ATHENA
User’s Manual
SILVACO
4701 Patrick Henry Drive, Bldg. 1
Santa Clara, CA 95054
Telephone
(408) 567-1000
Internet:
http://www.silvaco.com
April 14, 2008
ATHENA
User’s Manual
Copyright 2008
Silvaco
4701 Patrick Henry Drive, Building #6
Santa Clara, CA 95054
Phone:
Web:
(408) 567-1000
www.silvaco.com
Notice
The information contained in this document is subject to change without notice.
Silvaco Data Systems, Inc. MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS
MATERIAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTY OF FITNESS
FOR A PARTICULAR PURPOSE.
Silvaco Data Systems, Inc. shall not be held liable for errors contained herein or for incidental or
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into another language without the prior written consent of Silvaco Data Systems, Inc.
VIRTUAL WAFER FAB, VWF MANUFACTURING TOOLS, VWF AUTOMATION TOOLS,VWF INTERACTIVE
TOOLS DECKBUILD, TONYPLOT, DEVEDIT, TONYPLOT3D, DEVEDIT3D, MASKVIEWS, ATHENA,
SSUPREM4, MC IMPLANT, OPTOLITH, ELITE, MC DEPO/ETCH, SSUPREM3, SPDB, ATLAS, S-PISCES,
BLAZE/BLAZE3D, GIGA2D/3D, MIXEDMODE2D/3D, SIC, FERRO, QUANTUM2D/3D, LUMINOUS2D/3D,
LED, VCSELS, LASER, TFT2D/3D, OTFT, OLED, NOISE, DEVICE3D, THERMAL3D, ATLAS
INTERPRETER, MERCURY, FASTBLAZE, FASTNOISE, FASTGIGA, FAST ATLAS C-INTERPRETER, MOCASIM,
VICTORY, HARM, ZENITH, VISION, MIXSIM, TCAD DRIVEN CAD, SIMULATION STANDARD, CONNECTING
TCAD TO TAPEOUT, AND TCAD OMNI are trademarks of Silvaco Data Systems, Inc.
All other trademarks mentioned in this manual are the property of their respective owners.
© 2008 by Silvaco Data Systems, Inc.
Silvaco
iii
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ATHENA and ATLAS.
iv
Table of Contents
Chapter 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-1
1.1: Athena Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1: Using This Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2: Technical Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2: Athena Features and Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.1: Using ATHENA With Other SILVACO Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2.2: The Value Of Physically-Based Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-1
1-1
1-1
1-2
1-3
1-4
Chapter 2
Tutorial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1
2.1: Getting Started. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1
2.1.1: Running ATHENA Under DeckBuild . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-1
2.1.2: Loading And Running ATHENA Standard Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-2
2.2: Operation Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
2.2.1: Interactive Mode With DeckBuild . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
2.2.2: Batch Mode With Deckbuild . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
2.2.3: No Windows Batch Mode With Deckbuild. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-5
2.2.4: Running ATHENA inside DeckBuild . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-6
2.3: Creating a Device Structure Using ATHENA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7
2.3.1: Procedure Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7
2.3.2: ATHENA Input/Output. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-7
2.3.3: Creating An Initial Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-8
2.4: Choosing Models In SSUPREM4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-30
2.4.1: Implantation, Oxidation, RTA, Diffusion and Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-30
2.4.2: The Reason for Multiple Models for Each Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-30
2.4.3: Choosing an Appropriate Model Using the Method Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-30
2.4.4: Changing the Method Statement During the Process Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-31
2.4.5: Modelling the Correct Substrate Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-32
2.4.6: Simulating Rapid Thermal Anneals (RTA) Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-38
2.4.7: Simulating Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-39
2.4.8: Simulating the Epitaxy Process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-40
2.5: Calibrating ATHENA for a Typical MOSFET Flow. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42
2.5.1: Input Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-42
2.5.2: Tuning Oxidation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-43
2.5.3: Tuning Implantation Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-45
2.5.4: Tuning Diffusion Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-46
2.5.5: Related Issues on using the Device Simulator ATLAS for MOS Process Tuning. . . . . . . . . . . . . . . . . . . 2-46
2.6: Calibrating ATHENA for a Typical Bipolar Process Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-48
2.6.1: Tuning Base and Collector Currents – All Regions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-49
2.6.2: Tuning the Base Current – All Regions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-49
2.6.3: Tuning the Collector Current – All Regions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-50
2.6.4: The Base Current Profile – Medium Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-51
2.6.5: The Base Current Profile – Low Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-52
2.7: Using ATHENA for Simulating SiGe Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-54
2.7.1: METHOD Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-54
2.7.2: MATERIAL Statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2-54
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ATHENA User’s Manual
2.7.3: DEPOSIT Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7.4: DIFFUSE Statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8: Using Advanced Features of ATHENA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8.1: Structure Manipulation Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8.2: Deposition and Wet/Dry Etching using the Physical Models in ATHENA/ELITE . . . . . . . . . . . . . . . . . . . .
2.8.3: MaskViews Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9: Using ATHENA/OPTOLITH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9.1: Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9.2: Creating A Mask. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9.3: Illumination System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9.4: The Projection System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9.5: Imaging Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9.6: Defining Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9.7: Structure Exposure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.9.8: CD Extraction, Smile Plots, And Looping Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10: Adaptive Meshing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10.1: Introduction to Mesh Adaption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.10.2: Interface Mesh Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-54
2-55
2-56
2-56
2-59
2-65
2-74
2-74
2-74
2-77
2-79
2-80
2-82
2-82
2-84
2-86
2-86
2-89
Chapter 3
SSUPREM4 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1
3.1: Diffusion Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-1
3.1.1: Mathematical Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-2
3.1.2: The Fermi Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-5
3.1.3: Impurity Segregation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-6
3.1.4: The Two Dimensional Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-7
3.1.5: The Fully Coupled Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-16
3.1.6: Electrical Deactivation and Clustering Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-18
3.1.7: Grain-based Polysilicon Diffusion Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-21
3.2: Advanced Diffusion Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-23
3.2.1: Classical Model of Dopant Diffusion (CDD) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-24
3.2.2: Solid Solubility Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-31
3.2.3: Interstitials Clusters Model (IC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-31
3.2.4: Vacancy Cluster Model (VC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-33
3.2.5: Electrical Deactivation and Clustering Models (DDC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-34
3.2.6: Typical Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-36
3.3: Oxidation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-44
3.3.1: Numerical Oxidation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-46
3.3.2: Compress Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-47
3.3.3: Viscous Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-48
3.3.4: Linear Rate Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-50
3.3.5: Parabolic Rate Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-57
3.3.6: Mixed Ambient Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-58
3.3.7: Analytical Oxidation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-58
3.3.8: Recommendations for Successful Oxidation Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-59
3.4: Silicidation Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-64
3.5: Ion Implantation Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-66
3.5.1: Analytic Implant Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-66
3.5.2: Multi-Layer Implants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-70
3.5.3: Creating Two-Dimensional Implant Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-72
3.5.4: Monte Carlo Implants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-76
3.5.5: Ion Implantation Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3-87
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Table of Contents
3.5.6: Stopping Powers in Amorphous Materials and Range Validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6: Deposition Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.1: Deposition of Doped Layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.2: Grid Control During Deposit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6.3: Epitaxy Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7: Etching Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8: Compound Semiconductor Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.1: Diffusion Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.8.2: Implantation Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9: SiGe/SiGeC Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9.1: Deposition of SiGe/SiGeC Epitaxial Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9.2: Boron Diffusion in SiGe/SiGeC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.9.3: Boron Transient Diffusion Suppression by Carbon Incorporation Models. . . . . . . . . . . . . . . . . . . . . . . . .
3.10: Stress Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-89
3-91
3-91
3-91
3-91
3-92
3-93
3-93
3-94
3-95
3-95
3-95
3-96
3-97
Chapter 4
ELITE Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1
4.1: Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-1
4.2: String Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-2
4.3: Deposition Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4
4.3.1: Conformal Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4
4.3.2: CVD Deposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4
4.3.3: Unidirectional Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-4
4.3.4: Dual Directional Deposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-5
4.3.5: Hemispheric Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-6
4.3.6: Planetary Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-7
4.3.7: Conical Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-9
4.3.8: Monte Carlo Deposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-10
4.3.9: Custom Deposition Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-11
4.4: Etch Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12
4.4.1: Isotropic Etch Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12
4.4.2: RIE Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-12
4.4.3: Dopant Enhanced Etching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14
4.4.4: Plasma Etch Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14
4.4.5: Monte Carlo Etching Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-14
4.5: Reflow Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-20
4.6: Chemical Mechanical Polish (CMP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21
4.6.1: Hard Polish Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-21
4.6.2: Soft Polish Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4-23
Chapter 5
OPTOLITH Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1
5.1: Overview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-1
5.2: The Imaging Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-2
5.3: Optical System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-7
5.3.1: Discretization Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-7
5.3.2: Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-7
5.3.3: Computation Time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-8
5.4: The Exposure Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-9
5.5: Photoresist Bake Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-12
5.6: The Development Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-13
5.6.1: Dill’s Development Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5-13
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5.6.2: Kim’s Development Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.3: Mack’s Development Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.4: Trefonas’ Development Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.6.5: Hirai’s Development Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7: Proximity Printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.1: General Description of Proximity Lithography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.2: Theory of Proximity Printing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.7.3: Simulation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-13
5-14
5-14
5-14
5-15
5-15
5-15
5-17
Chapter 6
Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1
6.1: Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1
6.1.1: Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-1
6.1.2: Continuation Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-2
6.1.3: Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-2
6.1.4: General Syntax Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-2
6.1.5: Command Line Parsing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-3
6.2: ATHENA Statements List . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-4
6.2.1: Structure and Grid Initialization Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-4
6.2.2: Structure and Mesh Manipulation Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-4
6.2.3: Simulation Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-5
6.2.4: Model Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-5
6.2.5: Special DECKBUILD Statements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-6
6.2.6: Post-processing Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-6
6.2.7: Execution Control Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-6
6.2.8: Obsolete Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-6
6.2.9: Standard and User-Defined Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-7
6.2.10: Standard Impurities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-8
6.3: ABERRATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-9
6.4: ADAPT.MESH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-11
6.5: ADAPT.PAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-12
6.6: BAKE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-14
6.7: BASE.MESH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-15
6.8: BASE.PAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-16
6.9: BOUNDARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-17
6.10: CLUSTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-18
6.11: COMMENT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-19
6.12: CPULOG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-20
6.13: DEPOSIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-21
6.14: DEVELOP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-24
6.15: DIFFUSE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-25
6.16: DISLOC.LOOP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-28
6.17: ELECTRODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-29
6.18: EPITAXY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-30
6.19: ETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-32
6.20: EXPOSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-35
6.21: EXTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-37
6.22: FOREACH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-38
6.23: GO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-39
6.24: HELP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-40
6.25: ILLUM.FILTER . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-41
6.26: ILLUMINATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-42
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Table of Contents
6.27: IMAGE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-43
6.28: IMPLANT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-45
6.29: IMPURITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-49
6.30: INITIALIZE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-52
6.31: INTERSTITIAL and VACANCY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-54
6.32: LAYOUT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-57
6.33: LINE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-59
6.34: MASK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-61
6.35: MATERIAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-62
6.36: METHOD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-64
6.37: MOMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-70
6.38: OPTICAL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-72
6.39: OPTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-73
6.40: OXIDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-74
6.41: POLISH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-78
6.42: PRINT.1D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-79
6.43: PRINTF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-80
6.44: PROFILE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-81
6.45: PROJECTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-83
6.46: PUPIL.FILTER. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-84
6.47: QUIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-85
6.48: RATE.DEPO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-86
6.49: RATE.DEVELOP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-88
6.50: RATE.DOPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-90
6.51: RATE.ETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-91
6.52: RATE.POLISH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-95
6.53: REGION. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-96
6.54: RELAX. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-97
6.55: SELECT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-98
6.56: SET . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-100
6.57: SETMODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-101
6.58: SILICIDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-102
6.59: SOURCE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-103
6.60: STRESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-104
6.61: STRETCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-105
6.62: STRIP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-106
6.63: STRUCTURE. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-107
6.64: SYSTEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-109
6.65: TONYPLOT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-110
6.66: TRAP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-111
6.67: UNSETMODE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6-112
Appendix A
C-Interpreter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1
A.1: C-Interpreter Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1
A.2: Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A-1
Silvaco
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ATHENA User’s Manual
Appendix B
Default Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B-1
B.1: Oxidation Rate Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.1: Dry Ambient For <111> Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.2: Wet Ambient for <111> Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.3: Orientation Factors For Linear Coefficients (both Ambients). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.4: Pressure Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.5: Chlorine Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.6: Doping Dependence Of Oxidation Rate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.7: Coefficients for the Analytical Guillemot Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.8: Numerical Oxidation Coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.9: Stress-dependent Growth Model Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.10: Mechanical Parameters For Stress Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.11: Linear Coefficients Of Thermal Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.1.12: Volume Expansion Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.2: Impurity Diffusion Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.3: Impurity Segregation Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.4: Interface Transport Coefficients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.5: Solid Solubility In Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.6: Point Defect Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.7: Defect Interface Recombination Parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.8: Defect Growth Injection Interface Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.9: Material Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B-1
B-1
B-1
B-2
B-2
B-3
B-3
B-3
B-4
B-4
B-4
B-5
B-5
B-5
B-6
B-7
B-7
B-8
B-8
B-9
B-9
Appendix C
Hints and Tips. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C-1
Appendix D
ATHENA Version History . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-1
D.1: ATHENA Version 5.16.0.R Release Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.1.1: SSUPREM4 Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.1.2: Optolith Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.2: ATHENA Version 5.14.0.R Release Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.2.1: SSUPREM4 Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.2.2: ELITE Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.2.3: OPTOLITH Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.3: ATHENA Version 5.10.7.R Release Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.4: ATHENA Version 5.10.0.R Release Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.4.1: General Features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.4.2: SSUPREM4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.4.3: ELITE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.5: ATHENA Version 5.8.0.R Release Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.5.1: SSUPREM4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.5.2: ELITE Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.5.3: OPTOLITH Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.5.4: Miscellaneous Features and Bug Fixes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.6: ATHENA Version 5.6.0.R Release Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.6.1: SSUPREM4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.6.2: ELITE Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.6.3: Miscellaneous Features and Bug Fixes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.7: ATHENA Version 5.4.0.R Release Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
D.7.1: SSUPREM4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x
D-1
D-1
D-2
D-2
D-2
D-2
D-2
D-3
D-4
D-4
D-4
D-5
D-5
D-5
D-6
D-6
D-6
D-7
D-7
D-8
D-8
D-8
D-8
Silvaco
Table of Contents
D.7.2: FLASH Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-9
D.7.3: OPTOLITH Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-9
D.7.4: ELITE Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-9
D.7.5: Miscellaneous Features and Bug Fixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-9
D.8: ATHENA Version 5.2.0.R Release Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-9
D.8.1: Ion Implant BCA Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-9
D.8.2: Miscellaneous Features and Bug Fixes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-10
D.9: ATHENA Version 4.5.0.R Release Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-10
D.9.1: SSUPREM4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-10
D.9.2: ELITE Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-11
D.9.3: Generic ATHENA Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-11
D.10: ATHENA Version 4.0.0.R Release Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-11
D.10.1: SSUPREM4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-11
D.11: ELITE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-14
D.12: OPTOLITH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-14
D.13: ATHENA Version 3.0.1.R Release Notes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-14
D.13.1: ATHENA Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-14
D.13.2: ELITE Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-18
D.13.3: FLASH Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-20
D.13.4: OPTOLITH Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-20
D.13.5: Known Bugs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-20
D.14: ATHENA Version 2.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-20
D.14.1: ATHENA Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-20
D.14.2: SSUPREM4 Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-21
D.14.3: ELITE Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-22
D.14.4: OPTOLITH Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-22
D.14.5: FLASH Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-23
D.15: ATHENA Version 1.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-23
D.16: SSUPREM4 Version 6.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-24
D.17: SSUPREM4 Version 5.1.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-25
D.18: SSUPREM4 Version 5.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-25
D.19: SSUPREM4 Version 5.0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-26
D.20: Additional SSUPREM4 Changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-27
D.20.1: Oxidation method defaults to compress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D-27
Appendix E
SUPREM4 and TSUPREM3 Compatibility Features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E-1
E.1: General Syntax Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.2: Execution Control Capabilities Provided by Deckbuild . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.2.1: DEFINE Statement and Substitutions Capability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.2.2: IF/ELSEIF/ELSE/IF.END Capability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.2.3: LOOP/L.END/ASSIGN/L.MODIFY Capability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.3: MESH Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.4: Using MASK statement with the parameter IN.FILE and XLINES for Automatic grid generation
in the horizontal direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.5: Using mask information with the EXPOSE MASK=<maskname> statement. . . . . . . . . . . . . . . . . . . . . . . .
E.6: Aliases and substitutions for some statements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.7: Changes in the INITIALIZE statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.8: Changes in the DEPOSIT statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.9: Changes in the DIFFUSE statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.10: Changes in the ETCH statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.11: Changes in the STRUCUTURE (SAVEFILE) statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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E.12: Changes in the IMPLANT statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.13: Changes in the ELECTRODE statement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.14: Changes in the METHOD statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
E.15: Changes in the MATERIAL statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Chapter 1:
Introduction
1.1: Athena Overview
ATHENA is a simulator that provides general capabilities for numerical, physically-based, twodimensional simulation of semiconductor processing. ATHENA has a modular architecture that the
following licensable tools and extensions:
•
ATHENA: This tool performs structure initialization and manipulation, and provides basic deposition and etch facilities
•
SSUPREM4: This tool is used in the design, analysis, and optimization of silicon semiconductor
structures. It simulates silicon processing steps such as ion implantation, diffusion and oxidation.
•
ELITE: This tool is a general purpose 2D topography simulator that accurately describes a wide
range of deposition, etch and reflow processes used in modern IC technologies.
•
OPTOLITH: This tool performs general optical lithography simulation including 2D aerial imaging, non-planar photoresist exposure, and post exposure bake and development.
1.1.1: Using This Manual
This chapter is an overview of ATHENA. For new users, read Chapter 2: “Tutorial”, especially the
sections that describe the simulator or modules that you have licensed. This chapter will give you a
basic understanding of what ATHENA can do and how it’s used. The remaining chapters will give you a
detailed understanding of ATHENA’s capabilities and how to access them. Appendix D: “ATHENA
Version History” gives information about the current version of ATHENA.
ATHENA is supplied with a number of example problem descriptions. You can access them through
DECKBUILD as described in the VWF INTERACTIVE TOOLS USER’S MANUAL, VOL 1. These examples
demonstrate the capabilities of ATHENA. The input files provided as part of these examples can
provide an excellent starting point for developing your own ATHENA input files.
1.1.2: Technical Support
If you have difficulties or questions relating using ATHENA, e-mail SILVACO Support at
support@silvaco.com.
When you send us an e-mail message, please:
1. Explain the problem or question in detail.
2. Include any input files that you have created.
3. Provide us with the version number of ATHENA and the version numbers of the VWF INTERACTIVE
TOOLS that you are using.
4. Include your business telephone number and fax number.
SILVACO support will contact you promptly and resolve your problem as quickly as possible.
User feedback helps further develop ATHENA. Please send your comments on the programs,
suggestions for improvements, and additional feature requests to support@silvaco.com.
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1.2: Athena Features and Capabilities
Table 1-1 shows the features and capabilities of Athena.
Table 1.1: Athena Features and Capabilities
Features
Bake
•
Time and temperature bake specification.
•
Models photoresist material flow.
•
Models photo-active compound diffusion.
C-Intepreter
•
Allows user-defined models for implant damage, Monte Carlo plasma
etching and diffusion in SiGeC.
CMP
•
Models Chemical Mechanical Polishing.
•
Hard and soft models or a combination of both.
•
Includes isotropical etch component.
•
Conformal deposition model.
Deposition
1-2
Capabilities
•
Hemispherical, planetary, and conical metallization models.
•
Unidirectional or dual directional deposition models.
•
CVD model.
•
Surface diffusion/migration effects.
•
Ballistic deposition models including atomistic positioning effects.
•
User-definable models.
•
Default deposition machine definitions.
Development
•
Five different photoresist development models.
Diffusion
•
Impurity diffusion in general 2D structures including diffusion in all
material layers.
•
Fully coupled point defect diffusion model.
•
Oxidation enhanced/retarded diffusion effects.
•
Rapid thermal annealing.
•
Models simultaneous material reflow and impurity diffusion.
•
Impurity diffusion in polysilicon accounting for grain and grain
boundary components.
Epitaxy
•
2D epitaxy simulation including auto-doping.
Etch
•
Extensive geometric etch capability.
•
Wet etching with isotropic profile advance.
•
RIE model
components.
•
Microloading effects.
•
Angle dependence of etchant source.
•
Default etch machine definitions.
•
Monte Carlo plasma etching.
•
Dopant enhanced etching.
that
combines
isotropic
and
directional
etch
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Introduction
Table 1.1: Athena Features and Capabilities
Features
Exposure
Imaging
Implantation
Oxidation
Silicidation
Capabilities
•
Model is based on the Beam Propagation Method simulating reflections
and diffraction effects in non-planar structures with capability to take
into account local modification of material optical properties the
absorbed dose.
•
Defocus and large numerical aperture effects.
•
Two dimensional, large numerical aperture, aerial image formation.
•
Up to 9th order imaging system aberrations.
•
Extensive source and pupil plane filtering for enhanced aerial images.
•
Full phase shift and transmittance variation mask capabilities.
•
Experimentally verified Pearson and dual Pearson analytical models.
•
Extended low energy and high energy implant parameter tables.
•
Binary Collision Approximation Monte Carlo calculations for crystalline
and amorphous materials.
•
Universal tilt and rotation capability for both analytic and Monte Carlo
calculations.
•
Compressible and viscous stress dependent models.
•
Separate rate coefficients for silicon and polysilicon materials.
•
HCL and pressure-enhanced oxidation models.
•
Impurity concentration dependent effects.
•
Ability to simulate the oxidation of structures with deep trenches,
undercuts, and ONO layers.
•
Accurate models for the simultaneous oxidation and lifting of
polysilicon regions.
•
Models for titanium, tungsten, cobalt, and platinum silicides.
•
Experimentally verified growth rates.
•
Reactions and boundary motion on silicide/metal and silicide/silicon
interfaces.
•
Accurate material consumption model.
1.2.1: Using ATHENA With Other SILVACO Software
ATHENA is normally used in conjunction with the VWF INTERACTIVE TOOLS. These tools include
DECKBUILD, TONYPLOT, DEVEDIT, MASKVIEWS and OPTIMIZER. DECKBUILD provides an interactive run time
environment. TONYPLOT supplies scientific visualization capabilities. DEVEDIT is an interactive tool for
structure and mesh specification and refinement, and MASKVIEWS is an IC Layout Editor. The
OPTIMIZER supports black box optimization across multiple simulators.
For more information about VWF INTERACTIVE TOOLS, see the VWF INTERACTIVE TOOLS USER’S MANUAL
VOLUMES 1 and 2.
ATHENA is also frequently used in conjunction with the ATLAS device simulator. ATHENA predicts the
physical structures that result from processing. These physical structures are used as input by ATLAS,
which then predicts the electrical characteristics associated with specified bias conditions. Using
ATHENA and ATLAS makes it easy to determine the impact of process parameters on device
characteristics.
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ATHENA can also be used as one of the core simulators within VIRTUAL WAFER FAB (VWF). VWF makes it
convenient to perform highly automated simulation-based experimentation. VWF is used in a way that
closely resembles experimental research and development procedures. Therefore, it links simulation
closely to technology development, resulting in greatly increased benefits from simulation use.
For more information about VWF, see the VWF AUTOMATION, CALIBRATION,
AND
PRODUCTION TOOLS USER’S
MANUAL.
1.2.2: The Value Of Physically-Based Simulation
Physically-based process simulators predict the structures that result from specified process
sequences. This is done by solving systems of equations that describe the physics and chemistry of
semiconductor processes. Detail analysis of various aspects of process simulation can be found in [1]
and [2].
Physically-based simulation provides three major advantages: it is predictive, it provides insight, and
it captures theoretical knowledge in a way that makes this knowledge available to non-experts.
Physically-based simulation is different from empirical modeling. The goal of empirical modeling is to
obtain analytic formulae that approximate existing data with accuracy and minimum complexity.
Empirical models provide efficient approximation and interpolation. Empirical models, however,
doesn’t provide insight, predictive capabilities, or capture theoretical knowledge. Physically-based
simulation is an alternative to experiments as a source of data. Empirical modeling can provide
compact representations of data from either source.
Physically-based simulation has become very important for two reasons. One, it’s almost always much
quicker and cheaper than performing experiments. Two, it provides information that is difficult or
impossible to measure.
Physically-based simulation has two drawbacks: you must incorporated are that all the relevant
physics and chemistry into a simulator and numerical procedures, and you must be implemented to
solve the associated equations. But these tasks have been taken care of for ATHENA users.
Physically-based process simulation tools users must specify the problem to be simulated. ATHENA
users specify the problem by defining the following:
•
The initial geometry of the structure to be simulated.
•
The sequence of process steps (e.g., implantation, etching, diffusion, exposure) that are to be simulated.
•
The physical models to be used.
The subsequent chapters of this manual describe how to perform these steps.
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Chapter 2:
Tutorial
2.1: Getting Started
This chapter is to help you start using ATHENA by providing a step-by-step tutorial centered on a
typical process simulation sequence. It explains how ATHENA uses the VWF INTERACTIVE TOOLS (i.e.,
DECKBUILD, TONYPLOT, MASKVIEWS, DEVEDIT, and OPTIMIZER). These tools make ATHENA easier to use
and they provide visualization and interface capabilities with other Silvaco tools. This tutorial
assumes that you are familiar with the basic features of the VWF INTERACTIVE TOOLS. For more
information about these tools, see VWF INTERACTIVE TOOLS USER’S MANUAL.
This chapter begins by explaining how to start ATHENA and continues with tutorials on how to use the
program. We recommend that you read Section 2.3: “Creating a Device Structure Using ATHENA”
before you move on to the section appropriate to the particular tool you will be using. This section
explains how to start ATHENA, how to load and run standard examples, and how to use the ATHENA
online help facility.
The following explanations assume that ATHENA has been properly installed. See the SILVACO
INSTALLATION, MIGRATION AND TROUBLESHOOTING GUIDE if you encounter installation difficulties.
2.1.1: Running ATHENA Under DeckBuild
DECKBUILD is an interactive graphic environment that is used for the following purposes:
•
Generating input files for process or device simulation or both,
•
Running simulations interactively,
•
Interfacing between different simulators,
•
Invoking other VWF Interactive tools.
To start ATHENA under DECKBUILD in interactive mode, enter the following UNIX command:
deckbuild -an
After a short delay, the Main Deckbuild Window (See Figure 2-1) will appear. The lower text window of
this window will contain the ATHENA logo and version number, a list of available modules, and a
command prompt. ATHENA is now ready to run. To become familiar with the mechanics of running
ATHENA under DECKBUILD, load and run some of the ATHENA standard examples.
The method described here is the recommended procedure for starting the program. There are other
methods and modes of running ATHENA. Section 2.2: “Operation Modes” or Section 2.8: “Using
Advanced Features of ATHENA” will describe these methods and modes.
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Figure 2-1: Main Deckbuild Window
2.1.2: Loading And Running ATHENA Standard Examples
DECKBUILD makes it possible to load and run a number of example simulation input files. To access the
ATHENA examples, select Main Control→Examples and the Deckbuild Examples Window will
appear (See Figure 2-2).
Groups of DECKBUILD examples are listed in the Section menu and are grouped according to the
simulator or simulation topic the example demonstrates. The Sub-section menu lists individual
example input files. To run examples, select one of the sections (e.g., ATHENA_IMPLANT) in the
Section menu. This will open a list of input file names. Short descriptions of the examples will appear
in the Examples Window.
Select one of the input files using the Sub-section menu or by double-clicking on the input file name
and a description of the selected input file will appear.
Press the Load Example button to load the selected input file into the Deckbuild Text Subwindow
(bottom panel of the window). The input file, along with other files associated with the input file
(structure files, setfiles for TONYPLOT, and layout files for MASKVIEWS), will be copied into your current
directory.
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Once the input file is in the Deckbuild Text Subwindow (bottom panel of the window), press the Run
button in the Main Deckbuild window or follow the special instructions in the Deckbuild Examples
Window to run the input file.
Most of the ATHENA examples contain preset calls to the graphical postprocessing tool TONYPLOT. One
or more plots will appear while the selected example is running.
If you are not familiar with DECKBUILD, use a simple example to learn the basic DECKBUILD features and
capabilities. For more information, see the VWF INTERACTIVE TOOLS USER’S MANUAL, VOL. I. This will
assist you in working through the rest of the tutorial. The details of these functions are described in
the VWF INTERACTIVE TOOLS USER’S MANUAL, VOL. I.
Figure 2-2: DeckBuild Examples Window
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Online Help
You can find information on ATHENA statements and syntax using the online help facility. You can
access this facility in interactive mode or through DECKBUILD. Typing help at the ATHENA> prompt
either in Interactive Mode or in the Deckbuild Text Subwindow will display a list of valid ATHENA
statements. The syntax for the help command is shown below.
HELP <command name>
This command will give you additional information about parameter names, types, initial values, and
a description of the parameters for the specified command.
To obtain more information on ATHENA default parameters (stored in a special file called athenamod),
select Command→Models... in the Main Deckbuild Window. This opens athenamod in a text editing
window, making it possible to read the file or copy and paste statements from the file into a DECKBUILD
Text Subwindow.
Select Command→Notes... to open a special information file that includes the current release notes
and a release history.
For more information about ATHENA syntax, statements, parameters, and their default values, see
Chapter 6: “Statements”.
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2.2: Operation Modes
ATHENA is normally used through the DECKBUILD run-time environment, which supports both
interactive and batch mode operation. We recommend that you always use ATHENA through
DECKBUILD. In this section, we present the basic information you need to run ATHENA in the
DECKBUILD environment. The VWF INTERACTIVE TOOLS USER’S MANUAL, VOL. I provides a more detailed
description of the features and capabilities of DECKBUILD.
2.2.1: Interactive Mode With DeckBuild
To start ATHENA under DECKBUILD, type:
deckbuild -an
at the UNIX system command prompt. The command line option -an instructs DECKBUILD to start
ATHENA as the default simulator.
To start with an existing input file, type:
deckbuild -an <input filename>
The run-time output shows the execution of each ATHENA command and includes error messages,
warnings, extracted parameters and other important output for evaluating each ATHENA run. When
you run ATHENA interactively, the run-time output is sent to the Deckbuild Text Subwindow of the
Deckbuild Application Window and you can save it as needed. You don’t need to save the run-time
output explicitly. The following command line, however, specifies the file name that will be used for
storing the run-time output:
deckbuild -an <input filename> -outfile <output filename>
In this case, the run-time output is sent to the output file and to the output section of the Deckbuild
Window.
2.2.2: Batch Mode With Deckbuild
To use DECKBUILD in a non-interactive or batch mode, add the -run parameter to the command that
invokes DECKBUILD. A prepared command file is required for running in batch mode. We advise you to
save the run-time output to a file because error messages in the run-time output will be lost when the
batch job completes.
deckbuild -run -an <input filename> -outfile <output filename>
Using this command requires a local X-Windows system to be running. The job runs inside a
DECKBUILD icon on the terminal and quits automatically when the ATHENA simulation is complete. You
can also run DECKBUILD using a remote display. For example:
deckbuild -run -an <input file> -outfile <output file> -display<hostname>:0.0
2.2.3: No Windows Batch Mode With Deckbuild
The -ascii parameter is required for completely non-X Windows operation of DECKBUILD. For
example:
deckbuild -run -ascii -an <input filename> -outfile <output filename>
This command directs DECKBUILD to run the ATHENA simulation without any display of the DECKBUILD
window or icon. This is useful for remote execution without an X windows emulator or for replacing
UNIX-based ATHENA runs within framework programs.
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When using batch mode, use the UNIX command suffix & to detach the job from the current command
shell. To run a remote ATHENA simulation under DECKBUILD without display, and then logout from the
system, use the UNIX nohup command before the following DECKBUILD command line:
nohup deckbuild -run -ascii -an <input filename> -outfile <output filename> &
2.2.4: Running ATHENA inside DeckBuild
Each ATHENA run inside DECKBUILD should start with the following command line:
go athena
A single input file can contain several ATHENA runs each separated with a go athena line. Input files
within DECKBUILD can also contain runs from other programs such as ATLAS or DEVEDIT along with the
ATHENA runs.
Running a given version number of ATHENA
You can modify the go statement to provide parameters for the ATHENA run. To run version 5.8.0.R,
the syntax is
go athena simflags=”-V 5.8.0.R”
Starting Parallel ATHENA
The -P option is used to set the number of processors to use in a parallel ATHENA run (only the MC
Implant module is parallelized starting ATHENA release 5.16.0.R). If the number of processors
specified by -P is greater than the number of processors available, it is automatically reduced to this
cap number. If -P parameter is not specified, ATHENA will run on all available processors
automatically. To run ATHENA on 4 processors, use the command:
go athena simflags=" -V 5.16.0.R -P 4"
Running ATHENA with a user-specified default parameter file
ATHENA supports the use of multiple default parameter files. These files have the default root
filename athenamod. To start ATHENA with athenamod.97, the syntax is
go athena simflags=”-modfile 97”
Running ATHENA In Standalone Mode (Without DeckBuild)
You can run ATHENA outside the DECKBUILD environment, but we don’t recommended it. If you don’t
want the overhead of the Deckbuild Window, use the No Windows Mode. Many important features
such as variable substitution, automatic interfacing to device simulation, and parameter extraction
are unavailable outside the DECKBUILD environment. To run ATHENA directly under UNIX, use the
following command line:
athena <input filename>
To save the run-time output to a file, don’t use the UNIX redirect command (>). Instead, specify the
name of the output file:
athena <input filename> -logfile <output filename>
Note: Some of the standard examples supplied with ATHENA will not run correctly outside of DECKBUILD.
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2.3: Creating a Device Structure Using ATHENA
2.3.1: Procedure Overview
ATHENA is designed as a process simulation framework. The framework includes simulator
independent operations and simulator specific functions that simulate different process steps (e.g.,
implant, RIE, or photoresist exposure). This section describes ATHENA input/output and the following
basic operations for creating an input file:
•
Developing a good simulation grid
•
Performing conformal deposition
•
Performing geometric etches
•
Structure manipulation
•
Saving and loading structure information
•
Interfacing with device simulators
•
Using different VWF INTERACTIVE TOOLS
These operations are relevant to all individual ATHENA process simulators. This part of the tutorial
should help you if you’re new to each of the process simulators.
The three sections of the tutorial: SSUPREM4, ELITE, and OPTOLITH are devoted to individual
simulators and should be read if you’re going to use those simulators.
2.3.2: ATHENA Input/Output
Before proceeding to the ATHENA operation, we will discuss how to provide ATHENA with input
information and the forms of output information available from ATHENA.
Input Information
The bulk of input information for ATHENA is usually provided in the form of input files. An input file is
a text file that can be prepared by using DECKBUILD (which will be described throughout the rest of the
tutorial) or any ASCII text editor (such as vi on any UNIX system, or textedit on a SUN system). The
individual lines of the text file are called statements. Each statement consists of a statement name and
a set of parameters that specify a certain step of a process simulation or model coefficients used during
subsequent simulation steps. See Chapter 6: “Statements”, Section 6.1: “Overview” for details on
statement syntax.
The remainder of this tutorial will introduce you to the task of creating good input files.
Since ATHENA uses a great deal of default information, much of the default information is stored in
several non-user-specified files. These files are as follows:
•
The athenamod file includes default parameters of physical models, diffusion and oxidation
coefficients, default parameters of numerical methods, characteristics of predefined deposition
and etching machines, and optical parameters of materials for lithography simulation.
•
The std_table and several svdp**** files in the implant_tables directory contain ion implantation
look-up tables.
•
Several files with suffix .mod in the pls and models directories contain parameters for advanced
diffusion models (Chapter 3: “SSUPREM4 Models”, Section 3.2: “Advanced Diffusion Models”).
•
The athenares file includes resistivity vs. doping concentration data.
It’s important to be aware that information from the athenamod file is loaded into ATHENA each time
it starts. You can override any of the athenamod default parameters by specifying an alternative
parameter in an input file or by specifying the entire models file using the -modfile option.
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Output Information
All run-time output generated by ATHENA will appear in the Deckbuild Text Subwindow when
running DECKBUILD, or in the current window (or specified output file) when running ATHENA
standalone. Run-time output can be grouped into two categories: Standard Output and Standard Error
Output.
Standard Output consists of the output from the PRINT.1D statements or the EXTRACT statement of
DECKBUILD or both, and the normal information messages generated by ATHENA. The number of
messages generated depends on the output mode chosen in the OPTION statement. The QUIET mode is
the default. Minimum output is generated in this case: all statements are echoed and the status of a
time consuming simulation is reported. The NORMAL option produces some additional output
information, including information about the current grid (e.g., number of nodes or triangles).
VERBOSE and DEBUG modes are useful for debugging but these options produce too much output for
any other purpose.
Standard Error Output consists of the warning and error messages describing syntax errors, file
operation errors, system errors, and internal inconsistencies.
Standard Structure File Format
The main channel of information exchange between ATHENA and other simulators and tools is the
Standard Structure File (SSF) format. SSF is a universal file format used by a number of Silvaco
simulation programs. The STRUCTURE statement of ATHENA creates a Standard Structure File, which
contains mesh and solution information, model information, and other related parameters.
The saved Standard Structure File can be used by the following:
•
ATHENA to re-initialize the structure and continue process simulation.
•
ATLAS or other device simulators to perform electrical analysis of the structure produced by
ATHENA.
•
TONYPLOT to graphically display a solution created by ATHENA.
•
DEVEDIT to generate an updated mesh and export the mesh and doping back to ATHENA or any
other simulator.
For more information on structure files, see “Saving a Structure File for Plotting or Initializing an
ATHENA Input file for Further Processing” Section on page 2-28.
2.3.3: Creating An Initial Structure
This section will describe how to use DECKBUILD’s Commands menu to create a typical ATHENA input
file. The goal of this section is not to design a real process sequence, but to demonstrate the use of
specific ATHENA statements and parameters, as well as some DECKBUILD features, to create a realistic
input file. You can find many realistic process input files among the examples and use them as a
starting point in your process simulation.
Defining Initial Rectangular Grid
Once DECKBUILD is running and the current simulator is set to ATHENA (see the VWF AUTOMATION,
CALIBRATION, AND PRODUCTION TOOLS USER’S MANUAL for more information), open and pin the Commands
menu as shown in Figure 2-3. Then, select Mesh Define.... and the ATHENA Mesh Define Menu will
appear. We recommend that you pin this popup because it will be used often in designing an initial
mesh.
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Figure 2-3: Commands Menu
Now, you can specify the initial rectangular grid. The correct specification of a grid is critical in process
simulation. The number of nodes in the grid Np has a direct influence on simulation accuracy and
time. A finer grid should exist in those areas of the simulation structure where ion implantation will
occur, where p-n junction will be formed, or where optical illumination will change photoactive
component concentration. The number of arithmetic operations necessary to achieve a solution for
processes simulated, using the finite element analysis method could be estimated as (Np)α, where α is
of order 1.5 - 2.0.
Therefore, to maintain the simulation time within reasonable bounds, the fine grid should not be
allowed to spill over into unnecessary regions. The maximum number of grid nodes is 20,000 for
ATHENA simulations, but most practical simulations use far fewer nodes than this limit.
To create a simple uniform grid in a rectangular 1 µm by 1 µm simulation area, click on the Location
field and enter a value of 0.0. Then, click on the Spacing field and enter a value of 0.10. Then, click
on the Insert button and the line parameters will appear in the scrolling list.
Note: ATHENA coordinate system has positive x axis pointed to the right along the structure surface and positive y axis
pointed down to the depth of the structure.
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In the same way, set the location of a second X line to 1.0 with a spacing of 0.1. You can either set the
values by dragging a slider or by entering a number directly.
Now, select the Y direction and set the lines with the same values as the X direction. You can now add
the comments at the Comment line. The ATHENA Mesh Define menu should appear as shown in
Figure 2-4.
Figure 2-4: ATHENA Mesh Define Menu
You can now write the menu-prepared mesh information into the input file. But first, preview the
rectangular grid by selecting the View... button and the View Grid window (Figure 2-5) will appear.
Notice that vertical and horizontal grid lines are distributed uniformly, and the 121 points and the 200
triangles will be generated.
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Figure 2-5: View Grid Window
A uniform grid such as the one shown in Figure 2-5 is inefficient for performing complex simulations.
Therefore, the grid must be improved. First, make a better grid in the y-direction. Usually, it’s
necessary to get better resolution for the depth profile after the ion implantation step. When adaptive
gridding capability isn’t used, apply preliminary knowledge of the process you are going to simulate.
Suppose you want to perform a 60 keV boron implant so that the implant peak would be around 0.2
µm. It is reasonable to make a finer grid at this depth. To achieve this, simply add one more Y-line by
setting the Location to 0.2 and the Spacing to 0.02. The new rectangular grid (Figure 2-6) will now
appear. Notice the number of points and triangles have increased to 231 and 400 respectively.
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Figure 2-6: New Rectangular Grid
The minimum spacing in the Y-direction is at 0.2 µm, and the spacing gradually increases toward the
bottom and the top of the structure. Since the spacing at y=0 is still 0.1, only 3 grid lines lie between 0
and 0.2 µm. You may want to make a finer grid at the top of the structure. To do this, select the top line
of the Y Location scrolling list, change the spacing to 0.03, and press the Insert button. The selected
line will be replaced by Y LOC=0.00 SPAC=0.03. If you then press the View... button, there will be 8
grid lines between y=0 and y=0.2 (Figure 2-7).
Figure 2-7: Inserting New Grid Lines
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To improve the initial grid in the x-direction, consider two things. First, make sure that a good 2D
profile resolution is specified under the mask edges. Second, make sure the vertical grid lines are
placed along future mask edges. To build half of a 0.6 µm MOS structure with the center of the gate at
x=0, there must be an additional X line at x=0.3 and spacing at this line must be small enough to
obtain good lateral resolution of source/drain implants. To add these items, return to the X direction
specification in the Mesh Define menu and insert an additional X line at x=0.3 with spacing = 0.02.
After this final insertion and adding any desired Comment information, the Mesh Define menu
should appear as shown in Figure 2-8. The grid will have 525 points and 960 triangles (see Figure 2-9).
Figure 2-8: ATHENA Mesh Define Menu
Figure 2-9: Redefined Grid
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Finally, write the Mesh Define information to the file by pressing the Write button. A set of lines like
these will appear:
GO ATHENA
# NON-UNIFORM GRID
LINE X LOC=0.00 SPAC=0.1
LINE X LOC=0.3 SPAC=0.02
LINE X LOC=1 SPAC=0.1
LINE Y LOC=0.00 SPAC=0.03
LINE Y LOC=0.2 SPAC=0.02
LINE Y LOC=1 SPAC=0.1
The first line (GO ATHENA) is called an autointerface statement and tells DECKBUILD that the
following file should be run by ATHENA.
Defining the Initial Substrate
The LINE statements specified by the Mesh Define menu set only the rectangular base for the
ATHENA simulation structure. The next step is the initialization of the substrate region with its
points, nodes, triangles, background doping, substrate orientation, and some additional parameters. To
initialize the simulation structure, select ATHENA Command Menu→Mesh Initialize... and the
Mesh Initialize Menu will appear (see Figure 2-10) .
Figure 2-10: Mesh Initialize Menu
Background doping can be set by clicking on the desired impurity box (e.g., Boron). The background
impurity concentration specification will then become active. If the None box is checked, the
concentration information will become inactive and will appear grayed out from the rest of the menu.
Select the desired concentration using the slider (e.g., 3.0) and select an exponent from the Exp: menu
(e.g., 14). This will give a background concentration of 3.0e14 atom/cm3. You can set background
concentration using the By Resistivity specification in Ohm•cm. For this tutorial, check the 2D box
in the Dimensionality field. This will run the simulation in a two-dimensional calculation. The other
items in this menu will be discussed in Section 2.8: “Using Advanced Features of ATHENA”.
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Note: Two-dimensional mode is used in this tutorial to demonstrate 2D grid generation and manipulation. In most cases,
however, it is unnecessary to change the Auto default in the Dimensionality item of the Mesh Initialize menu. ATHENA will
begin in 1D and will automatically switch to 2D mode at the first statement, which disrupts the lateral uniformity of the device
structure. This generally results in massive savings of computation time.
You can now write the mesh initialization information into the file by pressing the Write button. The
following two lines will appear in the Deckbuild Text Subwindow:
# INITIAL SILICON STRUCTURE
INIT SILICON C.BORON=3.0E14 ORIENTATION=100 TWO.D
Now, run ATHENA to obtain the initial structure. Press the Run button on the DECKBUILD control. The
following output will appear in the simulator subwindow:
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
# NON-UNIFORM GRID
LINE X LOC=0.00 SPAC=0.10
LINE X LOC=0.3 SPAC=0.02
LINE X LOC=1 SPAC=0.1
#
LINE Y LOC=0.00 SPAC=0.03
LINE Y LOC=0.2 SPAC=0.02
LINE Y LOC=1 SPAC=0.1
# INITIAL SILICON STRUCTURE
INIT SILICON C.BORON=3.0E14 ORIENTATION=100 TWO.D
STRUCT OUTFILE=.history01.str
The line STRUCT OUTFILE=.history01.str is automatically produced by DECKBUILD through the
history function. This function provides an important service when debugging new files, performing
“what if ” simulations, and visualizing the structure at different steps of simulation. This feature will
be used throughout the tutorial. Use any of the three methods to visualize the initial structure:
1. Click on the Tools menu button. DECKBUILD will then automatically save a temporary standard
structure file and invoke TONYPLOT with this file.
2. Click on the Main Control button and the Deckbuild Main Control popup will appear. Then,
click on the Plot Current Structure button. DECKBUILD will then automatically save a
temporary standard structure file and invoke TONYPLOT with this file.
3. Select (highlight) the name of a structure file (.history01.str in this case) and click on the
Tools or Plot Current Structure. DECKBUILD will then start TONYPLOT with the selected
structure file.
After a short delay, TONYPLOT will appear. It will have only regional and material information. Click on
the Plot menu button and the Display (2D Mesh) popup will appear. Select only the two left icons:
Mesh and Edges and the Initial Triangular Grid (Figure 2-11) will appear in TONYPLOT.
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Figure 2-11: Initial Triangular Grid
The grid in ATHENA consists of points connected to form a number of triangles. Each point has one or
more nodes associated with it. A point within a material region has one node, while a point which
belongs to several regions has several nodes. A node represents the solution (e.g., doping
concentration) in a particular material region at the point. For example, a given node may represent
solution values in silicon at a point with coordinates (0.0, 0.0); an entirely different node may
represent solution values in oxide at the same point (0.0, 0.0).
So, the previous INIT statement creates the <100> silicon region of 1.0 µm x 1.0 µm size, which is
uniformly doped with boron concentration of 3e14 atom/cm3. This simulation structure is ready for any
process step (e.g., implant, diffusion, Reactive Ion Etching). Before discussing the simulation of
physical processing using SSUPREM4, ELITE or OPTOLITH modules, it’s important to discuss structure
manipulation statements that can precede or alternate with physical process steps.
Simple Film Depositions
Conformal deposition can be used to generate multi-layered structures. Conformal deposition is the
simplest deposit model and can be used in all cases when the exact shape of the deposited layer is not
critical. Conformal deposition can also be used in place of oxidation of planar or quasi-planar
semiconductor regions when doping redistribution during the oxidation process is negligible.
To set the conformal deposition step, select the menu items Process→Deposit→Deposit... from the
Commands menu in DECKBUILD and the ATHENA Deposit Menu (Figure 2-12) will appear.
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Figure 2-12: ATHENA Deposit Menu
As shown, Conformal Deposition is the default. If it is known that the oxide layer thickness grown in a
process is 200 Angstroms, you can substitute this with conformal oxide deposition. Select Oxide from
the Material menu and set its thickness to 0.02 µm. It is always useful to set several grid layers in a
deposited layer. In this case, at least two grid layers are needed to simulate impurity transport
through the oxide layer. In some other cases (e.g., photoresist deposition over a non-planar structure),
a sufficiently fine grid is needed to accurately simulate processes within the deposited layer. There are
also situations (e.g., spacer formation) when several grid layers in a deposited material region are
needed to properly represent the geometrical shape of the region.
The grid in the deposited layer is controlled by Grid Specification parameters in the ATHENA
Deposit Menu. Set the Total number of grid layers to 2, add a Comment, and click on the Write
button. The following lines will then appear in the Deckbuild Text Subwindow:
# GATE OXIDE DEPOSITION
DEPOSIT OXIDE THICK=0.02 DIVISIONS=2
The next step will be to deposit a phosphorus doped polysilicon layer of 0.5µm thickness. Select the
material Polysilicon, and set the thickness to 0.5. To add doping, select the Impurities box. The
Impurity Concentration section will be immediately added to the ATHENA Deposit Menu (See
Figure 2-13).
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Figure 2-13: Impurity Section of the ATHENA Deposit Menu
Click on the Phosphorus checkbox and set the doping level (e.g., 5.0x1019) using the slider and the
Exp menu. You can set a non-uniform grid in the deposited layer by changing the Nominal grid
spacing and the Grid spacing location parameters. To create a finer grid at the polysilicon surface,
set the total number of grid layers to 10, the Nominal grid spacing to 0.02 µm and the Grid
spacing location to 0.0 (at the surface). Then, click on the Write button and the following deposition
statement will be written in the input file as:
DEPOSIT POLY THICK=0.5 C.PHOSPHOR=5.0E19 DIVISIONS=10 \
DY=0.02 YDY=0.0 MIN.SPACING=0.001
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Use the Cont button to continue the ATHENA simulation. This will create the three layer structure
shown in the left plot of Figure 2-14. The MIN.SPACING parameter preserves the horizontal mesh
spacing for high aspect ratio grids. ATHENA tries to reduce high aspect ratio grids and MIN.SPACING
stops this. To get a finer grid not at the polysilicon surface but in the middle of polysilicon layer, change
YDY to 0.2. This puts on a finer grid at a distance of 0.2µm from the surface of the structure. You can
do this by positioning the cursor in the input file and backspacing over existing text, or entering new
text. For example:
DEPOSIT POLY THICK=0.5 C.PHOSPHOR=5.0E19 DIVISIONS=10 \
DY=0.02 YDY=0.2
It is possible to see the effect of changing the YDY. parameter within the polysilicon without rerunning
the whole input file. To do this, highlight the previous statement (DEPOSIT OXIDE...), select Main
Control→Init from History button, and press the Cont button. The new history file can then be
loaded into TONYPLOT (see the right plot in Figure 2-14).
Figure 2-14: Grid Control for Deposition
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Simple Geometrical Etches
The next step in this tutorial process simulation is to define the polysilicon gate definition. (Implant
and thermal steps will be discussed in Section 2.4: “Choosing Models In SSUPREM4”). To set a
geometrical etch step, select Process→Etch→Etch... from the Command menu of DECKBUILD. The
ATHENA Etch Menu (Figure 2-15) will appear.
Figure 2-15: ATHENA Etch Menu
The Geometrical etch is the default method. Other methods will be discussed in Section 2.8.2:
“Deposition and Wet/Dry Etching using the Physical Models in ATHENA/ELITE”. Select Polysilicon
from the Material menu. This example will use a polysilicon gate edge at x=0.3 and set the center of
the gate at x=0.0 for the initial grid. Therefore, polysilicon should be etched to the right from x=0.3. To
do so, select Right from the Geometrical type, and set the Etch location to 0.3. This will give the
following statement:
# POLY DEFINITION
ETCH POLY RIGHT P1.X=0.3
The structure created by this ETCH statement is shown in the left hand plot of Figure 2-16.
You can obtain an arbitrary shape of geometrical etching by using the Any Shape button. For
example, to make a tilted etch, specify X and Y locations of four Arbitrary points as shown in Figure
2-17.
The following four etch lines will be inserted into the input file:
# POLY DEFINITION
ETCH POLY START X=0.2 Y=-1
ETCH CONT X=0.4 Y=1
ETCH CONT X=2 Y=1
ETCH DONE X=2 Y=-1
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Figure 2-16: Structure Created by Etch Statement
Figure 2-17: Arbitrary Etch
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If this input file fragment is runned instead of the previous one (using the INIT statement from the
History capability), the structure after this etch sequence will appear as displayed in the right hand
plot in Figure 2-16. ATHENA etches all polysilicon material within the specified polygon. The polygon
etch can consist of any number of points. If you use the Insert button, an additional point will appear
after the currently selected point.
An additional option for geometrical etching is a dry etch with a specified thickness. This can be used
for spacer formation as follows: deposit an oxide of a specified thickness (e.g., 0.2µm) and then etch the
same thickness again.
# CLEAN GATE OXIDE
ETCH OXIDE DRY THICK=0.03
# SPACER DEPOSITION
DEPOSIT OXIDE THICK=0.2 DIVISIONS=8
# SPACER ETCHING
ETCH OXIDE DRY THICK=0.23
The dry etching step etches the specified material in the region between the top (exposed) boundary of
the structure and a line obtained by translating the boundary line down in the Y direction. The etch
distance is specified by the THICK parameter. Figure 2-19 shows the resulting spacer.
Reducing Grid Points in Non-Essential Areas using the Relax Parameter
The previous sections demonstrate that the quality of the grid is extremely important for ATHENA
simulation. The rectangular based grid generated by the INITIALIZE or DEPOSIT statements may
remain intact in those areas not involved in the process steps affecting the grid (e.g., etching or
oxidation). The Grid Relax capability allows the spacing to be increased in such areas at any point
during the simulation. This capability is useful for two reasons. First, the initial small spacings are
propagated throughout the structure. For example, the fine grid in the X-direction shown in Figure 2-9
may be needed only in the upper portion of the structure where doping occurs. Eliminating some grid
lines and points in the lower portion of the structure will not affect the accuracy of implant and
diffusion simulation. Second, it is always necessary to set a fine grid in the area where ion
implantation takes place, but the fine grid may be uneccessary after the profile is leveled-off during
thermal steps. So, relaxation of an initially fine grid may save simulation time during subsequent
steps. Parameters for the RELAX statement are set from the ATHENA Relax Menu (Figure 2-18).
Figure 2-18: ATHENA Relax Menu
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To open this menu, select Structure→Relax... in the DECKBUILD Commands menu. You can preform
grid relaxation over the whole structure if you select Entire Grid, or within a selected rectangular
area, if you choose Selected and specify Xmin, Xmax, Ymin, and Ymax in Location Select.
Selecting a material from the Material menu specifies which material region will be affected by the
grid relax operation. The default is all materials within the specified area. You can perform the grid
line elimination either in one direction or in both directions by selecting X direction, Y direction, or
Both. The X direction, Relax, cannot be performed for individual materials except for the substrate.
To understand how the relax function changes a grid, we will use the structure we have obtained after
spacer formation was specified (Figure 2-19). If we relax the entire grid in both directions
(Figure 2-20), the following lines will be inserted into the tutorial input file:
# RELAX EVERYWHERE
RELAX DIR.X=T DIR.Y=T
Figure 2-19: Spacer Formation using Dry Etch
The resultant grid is shown in the upper-right corner of Figure 2-20.
The total number of grid points is reduced from 708 to 388. When comparing with the grid before
relaxation (upper-left corner of Figure 2-20), note that the grid within the oxide spacer and polygate
has not changed. This is due to three factors:
•
the relax algorithm works only with rectangular base grid,
•
it never eliminates grid lines adjacent to a region boundary,
•
the relaxed area should be at least five by five grid points.
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Within silicon, each second horizontal line is eliminated. The lower part of each second vertical line is
also eliminated. This happens because the algorithm doesn’t allow the formation of obtuse triangles.
Figure 2-20: Grids after Various Relax Operations
If you don’t want the grid to be relaxed above y=0.3, choose Selected and set all four boundaries in the
Relax box. This will give the following RELAX statement:
# RELAX LOWER HALF OF THE STRUCTURE
RELAX X.MIN=0.00 X.MAX=1.00 Y.MIN=0.3 Y.MAX=1.00 DIR.X=T DIR.Y=T
In this case, the number of grid points is 567. The grid above y=0.3 remains intact (see the plot in
lower-left corner of Figure 2-20) and the elimination in X and Y- directions happens only below y=0.3.
To increase spacing only in the X-direction in the area below y=0.3, select the X direction and leave
the Area and Location Selections as before. This will give the following Relax statement:
# RELAX LOWER HALF ONLY IN X-DIRECTION RELAX X.MIN=0.00 X.MAX=1.00 Y.MIN=0.3
Y.MAX=1.00 DIR.X=T DIR.Y=F
Note: The only difference is that instead of DIR.Y=T, the statement contains DIR.Y=F, which prevents elimination in Ydirection. This gives 638 grid points and a different pattern of elimination (see the plot in the lower-right corner of Figure 2-20).
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You can also apply several consequent RELAX statements to achieve grid elimination in different areas
of the structure.
An important thing to remember about the RELAX capability is that it allows you to avoid creating
obtuse triangles and avoid relaxing directly on the material boundaries. This sometimes results in no
relaxation or grid relaxation in a subset of the desired area. The most desirable method for complete
control over gridding is by using DEVEDIT as described briefly in this chapter and in the VWF
INTERACTIVE TOOLS User’s Manual, Vol. II.
Reflecting a Structure in the “Y” Plane using the Mirror Parameter
This tutorial process simulation has been building one half of a MOSFET-like structure. At some point
in the simulation, you will need to obtain the full structure. This must be done before exporting the
structure to a device simulator or setting electrode names. In general, structure reflection should be
performed when the structure ceases to be symmetrical (e.g., a tilted implant, an asymmetrical
etching, or a deposition takes place), or when a reflecting boundary condition no longer applies to the
side, which is going to be the center of the structure.
This example will explain how to mirror the structure at its left boundary. To mirror the structure,
select Structure→Mirror in the Commands menu (Figure 2-21).
Figure 2-21: ATHENA Mirror Menu
Then, press the Write button to write the following statement to the input file:
STRUCT MIRROR LEFT
The resulting structure is shown in Figure 2-22.
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Figure 2-22: ATHENA Reflect Capability
The left half of the structure is a complete mirror copy of the right part, including node coordinates,
doping values, and so on. Beware of rounding errors when mirroring. If the boundary of reflection is
not smooth to within 0.1 angstroms, some points will be duplicated.
Specification of Electrodes in ATHENA
The ultimate goal of an ATHENA simulation is usually to create a device structure (material layers
plus doping), which then can be used by a device simulator (usually ATLAS) for electrical
characterization. Although ATLAS is able to specify the locations of electrodes, in many cases
specifying electrodes must be done in ATHENA. For example, it is impossible to specify an electrode
location in ATLAS when the electrode does not consist of straight segments. Also, when specifying
electrodes in ATHENA, it is useful to transfer electrode layer information from layout to electrical tests
in a device simulator (see the description of the auto-electrode capability in the MASKVIEWS Chapter
of the VWF INTERACTIVE TOOLS USER’S MANUAL, VOL. II).
ATHENA can attribute an electrode to any metal, silicide, or polysilicon region. A special case is the
backside electrode, which can be placed at the bottom of the structure without having a metal region
there. If you deposit 0.1 µm aluminum layer on the full structure after reflection (Figure 2-22) using:
DEPOSIT ALUMIN THICK=0.1
and etched the following part of the layer between x=-0.8 and x=0.8, using the Any Shape
specification in the Athena Etch Menu (See Figure 2-15):
ETCH ALUMINUM START X=-0.8 Y=-20
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ETCH CONT X=-0.8 Y=20
ETCH CONT X=0.8 Y=20
ETCH DONE X=0.8 Y=-20
you will now have the structure shown in Figure 2-23.
Figure 2-23: MOSFET Structure with Electrodes
You can now use the ATHENA Electrode menu (see Figure 2-24) by selecting
Commands→Structure→ Electrode.... To set an electrode at a specified position, select the
Specified Position button, type in the X Position (e.g., -0.9) and Name (for example, source), and
press the Write button. The following statement will appear in the input file:
ELECTRODE NAME=SOURCE X=-0.9
Similarly, specify the drain electrode:
ELECTRODE NAME=DRAIN X=0.9
The polysilicon gate electrode specification has the same format. For this structure it can be done the
same way as for source or drain:
ELECTRODE NAME=GATE X=0.0
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If the polysilicon layer is not the topmost layer at x=0, the Y Position can be specified. In this case,
check the Y Position checkbox and type in a y coordinate within the polygate layer (e.g., -0.2). If Y is
not specified and the electrode is not on top, ATHENA will look for the electrode in the underlying
layers. If it fails, an error will be reported. To specify a backside electrode, select Backside from the
Electrode Type field and type in a name (see also Figure 2-24) .
Figure 2-24: ATHENA Electrode Menu
The following backside electrode statement will appear in the input file:
ELECTRODE NAME=BACK BACKSIDE
If an electrode name is not specified, DECKBUILD issues the error message: NO ELECTRODE NAME
SPECIFIED and the command is not written to the input file.
If an incorrect position for electrode is specified, for example:
ELECTRODE NAME=JUNK X=0.6
ATHENA will output the following warning message: Cannot find the electrode for this
structure. Electrode statement ignored and ignores the statement.
Saving a Structure File for Plotting or Initializing an ATHENA Input file for Further Processing
As mentioned in the “Standard Structure File Format” Section on page 2-8, the DECKBUILD history
function saves structure files after each process step. In many cases, however, you need to save and
initialize structures independently. There are several reason why it’s needed to save and initialize
structures independently.
The first reason is because the stack for the history files is limited (50 by default). The second reason is
because it is usually undesirable to keep dozens of history files on disc (each of which occupy hundreds
of Kbytes) after the DECKBUILD session ends. The third reason is because users often want to save the
structure information generated after key process steps (e.g., final structure)
To save or load a structure, use the ATHENA File I/O Menu (See Figure 2-25) by selecting
Commands→File I/O.... Specify a file name (the file extension.str is recommended for all ATHENA
structure files) and press the Save button. The following line will appear in the input file:
STRUCT OUTFILE=TUTOR.STR
You can reload this file (tutor.str) back into ATHENA at any time during the current DECKBUILD
session or during any subsequent session. To reload the structure file, press the Load button on the
ATHENA File I/O menu. The following INIT statement will appear:
INIT INFILE=TUTOR.STR
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Figure 2-25: ATHENA File I/O Menu
Note: Only the structure will be reloaded if ATHENA is restarted before this INIT statement. Any parameters or
coefficients that were set during previous simulations must be reset if they are needed. This structure file can also be used by
any device simulator or DEVEDIT.
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2.4: Choosing Models In SSUPREM4
2.4.1: Implantation, Oxidation, RTA, Diffusion and Epitaxy
This section describes how to simulate process steps (e.g., implantation, diffusion/oxidation, epitaxy,
and silicidation) specific to the SSUPREM4 module of ATHENA. Also discussed, are the SSUPREM4
model statements, such as METHOD, OXIDE, MATERIAL, and IMPURITY.
For more information about SSUPREM4, see Chapter 3: “SSUPREM4 Models”. For more information
about the MODEL statements, see Chapter 6: “Statements”.
When simulating any process involving dopant or its diffusion or both, it is absolutely critical for
simulation accuracy to use the appropriate model. Process steps where correct choice of models are
vital include implantation, diffusion, rapid thermal annealing, oxidation, and epitaxy. This section
provides specific advice on which models should be used for each process step.
2.4.2: The Reason for Multiple Models for Each Process
The key to simulating any dopant related process is to accurately account for damage in the
semiconductor. For example, in silicon processing, typical implantation doses can cause sufficient
damage to the substrate to enhance dopant diffusion rates by three orders of magnitude or more, so
choosing the wrong model in this instance will result in inaccurate results.
Well known device anomalies such as the Reverse Short Channel Effect in MOS processing or the
emitter push effect in bipolar processing are wholly the result of such damage enhanced diffusion.
Other processes that consume the semiconductor, such as oxidation and silicidation also inject damage
into the substrate. This must be accounted for if accurate dopant profiles are a requirement.
This section aims to provide you with a set of rules outlined, indicating the correct model that can be
used most of the time without you having a detailed knowledge of the physics involved. The usual
rules of model selection apply here. The more complicated the model, the greater the simulation time.
There is always a compromise between simulation accuracy and simulation time. The following
sections describe when to use the hierarchy of models so that the most complicated models are only
used when you make a significant difference to the result.
2.4.3: Choosing an Appropriate Model Using the Method Statement
The hierarchy of diffusion and damage models available is broadly related to the maximum level of
damage already in the semiconductor or the maximum level of damage that the next process step is
likely to introduce at any particular time during the process flow. The level of damage in the
semiconductor at any one time is not a static quantity but will depend on when and how much damage
was induced by a process step and how much annealing has occurred in subsequent thermal steps. The
range of models available to you can account for all of the above effects and allows accurate simulation
of dopant diffusion if appropriate models have been chosen.
The choice of model or combination of models for any of the process steps described above is defined in
the METHOD statement. The METHOD statement serves a number of functions but in the context of
defining damage models the METHOD statement is used for two purposes.
The first purpose is to specify models for how damage is induced during processes such as
implantation or oxidation. The second purpose is to specify how that damage anneals and diffuses in
subsequent or concurrent thermal processes.
It’s important to realize that the METHOD statement must be placed above the line, specifying the
process step or steps to which it refers in the input file. Any number of method statements can be used
in an input file allowing you to change the models at will during the process flow to optimize the speed
and accuracy of the simulation. The models specified in the METHOD statement will hold true for all
processes that follow it until it’s updated by a subsequent method statement.
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Table 2-1 below indicates a recommended method statement for typical processes. It should be
realized that these statements are hierarchical, so there is no accuracy lost if a more complicated
model is used where a simpler one would suffice. The only downside here is a longer simulation time.
The table below starts off with the simplest of models and progresses to the more complicated ones.
Table 2-1. Recommended Method Statements for Typical Processes
Method Statement Syntax
Suitability of using this method syntax
method fermi
Use only before undamaged silicon diffusions, where doping
concentrations are less than 1e20/cm3 and no oxidizing
ambient is present.
method two.dim
Use before implant doses less than 1e13/cm2 and for
oxidations.
method full.cpl
cluster.dam high.conc
Use before implant doses greater than 1e13/cm2
2.4.4: Changing the Method Statement During the Process Flow
It has previously been stated that the disadvantage of using the most advanced and complex models is
the time involved during diffusion cycle simulation. Accordingly, there is an incentive during complex
process simulations to switch back to a simpler model during a diffusion cycle when the majority of the
damage created by a previous implant has been annealed. We will show you when to switch to a
simpler model.
If the process being modeled has involved implantation or oxidation at any stage, we advise not to use
the fermi model. An exception to this would be in some power devices with very long diffusion times
where the exact nature of surface damage would have little impact on the final distribution of the
dopant and simulation time is at a premium.
In reality, for most small geometry processes, the question of switching models becomes one of when to
add a new method statement that changes from:
METHOD FULL.CPL CLUSTER.DAM HIGH.CONC
to
METHOD TWO.DIM
after a high dose implant.
Switching guidelines
A simple guideline to follow when to switch method statements during a process flow is by switching
back to the TWO.DIM model if the anneal temperature is greater than 900° and the device has been
annealed for at least one minute, following an implant where the dose is greater than 1e13/cm2.
For a more accurate guideline, see the Chapter 3: “RTA Diffusion Modelling”. Table 3-6 shows the
anneal temperature/time combinations required for 95% of the clusters formed during high dose
implants to dissolve. Modeling these dopant/defect clusters requires the fully coupled (full.cpl) and
cluster damage (cluster.dam) models. Only when these clusters have dissolved can the two.dim
model be used without significant loss of simulation accuracy. As a general rule, we recommend that
the method statement be changed to method two.dim only after a diffusion time that is at least two
or three times as long as the values quoted in the table.
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If you wish to be certain of when it’s safe to switch models, the recommended procedure is to save a
structure file at the point of interest, load the file into TONYPLOT and perform a 1D cutline. Plot the
clusters and interstitials. If the cluster concentration is still visible, it’s too early to switch models.
For power devices, where simulation time is at a premium, the same method already described should
be used. But instead of using the cluster concentration as a guide of when to switch models, the
interstitial concentration should be used as the guide as to when to switch models one more time from
the TWO.DIM model to the basic FERMI model. When the interstitial concentration near the surface
during a very long anneal has been reduced to only marginally above the background level at the
anneal temperature concerned, the method statement can be switched to METHOD FERMI to greatly
reduce the simulation time. The interstitial background level will be the level deep in the substrate
where little damage has occurred.
2.4.5: Modelling the Correct Substrate Depth
An important and often overlooked aspect of the correct modeling of dopant diffusion is the choice of
substrate depth. It has been mentioned previously that the rate of dopant diffusion is highly
dependent on the level of damage in the substrate. Therefore, the accurate modeling of dopant
diffusion requires the accurate modeling of substrate damage, particularly the movement of
interstitials. In general, the interstitials created directly or indirectly by implantation and oxidation
tend to diffuse much greater distances than the dopant. The substrate depth chosen for modeling
purposes must therefore be deep enough to allow the interstitial concentrations to return to
background levels at the bottom of the simulated substrate, even if no dopant diffusion occurs at this
depth.
Figure 2-26: Interstitials can move far into the substrate even after a short 10min anneal
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Figure 2-26 shows typical diffusion profiles of interstitials after a 1e15/cm3 20keV Boron implant at
various anneal times. After only a 10 minute anneal, the interstitials have diffused 8um into the
substrate.
Interstitials, like dopant, require a concentration gradient in order for overall diffusion to take place.
For example, if the concentration gradient of interstitials is removed by having too shallow a substrate
depth, the concentration of interstitials will start to pile up because they are no longer being removed
through diffusion into the bulk of the substrate. If the level of modeled interstitials becomes too high,
the diffusion of dopant, even near the surface of the substrate, will also be too high and the simulation
will be inaccurate.
Figure 2-27: Effect on boron diffusion profile when too small a substrate depth is used in the simulation
Figure 2-27 shows the boron profiles for two identical anneals, the only difference is the depth of the
simulated substrate. You’ll see that a shallow modeled substrate always results in more total diffusion,
even though the substrate depth was greater than the total diffusion depth in both cases.
Modeling a deep substrate doesn’t need to involve a huge number of extra mesh points, since the mesh
points can be placed quite far apart near the bottom of the substrate. All that is required of the mesh
points near the bottom of the substrate is that there be sufficient to model the gradient of interstitials
in this region. The number of additional mesh points can be further reduced in the X-direction by the
using several RELAX statements.
For normal small geometry MOSFET/Bipolar processing, a substrate depth of 20 µm should be more
than adequate. This depth can be reduced by plotting the vertical interstitial profiles at various points
in the process to find the maximum depth of interstitial diffusion. There is little to be gained by
reducing the depth of simulation, however, if the combination of large grid spacing is deep in the
substrate and the RELAX statement is used appropriately.
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Simulating Ion Implantation
Ion implantation is the main method used to introduce doping impurities into semiconductor device
structures. Adequate simulation of the ion implantation process is very important because modern
technologies employ small critical dimensions (CDs) and shallow doping profiles, high doses, tilted
implants and other advanced methods.
The IMPLANT statement can be set by using the ATHENA Implant Menu (Figure 2-28). To open this
menu, select Process →Implant... in the Commands menu.
Figure 2-28: ATHENA Implant Menu
The following gives the minimum set of parameters that should be specified:
•
Name of implant impurity (e.g., boron)
•
Implant dose using the slider for the pre-exponential value (e.g., 4.0) and the Exp menu for the
exponent (e.g., 12)
•
Implant energy in KeV (e.g., 60)
•
Tilt angle in degrees (e.g., 7°)
•
Rotation angle in degrees (e.g., 30°)
All other parameters can use their default values.
Press the Write button and the following statement will appear in the input file.
# CHANNEL IMPLANT
IMPLANT BORON DOSE=4.0E12 ENERGY=60 PEARSON TILT=7 ROTATION=30 \
CRYSTAL
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All of the parameters in the statement above are self-explanatory except CRYSTALLINE. The
CRYSTALLINE parameter indicates that for all analytical models, the range statistics extracted for a
single silicon crystal will be applied (when available). If AMORPHOUS is selected, the range parameters
measured in pre-amorphized silicon will be used (when available). The CRYSTALLINE parameter also
has another meaning for the Monte Carlo or BCA implant models. It invokes the Crystalline Material
Model which takes channeling into account. Note that the latter model is much slower (5 - 10 times)
than the Amorphous Material Model. The Crystalline Material Model is the default model for BCA or
Monte Carlo simulation.
For a detailed description of ion implant model selection, see Chapter 3:
Section 3.5: “Ion Implantation Models”.
“SSUPREM4 Models”,
You can specify tilt and rotation angles of the ion beam. Positive tilt angles correspond to the ion beam
coming from the top left. Specifying the rotation angle makes sense only for non-zero tilt angles. Zero
rotation means that the ion beam vector lies in the plane parallel to the 2D simulation plane. 90°
rotation means that the ion beam vector lies in the plane perpendicular to the simulation plane.
Selecting Continual rotation causes SSUPREM4 to rotate the wafer, i.e., implantation will be
performed at 24 different rotation angles from 0 to 345°, in increments of 15°.
There are several damage models available in SSUPREM4. These models allow you to estimate
distributions of various defects generated after ion implantation. For more details about the damage
models and their effect on subsequent diffusion, see Chapter 3: “SSUPREM4 Models”, Section 3.5.5:
“Ion Implantation Damage”.
When the Monte Carlo model is selected, you can specify several additional optional parameters (See
Figure 2-29). The first three parameters are related to the Damage model (Point defects, {311}-clusters,
and dislocation loops). The three others control Monte Carlo calculation (initial random number,
number of trajectories, and smoothing). See Table 2-2 for a quick reference of ATHENA implant models.
Table 2-2. ATHENA Implant Model Reference
Process
Model
Assumption
Recommendation
Implant
SIMS Verified Dual
Pearson (SVDP) - Default
Empirical
See Chapter 3: “SSUPREM4 Models”,
Table 3-7.
Single Pearson
Analytic
All other cases
Monte Carlo
Monte or BCA
Statistical
Multi-layer structures: angled implants
into a structure where many ions could
be reflected (trenches); when channeling
is not described by SVDP; high or very
low energy
Amorphous
No channeling
effect is
included
Most of implant profile is within amorphous materials (oxide, polysilicon, preamorphized silicon); channeling is negligible or not important
Crystal - Default
Channeling
effect is
included
When channeling effects are important:
light ions (boron, phosphorus)_, zero or
close to 0° tilt, implant through thin
amorphous layer into crystalline substrate
Silicon
Type
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Figure 2-29: ATHENA Implant Window
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Simulating Diffusion
Simulation of thermal process steps is a focal point of SSUPREM4. The hierarchy of diffusion and
oxidation models is described in this chapter and in Chapter 3: “SSUPREM4 Models”, Sections 3.1:
“Diffusion Models” and 3.3: “Oxidation Models”. This section will demonstrate how to set different
parameters and models of diffusion, oxidation and silicidation. The last process will take place only if
at least one refractory metal or silicide layer is present in the structure.
The parameters and models of a diffusion/oxidation step can be prepared from the ATHENA Diffuse
Menu. (Figure 2-30).
Figure 2-30: ATHENA Diffuse Menu
To open this menu, select Process→Diffuse... in the Deckbuild Commands menu. The Diffuse menu
has four sections. Only the Time/Temperature and Ambient fields appear initially. The
Impurities and Models fields appear only when the corresponding check boxes are selected.
The minimum set of diffusion step parameters is as follows:
•
Time (e.g., 60 minutes)
•
Temperature (e.g., 1100° Celsius)
•
Gas pressure (1 atmosphere is default)
The following input file statements will appear:
# DRIVE-IN
DIFFUSE TIME=60 TEMP=1100 NITRO PRESS=1.00
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If you choose the Ramped box and End Temperature or Temperature rate, a ramped temperature
thermal step is simulated. The temperature rate is a variable by default, but it can be set to a specific
constant temperature rate by selecting Constant in the Rate box. If the End Temperature is set to
1000, the following lines appear:
# RAMPING DOWN
DIFFUSE TIME=60 TEMP=1100 T.FINAL=1000 NITRO PRESS=1.00
The same pull down menu used for inert diffusions is also used for oxidations described in the
“Simulating Oxidation” Section on page 2-39. But, since there are special considerations for inert
diffusions which come under the category of Rapid Thermal Anneals (RTA), the special notes
pertaining to this specific set of conditions are described in the next section. These notes are very
important for accurate simulation of high temperature, short duration anneals. We recommend that
you read these notes before attempting to write the RTA section of the input file.
2.4.6: Simulating Rapid Thermal Anneals (RTA) Notes
The usual reason for employing a Rapid Thermal Anneal (RTA) in a process flow is to anneal out
damage in the substrate that has been caused by a previous process step, usually an implant, while at
the same time minimizing dopant diffusion. Dopant activation also occurs during this process. These
anneals are usually high in temperature and low in duration for sound device physics reasons.
Once again, the key to accurate simulation of RTA lies in the accurate simulation of substrate damage
behavior. The role of interstitials in enhanced dopant diffusion has already been explained in Section
2.4: “Choosing Models In SSUPREM4” to become familiar with the role of interstitials during process
simulation.
The reason why an RTA usually employs high temperatures and short durations is because for a given
high dose implant, if an anneal duration is selected so that a fixed percentage of the damage is
annealed, the lower the anneal temperature, the more dopant diffusion occurs.
The above statement requires an explanation since intuitively, the opposite would seem more likely. A
descriptive explanation of what is happening can be informative if the two extremes of anneal
temperature are considered.
For the lowest anneal temperatures, the damage anneal rate is almost zero, so dopant diffusion rates
are enhanced by a factor of 1000°C or more for the long time periods required to remove the damage.
This results in high total dopant diffusion.
For the highest temperature anneals, a significant percentage of damage removal occurs in a fraction
of a second. Almost zero damage enhanced diffusion or total diffusion occurs in this instance, and the
anneal time to remove the damage is very short. Extrapolating between these extremes provides a
qualitative explanation of what occurs for intermediate temperature anneals.
Two important points have now been established:
1. For sound device physics reasons, most RTA processes consist of high temperature, short duration
anneals.
2. Damage-enhanced diffusion will only occur for a few seconds at typical RTA temperatures.
For accurate simulation of RTA, the second point is most important and often wrongly neglected.
Suppose an RTA consists of a 10 second ramp up to 1000°C, followed by a 20 second anneal and a 10
second cool down. From the second point, it is apparent that most of the Total Dopant Diffusion would
have taken place during the Ramp Up Phase of the RTA.
Therefore, always model the temperature ramp up accurately when simulating an RTA process. In
most cases, the ramp down can be neglected, since all the diffusion has already taken place at the
beginning when the silicon was still damaged.
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2.4.7: Simulating Oxidation
It has already been stated that the pull down menu for simulating oxidations is the same as that for
simulating inert diffusions described in the “Simulating Diffusion” Section on page 2-37. See this
section for advice on selecting the appropriate pull down menu from DECKBUILD.
The default method for oxidation is Compress. In SSUPREM4 examples there are a number of
examples which illustrate the use of different models for different processes and structures.
In our previous example described in the “Simulating Diffusion” Section on page 2-37, if the next
temperature step is going to be at a constant temperature of 1000°C in dry O2 with 3% of HCL in the
ambient, select the Dry O2 box and set HCL% equal to 3 in the Ambient section of the Diffuse menu.
The following input file fragment will appear:
# GATE OXIDE
DIFFUSE TIME=60 TEMP=1000 DRYO2 PRESS=1.00 HCL.PC=3
If the ambient is a mixture consisting of more than one oxidant, the total oxidation rate will depend on
the combined effect of all species in the ambient. To specify the contents of the ambient mixture, select
t he Gas Flow button in the Ambient section and an additional ATHENA Gas Flow Properties Menu
(Figure 2-31) will appear.
Figure 2-31: ATHENA Gas Flow Properties menu
If the Gas Flow components are selected, as shown in Figure 2-31, the following statement will be
generated:
# GATE OXIDE
DIFFUSE TIME=60 TEMP=1000 F.H2O=5.3 F.HCL=0.06 F.O2=8.0 \
PRESS=1.00
One or several impurities can be present in the ambient. To set ambient in the Impurity
Concentration section of the ATHENA Diffuse Menu (See Figure 2-30), check the corresponding
checkboxes, and set the values using sliders and the Exp menus.
For example, by selecting the appropriate boxes and values, the following DIFFUSE statement will be
inserted into the input file:
# FIELD OXIDE
DIFFUSE TIME=100 TEMP=850 T.FINAL=1060 WETO2 PRESS=1.00 \
HCL.PC=0 C.ARSENIC=9.0E19 C.PHOSPHOR=4.0E20
Several other parameters not included on the menu are available in the DIFFUSE statement (Chapter
6: “Statements”, Section 6.15: “DIFFUSE”). The DUMP, DUMP.PREFIX, and NO.DIFF parameters
can be useful. DUMP and DUMP.PREFIX can be used to make a movie using TONYPLOT. The NO.DIFF
parameter specifies that impurity redistribution will be neglected. This provides a good approximation
for low temperature processes, such as silicidation.
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Several other model specification statements are important for diffusion processes. These are as
follows:
•
IMPURITY, INTERSTITIAL, and other impurity and point defect statements, which specify model
parameters (e.g., diffusivity or segregation) of these species.
•
The OXIDE statement, which specifies parameters for different oxidation models.
•
The MATERIAL statement, which specifies some basic parameters for all materials.
•
The SILICIDE statement, which specifies silicidation coefficients.
Table 2-3 shows the basic diffusion and oxidation models.
Table 2-3. Basic Diffusion and Oxidation Models
Process
Model
Assumption
Recommendation
Diffuse
Fermi- Default
Defect in equilibrium
For undamaged substrates in inert
ambients
two.dim
Transient defect diffusion
during oxidation, and after medium
dose implant (e.g., OED)
full.cpl
Defect and impurity
binding energy model
Post high dose implant & co-diffusion
effects, but execution time is high
Vertical
Planar
1D oxidation only (should never be
used)
Compress- Default
Non-planar with linear flow
2D oxidation (e.g. birds beak)
Viscous
Elastic
Non-planar with nonlinear flow
2D oxidation (e.g. birds beak with thick
Si3N4, however, execution time is
higher
Oxidation
For a detailed description of all diffusion and oxidation models, see Chapter 3: “SSUPREM4 Models”,
Sections 3.1: “Diffusion Models” and 3.3: “Oxidation Models”.
2.4.8: Simulating the Epitaxy Process
ATHENA/SSUPREM4 can simulate a high temperature silicon epitaxial processes. The epitaxy process
is considered as a combination of deposit and diffuse processes. Therefore, processes such as
autodoping from a highly doped buried layer into a lightly doped epitaxial layer can be simulated.
Diffusion parameters for epitaxial silicon, however, are considered the same as for single crystal
silicon.
The epitaxy process is defined in the ATHENA Epitaxy Menu (Figure 2-32). To open this menu, select
Process→Epitaxy in the Commands menu. The ATHENA Epitaxy Menu consists of five sections:
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•
The Time/temperature section selects temperature step parameters in the same way as in the
DIFFUSE statement.
•
The Thickness/rate section selects either the total thickness of the epitaxial layer, or the deposit
rate in microns/minute. In the latter case, the total thickness will be determined by the rate and
time.
•
The Grid Specification section specifies the vertical grid structure within the grown epitaxial
layer. All grid parameters are equivalent to those of the ATHENA Deposit Menu
(See Figure 2-12).
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•
The Ambient section is where the gas pressure can be modified to the value used in the Epitaxial
Chamber.
•
The Impurity Concentrations section specifies the growing epitaxial layer in the same way as
in the DIFFUSE statement.
All parameters in the last three groups are optional. If the parameters of an epitaxial step are set
exactly as shown in Figure 2-32, the following statement will appear in the input file:
# EPI-LAYER
EPITAXY TIME=30 TEMP=900 T.FINAL=1000 THICKNESS=5 DIVISIONS=20 \
DY=0.05 YDY=0.00
Note: The diffusion during the epitaxy process will use the Diffusion Model Set in the most recent METHOD statement. If you
need another METHOD statement, include it before the EPITAXY statement.
Figure 2-32: ATHENA Epitaxy Menu
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2.5: Calibrating ATHENA for a Typical MOSFET Flow
This section of the manual provides information on which parameters should be tuned in the input file
to provide predictive simulations using a typical MOSFET process flow. We assume you are now
familiar with the mechanics of making an input file and using the correct methods and models (see
Section 2.4: “Choosing Models In SSUPREM4”). For example, incorrect use of the METHOD statement
will invalidate the rest of the following section.
Calibrating an ATHENA input file for a typical MOS process flow involves using the device simulator,
ATLAS, since electrical measurements from the MOSFETs in question often represents the majority of
the physical data available for calibration. This can be thought as a paradox since ATLAS would also
have to be correctly calibrated. The reason that this doesn’t present a problem is discussed below.
An important point to remember when using Technology Computer Aided Design (TCAD) is that the
most critical task is to accurately model the process flow.
Note: For accurate MOSFET simulation, you should invest 90% of the time in achieving an accurate process simulation,
while only investing 10% of the time in fine-tuning the device simulation.
The reason for this, especially for silicon technologies, is that the device physics, in general, is
understood. For silicon, not only is the physics well understood, it is also well characterized, so most of
the default values in ATLAS will be correct. Therefore, the calibration of an ATHENA process file does
not involve the calibration of well known quantities such as diffusion coefficients. Instead, the
calibration involves variables that are process and production line dependent. For example, the
damage caused by an implant cannot be determined exactly, since it is dose rate dependent and can be
influenced by beam heating of the substrate, which is dependent on the carousel rotation speed and
the efficiency of the cooling system.
Note: If the process has been correctly modeled, the device simulation will also be accurate if appropriate models have been
chosen.
If a simulated device exhibits electrical characteristics that are totally inaccurate, you may have done
something wrong in the process simulation. Do not make the mistake of changing well known default
values in the simulators to make a curve fit one set of results because this will lead to poor predictive
behavior. Try and find the cause of a discrepancy.
2.5.1: Input Information
It may seem obvious but must be emphasized that an accurate process flow is vital for simulation
accuracy, especially for Rapid Thermal Anneals (see Section 2.4.6: “Simulating Rapid Thermal
Anneals (RTA) Notes” for details). Other process information required is an accurate cross-section of
the oxide spacer. Modeling the spacer profile accurately ensures the lateral damage distribution due to
the subsequent source-drain implants is correctly modeled.
Turning to electrical data, the most important device electrical data is a plot of threshold voltage
versus gate length for the NMOS devices. Figure 2-33 shows typical plots of threshold voltage versus
gate length. In this figure, the RTA anneal temperature and times were varied to show the various
profiles that can be expected. A more typical plot is represented by the 1000°C RTA profile, showing a
peak value around 1-2 microns with a tail off for longer or shorter gate lengths.
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Figure 2-33: A plot of Threshold Voltage vs. Gate Length for NMOS devices
Gate oxide thickness measurements are also required. Be careful here if oxide thickness is measured
with capacitance-voltage (C-V) methods, since quantum effects in very thin oxides (less than 5nm) can
lead to inaccuracies because the actual location of the peak concentration of the accumulation charge
is not at the interface as classic physics predicts but a short distance into the silicon. Use the QUANTUM
model in ATLAS to match accumulation capacitance with oxide thickness for very thin oxides.
Other useful electrical input information is data that won’t be used now but later for the calibration
process itself, testing the predictive nature of the simulation. Typical device characteristics used for
predictive testing includes threshold voltage versus gate length measurements for a non-zero
substrate bias.
2.5.2: Tuning Oxidation Parameters
During oxidation, interstitials are injected into the silicon substrate by the advancing interface. The
first parameter to tune is the fraction of consumed silicon atoms that are re-injected back into the
substrate as interstitials. In ATHENA, the related tuning parameter is called THETA.0 and is defined
in the INTERSTITIAL statement. THETA.0 has been found to be slightly different for wet and dry
oxides. The default value is reasonably accurate for dry oxides but some tuning may be required for
wet oxidation.
The major effect of interstitial injection during gate oxidation is to create enhanced diffusion of the
threshold adjust implant. The measured threshold voltage of the final device is very sensitive to the
dopant concentration near the silicon-gate oxide interface. Consequently, threshold voltage
measurements are a sensitive indicator of interstitial behavior. Oxidation, however, is not the only
source of interstitial injection. The source-drain and LDD implants also induce a large concentration of
interstitials. In order to isolate oxidation enhanced diffusion, the threshold voltage of a long gate
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length device is used, preferably where L=20 µm or more, so that the threshold voltage will be little
influenced by damage near the source-drain regions.
Interstitials injected by source-drain implant damage can travel up to 10 µm along the surface before
recombination takes place. A gate length of 20 µm is recommended as the minimum gate length for
calibration so this can allow the interstitials to diffuse 10 µm along the surface from both the source
and drain ends without effecting diffusion near the center of the device. In summary, tuning THETA.0
involves the comparison of modeled and measured threshold voltage data for a long gate-length device.
THETA.0 can be rapidly tuned by taking a one dimensional (1D) vertical cutline through the center of
the gate and doing a 1D process simulation. You can either tune THETA.0 manually or by using the
Optimize function in DECKBUILD. Theta.0 is tuned until the measured and simulated data of the long
channel threshold voltage correspond. The fine tuning of THETA.0 is performed by using a full 2D
simulation.
Figure 2-34 shows a typical dependence of extracted threshold voltage on the Theta.0 tuning
parameter. Realistic values of THETA.0 correspond to the rising part of the curve. The glitch in the
curve is due to rounding errors in the EXTRACT statement used to calculate the threshold voltage due
to the automatic and independent mesh generated in the EXTRACT statement. The mesh can be
changed from its default value shown here to eliminate this effect. But close examination reveals that
the error is only a few millivolts off, which is accurate enough for most process parameter extractions.
Figure 2-34: A Typical Dependence of Extracted Threshold Voltage
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2.5.3: Tuning Implantation Parameters
You can now tune two implantation parameters by using the threshold voltage versus gate length
data. The peak value of threshold voltage for a given process flow (the reverse short channel effect) will
be a function of the initial implant damage caused by the LDD and source-drain implants. Since these
implants have a high total dose and damage, the tuning parameter here is the clustering factor. In
ATHENA, this parameter is called CLUST.FACT and is defined in the CLUSTER statement. The higher
the clustering factor, the greater the damage, and the greater the diffusion, the greater the reverse
short channel effect.
Figure 2-35 shows the effect on the threshold voltage of changing the CLUST.FACT parameter for a
typical process flow.
Figure 2-35: How Changing the clust.fact parameter affects the threshold voltage
The second implantation parameter that can now be tuned is the lateral spread of the implant near
the surface. In ATHENA, this parameter is called LAT.RATIO1 and is defined in the IMPLANT
statement. The lateral spread of the source-drain and LDD dopant is responsible for the classical short
channel effect, where the threshold voltage reduces for very short channel lengths. Simply tune the
LAT.RATIO1 parameter until the onset of classical short channel effects of simulated and measured
data correspond. If the LAT.RATIO1 is increased, the onset of the classical short channel effect will
occur for longer gate lengths.
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2.5.4: Tuning Diffusion Parameters
The final part of the threshold voltage versus gate length curve can now be used to tune the surface
recombination rate of interstitials. In ATHENA, this parameter is called KSURF.0 and is specified in
the INTERSTITIAL statement. The surface recombination of interstitials will dictate the roll-off rate of
threshold voltage from its peak value (reverse short channel effect) to the long gate length value. Once
again, simply tune KSURF.0 until the long channel threshold voltage roll off rate matches that of the
measured data.
PMOS Tuning
PMOS devices are a special case since the boron doped Source/Drain implants overall tend to absorb
interstitials rather than emit them. The reverse short channel effect in buried channel PMOS devices
can be caused by high angle implants. If high angle implants are used, the reverse short channel effect
can be tuned using the LAT.RATIO1 parameter in the IMPLANT statement.
2.5.5: Related Issues on using the Device Simulator ATLAS for MOS Process Tuning
It should now be known that calibrating an ATHENA process file involves using the device simulator
ATLAS to a significant extent. Hence, it’s imperative that the use of the device simulator doesn’t create
additional errors, rendering the process calibration results invalid.
Fortunately, the device physics involved in simulating the conditions required to extract a threshold
voltage are not demanding. The drain voltage required to extract a threshold voltage is only 50-100mV
so effects such as impact ionization can be neglected. The field perpendicular to the gate is also
relatively low around the threshold voltage so field effects in this direction will do little effect. We
recommend, however, using at least the models SRH and CVT during the calculation. Other parameters
for silicon are sufficiently well known for silicon to the point that the results from the device simulator
are reliable.
The first important point is to ensure that you let the device simulator calculate the work function of
the gate electrode from the simulated doping profile rather than assigning a value to it. This means,
making sure that the polysilicon gate is not itself defined as an electrode but rather a layer of metal,
usually aluminum, is deposited on top of the polysilicon gate. Therefore, this metal layer is the film
defined as the electrode. Do not assign a work function to this deposited metal electrode to ensure that
it behaves as an ohmic contact rather than a Schottky contact. The effective work function of the poly
gate will then be correctly calculated from the doping profile in the polysilicon.
An important area for accuracy in MOSFETs is modeling the inversion region under the gate. As it is,
this charge that is responsible for current conduction in the device. The inversion region charge under
the gate-only extends approximately 30 Angstroms into the silicon. The inversion region charge
density under the gate falls off rapidly with depth into the silicon. It is imperative that there are
several mesh points in the Y direction in this inversion region to model the drain current correctly.
Accordingly, we recommend that the mesh spacing under the gate be no more than 10 Angstroms (1
nm).
You would think that a 10 Angstrom mesh under the gate would result in a huge number of mesh
points. But, there only needs to be approximately three mesh points within the inversion region in the
Y direction. The grid spacing can increase rapidly in spacing away from the oxide-silicon interface.
Figure 2-36 shows the effects of changing the mesh spacing at the interface on the simulated drain
current. You can see from this figure that too coarse of a mesh always results in too high of a current
simulated.
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Figure 2-36: The effect of changing the mesh spacing at the interface on the simulated drain current
If contact resistance is a problem, then include it in the CONTACT statement. The resistance added to
the CONTACT statement should be the measured resistance per contact divided by the number of
contacts on each individual electrode. Obviously for D.C. measurements, the resistance on the gate
contact will have no effect on the results since no current flows in this direction.
Checking the Predictive Powers of Tuned Process Parameters
If the process simulation has been correctly tuned, the process and device simulators should have
predictive powers. To check the validity of the tuning process, use a new set of electrical data that was
not used during the tuning process. For example, a good alternative set of data is to check the
threshold voltage versus gate length for a non-zero voltage applied to the MOSFET body contact.
Conclusion
Using just one set of easily obtained measured electrical data, namely a plot of threshold voltage
versus gate length, you can obtain most of the tuning parameters required for accurate process
simulation. The other most important piece of data required is an accurate measurement of the gate
oxide thickness, which is routinely measured in any instance.
You have been given specific advice as to which process and device models to use for each process in
order to get the best results out of the simulation software. In particular, the correct use of models for
the implantation and diffusion processes is stressed, as this has a dramatic effect on MOSFET
characteristics, especially as anneal times and device dimensions decrease.
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2.6: Calibrating ATHENA for a Typical Bipolar Process Flow
As with MOS calibration text, we assume you are familiar with the mechanics of making an input file
and using the correct methods and models (see Section 2.4: “Choosing Models In SSUPREM4”). For
example, incorrect selection of diffusion models defined in the METHOD statement would invalidate the
remainder of the following section.
Calibrating a bipolar process flow entails matching the two parameters, base current and collector
current versus base emitter voltage to measure results throughout the full operating range of the
device. By implication, the current gain of the device (Ic/Ib) will also be matched. All of the following
paragraphs refer to the standard plot of collector and base currents measured against the base-emitter
voltage, Vbe, unless it’s specifically stated otherwise. This standard IV graph is usually referred to as
the Gummel Plot.
Another way of plotting the same information in a different format that can prove useful is a plot of
current gain, hfe, versus the log of the collector current. This graph, however, is a derivation of the
same information that makes it less clear as to which current is increasing or decreasing for each
change. Therefore, a less useful graph when it comes to understanding exactly what is happening to
the collector and base currents.
The full operating range of a bipolar junction transistor (BJT) consists of three general regions defined
by the current density injected into the base. These three operating regions are usually described as
low, medium, and high current injection regimes. The medium injection region is the most important
part of the curve to model correctly as this represents the typical operating condition of the BJT. Each
of the three operating regions is dominated by a different physical phenomenon. Therefore, successful
modeling of a BJT involves matching both the base and collector currents in each of the three general
operating regions, making a total of six areas for calibration. The derived parameter, hfe, is also a good
parameter to monitor, since this is sensitive to errors in the ratio of collector to base current.
The following text suggests an approach and describes which of the six regions are effected by each
change. The general technique is to calibrate the parameters that have the greatest effect on device
performance in all regions first and then to move on to more subtle phenomenon that effect certain
parts of the base or collector currents or both. In general, matching the collector current for all
injection regions is less problematic than matching the base current at the extremes of the injection
regions. Consequently, there are more sections on tailoring these parts of the curve. The text is divided
into the following sections:
1.
2.
3.
4.
5.
6.
Tuning Base and Collector Currents – All Regions
Tuning the Base Current – All Regions
Tuning the Collector Current – All Regions
The Base Current Profile – Medium Injection
The Base Current Profile – Low Injection
Conclusions
If you follow this order, there should be a reasonable correlation between measured and simulated
data. Most of the tuning parameters, however, have some degree of interdependency to the extent of
which is also device design specific. Therefore, some degree of iteration of the tuning parameters is to
be expected.
When tuning bipolar transistors, there is a greater emphasis to accessing tuning parameters by using
the device simulator, ATLAS, compared to optimizing MOSFETs, where most tuning parameters are
process-related. A powerful combination is the tuning of a BiCMOS process where you can use the
MOSFET part of the process flow to tune the process parameters, while using the Bipolar part of the
flow to tune ATLAS. This technique should yield a high degree of predictability in the results.
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Tuning the process simulator parameters in ATHENA are mainly required to model effects, such as the
implantation induced defect enhanced diffusion responsible for the Emitter Push Effect, which is
essential to obtain the correct depth of the base-collector junction. The correct process modeling of the
out diffusion of dopant from the poly-emitter into the mono-crystalline substrate is also critical to
obtaining well-matched IV curves. Another critical process modeling area is the base implant, because
it is essential to match measured and modeled base resistance for correct modeling of the collector
current. These and other issues are discussed in these sections.
2.6.1: Tuning Base and Collector Currents – All Regions
The most important parameter to model the general level of base and collector currents is the device
measurement temperature. The base and collector currents are strongly influenced by temperature
changes, as small as a few degrees centigrade. A significant effort should be made to determine the
exact temperature of the device during measurements before calibration is attempted. This
temperature should be input into ATLAS in the MODELS statement using the TEMPERATURE=<n>
parameter. An increase in temperature will cause an increase in base and collector currents.
2.6.2: Tuning the Base Current – All Regions
A critical region for poly-emitter bipolar devices is the interface between the poly-emitter and the
mono-crystalline silicon. This region is difficult to process simulate directly as the interface between
the polysilicon emitter and single crystalline silicon usually consists of a thin, uneven and possibly
non-continuous film of oxide. This is simulated by calibrating the overall effect of this interface with
ATLAS. The tuning parameter is the surface recombination velocity at this interface for electrons
(VSURFN for PNP devices) or holes (VSURFP for NPN devices). This will only be effective for thin
emitters where at least a fraction of the holes (for NPN devices) can reach the emitter before
recombination.
The surface recombination velocity parameter not only affects the base current, it also affects the base
current in all of the operating regions. Therefore, it is a powerful parameter to approximately match
the base current and gain throughout the full operating range. In some cases, the base current may be
less affected in the very high and very low injection regions by changes in the surface recombination
velocity, and adding some scope to fine tuning the profile of the base current versus base-emitter
voltage curve.
It is important to define the poly-emitter as an electrode so it can define the interfacial surface
recombination velocity, VSURFN and VSURFP, using the CONTACT statement. This is in contrast to the
MOSFET calibration text where we strongly advise you not to define the polygate as an electrode. Be
sure not to get these two confused. The parameter that activates the recombination velocity is
SURF.REC, which is also in the CONTACT statement. For example, an NPN BJT statement would be:
CONTACT NAME=emitter N.POLYSILICON SURF.REC VSURFP=1.5e5
A lower value of recombination velocity, VSURFP, will reduce the base current and increase the gain,
hfe. The reverse is also true.
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2.6.3: Tuning the Collector Current – All Regions
Figure 2-37 shows the parameter that affects the collector current over the entire range is the intrinsic
base resistance. The base resistance is primarily determined by the dose of the base implant(s). An
increase in the base implant dose will decrease the intrinsic base resistance and decrease the collector
current in all injection regions. In some cases, however, the collector current may be affected a little in
the very high injection region, giving scope for fine tuning the profile of collector current versus baseemitter voltage.
Figure 2-37: Effect of base doping profile on low injection base current in BJT
If the pinched or intrinsic base sheet resistance is a measured parameter, the simplest way to match
measured and simulated data is to make slight changes to the base implant dose so that the simulated
dose is not outside the expected error in actual implanted dose in conjunction with the error in
percentage activation.
In some designs, where the base contact is close to the collector contact or the base contact is the
substrate or is generally wide, the collector current can also influence all current injection regions by
specifying a surface recombination velocity at the base contact. For a typical design with a buried n+
collector and surface contacts, the surface recombination velocity at the base contact may have little
affect on the collector current.
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2.6.4: The Base Current Profile – Medium Injection
In ATLAS, there are two major parameters that have a significant affect on the base current in the
medium injection regime. These parameters are the Poly-emitter Work Function and the Bandgap
Narrowing Effect. These parameters are described below.
Poly-emitter work function
If the poly-emitter is described as N.POLYSILICON in the CONTACT statement for an NPN device, as
already described, the Poly-emitter Work Function is then set to 4.17V and is correct for saturation
doped n++ polysilicon. But if the poly-emitter is not saturation-doped, the work function will differ
from this ideal and have a pronounced affect on the base current and current gain in the medium
injection regime as shown in Figure 2-38. The work function of the poly-gate can vary from 4.17V for
n++ poly-silicon to (4.17V + Eg) for p++ polysilicon, depending on the position of the Fermi-Energy.
Changing the work function of the poly-emitter by just 0.1V from 4.17V to 4.27V can often reduce the
current gain in half in the medium injection regime, so it’s very important to assign the correct value.
The CONTACT statement below assigns a work function of 4.27eV to the poly-emitter, while keeping the
other parameters the same as before.
CONTACT NAME=emitter SURF.REC VSURFP=1.5e5 WORKFUN=4.27
The poly-emitter work function can be calculated by measuring the position of the Fermi-Energy at the
poly-silicon/silicon interface relative to the conduction band and adding this value to 4.17V. For
example, if the Fermi-Energy is measured as being 0.1eV from the conduction band edge, the work
function of the poly-emitter set in the CONTACT statement should be set to 4.17 + 0.1 = 4.27V.
Figure 2-38: Effect of emitter contact work function on bipolar gain
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Bandgap Narrowing Effects
If the BIPOLAR parameter is stipulated in the MODELS statement in ATLAS, bandgap narrowing is
included automatically. The inclusion of bandgap narrowing in the MODELS statement is strongly
advised since this phenomenon has a significant effect on the current gain of the device. But, to
validate the default Klaassen bandgap narrowing model, you should also use the Klaassen mobility
model. Use the additional keyword KLA in the MODELS statement to activate this model. For example:
MODELS BIPOLAR KLA
The parameters in the Klaassen bandgap narrowing model are user-definable in the MATERIAL
statement and described in the “Physics” Chapter of the ATLAS USER’S MANUAL, VOL. I. There are three
user-definable parameters for the Klaassen band gap narrowing model. The BGN.E parameter has a
linear dependency on doping concentration and has the default value of 6.92e-3 volts. BGN.C has a
square root dependency with doping concentration and has the default value of 0.5. BGN.N is the value
of doping where band gap narrowing effectively starts to take effect and has a default value of 1.3e17/
cm3. The equivalent default setting consequently should be written as:
MATERIAL BGN.E=6.92e-3 BGN.C=0.5 BGN.N=1.3e17
You can alter these parameters to modify the current gain of the device in the medium injection
regime. For example, reducing the linear parameter from 6.92e-3 to 6.5e-3 is sufficient to cause a
significant increase in current gain in the medium injection region. Although the bandgap narrowing
parameters affect both collector and base currents, the base current is affected to a greater degree. The
most sensitive plot to see the effect of small changes to bandgap narrowing is a plot of current gain
versus log of collector current. A reduction in bandgap narrowing will result in an increase in current
gain in the medium current injection region.
2.6.5: The Base Current Profile – Low Injection
This is one case where there is an interdependency on one parameter, since the intrinsic base
resistance not only affects the collector current in all regions (see the previous section) Figure 2-37,
however, also has an effect on the base current in the low injection region.
For a small range of implant doses around the optimum, the base doping concentration will also affect
the position of the knee or the rate or both of fall off of the base current in the low injection operating
region of the device. This is most noticeable as a loss of current gain in the low injection region for the
alternative standard plot of current gain versus collector current. An increase in the base implant
reduces the intrinsic resistance and typically increases the base current in the low injection region,
resulting in a decrease in current gain for very low currents.
A similar effect to increasing the base doping is observed if the base doping is kept constant but the
overall doping is reduced in the mono-crystalline silicon region of the emitter. You can tune the doping
profile in the mono-crystalline region of the emitter using three parameters in ATHENA. The main
physical effect of these ATHENA parameters is to change the doping profile of the emitter in the monocrystalline silicon. These process parameters are as follows:
•
The total interstitial concentration in the poly-emitter.
•
The dopant segregation effects in the poly-emitter.
•
The dopant velocity across the silicon/polysilicon boundary.
The first process parameter will affect how quickly the dopant in an implanted poly-emitter reaches
the silicon/polysilicon boundary during the RTA diffusion and therefore affects the total diffusion of
dopant into the single crystalline part of the emitter and the base width doping profile.
The second process parameter affects dopant pile-up at the poly-silicon/silicon boundary and therefore
the source doping concentration at the mono-crystalline interface. Once again, this will affect the
overall doping profile of the emitter in the mono-crystalline region of the device.
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The third process parameter affects the velocity of transport of dopant across the polysilicon/silicon
boundary with similar effects to the parameters above.
You can use these parameters to tailor the emitter doping profile in the mono-crystalline silicon region
to match available measured data, usually in the form of SIMS or capacitance information. An
accurate profile of dopant in the poly-silicon part of the emitter is not too important if measured data
concerning interfacial dopant concentrations is available. This is because the work function of the
poly-emitter will be set in ATLAS by defining the poly-emitter as an electrode. All you need to calculate
the correct work function at the poly-silicon emitter is the interfacial doping concentration at the polysilicon/silicon interface on the poly side of the junction. See the “Poly-emitter work function” Section on
page 2-51 for setting the correct work function for the poly-emitter .
Conclusions
By using a logical combination of tuning parameters available in both the process simulator (ATHENA)
and the device simulator (ATLAS) and with the influence of each parameter, you can get a good match
for bipolar transistors for most device designs.
Since it is usually less problematic to match the collector current for all levels of applied base-emitter
voltage compared to the matching of base current, you will probably find that more time is spent
trying to match the base current for very small and very large values of applied base-emitter voltage.
You should, however, spend a good amount of time on making sure that the correct process models are
used in the process flow to reduce the overall uncertainty as to which parameters require calibration.
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2.7: Using ATHENA for Simulating SiGe Process
The recommended method for simulating SiGe process is to treat germanium as a dopant in silicon
rather than depositing the SiGe material. This is because it allows boron diffusivities to be germanium
concentration dependant by using the model.sige parameter in the METHOD statement. You can also
define SiGe related parameters in the MATERIAL statement.
The example below show a typical set of statements for depositing a 200A thick trapezoid profile SiGe
base region in an HBT may be as follows:
METHOD
FULL.CPL MIN.TEMP=600 MODEL.SIGE
MATERIAL SILICON NIFACT.SIGE=100 EAFACT.SIGE=1.5 NO.FLIP
DEPOSIT SILICON THICK=0.02 DIVISIONS=8 C.BORON=5E18 \
C.GERMANIUM=1E22 F.GERMANIUM=1E21
DIFFUSE TIME=4 TEMP=650 NITRO PRESS=1
This section will give a brief explanation of the statements and possible variances. A more detailed
description of the individual parameters are given in the ATHENA notes files and in Chapter 6:
“Statements”.
2.7.1: METHOD Statement
FULL.CPL is the recommended diffusion model for boron to obtain the best accuracy. It is, however,
slower than other diffusion models due to the larger number and more complex inter-relations taken
into account.
MIN.TEMP is required if the deposition temperature is below 700°C, which is the minimum calibrated
temperature for ATHENA in standard processing. Select a MIN.TEMP value below the deposition
temperature otherwise, no diffusion will be calculated. The MODEL.SIGE parameter invokes the silicon
germanium models.
2.7.2: MATERIAL Statement
The following statement specifies reasonable user-definable parameters for the SiGe models in the
material silicon.
MATERIAL SILICON NIFACT.SIGE=100 EAFACT.SIGE=1.5 NO.FLIP
The NO.FLIP parameter prevents automatic mesh optimization, which preserves the user-defined x
grid spacing. ATHENA often will try to remove what it believes are excessive grid points during
DEPOSITION/ETCH statements. It is not advisable to remove mesh points in the base of an HBT, which
is the usual SiGe application.
2.7.3: DEPOSIT Statement
This statement is used to specify the material (silicon), thickness, gridding, and doping parameters.
Once you specify these parameters, specify the germanium dopant concentration either as a constant
or as a graded doping profile as shown in the example.
To calculate the doping required, the total number of atoms in silicon is taken to be 5e22/cm3 for
simplicity. Therefore, a doping of 1e22/cm3 of germanium is a 20% concentration. Other concentrations
are calculated in proportion to this, so a final concentration at the end of the deposition of 1e21
represents a 2% concentration of germanium. Therefore, the example deposits a 200A thick SiGe film
with an initial germanium concentration of 20% and a final germanium concentration of 2%.
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2.7.4: DIFFUSE Statement
Since this example above used the DEPOSIT statement, the thermal budget for deposition is simulated
by an inert diffusion for the deposition time. A typical deposition temperature is around 650°C.
Generally, a typical SiGe HBT device would have a base profile consisting of boron and non-boron
doped regions together with a tapered germanium profile at both ends of the base. In this case, simply
specify the DEPOSIT and DIFFUSE statements in several stages. You can also use several EPITAXY
statements to do the same thing.
At the end of the process simulation, the germanium dopant profile has to be converted into SiGe
material with a variable X composition to pass the device into ATLAS. To do this, type in the following
STRUCTURE command example.
STRUCT OUTFILE=HBT.STR SIGE.CONV
This will save a structure call HBT.str and converts the germanium dopant profile into the correct X
composition SiGe material.
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2.8: Using Advanced Features of ATHENA
2.8.1: Structure Manipulation Tools
Using the Structure FLIP Capability
The Structure FLIP capability allows you to flip the structure in the x axis. The STRUCT FLIP.Y
statement causes the structure to be vertically flipped.
This operation can be useful if some process steps (e.g., etching, deposition, or implant) take place from
the backside of the wafer. By using this statement, you can flip a structure, perform these steps, and
then flip it back.
Using the Stretch Capability
In some cases, a device characterization as a function of length is of interest. For example, the drain
current characteristics depend strongly on the gate length. The Stretch capability makes it possible to
generate a number of MOSFET structures with different gate lengths from one ATHENA simulation.
The structure obtained so far in this tutorial (See Figure 2-22) has a gate length of 0.6 µ. To increase
the gate length to 1.5µ, use the STRETCH command. To use this capability, select Structure→Stretch
in the Commands menu and the ATHENA Stretch menu (Figure 2-39) will appear.
Figure 2-39: ATHENA Stretch Menu
Then, select Stretch→Polysilicon (upper-left hand corner). Next, set Stretch Length to 1.5µ, and
choose 10 as the number of Grid Divisions. Then, press the Write button and the following command
will appear in the input file:
# STRETCH TO 1.5 MICRONS
STRETCH LENGTH=1.5 POLY SNAP DIVISION=10
As a result, the polygate will be stretched from its initial length of 0.6 µ (left plot in Figure 2-40) to
1.5µ (right plot in Figure 2-40).
Ten additional vertical grid lines will be inserted in the center of the gate area. The LENGTH
parameter of the STRETCH command can serve as a split parameter for the Virtual Wafer Fab Split
Experimentation capability. For more information about this capability, see the VWF AUTOMATION AND
PRODUCTION TOOLS USER’S MANUAL.
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Another use of the Stretch capability is in the simulation of large power device structures, where
active areas are uniform everywhere except in close proximity to the mask edges and are separated
from each other by long non-active or isolation regions. You can simulate a shrunken structure and
then stretch the active or non-active or both areas to the actual widths. This will also save a
tremendous amount of simulation time.
Figure 2-40: Using Stretch Function for a MOSFET Structure
Note: The stretch function can save a great deal of CPU time.
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Using ATHENA In 1D Mode
You can increase the simulation speed by running ATHENA in 1D mode. ATHENA automatically runs
in 1D mode by default initially. The simulation will automatically converts to 2D mode when you
perform a two dimensional simulation process, such as ETCH or EXPOSE. Simple operations such as
conformal deposits, oxidation, and diffusion run faster in 1D mode.
The deposition and etch sequences displayed in Figure 2-41 show a sequence of 1D depositions with an
automatic conversion to 2D at the first etch.
Initial
silicon
Fast 1D
calculation
Epitaxy or
other
blanket
processing
Fast 1D
calculation.
Gate
formation
or other
2D step
Automatically
transformed to
2D calculation.
Process
completion
2D calculation
Figure 2-41: Automatic 1D to 2D Conversion
Figure 2-41 shows another aspect of 1D mode. In this case, the INITIALIZE command is specified with
the parameters ONE.D and X.LOC=<n> (see Chapter 6: “Statements”, Section 6.30: “INITIALIZE”).
ONE.D specifies that a one dimensional calculation is to be done at the location X.LOC.
In the case of Figure 2-40, 1D profiles are generated at different X locations of a complicated BiCMOS
structure. This allows you to quickly check of the overall process using the 1D mode.
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+
N
P+
+
P
N
P+
N
P+
Build a complete
2D process
description
(i.e. BiCMOS).
N+
P - Substrate
Quickly calculate
1D profiles at key
locations using
the 1D mode.
Modify process
description to
produce desired
characteristics
at key locations.
N+
P
P+
N+
P+
N
P+
Simulate the
complete 2D
process only
once!
N+
P - Substrate
Figure 2-42: Use of One Dimensional Mode
2.8.2: Deposition and Wet/Dry Etching using the Physical Models in ATHENA/ELITE
This section describes the deposition and etch capabilities of the ELITE module of ATHENA using
ATHENA/ELITE default machines
To use ATHENA/ELITE‘s physically based deposition and etch models, use at least one of the following
steps:
1. Use one of the predefined machines described in Chapter 4: “ELITE Models”, Section 4.4: “Etch
Models”.
2. Within your input file, modify the specification of one of these predefined machines to fit your
process
3. Define a custom machine
4. Invoke a prepared file that defines machines of interest
For example, one of the predefined machines is named PE4450. This machine deposits aluminum at a
rate of 1 micron/minute from a hemispheric source.
To simulate the effects of two minutes of operation of this machine, open the ATHENA Deposit Menu
and select the Machine checkbox. The section PARAMETERS TO RUN THE DEFINED MACHINE
will appear in the menu (See Figure 2-43). In this section, specify PE4450 as the Machine Name, the
Time of run (2.0), and the time units (menu box beside the Time of run field) as minutes.
We recommend that you specify the Total number of grid layers in the deposited material region. If
you set this number to 10, it will insert the following ATHENA/ELITE DEPOSIT statement:
# USING DEFAULT DEPOSIT MACHINE PE4450
DEPOSIT MACHINE=PE4450 TIME=2.0 MINUTES DIVISIONS=10
You can specify impurity concentrations in the deposited region in the Impurity concentration
section of the ATHENA Deposit Menu by clicking on the Impurities box.
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Figure 2-43: ATHENA Deposit Menu with Machine Section
Modifying ATHENA/ELITE Default Machines
The file athenamod defines PE4450 as follows (Notice that a ( \ ) is used to concatenate or continue a
long input line):
RATE.DEPO MACHINE=PE4450 ALUMINUM \
U.M SIGMA.DEP=.35 HEMISPHE DEP.RATE=1.0 \
ANGLE1=72 ANGLE2=-70
The machine is modeled with a hemispherical deposition model. The deposition rate is 1 micron/
minute. The logical parameter, U.M, specifies what units are used, in this case, microns per minute.
Finally, the angles of incidence of the hemispherical deposition with respect to the surface normal are
specified with the ANGLE1 and ANGLE2 parameters. You can modify these characteristics of the
machine PE4450 by copying the specification to the input file and using an ASCII editor. For example:
RATE.DEPO MACHINE=PE4450 ALUMINUM \
U.M SIGMA.DEP=.35 HEMISPHE DEP.RATE=.5 \
ANGLE1=72 ANGLE2=-70
redefines machine PE4450 to have a deposition rate of 0.5 micron/minute.
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Defining ELITE Deposition Machines
You can define your own deposition machine using the ATHENA Rate Deposit menu (Figure 2-44). To
open this menu, select Process→Deposit→Rate Deposit in the Commands menu. Machine
definition requires the specification of five general parameters and one or several model-specific
parameters. The general parameters that must be specified are the following:
•
Machine name (e.g., TEST01): This parameter uniquely identifies the machine.
•
Material name (e.g., aluminum): A user-defined material.
•
Machine (model) type (e.g., unidirectional): You can select one of six models by pressing the
appropriate button.
•
Deposition (rate units specifier e.g., A/min): You can select one of seven unit specifiers from the
menu.
•
Deposition rate (e.g., 1000): This parameter is specified in the user-selected units.
The SIGMA.DEP parameter is optional and defaults to 0.2.
The SMOOTH.WIN and SMOOTH.STEP parameters provides an alternative to a complete reflow
calculation. It allows a geometric averaging over a window of width (SMOOTH.WIN) microns that is
performed over a number of steps (SMOOTH.STEP). These parameters perform a post-deposition
smoothing that effectively emulates a reflow process. The wider smoothing window produces a more
intensive surface redistribution of the deposit material. The default number of smoothing operations
(1) is adequate for most applications.
One or several model-specific parameters are attributed to each model. For example, only the ANGLE1
parameter is required for the unidirectional model. Table 2-4 indicates which parameters are required
for each model. The Machine Type section of the ATHENA Rate Deposit Menu includes only those
parameters that are relevant to the selected model. Each parameter has a default value which will be
inserted in the input file. If some of the parameters are undefined, the simulation may be invalid or
may produce unpredictable results.
If the ATHENA Rate Deposit menu is set as shown in Figure 2-44, the following RATE.DEPO statement
will be inserted into the input file.
RATE.DEPO MACHINE=TEST01 ALUMINUM A.S SIGMA.DEP=0.2 \
SMOOTH.WIN=0.1 SMOOTH.STEP=1 UNIDIREC \
DEP.RATE=1000 ANGLE1=0.00
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Figure 2-44: ATHENA Rate Deposit Menu
Table 2-4. Deposition Model Required Parameters
Parameters
Models
CVD
UNI
DUAL
HEMI
CONIC
PLANET
MONTE1
MONTE2
CUSTOM1
CUSTOM2
dep.rate
yes
yes
yes
yes
yes
yes
yes
yes
optional
yes
step.cov
yes
no
no
no
no
no
no
no
no
no
angle1
no
yes
yes
yes
yes
yes/no*
yes
yes
no
no
angle2
no
no
yes
yes
no
yes
no
no
no
no
c.axis
no
no
no
no
yes
yes
no
no
no
no
p.axis
no
no
no
no
yes
yes
no
no
no
no
dist.pl
no
no
no
no
no
yes/no *
no
no
no
no
sigma.dep
no
optional
optional
optional
optional
optional
optional
optional
no
yes
smooth.win
no
optional
optional
optional
optional
optional
optional
optional
optional
optional
smooth.step
no
optional
optional
optional
optional
optional
optional
optional
optional
optional
* To use the planetary model, either the ANGLE1 or the DIST.PL parameter must be specified. These parameters are mutually exclusive.
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Defining ELITE Etch Machines
An ATHENA/ELITE etch machine can be defined using the ATHENA Rate Etch Menu (Figure 2-45).
To open this menu, select Process→Etch→Rate Etch in the Commands menu. The machine
definition requires the specification of four general parameters and one or several model-specific
parameters.
The general parameters that must be specified are as follows:
•
Machine name (e.g. TEST02): This parameter uniquely identifies the machine.
•
Material name (e.g., silicon): A user -defined material can also be specified.
•
Machine type (e.g., Wet Etch): You can select one of three models by pressing the appropriate
button.
•
Etch rate units specifier (e.g., A/min): You can select one of seven unit specifiers from the menu.
One or several model-specific parameters are attributed to each model. For example, only the
ISOTROPIC rate parameter is required for the Wet Etch model.
Table 2-5 indicates which parameters are required for each of the three models. The Parameters for
Specific Machine Type section of the Rate Etch menu includes only those parameters, which are
relevant to the selected model.
If the ATHENA Rate Etch Menu is set as shown in Figure 2-45, the following RATE.ETCH statement
will be inserted into the input file:
# TEST02 ETCHING MACHINE
RATE.ETCH MACHINE=TEST02 SILICON U.M WET.ETCH ISOTROPIC=0.03
Figure 2-45: ATHENA Rate Etch menu
If several materials are present in the structure to be etched, etch rates for each material type should
be specified in separate RATE.ETCH statements.
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Table 2-5. Allowable Etch Model Parameters
Parameters
wet.etch
rie
isotropic
yes
yes
directional
no
yes
divergence
no
yes
chemical
no
yes
Using A Specified Etch Machine
When etch rates for a specific machine are specified using RATE.ETCH statements, you can simulate
the effects of the operation of this machine. To simulate the etch process using a specified etch
machine, open the ATHENA Etch Menu and check the Etching Machine box. The Parameters to
Run the Defined Machine section will appear in the menu (See Figure 2-46).
Figure 2-46: ATHENA Parameters to Run the Define Machine Etch Menu Section
The Machine Name (TEST02), the time units (e.g., minutes) and the Time of run (e.g., 1.0) must be
specified. There are also two tuning parameters that control time stepping during the etch process. To
improve the smoothness of the etch surface, decrease the maximum time step parameter, DT.MAX,
from its default value of 10 percent of the specified Time of Run value.
If you set the ATHENA Etch Menu as shown in Figure 2-46, the following ETCH statement will appear
in the input file when you press the WRITE button.
# 1 MINUTE ETCHING USING TEST02 ETCH MACHINE
ETCH MACHINE=TEST02 TIME=1.0 MINUTES DT.MAX=0.25
A new parameter, DX.MULT, will be added to the ETCH statement to allow enhanced discretization
during individual ELITE Etch steps. Increasing the value of DX.MULT from its default value of 1.0 will
result in larger surface segments and a reduced discretization. Decreasing DX.MULT will result in
better discretization in both space and time during the etch calculation. Reducing the value of this
parameter allows realistic modeling of wet etches that previously were poorly resolved. Use the
DX.MULT is preferable to the use of DT.MAX.
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2.8.3: MaskViews Interface
This section describes an alternative to the manual specification of grid and etch steps described in
Section 2.3: “Creating a Device Structure Using ATHENA”.
Defining Initial Rectangular Grid Using MaskViews
An initial rectangular grid can also be defined by using Silvaco’s IC layout editor, MASKVIEWS.
MASKVIEWS is designed specifically for interfacing IC layout information with process and device
simulators. For more detailed information about MASKVIEWS and its interface with DECKBUILD, see the
VWF INTERACTIVE TOOLS USER’S MANUAL, VOL. I. This section gives several practical suggestions on how to
prepare a good initial grid for ATHENA.
With MASKVIEWS, you can omit ATHENA mesh definition statements because you can include the
gridding information in the layout file. When using MASKVIEWS to provide line information, DECKBUILD
will comment out existing line commands when it loads the MASKVIEWS information.
Load the example, 34.11 anex11.in, from the MaskViews-ATHENA section of the Deckbuild
Examples Window (See Figure 2-2). Then, select MaskViews→Starting MaskViews from the Tools
menu of DECKBUILD to open MASKVIEWS Layout Files Popup (Figure 2-47).
Figure 2-47: MaskViews Layout Files Popup
Choose the anex11.lay layout file from the scrolling list and press the Start MaskViews button.
The MASKVIEWS window will then appear as shown in Figure 2-48.
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Figure 2-48: MaskViews Window
This section will describe how to modify a grid specification for ATHENA. First, set the grid in the Y
direction by selecting Grid→Y... from the Define menu. Figure 2-49 shows the Vertical Grid Control
popup will appear.
You can add, modify, and delete the lines for ATHENA initial rectangular grid exactly the same way as
using the ATHENA Mesh Define menu from DECKBUILD as previously described. Note that the
Distance parameter is equivalent to the location parameter in ATHENA. Also, the Add button is
equivalent to the Insert button of the ATHENA Mesh Define Menu. Then, press Return after entering
the Distance or the Spacing values.
If the Distance and Spacing are set as shown in Figure 2-49, the grid will be the same in the Ydirection as the grid produced using the ATHENA Mesh Define Menu.
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Figure 2-49: Vertical Grid Control Popup
MASKVIEWS also controls the initial ATHENA grid in the X-direction. MASKVIEWS generates ATHENA line
statements for each mask edge on valid layers crossed by a cutline. The grid spacing and the validation
of layers can be set by the ATHENA Grid Control Menu (See Figure 2-50). To open this menu, select
Grid→X... from the Define menu.
Figure 2-50: ATHENA Grid Control Menu
Figure 2-50 shows the line locations and spacings preset for the POLY layer. This set of parameters
means that for each POLY edge crossed by a cutline, three line statements are to be inserted into the
ATHENA input file. The first line will be located exactly at the edge and the spacing will be 0.05µm.
The second line will be inside the POLY layer, 0.3µm from the edge, and spacing at this line is 0.15µm.
The third line will be outside the POLY layer, 0.2µm from the edge, and its spacing will be set to 0.1µm.
You can choose the current edit layer by selecting the Name button (located underneath the Layers
Menu) for the layer in the key list of MASKVIEWS (Figure 2-48). If you select AAD, then only set one line
for an edge of the AAD layer because offset distances are equal to 0.0. We recommend that only one line
be set for unimportant layers. It’s also important to validate only those layers that are going to be used
in ATHENA MASK statements.
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When grid parameters are set for all valid layers, a cutline can be chosen. Click on the Write File
button and the Select First End Of Athena Cross Section Line Popup will appear at the bottom of the
MaskViews Window. Press the select (left) mouse button at the desired point in the layout (e.g., within
the VIA2 region in the upper left corner of the layout). You will be prompted to select another end of
the cross section line. Then, drag the pointer and press the select mouse button on the other end of the
selected cutline. Figure 2-51 shows the Athena Cutline Popup will then appear. This shows the exact
location of the cutline. You can now preview the mask and grid information generated by MASKVIEWS.
Press the Preview button and the Display Masks Window will appear as shown in Figure 2-52.
Figure 2-51: ATHENA Cutline Popup
Figure 2-52: Display Masks Window
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The additional information on the number of lines, points, and triangles is also displayed in this
window. If the grid does not appear as shown in Figure 2-52, select the Options Grid box and the
Display Masks box in the Properties... menu (Figure 2-53).
Figure 2-53: Properties Menu
To select another cutline location, press the Done button in the Athena Cutline Popup and repeat the
cutline selection process for the desired cutlines one at a time. If you’re not satisfied with the grid, you
can modify the X... or Y... or both settings. You can then preview the modified grid without selecting
another cutline. For example, if the Spacing at edge in the Athena Cutline Popup (see Figure 2-51) is
decreased from 0.05 to 0.025, a finer grid will be obtained at both POLY gate edges (see Figure 2-52).
When the location of a cutline and the corresponding grid are satisfactory, the cutline information can
be stored or used either as a Cut file or as a cutline object.
You can save the Cut file by pressing the Write button in the ATHENA Cutline Popup. You can then
load this file into DECKBUILD for use in ATHENA by selecting MaskViews→Cutfiles... from the Tools
menu in the DECKBUILD window. The MaskViews Cut Files popup (Figure 2-54) will then appear. Select
the desired *.sec* file and press Load.
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Figure 2-54: MaskViews Cutline Files Window
You can now select any preview as shown in Figure 2-52. Press the Select mouse button anywhere
within the Display Masks window and the cutline icon will appear. Without releasing the Select mouse
button, drag the icon into the MASKVIEWS Cut Files Window and drop it by releasing the Select mouse
button.
Several cutlines with different locations and grids can be dragged and dropped in this fashion. You can
then load them into DECKBUILD for use by ATHENA.
When ATHENA is loaded with a cutline, DECKBUILD will comment out all existing line statements and
will automatically run line statements generated by MASKVIEWS. For example, the following output
will appear in the DECKBUILD Text Subwindow if the default.sec.1 generated for the CMOS
Inverter is loaded.
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
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LINE
LINE
LINE
LINE
LINE
LINE
LINE
LINE
LINE
LINE
LINE
LINE
LINE
LINE
LINE
X
X
X
X
X
X
X
X
X
X
X
X
Y
Y
Y
LOC=0.000 SPAC=0.100 TAG=LEFT
LOC=0.300 SPAC=0.100
LOC=0.500 SPAC=0.100
LOC=0.600 SPAC=0.100
LOC=0.800 SPAC=0.050
LOC=1.100 SPAC=0.150
LOC=1.500 SPAC=0.150
LOC=1.800 SPAC=0.050
LOC=2.000 SPAC=0.100
LOC=2.100 SPAC=0.100
LOC=2.300 SPAC=0.100
LOC=2.600 SPAC=0.100 TAG=RIGHT
LOC=0.00 SPAC=0.03 TAG=TOP
LOC=0.20 SPAC=0.02
LOC=1.00 SPAC=0.10 TAG=BOTTOM
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Using MaskViews for Generating Masks in ATHENA
The dry etching capability of ATHENA and the physical etching capability of ATHENA/ELITE can be
used in conjunction with the mask generating capability provided by DECKBUILD and MASKVIEWS. A
cutline loaded into DECKBUILD has information on the x-location of the photomask edges. You should
specify the sequence of mask creation and stripping steps in the ATHENA input file. This can be done
by selecting the Tools→Maskviews→Cutfiles option from DECKBUILD when ATHENA is active, which
will open the MASKVIEWS Cutline Popup.
Names of all available mask layers are in Figure 2-55. When you select a name (e.g., POLY) from the
list, press the Apply Mask button and the following lines will appear in the input file.
# DEFINING POLY MASK
MASK NAME="POLY"
Figure 2-55: ATHENA Photo Popup
During runtime, DECKBUILD converts the MASK statement into a DEPOSIT statement, followed by a
series of ETCH statements. The mask thickness and material type are defined in the MaskViews
Layers Popup (Figure 2-56) in the Define menu of MASKVIEWS.
Figure 2-56: MaskViews Layers Menu
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Two types of mask material are available: Photoresist and Barrier. The real thickness of a photoresist
layer should be specified because it can be used as a mask for implantation. Barrier is a fictitious
material. It is impenetrable for any implants and can serve only as a masking material. This material
is implemented in ATHENA for the purpose of simplifying simulation of mask deposition over highly
non-flat structures. A region to be etched may be any area not containing a mask on a clear field layer
or any area containing a mask on a dark field area. You can specify this in the Field section in the
MaskViews Layers Popup. In the case of the POLY mask and cutline in Figure 2-56, the barrier layer
will be etched to the left of x=0.8, and to the right to x=1.8. The following echo output will appear in
the Deckbuild Text Subwindow as the result of defining of the POLY mask:
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
ATHENA>
# DEFINING POLY MASK
## MASK NAME="POLY"
DEPO BARRIER THICK=0.10
STRUCT OUTFILE=.HISTORY.9
ETCH BARRIER START X=-0.100 Y=-20
ETCH CONT X=-0.100 Y=20
ETCH CONT X=0.800 Y=20
ETCH DONE X=0.800 Y=-20
STRUCT OUTFILE=.HISTORY.10
ETCH BARRIER START X=1.800 Y=-20
ETCH CONT X=1.800 Y=20
ETCH CONT X=2.800 Y=20
ETCH DONE X=2.800 Y=-20
STRUCT OUTFILE=.HISTORY.11
If the Reverse Mask box is checked in the ATHENA Photo popup, the following lines will be inserted
into the input file:
# DEFINING POLY MASK
MASK NAME="POLY" REVERSE
and the effect of the field attribute is reversed (i.e., the barrier area will be etched between x=0.8 and
x=1.8).
When the mask is defined, the ATHENA dry etch capability can be used to etch the specified thickness
of a material not covered by the mask. After the dry etch is complete, strip the mask by clicking the
Strip Mask button in the ATHENA Photo popup. A typical mask definition fragment should appear as
follows:
# POLY DEFINITION
MASK NAME="POLY"
ETCH POLY THICK=0.5
STRIP
If the cutline from Figure 2-51 is loaded, this will give the structure shown in upper plot of
Figure 2-57. If the reverse parameter is added, the structure will appear as shown in the lower plot of
Figure 2-57.
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Figure 2-57: Using Mask Capability for POLY Definition
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2.9: Using ATHENA/OPTOLITH
2.9.1: Overview
ATHENA/OPTOLITH is designed as an optical lithography tool integrated into a complete process
framework. Specific functions of ATHENA/OPTOLITH include 2D aerial image formation, 2D photoresist
exposure and development, post exposure bake, and post processing capabilities such as CD extraction
for generating SMILE plots. This section of the tutorial describes ATHENA/OPTOLITH input/output
and the following basic operations for creating a typical input file for optical lithography:
•
Creating an input mask using MASKVIEWS or the LAYOUT command
•
Designing custom or standard illumination systems
•
Projection Fourier plane filtering
•
Imaging controls
•
Properties of materials
•
Structure exposure, post exposure bake, and development
•
CD extraction, SMILE plots, and looping procedures
This section of the tutorial assumes that you are familiar with the general operation of ATHENA. This
includes familiarity with the command language used to generate structures, as well as a general
knowledge of the use of the VWF INTERACTIVE TOOLS. Specific features that refer particularly to
OPTOLITH will be explained here.
2.9.2: Creating A Mask
A mask can be created using the MASKVIEWS tool supported by the VWF INTERACTIVE TOOLS, or by using
the LAYOUT command. MASKVIEWS facilitates the creation of complicated masks and can import
different mask data formats, such as the GDS2 stream format. In the case of simple masks containing
one or two features, it may be simpler to use the LAYOUT command.
MaskViews
Once you select MaskViews from the Tools/MaskViews menu, press the Start MaskViews button
and the MASKVIEWS window will appear. Then, press the Properties... button and the MASKVIEWS
Properties popup will appear (See Figure 2-58).
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Figure 2-58: MASKVIEWS Properties Popup showing the Simulation Menu
Open the Simulator menu and select the ATHENA/OPTOLITH menu item. Customized controls for
MASKVIEWS/OPTOLITH will appear in the MASKVIEWS window. The colored buttons on the right side of
the window are discrete controls for phase in degrees and intensity transmittance. The buttons first
appear as phase. To change to transmittance, open the Phases menu above the buttons and select the
Transmittances menu item. This will change the buttons from phase to transmittance controls.
Continuous controls for phase and transmittance are located directly below the colored buttons.
The mask can now be designed using the mouse driven line writer following the description outlined in
the MASKVIEWS chapter of the VWF INTERACTIVE TOOLS USER’S MANUAL, VOL. I. Once the mask is created,
it should be saved to a file with a name ending in a .lay extension for future editing. It is important to
be aware that there are two types of files that can be saved from a MASKVIEWS layout information.
The first type is the layout file. This file includes the information about layers and mask features. To
store this information, select the Files Save menu item in the MASKVIEWS screen. The second type of
file that can be saved from MASKVIEWS is a file that is similar to the layout file but is written to
interface with ATHENA/OPTOLITH. The file to be used by OPTOLITH is created by pressing the Write
File button in the MASKVIEWS window. The Optolith Simulation Popup will appear (Figure 2-59).
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Figure 2-59: OPTOLITH Simulation Control Popup
Enter the desired file name, which should end with a .sec extension, and proceed to the next step.
Note that at the bottom of the MASKVIEWS window the message: Select first corner of OPTOLITH
simulation area will appear. MASKVIEWS is now prepared for the selection of the image window. The
image window describes the area where intensity will be calculated. Click on the desired area for
intensity calculation to create the first corner of the OPTOLITH simulation area. The message: Select
the other corner of OPTOLITH simulation area will then appear at the bottom of the MASKVIEWS
window. Click on the desired second corner. Once this second point is selected, the coordinates of the
image window’s lower left and upper right corners will be displayed in the OPTOLITH Simulation
Control Popup. Press the Write button to save the OPTOLITH mask file. The input file created by
MASKVIEWS is loaded into OPTOLITH by the IMAGE command, which is described in Section 2.9.5:
“Imaging Control”.
To modify the layers, open the Define menu in the MASKVIEWS Window (See Figure 2-48) and select
Layers menu item. The Layers Popup (Figure 2-60) will then appear.
Figure 2-60: Layers Popup
If you select Dark, the field background will be dark and the features will have the intensity
transmittance (T), where T is user-defined. If you select Clear, the intensity transmittance
automatically becomes [1 - T].
Only rectangular features are used in the imaging module. MASKVIEWS automatically converts
triangles or polygons to a set of parallel rectangles. Finer resolution on these rectangles can be
obtained by changing the resolution on the Screen... popup under the Define menu.
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Mask Layout
In the LAYOUT command, each mask feature is defined with one command line. For example:
LAYOUT X.LO=-0.5 Z.LO=-5.0 X.HI=0.5 Z.HI=5.0 TRANS=1 PHASE=0
defines a 1µ wide line that is 10m long. The mask has an intensity transmittance of one and a phase of
0°. The LAYOUT command can be repeated as often as desired. The number of mask features is limited
only to the amount of memory available. The LAYOUT LAY.CLEAR command will remove all previous
mask features from memory. Overlapping mask features will cause an error. The OPAQUE and CLEAR
parameters can be specified in the IMAGE command. This will not reverse polarity as it does in
MASKVIEWS.
2.9.3: Illumination System
The Illumination System is defined using two statements: ILLUMINATION and ILLUM.FILTER.
ILLUMINATION defines the illuminating wavelength, the possible x and z tilt of the optical system and
the relative intensity, which is usually set to 1. ILLUM.FILTER defines the shape of the illumination
system. The general shapes available are CIRCLE, SQUARE, GAUSSIAN, ANTIGUASS, and SHRINC. The
extent of the source must be defined to be within a square centered at the origin as shown in
Figure 2-61.
The extent of the source is defined by the coherence parameter, SIGMA. SIGMA defines the radius for
circular sources (CIRCLE, GAUSSIAN, and ANTIGAUSS), the x and y intercepts for square sources, and
the radius of each individual SHRINC source element as shown in Figure 2-62.
In all cases, anything outside of the square defined by SIGMA=1 will be ignored. The SHRINC source
position is defined by the RADIUS and ANGLE parameters as shown in Figure 2-62. The SHRINC source
can be defined by the command:
ILLUM.FILTER SHRINC RADIUS=0.25 ANGLE=45 SIGMA=0.1
1
Source
-1
1
Region
-1
Figure 2-61: Maximum Extent of the Source Region
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Sigma
Sigma
-Sigma
Sigma
- Sigma
CIRCLE
SQUARE
Sigma
Radius
+ Angle
SHRINC
Figure 2-62: Three Different Source Types
Arbitrary sources can be defined by using the ANGLE and RADIUS parameters. Phase and intensity
transmittance of each source element are controlled by the parameters PHASE and TRANSMIT. By
positioning each source element in the source region, you can simulate any type of source. To simulate
a SHRINC source, enter the following command lines:
ILLUM.FILTER
ILLUM.FILTER
ILLUM.FILTER
ILLUM.FILTER
CIRCLE
CIRCLE
CIRCLE
CIRCLE
SIGMA=0.1
SIGMA=0.1
SIGMA=0.1
SIGMA=0.1
RADIUS=0.25
RADIUS=0.25
RADIUS=0.25
RADIUS=0.25
ANGLE=45
ANGLE=135
ANGLE=225
ANGLE=315
If overlapping sources are defined, a warning is issued and the most recent source is used. If the
overlap is partial, only the overlap area is overwritten by the most recent source.
Annular filters can also be superimposed on the source. There are two types of annular filters: Square
and Circle. Annular filters have a multiplicative effect on the source. Because of this, be careful when
defining a complex source and a complex filter. The following example of an annular source of inner
radius 0.4 and outer radius 0.6 is given below.
ILLUM.FILTER CIRCLE SIGMA=0.6
ILLUM.FILTER CIRCLE INNER.RAD=0.0 OUTER.RAD=0.4 TRANSMIT=0.0
In the first statement, the SIGMA parameter defines the outer radius. In the second statement, an
opaque spot is defined as an annular filter (see Figure 2-63).
The source must be described before the filter or the command will be ignored and a warning will be
given. The CLEAR.FILTER parameter is used to remove all pre-existing filters and sources.
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Sigma = 0.6
Figure 2-63: Annular Source
2.9.4: The Projection System
The Projection System is defined using two statements: PROJECTION and PUPIL.FILTER. The
PROJECTION command is used to define the numerical aperture and flare of the projection system. The
PUPIL.FILTER command describes the shape of the projection system and the possible filters of the
projection system. The shape of the projector pupil can be square or circular. The circular pupil has the
option of having a Gaussian or anti-Gaussian transmittance profile. Filtering of the Fourier spectrum
can be performed by using annular filters. The filters have a multiplicative effect on the transmittance
and phase in the projector pupil. The following example creates an opaque square at the origin:
PUPIL.FILTER SQUARE
PUPIL.FILTER SQUARE INNER.RAD=0.0 OUTER.RAD=0.1 TRANS=0.0
This creates the following projection pupil (Figure 2-64):
1
0.1
-1
1
-0.1
0.1
-0.1
-1
Figure 2-64: Projection Pupil
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The maximum extent of the projector pupil plane is +1 or -1 in both dimensions. A filter exceeding
these dimensions will be ignored and a warning will be issued.
2.9.5: Imaging Control
The image calculation is done by the IMAGE command and its associated parameters. The mask to be
imaged will already be defined either by a MASKVIEWS *.sec file or by the LAYOUT command. If a
MASKVIEWS *.sec file is used, the IMAGE command will be of this form:
IMAGE INFILE=*.sec ...
If the mask is defined using the LAYOUT command, the mask features will be stored in memory and the
only required input related to mask features is the OPAQUE/CLEAR specification. OPAQUE specifies the
background intensity transmittance to be zero. CLEAR specifies the background intensity
transmittance to be one. OPAQUE is the default setting. OPAQUE and CLEAR cannot be used with an
input file from MASKVIEWS.
The Image Window (not the Computational Window) is specified with the parameters: WIN.X.LOW,
WIN.Z.LOW, WIN.X.HI, and WIN.Z.HI. These parameters define the minimum and maximum
range of the x and z values (see Figure 2-65). The aerial image is then calculated only inside this
window. This allows for faster computation when you only want a cross section. If you want a simple
cross section, set the window parameters for z (WIN.Z.LO, WIN.Z.HI) to the same value for a cross
section parallel to the x-axis.
This value(WIN.Z.LOW = WIN.Z.HI) gives the location of the cross-section.
z
WIN.Z.HIGH
WIN.X.LOW
Image
WIN.X.HIGH
x
Window
WIN.Z.LOW
Figure 2-65: The Image Window can be Placed Anywhere in the XZ Window
The resolution in the image window can be controlled by two different sets of parameters. The first set
is DX and DZ. DX and DZ are the resolution in micrometers for the x and z directions. The second set,
X.POINTS and Z.POINTS, is based on the number of points in each direction. The resolution will be
the length of the side of the image window divided by the number of points. To study the defocus of the
aerial image, use the DEFOCUS parameter. DEFOCUS uses units of micrometers.
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The N.PUPIL parameter specifies the computational window. If N.PUPIL is not specified, it is
automatically calculated to a size that encompasses all mask features. In these cases, you can set the
computational window manually using the following formula:
length ⋅ NA
N.PUPIL = ------------------------- * 2
2-1
lambda
where length is the intercept coordinate for the x and z axes of a square centered at the origin that
delimits the Computational Window as shown in Figure 2-66.
z
Computational
x
Window
Figure 2-66: The Computational Window is Always Centered at the Origin
Once you calculate the image, you can store it in a standard structure file by using the STRUCTURE
OUTFILE=*.STR INTENSITY command.
The INTENSITY modifier identifies the file to be different than a standard structure. This file can later
be initialized into memory and used without running the imaging module. To initialize an intensity
file, type:
INITIALIZE INFILE=*.STR INTENSITY
The intensity modifier again specifies the type of file. An intensity file initialized in this fashion is
useful only for exposures that use the vertical propagation model.
N.PUPIL also affects the accuracy of the aerial image calculation. A higher N.PUPIL value increases
the number of source points by a factor (2*N.PUPIL+1) squared, and increases the accuracy and the
computation time.
Note: The Image Window and the Computational Window are not linked. The computational window is automatically
adjusted to include all mask features, unless otherwise specified in the IMAGE command. This means that the entire mask will
be used in the image calculation. You can use the Image Window to calculate a part of the entire image to increase the
simulation speed. You can override the selected image in the IMAGE command by specifying new window coordinates.
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Aerial image intensity distributions can be added together by specifying MULT.IMAGE on repetitions of
the IMAGE command. You can add any number of images together. The first IMAGE statement
shouldn’t contain the boolean parameter, MULT.IMAGE, because the preceding aerial images are erased
from memory. You can weigh of the aerial images by using the INTENSITY parameter on the
ILLUMINATION command.
ONE.DIM is a new parameter that has been added to the IMAGE command. It allows you to calculate
one dimensional aerial images. This is used primarily for increasing speed in the exposure calculation
for repetitive line width calculations.
2.9.6: Defining Material Properties
There are two statements in ATHENA/OPTOLITH that relate to material properties: OPTICAL and
RATE.DEVELOP. The OPTICAL command sets the complex index of refraction for a single material at a
given wavelength. The RATE.DEVELOP command sets development rate parameters for each resist
defined in the resist library. Default values for these material parameters are located in the
athenamod file, which can be viewed in DECKBUILD by selecting the Models... item from the Command
menu. You can change any of these parameters by entering the command with the new values. For
example, to change the index of refraction of silicon at the wavelength of 0.365 µm, enter:
OPTICAL SILICON LAMBDA=0.365 REFRAC.REAL=6.522 REFRAC.IMAG=2.705
To enter resist parameters at wavelength of 0.407µm, use the RATE.DEVELOP command as follows:
RATE.DEVELOP NAME.RESIST=AZ135OJ LAMBDA=0.407 \
A.DILL=0.88 B.DILL=0.077 C.DILL=0.018 E1.DILL=5.63 \
E2.DILL=7.43 E3.DILL=-12.6
Photoresist parameters for development or diffusivity (DIX.0, DIX.E) can be entered separately from
exposure parameters without specifying the wavelength. The photoresist name must always be
specified. When specifying Dill exposure parameters (A, B, and C), specify the wavelength as these
parameters vary with wavelength.
2.9.7: Structure Exposure
Exposure, post exposure bake, and development each have separate statements (EXPOSE, BAKE, and
DEVELOP) respectively. In order to use these three statements, some initial requirements must be met.
First, an intensity cross section or Fourier Spectrum data must be available. Second, you must create a
structure including photoresist using the techniques described in Section 2.3: “Creating a Device
Structure Using ATHENA”.
This intensity cross section can come from three different places. The first method is by running the
imaging module prior to exposure. This puts the intensity data array into memory. The second method
is by initializing with an intensity data array that has been stored in a standard structure file (see
Section 2.9.5: “Imaging Control”) using the following command:
INITIALIZE INFILE=*.STR INTENSITY
The INTENSITY qualifier lets ATHENA know that this is an intensity file, as opposed to a standard
structure file. After this command is entered, the intensity data array will be placed in memory.
Wavelength will be stored in this file and can be changed only by re-running the imaging module.
The third method of entering an intensity cross section is through a user data file. The file should
contain the wavelength, the number of data points, and the intensity and position of each point. The
first line of this file should contain the wavelength in micrometers. The second line should contain the
number of points. The following line should contain the position and then the intensity of the first
point on the same line. This should be repeated for each point. This input file is read in the EXPOSE
command using the following format:
EXPOSE INFILE=*.EXP
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Once the intensity array is initialized or when the Fourier spectrum data is in memory through the
IMAGE command, you can expose a structure if it exists in memory and if it has photoresist as its top
layer(s). You can either create the structure in the input file or initialize it as described in Section 2.3:
“Creating a Device Structure Using ATHENA”.
The EXPOSE command has many parameters that control the accuracy and speed of the exposure
simulation, as well as related imaging parameters. The following parameters control simulation speed
and accuracy and are unnecessary for a preliminary simulation.
FLATNESS, NUM.REFL, FRONT.REFL, BACK.REFL, ALL.MATS
The most important of these parameters is the FLATNESS parameter. If FLATNESS is set equal to zero,
the algorithm uses the entire grid for the calculation and may lengthen the simulation time. The
remaining parameters refer to the image to be exposed. Both TE and TM modes are available in
exposure, but they must be performed separately. Select TE by adding the PERPENDICULAR
parameter to the EXPOSE command, or select TM by entering the PARALLEL parameter. TE is the
default. The exposure dose is also defined in the EXPOSURE command in units of mJ/cm2 using the
DOSE parameter.
Exposures can be made with either coherent or incoherent sources. Coherent sources are described by
SIGMA=0.01 in the IMAGE command. This defines a small enough source so that only one
discretization point is included. If a large SIGMA is defined and discretization of the source allows at
least three source points in the x (or z) direction, then three points from the source will be used in the
bulk image calculation with equal weight given to each point. The points chosen will be the central
point and the outermost points, or the dimension of the chosen cross section (x or z). If multiple sources
are defined using the ILLUM.FILTER command, then the central point of each SOURCE defined is used
for calculating the bulk image in the exposure. The latter allows an arbitrary amount of source points
to be simulated for the bulk image calculation. This is done by specifying many small adjacent sources
and one point will be taken from each source.
You can add bulk image exposures together by specifying MULT.EXPOSE on repetitions of the EXPOSE
command. Any number of exposures can be added together. The first EXPOSE statement should not
contain the boolean parameter MULT.EXPOSE because the preceding exposures are erased from
memory. You can weigh the exposures by using the DOSE parameter on the EXPOSE command.
The final four parameters: X.CROSS, Z.CROSS, CROSS.VALUE, and X.ORIGIN all refer to the aerial
image cross section. The boolean parameters (X.CROSS or Z.CROSS) define the cross-section to be
parallel to the x-axis or the z-axis respectively. CROSS.VALUE specifies the z location of X.CROSS, or
the x location of Z.CROSS. These parameters are especially useful when several cross sections from the
one large, two dimensional aerial image will be simulated. X.CROSS is the default. If CROSS.VALUE is
unspecified, the center of the image window, defined in the imaging module, will be used as
CROSS.VALUE. X.ORIGIN allows the aerial image cross section to be shifted laterally in the two
dimensional exposure simulation.
Post Exposure Bake
The BAKE command can be invoked by using only one parameter DIFF.LENGTH (the diffusion length).
For a post exposure bake of 60 seconds at a temperature of 125°C, the recommended diffusion length is
between 0.05 and 0.1 micrometers. The BAKE command can also be used by specifying TIME and
TEMPERATURE in C°.
Development
The development module offers a choice of six different development models. As mentioned before,
model parameters are specified in the RATE.DEVELOP command. After the development model is
selected, the three primary parameters for the DEVELOP command are: TIME (in seconds), STEPS, and
SUBSTEPS.
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TIME is the total development time. STEPS specifies the number of times the structure has to be
regridded. SUBSTEPS is the total number of times the development line has to be moved. Each substep
is performed for a time increment equal to TIME/(STEPS*SUBSTEPS). After each regridding of the
structure, you can dump out a standard structure file to show the progress of the development. To do
this, specify the parameter DUMP=1. To name the structure file to be dumped, specify
DUMP.PREFIX=<name> and the structure will be created in the local directory with the name
<name>**.str, where ** is the current development time.
Post Development Bake
A physically-based reflow of the developed photoresist is available. Specify it by using the BAKE
command and the boolean parameter REFLOW along with TIME and TEMPERATURE.
2.9.8: CD Extraction, Smile Plots, And Looping Procedures
CDs are extracted from the structure using the function MAT1|MAT2(y). This gives the horizontal
intersection of material number 1 and material number 2 at the value y. To extract a CD from a profile,
the following format is used.
(GAS|PHOTO(1.4) - PHOTO|GAS(1.4))
This will give the CD at the horizontal line y=1.4.
To generate swing curves, use the FOREACH and END statements for looping. The example below shows
the input language used to perform the loop.
PRINTF ATHENA > SWING
PRINTF 16 2 2 > SWING
PRINTF THICKNESS > SWING
PRINTF CDS > SWING
FOREACH J (0.1 TO 0.5 STEP 0.25)
INITIALIZE INFILE=ANOPEX15.STR
DEPOSIT NITRIDE THICK=J DIV=1 MIN.SPACE=0.01
DEPOSIT PHOTORESIST NAME.RESIST=ZZZ THICK=1 DIV=30 MIN.SPACE=0.01
EXPOSE DOSE=150 NUM.REFL=3 NA=0 FRONT.REFL=1
BAKE DIFF.LENGTH=0.05
STRUCTURE OUTFILE=ANOPEX15.J.STR2
DEVELOP MACK TIME=45 STEPS=9 SUBSTEPS=10
STRUCTURE OUTFILE=ANOPEX.15.J.STR3
PRINTF J (ZZZ|GAS(1.4+J) - GAS|ZZZ(1.4 + J)) > SWING
END
This creates an output file called SWING. The first command writes the name of the framework. The
second command writes the number of rows, number of columns, and number of titles (see the
TONYPLOT chapter in the VWF INTERACTIVE TOOLS USER’S MANUAL, VOL I).
The FOREACH statement signals the beginning of the loop. The END statement terminates the loop. J is
the parameter to be varied in the loop. In this case, it is the thickness of the nitride layer.
The final PRINTF statement prints the data to the file. First, the thickness J, and then the CD at
y=1.4+J. In the DECKBUILD input file, enter the command:
tonyplot -da SWING
and a plot of the swing curve will appear. This command can also be written in the input file after the
loop.
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To generate SMILE plots (focus-exposure latitude curves), you need to require a double loop. The input
language used for a typical double loop is shown below.
PRINTF ATHENA > SMILE
PRINTF 24 3 3 > SMILE
PRINTF DEFOCUS > SMILE
PRINTF CDS > SMILE
PRINTF DOSE > SMILE
FOREACH I (200 TO 300 STEP 25)
FOREACH J (-1.5 TO 1.5 STEP 0.5)
INITIALIZE INFILE=ANOPEX12.STR1
IMAGE DEFOCUS=J WIN.X.LO=.5 WIN.X.HI=.5 WIN.Z.LO=0 WIN.Z.HI=0 \
CLEAR
EXPOSE DOSE=I
BAKE DIFF.LENGTH=0.05
STRUCT OUTFILE=ANOPEX12.J.I.STR
DEVELOP MACK TIME=45 STEPS=5 SUBSTEPS=10
STRUCTURE OUTFILE=ANOPEX12.J.I.STR3
PRINTF J (ZZZ|GAS(1.4) - GASS|ZZZ(1.4)) I > SMILE
END
In this smile plot example, exposure DOSE is varied in the outer loop and DEFOCUS is varied in the
inner loop.
The output is written to a file called SMILE. The difference between the smile plot and the swing plot is
that smile plots must distinguish between several types of data. To do so, a third column called Group
is added (see the TONYPLOT chapter in the VWF INTERACTIVE TOOLS USER’S MANUAL, VOL I). The final
PRINTF statement prints DEFOCUS (J), CDs, and DOSE (I). To display the plot, outside of
DECKBUILD, enter the tonyplot -da SMILE command and the plot will appear. In the TonyPlot
Window, select Plot/Display and a popup will appear. Then, pull down the Group menu and select
the Dose menu item. This will group the set of plots for each exposure dose.
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2.10: Adaptive Meshing
2.10.1: Introduction to Mesh Adaption
ATHENA has a built-in mesh adaption module that automatically adapts the grid to dopant profiles.
Used together with implantation and diffusion, the module can achieve more optimized accuracy of a
given profile’s representation for a given number of grid points. This relieves you to some extent from
the time consuming mesh generation task in the simulation structure preparation stage. It will also
improve the accuracy and speed of the subsequent diffusion/oxidation/epitaxy stages where impurity
profiles change with time.
The algorithm used was suggested in [3], [4]. It uses an efficient local error estimator and a
triangulation scheme suitable for complex two-dimensional moving boundary problems.
Adaption During Ion Implantation
Ion implant is a common process step to introduce impurities into the substrate to form active device
regions. Prior to the implant step, it is difficult to determine the required mesh density distribution
because the exact dopant profile is unknown before processing. Thus, you can only estimate the profile
and required mesh. It’s a time consuming process to specify mesh generation statements to create the
mesh with a density conforming to an estimated profile. Graphical tools, such as DEVEDIT, can make
this easier. But it can’t totally eliminate the process. With the Adaptive Meshing module, you can
overcome these difficulties to a larger extent.
The program uses an iterative algorithm to determine the required mesh density distribution to
accurately conform to the implanted profile, and will automatically generate the additional required
mesh. The algorithm is illustrated with the flow chart depicted in Figure 2-67.
Previous Mesh
Dopant Implant
Clear Dopant
+ Increase Adaptive
Meshing critera
Mesh Adaption
N
Accurate
Implanted
Profile
Distribution?
Y
Continue
Figure 2-67: Flow Chart of Mesh Adaption Algorithm
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Adaption During A Heat Cycle
During the diffusion/oxidation/epitaxy processes, impurity profiles are usually changing continually
with each elapsed time step. An initially generated optimal mesh will not conform to the time varying
dopant profile. If the impurity profiles change substantially during the process, the mesh density
distribution will be different from the dopant contour distribution, causing both accuracy and speed
problems.
During simulation, the total time of a diffusion/oxidation/epitaxy process is usually divided into many
small time steps, with profiles changing gradually between time steps. Using the Adaptive Meshing
module, you can perform a mesh adaption after each time step. This allows the mesh to conform to the
dopant after a time step.
The difference between the dopant contours and the change in the mesh density distribution will thus
be limited to the difference of dopant profiles between time steps. This difference is substantially
smaller than that over total diffusion time. Thus, mesh adaption can allow more accuracy and
minimize the mesh density for the dopant representation at any given time.
A Simple Example:
GO ATHENA
LINE X LOC=0.00 SPAC=0.1
LINE X LOC=2.00 SPAC=0.1
LINE X LOC=0.00 SPAC=0.1
INIT SILICON C. ARSENIC=10E14
DIFF TIME=50 TEMP=950 DRYO2
DEPOSIT POLY LEFT PL.X=1.2
ETCH POLY LEFT PL.X=1.2
STRUCT OUTF=MOS_0.STR
#PERFORM ADAPTIVE MESHING FOR BOTH IMPLANT AND DIFFUSION
METHOD ADAPT
IMPLANT BORON DOSE=1.0E13 ENGERY=15 PERSON TILT=0
STRUCT OUTF=MOS_1.STR
DEPOSIT OXIDE THICK=.35 DIV=6
ETCH OXIDE THICK=.35
IMPLANT BORON DOSE=1.0E14 ENGERY=15 PERSON TILT=0
STRUCT OUTF=MOS_2.STR
DIFFUSE TEMP=1000 TIME=30
STRUCT OUTF=MOS_3.STR
QUIT
LISTING 1: A SIMPLE EXAMPLE OF IMPLANT ADAPTIVE MESHING
This simple example creates a LDD MOS device structure. The initial simple mesh is specified with the
four LINE statements. This initial mesh is referred to as a base mesh and options for its formation will
be discussed the “The Mechanics of the Base Mesh Formation” Section on page 2-89. After some initial
1D processing, the adaptive meshing function is invoked. Subsequently, automatically adds mesh that
conforms well to the two implanted Boron profiles. During the final DIFFUSE statement, Boron has
been driven down into the substrate and tessellated with the initial simple mesh. The mesh
adaptation module adapts after each time step. This results in meshing conforming to the Boron
profile throughout the diffusion process.
The mesh adaption module is invoked during the simulation by specifying boolean flag ADAPT on the
METHOD command preceding IMPLANT, DIFFUSE, or EPITAXY statements. The syntax behind this
simple example using the mesh adaption module is shown below.
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Three statements are available to access the mesh adaptation module, they are briefly described as the
following. The METHOD statement is used to control numerical algorithms. When METHOD ADAPT is
specified, the mesh adaptation algorithm will be used. If you specify METHOD ADAPT=false, the mesh
adaptation algorithm will be turned off. ADAPT is off by default.
ADAPT specifies that the adaptive meshing should be performed on any of the following IMPLANT,
DIFFUSE or EPITAXY statements. Adaptation is performed by following each step on each DIFFUSE/
EXPITAXY statement. IMPLANT.MES specifies which adapting algorithm to use on IMPLANT
statements. Currently, IMPLANT.MES=0 corresponds to the University of Florida’s algorithm. This is
the default. Also currently, this is the only recommended algorithm. There are four other parameters
on the METHOD statement that specify mesh smoothing.
They are as follows:
•
ETCH.SMOOTH specifies that mesh smooth operation will be performed after etch.
•
DEPO.SMOOTH specifies that mesh smooth operation will be performed after deposit.
•
DIFF.SMOOTH specifies that mesh smooth operation will be performed after diffusion.
•
STEP.SMOOTH specifies that mesh smooth operation will be performed after each diffusion time
step. These four parameters are currently set as default.
The ADAPT.PAR statement is used to set parameters to adjust the mesh adaptation process. The
parameters available on the ADAPT.PAR statement are the following. Specify material regions to be
adapted, such as SILICON, OXDIDE, and POLYSILICON. This may be one or several materials at a
time. The default impurities include such as I.BORON or I.ARSENIC. Specify impurities to be adapted
on. This may be one or several impurities at a time. The DISABLE parameter specifies materials/
impurities given disabled to be effective on mesh adapting or smoothing. The MAX.ERR parameter
specifies the maximum errors allowed before adding points to the mesh (unitless). Errors calculated
above this value cause points to be added. The MIN.ERR parameter specifies the minimum error below
which points may be deleted from the mesh (unitless). Error calculated below this value causes points
to be removed. Both MAX.ERR and MIN.ERR are calculated using the Bank-Weiser Error Estimator
which is defined as
2 ∆ ( Ci )
c = h * -------------( Ci )
2-2
where h is the average of the edge lengths associated with node i. Ci is the impurity concentration at
node i. The parameter, CONC.MIN, specifies the minimum impurity concentration below which
adapting will stop (units 1.0/cm3).
The ADAPT.MESH statement is used to do mesh adaptation for a given device structure without
coupling implant diffusion/epitaxy to the process. Therefore, the mesh adaptation module can be used
to assist the manual mesh generation process. The following parameters are available on the
ADAPT.MESH statement:
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•
ADAPT specifies a stand alone adaptive meshing step should be performed to refine or relax the
current mesh based on the material/impurity specification given on the ADAPT.PAR statement
(default false).
•
ADAPT.COUNT specifies that stand alone annealing be performed during the execution of the
ADAPT.MESH statement (default false).
•
SMTH.COUNT specifies the number of smooth loops during the smoothing algorithm.
Silvaco
Tutorial
Adaptive Meshing Control
Adaptive meshing may be used in several different modes and has several statements to control it.
This section describes the adaptive meshing related statements and how to use them. Table 2-6 list
these statements.
Table 2-6. Summary of Adaptive Meshing Control
Parameter
Description
METHOD
Switches the various automated adaption modes on and off.
ADAPT.MESH
Invokes a stand alone adaption of the mesh at a specific point.
ADAPT.PAR
Control both the stand alone adaption and the automatic adaption meshing
criteria.
GRID.MODEL
Describes an external template file, containing mesh related statements specific
to a general technology or device.
BASE.MESH
Defines the 1D starting point of a mesh for an adaptive mesh based simulation.
BASE.PAR
Specifies the adaption criteria for the base mesh only.
The Mechanics of the Base Mesh Formation
ATHENA uses adaptive meshing in both 1D and 2D modes. ADAPT.PAR parameters control both these
modes. The concept of the Base Mesh, however, needs to be described. A typical simulation (e.g., a
MOS) is simulated in 1D initially and then switched to 2D during mid-process flow, perhaps at the
Poly Gate definition process step. Here, the mesh is extruded from 1D to 2D and the result is the base
mesh. The Base Mesh then forms the basis, and is the starting point, for 2D Adaptive Meshing. The
mesh quality of this base mesh is important for success of future adaption for example, during sourcedrain implants and anneals.
2.10.2: Interface Mesh Control
The Interface Mesh Control is used to control the mesh in the vicinity of a material interface. This
function allows you to add grid lines, for example, to run along under the gate of MOSFET at some
distance from the Si/Si02 interface. The Interface Mesh Control is often useful for adding mesh as
required by highly mesh dependent mobility models during a following device simulation. It is also
useful to be able to add mesh for better segregation modeling. The ADAPT ADD.I.LINE=n command
controls the addition of a new mesh line. Two materials are specified as parameters to the command
defining an interface or a set of interfaces. The mesh line is added to MATERIAL1 as follows:
ADAPT.MESH ADD.I.LINE=0.001 MATERIAL1 / MATERIAL2
For example, in the case of adding an additional mesh line to the SILICON in the channel region of a
MOSFET:
ADAPT.MESH ADD.I.LINE=0.001 SILICON / OXIDE
The structural transition from 1D to 2D to create a base mesh is controlled by the BASE.PAR
parameters. Figure 2-68 indicates the flow of events towards the formation of a base mesh and beyond
in the case of MOSFET device.
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Commands
Base. Mesh
INIT
Method
Adapt
Action on Structure
Define
Initial ID
Mesh
Define
Width +
Depth
ID Adaptive
Meshing
Simulation
Adapt.Par
Base.Par
ETCH Left.....
Adapt.Par
Define Mesh Rules
for ID to 2D
Transition
Switch from ID
to 2D Simulation
Modify 2D
Adaptive Meshing
Criteria
Simulate to
Complete
Figure 2-68: MOSFET Device Mesh Formation Flow
The base mesh quality is important to allow a subsequent adaption in 2D. The adjacent ratio of
elements, both in 1D and 2D relate directly to the smoothness of the final mesh quality.
The generation of a high quality adapted mesh starts with the BASE.MESH command. Here, the 1D
mesh is defined from where the final 2D mesh will evolve. The BASE.MESH command defines a 1D
structure as a stack of up to five layers. Five layers are used to define the five layers of a Bipolar
device. Each layer is described as having a thickness: SURF.LY, ACTIVE.LY EPI.LY, SUB.LY, and
BACK.LY and an associated mesh spacing per layer, SURF.DY, ACTIVE.DY, EPI.DY, SUB.DY, and
BACK.DY. The whole structure can also be offset in space with the point of origin determining the top
left hand corner of the structure. The OFFSET.X and OFFSET.Y parameters are used for this purpose.
An example of using the offset command might be defining the starting surface of an initial
structure an epi thickness below the zero position. That way, the subsequent geometrical calculations
are made easier.
Figure 2-69 indicates the relationship of the BASE.MESH command to the initial 1D structure mesh.
2-90
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Tutorial
Figure 2-69: Initial 1D Structure Relationship
The BASE.MESH parameters should be considered alongside the BASE.PAR parameters. When forming
a base mesh, there are three objectives to remember regarding the quality of mesh. These objectives
are as follows:
•
1D dopant information is neither lost in the 2D transition nor overly refined upon, resulting in
overly dense BASE.MESH (See Figures 2-70 and 2-71).
•
Little or few flat triangles exist in regions and materials of importance. (See Figure 2-74).
•
The adjacent triangle ratio, in both X, and Y directions, is not abrupt in spacial regions of
importance to the device (See Figure 2-75).
Controlling the quality of the BASE.MESH, formed at the 1D-2D transition, is achieved with the
BASE.PAR command parameter. Specific materials can be assigned different parameters. The
GRAD.SPACE parameter controls the Vertical Adjacent Triangle Ratio Quality, while the RATIO.BOX
parameter controls the lateral Adjacent Triangle Ratio. These two statements can be thought of as
operating upon the 1D and 2D simulation segments respectively during 1D simulation. Only the
adjacent spacing ratio can be controlled in the vertical profile with the GRAD.SPACE parameter.
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Subsequently, at the point of 2D transition, the RATIO.BOX parameter is used to trade off mesh
quality for mesh density.
The INIT command includes the parameters: WIDTH.STR and DEPTH.STR. These parameters define
the size of the initial structure and will truncate the previous BASE.MESH defined structure.
Figures 2-74 and 2-75. show an example of this base mesh and of the subsequent 2D diffusion.
Figure 2-70: Mesh that is too coarse leads to Dopant Information Loss
Figure 2-71: Too Dense Mesh Causes Too Much CPU Time during Subsequent Simulation
2-92
Silvaco
Tutorial
3. (i)
Large
Adjacent
Triangle
Ratios
3. (ii)
Reasonable
Adjacent
Triangle
Ratios
Figure 2-72: Large and reasonable Adjacent Triangle Ratios
A
B
C
B/A = GRAD.SPACE
D
C/D = RATIO.BOX
Figure 2-73: Base Mesh Formation
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ATHENA User’s Manual
Figure 2-74: Automatic Base Mesh Generation
Figure 2-75: Ion Implantation Adaption on New Base Mesh
2-94
Silvaco
Chapter 3:
SSUPREM4 Models
3.1: Diffusion Models
The diffusion models in ATHENA describe how implanted profiles of dopants/defects (see the Note
below) redistribute themselves during thermal treatment, due to concentration gradients and internal
electric fields. When modelling the actual diffusion process, there are additional effects to consider
such as impurity clustering, activation, and how interfaces are treated. Fundamentals of the models
described in this section could be found in [5], [6], and [7].
Note: In the following sections, the terms impurity and dopant shall be used interchangeably, although an impurity doesn’t
necessarily have to be a dopant. Also the term, defect, shall mean the same as point defect, unless otherwise indicated in the
context.
Diffusion of dopants and point defects in SSUPREM4 is described by a number of user-specifiable
models. The three most basic models are the following:
•
The Fermi diffusion model.
•
The two dimensional diffusion model.
•
The fully coupled diffusion model.
The models are natural extensions of each other in the sense that the Fermi model is included in the
two dimensional model, which is included in the fully coupled model. The two significant differences
between them are the way point defects are represented and treated throughout the simulation, and
how the specific dopant diffusivities are formulated. The selection of which model to use will depend
upon the existence or the generation of point defects during the diffusion process and the dopant
concentrations within the silicon. Careful reading of the following sections is critical to understanding
which model to use.
All three models rely on the concept of Pair Diffusion, which says that a dopant atom cannot diffuse on
its own – it needs the assistance of a point defect (a silicon self interstitial or a lattice vacancy) in the
near vicinity as a diffusion vehicle. If there is a non-vanishing binding energy between the two, they
can move as one entity (a pair) through a number of jumps and inversion cycles before eventually
breaking up. When speaking of dopant diffusivity within the scope of these models, one actually means
the diffusivity of the pair as a whole. A point defect, however, can either diffuse freely or as a
participant in a dopant-defect pair. The diffusivity of a free point defect can actually be different from
the diffusivity of a point defect pair.
All diffusion models in ATHENA also use the concept of Chemical and Active Concentration Values.
The chemical concentration is the actual implanted value of the dopant but when dopants are present
at high concentrations, clustering or electrical deactivation can occur so that the electrically active
concentration may be less than the corresponding chemical concentration. This is described Section
3.1.6: “Electrical Deactivation and Clustering Models”.
ATHENA creates structures that can have multiple materials and interfaces such as the polysiliconoxide-silicon interface in MOSFETs. Each interface within ATHENA has boundary or interface
conditions that model impurity segregation. The model details are described later in this chapter. You
should, however, be aware that the gas/solid interface (the surface of the silicon if exposed) and solid/
solid interfaces have been strictly modelled within ATHENA. Effects such as dopant loss from exposed
silicon and dopant pile-up at interfaces are simulated.
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ATHENA User’s Manual
3.1.1: Mathematical Description
The mathematical definition of a diffusion model includes the following specifications for every
diffusing species present:
•
a Continuity Equation (often called a Diffusion Equation).
•
one or more flux terms.
•
a set of boundary and interregional interface conditions.
In the case of impurity diffusion in semiconductors, we need a set of equations for each dopant present
and for each type of point defect if point defects are explicitly represented in the model. Since dopants
can only diffuse as participants in dopant-defect pairs, the dopant continuity equation is actually a
continuity equation for defect-dopant pairs.
The formulation of the continuity equation have a number of built-in assumptions:
•
•
•
Electronic processes take place on a time scale, which is much smaller than the time scale of all
other processes (adiabatic approximation).
The pairing reaction between dopants and defects is assumed to always be in equilibrium. This
may not be the case, especially at a low temperature, but would pose a much harder and more CPU
intensive numerical problem to solve.
Mobile dopants are electrically active and vice versa.
Models that explicitly take pair populations into account have been implemented by various research
groups. But all these models suffer from the lack of established experimental data, such as binding
energies, or pairing coefficients, for which reason the predictability of these models is questionable.
The lack of data, especially for the energy levels of the different charge states of the point defects in
the band gap at typical diffusion temperatures, poses a serious gap in our knowledge. Some of these
energy levels have been measured in low temperature experiments such as DLTS (deep level transient
spectroscopy), but no one knows how these levels adjust themselves relative to the band edges when
the band gap narrows as a function of increasing temperature.
Van Vechten [8] has theoretically argued that the acceptor states (0/- and -/=) and the donor states (+/
++ and +/0) of the mono vacancy follow the conduction band edge with increasing temperature.
Mathiot [5], however, chooses to scale the positions of the energy levels relative to the band edges with
the size of the band gap.
In addition to the models described above, which are all specific for dopants and point defects in
silicon, there is a smaller number of hard coded models that are used for other materials such as oxide
or poly.
In the sections that follow, we apply standard notation used in the literature for dopants, point defects
(interstitials and vacancies) and the different charge states as shown in Table 3-1. In Table 3-1, the x
designates the neutral charge state. - is a single negatively charged state. = is a double negatively
charged state.
Table 3-1. Notational standards in diffusion literature
3-2
Physical Entity
Generic Symbol
Replacement Values
Dopant
A
B, P, As, Sb,...
Point Defect
X
I, V
Charge State
c
x, -, =, +, ++
Silvaco
SSUPREM4 Models
Many physical entities or parameters are temperature-dependent. In ATHENA, this dependence upon
temperature is modelled by the Arrhenius expression (unless otherwise indicated):
Q.E
Q ( T ) = Q.0 exp  – ---------- 
 kT 
3-1
where:
• Q.0 is the pre-exponential factor,
• Q.E is the activation energy,
• k is the Boltzmann constant,
• T is the absolute temperature.
Generic Diffusion Equation
All diffusion models, whether they are the Fermi, the two dimensional or the fully coupled model,
follow the same generic mathematical form of a continuity equation. A continuity equation merely
expresses particle conservation, that is, the rate of change with time of the number of particles in a
unit volume must equal the number of particles that leave that volume through diffusion, plus the
number of particles that are either created or annihilated in the volume due to various source and sink
terms.
This basic continuity equation for the diffusion of some particle species (C) in a piece of semiconductor
material is a simple Second Order Fick’s Equation [9]:
∂ C Ch
------------ = –∇ JA + S
∂t
3-2
where CCh is the total particle (chemical) concentration, JA is the flux of mobile particles, ∇ is the
gradient operator, and S accounts for all source and sink terms. The difference between the total
(chemical) concentration and the actual mobile concentration is described in a later section entitled
Section 3.1.6: “Electrical Deactivation and Clustering Models”. In semiconductor diffusion problems,
there are generally two contributors to the particle flux.
The first contributor is an Entropy Driven Term, which is proportional to the concentration gradient of
mobile particles. The coefficient of proportionality, DA, is called the diffusivity. The second contributor
is a Drift Term, which is proportional to the local electric field. Notice that if there are several types of
electrically charged species present, this term establishes a coupling between them, since all charged
particles both contribute to and are influenced by the local electric field.
The Flux Term, JA, can be written as:
JA = –DA ( C ) ∇ CA + CA σ E
3-3
where CA designates the mobile impurity concentration, σ is the mobility, and E is the electric field. It
should also be observed that Equation 3-3 is non-linear, since both the diffusivity DA and the electric
field E in general depend on the concentration of all present species. In thermodynamical equilibrium,
kT
the Einstein relation relates mobility and diffusivity through the expression D = ------- σ .
q
Silvaco
3-3
ATHENA User’s Manual
Substituting for σ in Equation 3-3 is writing the particle charge as a signed integer, ZA, times the
elementary charge, q, giving us this Flux Expression.
J A = – D A ( C )  ∇ C A – Z A C A qE
-------

kT 
3-4
In insulator and conductor materials, the electric field is zero. In semiconductor materials, the electric
field is given by:
E = – ∇ψ = – kT
------ ∇ n
qn
3-5
where ψ is the electrostatic potential and n is the electron concentration. If charge neutrality is
assumed, then the electron concentration may be rewritten as:
 ND – NA  2
ND – NA
2
- +n
n = ------------------- +  ------------------2 
2
i

3-6
where ND and NA are the electrically active donor and acceptor impurity concentrations, and ni is the
intrinsic carrier concentration calculated as:
NI.E NI.POW
n i = NI.0 ⋅ exp  – ------------ T
 kT 
3-7
where you can specify the NI.0, NI.E, and NI.POW parameters in the MATERIAL statement. The
electrically active and mobile impurity concentrations are equivalent.
Boundary conditions
Boundary conditions within ATHENA are of mixed type and are expressed mathematically as:
α ⋅ CA + ( β ⋅ ∂n CA ) = R
3-8
where (α, β) are real numbers and ∂nCA designates the flux of CA across the boundary. The right hand
term, R, accounts for all source terms on the boundary. Boundary conditions are applied at two main
regions.
The first region is at the top of the simulation region (the surface). The second region is at the
inter-regional interfaces for which the species in question only has a meaningful existence in one of the
region materials (e.g., an interstitial on a silicon/oxide interface).
Interface conditions
Between any two regions there must be some control on how any impurity species can exist in the
vicinity of the interface. For every such interface, you must specify a Concentration Jump Condition
and a Flux Jump Condition.
The Concentration Jump Condition accounts for discontinuities in particle concentrations across
interfaces and encompasses particle transport across material interfaces due to different solid
solubility ratios of the impurity species in the two materials.
The Flux Jump Condition enables the formulation of interface source and sink terms such as surface
recombination, particle injection, and particle pile-up at a moving interface.
For all species, no flux boundary conditions are employed on the sides and at the bottom of the
simulation structure. This is hardwired into the software, which means it is not user-definable.
3-4
Silvaco
SSUPREM4 Models
3.1.2: The Fermi Model
The Fermi Model assumes that point defect populations are in thermodynamical equilibrium and thus
need no direct representation. All effects of the point defects on dopant diffusion are built into the pair
diffusivities. The main advantage for using the Fermi Diffusion model is it will greatly improve the
simulation speed, since it does not directly represent point defects and only needs to simulate the
diffusion of dopants. Also, the Fermi Model usually results in an easier numerical problem due to the
avoidance of “numerical stiffness”. But since point defects are not directly simulated, the Fermi model
cannot deal with certain process conditions in which the defect populations are not in equilibrium,
such as in wet oxidation (where Oxidation Enhanced Diffusion (OED) is important), emitter-base
diffusions and wherever implantation results in an initial high level of implant damage.
To use the Fermi Model, specify FERMI partameter in he METHOD statement.
In the Fermi Model, each dopant obeys a continuity equation of the form:
∂ C Ch
-------------- =
∂t
∑∇
X = I, V
• D AX  ∇ C A – Z A C A qE
-------

kT 
3-9
where CCh is the chemical impurity concentration, ZA is the particle charge (+1 for donors and -1 for
acceptors), DAV and DAI are the joint contributions to the dopant diffusivity from dopant-vacancy and
dopant-interstitial pairs in different charge states [5]. CA is the mobile impurity concentration and E is
the electric field. The terms DAV and DAI depend on both the position of the Fermi level as well as
temperature and are expressed as:
+ + n –2
x
– n 1
=
+ n –1
n 2
n
D AX (T,----) = D AX + D AX  ---- + D AX  ---- + D AX  ---- + D AX  ----
n 
n 
n 
n 
ni
i
i
i
i
3-10
where the temperature dependency is embedded in the intrinsic pair diffusivities, which are specified
by Arrhenius expressions of the type:
c 
 D .E AX
c
c
-
D AX = D.0 AX exp  – ------------------kT 

3-11
Table 3-2 shows the names of the pre-exponential factors, D.0, and activation energies, D.E, for each of
the charge states, c, of the various intrinsic pair diffusivity terms.
Pair charge states beyond two are unlikely to occur, which is why they have been omitted. Also, for
most dopants it is seldom that more than three of the terms above are non-vanishing.
Table 3-2. Table of intrinsic pair diffusivities for different pair types
Silvaco
Pair
Charge State
Pre--exponential
factor
Activation Energy
AV
x
DVX.0
DVX.E
AV
-
DVM.0
DVM.E
AV
=
DVMM.0
DVMM.E
AV
+
DVP.0
DVP.E
AV
++
DVPP.0
DVPP.E
3-5
ATHENA User’s Manual
Table 3-2. Table of intrinsic pair diffusivities for different pair types
Pair
Charge State
Pre--exponential
factor
Activation Energy
AI
x
DIX.0
DIX.E
AI
-
DIM.0
DIM.E
AI
=
DIMM.0
DIMM.E
AI
+
DIP.0
DIP.E
AI
++
DIPP.0
DIPP.E
Note: Since the point defect populations are by definition assumed to be in equilibrium in the Fermi model, there are no
separate continuity or boundary condition equations for these species. Additionally, neither the vacancy concentration, CI, nor
the interstitial concentration, CV, appear explicitly in Equations 3-9, 3-10, or 3-11.
3.1.3: Impurity Segregation Model
In multilayer structures, dopant segregation across material interfaces must be considered. Such
interfaces can represent either a solid/solid interface or a gas/solid interface (the surface).
Interface segregation is modeled empirically by a first order kinetic model for the interregional flux:
C1
F s = h 12 ⋅  -------- – C 2
M

12
3-12
where:
• C1 and C2 are the particle concentrations in the immediate vicinity of the interface in the
regions 1 and 2.
• h12 is the interface transport velocity.
• M12 is the segregation coefficient.
The transport velocity and segregation coefficients are temperature-dependent parameters defined
through the following Arrhenius expressions:
-----------------
h 12 = TRN.0 ⋅ exp  – TRN.E

kT 
3-13
-----------------
M 12 = SEG.0 ⋅ exp  – SEG.E

kT 
3-14
You can specify the parameters: TRN.0, TRN.E, SEG.0 and SEG.E in the IMPURITY statement. All
parameters are specified for only one direction, which is from region 1 to region 2.
The following is an example of the syntax used to change the segregation coefficients between oxide
and silicon. Two material names separated by a / to indicate the combination and the ordering of
materials for which these parameters are specified.
IMPURITY I.PHOSPHORUS SILICON /OXIDE SEG.0=30 TRN.0=1.66E–7
3-6
Silvaco
SSUPREM4 Models
Interface Trap Model (Dose Loss Model)
You can simulate the effect of dose loss at silicon/oxide interface by specifying the DOSE.LOSS
parameter in the METHOD statement. This model is based on the theory that the dopant diffusing
through silicon/oxide interface can be trapped into the trap sides located at the interface [10], [11]. A
modified equation for impurity flux is used in the Dose Loss Model.
F m = S m ( C m ( 1 – C T ⁄ C Tmax ) – M m C T )
3-15
where m=1,2 correspond to Si and SiO2, Mm = Cmss/CTmax, M12 = M1/M2, and S1 = 10S2. The CT
parameter is the real density of occupied trap sites at the interface and is found by solving the
following equation:
∂C T
= F1 + F2
∂t
3-16
where CTmax = 6.8 × 1014cm-3 for phosphorus and 2 x1014cm-3 for other dopants. The dose loss
transport coefficient S1 is calculated through the following Arrhenius expression:
-------------------------
S 1 = TRNDL.0 ⋅ exp  – TRNDL.E


kT
3-17
where the TRNDL.0 and TRNDL.E parameters can be specified in the IMPURITY statement.
3.1.4: The Two Dimensional Model
In this model, the point defect populations are directly represented and evolved in time. If there is a
super/supra saturation of point defects, it will affect the dopant diffusivity through a simple scale
factor, which goes to unity as the actual defect concentration approaches the equilibrium defect
concentration. Therefore with equilibrium defect profiles, the Two Dimensional Model merely reduces
to the Fermi Model, although in a more computational inefficient manner, since solving for point
defects is not required. The pair coupling between defects and dopants in this model is assumed to be
one-way. The diffusion of dopants is highly influenced by the diffusion of point defects, while the
diffusion of the point defects, however, is regarded as totally independent of dopant diffusion. Stated in
physical terms, this corresponds to a pairing between defects and dopants with zero binding energy.
To turn on the Two Dimensional Model, specify parameter TWO.DIM in the METHOD statement.
The Two Dimensional Model is based on the Fermi Model, so read the Fermi Model description before
continuing. The major difference between the Fermi Model and the Two Dimensional Model is the
direct representation and evolution of non-equilibrium point defect populations. Therefore, there are
three different sets of governing diffusion equations: one for dopants, one for point defect interstitials
and one of point defect vacancies. In addition, you also need to take into account the {311} cluster
formation and dissolution, bulk and interface recombination, and the generation of point defects
through oxidation. Each of these are described in detail in the following sections.
Dopants
The continuity equation for dopants is:
∂ C Ch
------------ = –
∂t
Silvaco
∑
∇•J AX
3-18
X = I, V
3-7
ATHENA User’s Manual


CX 
C X  qE
J AX = – f X D AX ∇  C A ---------  – Z A  C A --------- ------ C* 
 C *  kT
X
3-19
X
where CI and CV are the actual concentrations of interstitials and vacancies, and C*I and C*V are the
equilibrium concentrations. The fX factor is an empirical defect factor, which for interstitials is
assumed to be temperature-dependent through the following Arrhenius expression:
FI.E
f I = FI.0 exp  – -----------
 kT 
3-20
where the FI.0 and FI.E parameters can be specified in the IMPURITY statement. The value of fI is
clamped to a number between 0 and 1. The equivalent term for vacancies is calculated according to:
fV = ( 1 – fI )
3-21
The formulation of equation (Equations 3-18 and 3-19) is similar to the Fermi Diffusion Model except
for two elements. The additional term C X ⁄ C X
*
has been added to model the enhancement or
retardation of diffusion due to non-equilibrium point defect concentrations. The term fX takes into
account the knowledge that some impurities diffuse more by interstitials than by vacancies or vice
versa. Although this dependency is of a phenomenological character, it seems reasonable, and is the
one used by most diffusion simulators to account for the diffusion enhancement of dopants during
oxidation enhanced diffusion (OED) or transient enhanced diffusion (TED).
Remember the point defect equilibrium concentrations are temperature as well as Fermi level
dependent and can be calculated from the following expressions:
n +1
n +2
n –1
n –2
neu + neg  ----
+ dneg  ----
+ pos  ---- + dpos  ----
n 
n 
n 
n 
i
i
i
i C X∗ = C X∗ i ------------------------------------------------------------------------------------------------------------------------------------------------------------------neu + neg + dneg + pos + dpos
3-22
where CX*i represents the equilibrium defect concentrations of interstitials and vacancies under
intrinsic conditions, and the weight factors: neu, neg, dneg, pos, and dpos account for the distribution
of defects of different charge states under intrinsic conditions. All of these are assumed to be
temperature dependent through Arrhenius expressions of the following type:
------------------
neu = NEU.0 exp  – NEU.E

kT 
3-23
where the pre-exponential factors and activation energies, in this case NEU.0 and NEU.E, can be
specified in the VACANCY and INTERSTITIAL statements. Table 3-3 shows the complete set of
corresponding parameters.
For dopants, the boundary and interface conditions are identical to the ones stated in the Fermi Model.
3-8
Silvaco
SSUPREM4 Models
Table 3-3. Parameters for charge statistics and intrinsic point defect concentrations
Entity
Pre-exponential
factor
Activation Energy
neu
NEU.0
NEU.E
neg
NEG.0
NEG.E
dneg
DNEG.0
DNEG.E
pos
POS.0
POS.E
dpos
DPOS.0
DPOS.E
C X∗
CSTAR.0
CSTAR.E
i
Interstitials
The interstitial profile evolves with the following continuity equation.
∂ CI
-------- = – ∇•J I – R B + R T – R 〈 311〉
∂t
3-24
where JI is the flux of interstitials, RB is the bulk recombination rate of interstitials, RT accounts for
the capture or emission of interstitials by traps, and R{311} is the recombination rate of {311} clusters.
Each of these terms are described below.
The interstitial flux, JI, is calculated according to [5] with:
* C 
– J I = D I C I ∇  ------I-
 C*I 
3-25
which correctly accounts for the effect of an electric field on the charged portion of the interstitials,
C
I
- . DI is the diffusivity of free
taking the gradient of the normalized interstitial concentration, -------∗
CI
interstitials. Don’t confuse it with the pair diffusivity DAI, which was mentioned in Section 3.1.2: “The
Fermi Model”.
DI is calculated once again with the following Arrhenius expression:
----------
D I = D.0 exp  – D.E
 kT 
3-26
where the pre-exponential factor and activation energy (D.0 and D.E) can be set in the INTERSTITIAL
statement.
The bulk recombination rate (RB) is a simple reaction between vacancies and interstitials that
assumes that any interstitial will recombine with any vacancy, regardless of their charged states. This
assumption may overestimate the recombination rate. The equation is expressed as:
*
R B = K r ( C I C V – C I C V*)
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3-27
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ATHENA User’s Manual
where Kr is the bulk combination coefficient and specified as:
KR.E
K = KR.0 exp  – -------------
r
 kT 
3-28
where the parameters KR.0 and KR.E are user-definable in the INTERSTITIAL statement.
The interstitial trap rate (RT) model was first introduced by Griffin [12] to explain some of the wide
variety of diffusion coefficients extracted from different experimental conditions. The Trap Equation,
which describes the evolution of the empty trap population in time, is:
∗
∂ C ET
e
C I∗ ( C T – C ET )
- = – K T C ET C I – ----------------R = ----------∂t
∗
1–e
3-29
where:
• CT is the total trap concentration.
• KT is the trap capture rate.
• CET is the empty trap concentration.
• CI is the interstitial concentration.
• CI
•
∗
is the equilibrium interstitial concentration.
∗ ⁄C .
e* is the equilibrium empty trap to total trap ratio, e∗½ C ET
T
Both KT and e* are Arrhenius expressions that can be set in the TRAP statement with the total trap
concentration, RT, with the parameters shown in Table 3-4.
Table 3-4. Parameters for interstitial traps
Entity
Pre-exponential
factor
Activation Energy
KT
KTRAP.0
KTRAP.E
e*
FRAC.0
FRAC.E
CT
TOTAL
—
The trap equation is either derived from the simple reaction:
I+T
⇔ IT
3-30
or posed as a rate equation:
∂ C ET
------------ = – K T C I C ET + K r ( C T – C ET )
∂t
3-31
where Kr is the trap emission rate. In equilibrium, the left hand side of Equation 3-31 must vanish,
giving:
3-10
Silvaco
SSUPREM4 Models
K T C I∗ C ET
∗
= K r  C T – C ET


∗
⇔
∗ ⁄C 
C I∗  C ET
T

e∗ K r = K T ------------------------------------- = K T C I∗ ------------1 – e∗
∗ ⁄C 
1 –  C ET
T


3-32
Substituting this value for Kr into Equation 3-31 leads to the expression in Equation 3-32.
The recombination rate of {311} clusters (R{311}) in Equation 3-24 accounts for the release rate of
{311} interstitial clusters, which are small, rod-like defects that have been observed in Transmission
Electron Microscopy (TEM) studies after medium to high dose implantation of impurities into silicon.
Since a large fraction, if not all, of the excess interstitials after implantation are believed to exist in
this form, the time scale for dissolution of {311} clusters plays an important role for the duration of any
Transient Enhanced Diffusion (TED).
Think of these volume defects as small pockets of interstitials distributed throughout certain parts of
the doped regions, which are released during annealing; thus, acting as bulk sources of point defects.
Note: Actually, {311} defects are believed to be created from excess free interstitials during the earliest part of the annealing
cycle through a process called Ostwald ripening. But here, they’re considered as existing immediately after the implantation.
The cluster release rate follows a simple exponential decay in time specified by:
R 〈 311〉
∂C
∂t
1
t
{ 311 }
≡ – ----------------- = f ( x )  --- exp  – --
 
τ
τ
3-33
where f(x) is the as-implanted profile of {311} clusters, and τ is an Arrhenius type temperature
dependent time constant calculated from:
-----------------------------
τ = TAU.311.0 exp  – TAU.311.E

kT
3-34
where the TAU.311.0 and TAU.311.E parameters can be specified in the CLUSTER statement. The
profile, f(x), of the {311} clusters is created from a previous IMPLANT statement. For more information,
see Section 3.5.5: “Ion Implantation Damage”.
To activate this model, a previous IMPLANT statement has to introduce {311} clusters with the
CLUSTER.DAM flag in the METHOD statement. For example:
METHOD CLUSTER.DAM
CLUSTER BORON MIN.CLUSTER=1.0E17 MAX.CLUSTER=1.0E19 CLUST.FAC=1.4\
TAU.311.0=8.33e-16 TAU.311.E=-3.6 SILICON
IMPLANT BORON ENERGY=100 DOSE=1E15
Here, the METHOD statement switches the model on, and the CLUSTER (optional) statement decides the
location and scaling of the {311} cluster profile. In this example, clusters are present in the regions of
the substrate, where the chemical boron concentration is between 1.0e17 cm–3 and 1.0e19 cm–3, which
are scaled by a factor of 1.4 relative to the boron concentration.
Notice that the activation energy for TAU.311.E must be specified as negative, since the time constant
decreases with rising temperature.
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3-11
ATHENA User’s Manual
Interstitial Generation and Recombination at Interfaces
Interfaces present a moving boundary problem during a thermal oxidation. In this instance, there will
be a recombination rate at the interface, which will vary as a function of the interface velocity. Also as
a consequence of the silicon being consumed, there is a significant injection of interstitials into the
substrate. Within ATHENA, this is modelled by an interstitial flux boundary condition, as described by
Hu [13].
∂ n C I + K s  C I – C I∗  = G I
3-35
where:
• ∂nCI is the projection of the interstitial flux vector on an inward pointing unit vector normal to
the boundary.
• KS is the effective surface recombination rate for interstitials.
• GI is the generation rate at the interface of interstitials during annealing in an oxidizing
ambient.
In other words, Equation 3-35 shows that the number of interstitials generated on the surface, minus
the number of interstitials that recombine there, must equal the number of interstitials that diffuse
from the surface/interface into the substrate.
The effective surface recombination rate, KS, depends on the motion of the interface during oxidation
according to:
K
 v i  POW
K S = K SURF K RAT  ------------------
+1
 v i – max
3-36
where vi is the velocity of the interface, vi-max is the maximum interface velocity, and the parameters
KSURF, KRAT, and KPOW are calculated according to the following equations:
-------------------------
K SURF = KSURF.0 exp  – KSURF.E


kT
3-37
---------------------
K RAT = KRAT.0 exp  – KRAT.E

kT 
3-38
-----------------------
K POW = KPOW.0 exp  – KPOW.E

kT 
3-39
where the pre-exponential factor and exponent terms can be defined in the INTERSTITIAL and
VACANCY statements.
Surface recombination plays an important role in the relaxation of perturbed point defect profiles back
to their equilibrium values, which cannot happen by bulk recombination alone.
The surface generation rate, GI, controls the injection of point defects into the silicon during oxidation.
Two models have been implemented into ATHENA: the default model, GROWTH.INJ and TIME.INJ.
The moving interface can inject point defects into silicon and polysilicon.
The GROWTH.INJ parameter in the VACANCY or INTERSTITIAL statement will activate or deactivate
the growth dependent injection model. By default, this model is always turned on and is described
mathematically by the following equation.
3-12
Silvaco
SSUPREM4 Models
G
 v i  POW
G I = θ ⋅ VMOLE ⋅ v ⋅  ------------------
i v
i – max
3-40
where:
• θ is the fraction of silicon atoms consumed during growth that are injected into the bulk as self
interstitials.
• VMOLE is the lattice density of the consumed material.
• GPOW is a power parameter.
The values θ and GPOW are calculated from the following equations:
-------------------------
θ = THETA.0 exp  – THETA.E

kT
3-41
GPOW.E
G POW = GPOW.0 exp  – ------------------------

kT 
3-42
and the THETA.0, THETA.E, GPOW.0, GPOW.E, and VMOLE parameters can be specified in the
INTERSTITIAL and VACANCY statements.
As a general rule, the ratio θ ⁄ ( K RAT ⋅ K SURF ) should be maintained reasonably constant during
calibration. The entities, vi and vi–max have the same meaning as described for surface
recombination. The maximum interface velocity, vi–max, cannot be manipulated directly and will
change only when oxidation characteristics change.
The TIME.INJ parameter in the VACANCY or INTERSTITIAL statement activates the time dependent
injection model. It is defined as:
G IV = A ( t + t 0 )
T POW
3-43
where t is the total diffusion time in seconds, and A, t0 and Tpow are free parameters used for
calibration purposes and are calculated according to the following equations:
A.E
A = A.0 exp  – ---------
 kT 
3-44
T0.E
t 0 = T0.0 exp  – ------------
 kT 
3-45
TPOW.E
T POW = TPOW.0 exp  – -----------------------

kT 
3-46
Table 3-5 shows all user-specifiable model parameters for point defect boundary and injection
conditions.
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3-13
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Table 3-5. Parameters for specifying point defect boundary and injection conditions
Entity
Pre-exponential factor
Activation Energy
KSURF
KSURF.0
KSURF.E
KRAT
KRAT.0
KRAT.E
KPOW
KPOW.0
KPOW.E
A
A.0
A.E
t0
t0.0
t0.E
TPOW
TPOW.0
TPOW.E
Θ
THETA.0
THETA.E
VMOLE
VMOLE
—
GPOW
GPOW.0
GPOW.E
KSURF
KSURF.0
KSURF.E
Vacancies
The diffusion and flux equations for vacancies are largely similar to the interstitial equations
described above.
∂ CV
---------- = – ∇ ⋅ J V – R B
∂t
3-47
Here, JV is the flux of vacancies and RB is the bulk recombination rate.
The Vacancy Flux Expression is:
 CV 
-
– J V = D V C V∗ ∇  --------C ∗ 
V
3-48
which correctly accounts for the effect of an electric field on the charged portion of the vacancies by
C
V
- . The term DV is the diffusivity of free
taking the gradient of the normalized concentration -------∗
CV
vacancies, not to be confused with the pair diffusivity DAV, which was mentioned in Section 3.1.2: “The
Fermi Model”. The vacancy diffusivity is set according to the following equation:
D.E
D V = D.0 exp  – ----------
 kT 
3-49
where the D.0 and D.E parameters are set on the VACANCY statement.
3-14
Silvaco
SSUPREM4 Models
The bulk recombination rate, RB, is a simple reaction between vacancies and interstitials that
assumes that any interstitial is equally likely to recombine with any vacancy, regardless of their
charged states. This assumption may overestimate the recombination rate but is a commonly applied
assumption. The equation is expressed as:
*
R B = K r ( C I C V – C I C*V )
3-50
where Kr is the bulk combination coefficient and is specified as:
KR.E
K r = KR.0 exp  – -------------
 kT 
3-51
where the parameters KR.0 and KR.E are user-definable in the INTERSTITIAL statement. This is the
same equation for bulk recombination as described earlier for interstitial bulk recombination.
The boundary/interface conditions for vacancies are set similarly to those for interstitials except that
the VACANCY statements should be used instead of all INTERSTITIAL statements.
Dislocation Loop Based Enhanced Bulk Recombination
A topic of some debate in recent literature has been the creation of Dislocation Loops. Currently, the
exact physical nature of these defects is still under investigation. It is believed that they arise from
amorphizing implants and only exist at the edge of the amorphous layer. It has been suggested that
these loops grow through the absorption of interstitials during oxidation and perhaps shrink by the
emission of interstitials when annealed in nitrogen.
Due to the lack of proper scientific description, only a simple recombination model has been
implemented into ATHENA. This model introduces an additional sink of interstitials that is described
by the following expression:
R loop = damalpha  C I – C I ∗ 


3-52
where damalpha is a parameter you can set on the INTERSTITIAL statement. This additional
recombination is only applied to a region of the amorphizing implant controlled by the parameters
MIN.LOOP and MAX.LOOP in the DISLOC.LOOP statement.
As an example, the following statements will produce a region of dislocation loops where the
as-implanted phosphorus concentration is between 1e16 cm-3 and 1e18 cm-3. The damalpha
parameter is then set to 1e8 in this region. For example:
DISLOC.LOOP MIN.LOOP=1e16 MAX.LOOP=1e18 PHOSPHORUS
INTERSTITIAL SILICON DAMALPHA=1e8
IMPLANT PHOSPHORUS DOSE=1e15 ENERGY=120
This model should only be chosen when either the Two Dimensional or Fully Coupled Model is also
used. The two things to apply to this model are as follows:
• an implant has to create an amorphous layer
• immediately after the implant there is an anneal in a wet ambient
Even when these two criteria are met it is suggested to only apply this model when it is needed to
match experimental results.
The Steady State Diffusion Model
The Steady State Diffusion Model is a variant of the two dimensional diffusion model, which assumes
the point defect profiles are in a steady state. It is turned on with the METHOD STEADY command.
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ATHENA User’s Manual
Important Notes about Defect Diffusion
Point defects have larger diffusivities than dopants and may therefore diffuse down to the bottom of
the structure during a simulation. If the simulation structure is too shallow, you may get an
unrealistic high defect concentration in the regions where dopant profiles are present and
consequently too much dopant diffusion. Therefore, you may need to extend the depth of the
simulation space to provide an adequate sink for the point defects. To determine the depth of the
structure, you can estimate the characteristic defect diffusion lengths using:
l =
DX ∆ t
3-53
where DX is the defect diffusivity and ∆t is the total diffusion time. Simulations show that a depth of
20 to 50 microns is required in most cases. This restriction on the minimum structure depth poses a
threat to computational efficiency, whenever diffusion models that include point defects are employed.
But since the fine structure of the defect profiles near the bottom of the structure is not a feature of
particular interest for processing purposes, you can reduce the computational cost by making the grid
very coarse in this region.
Time Step Control
When using diffusion models that include the explicit representation and evolution of point defects, be
aware of time stepping issues. Although step size control between iterations is fully automated, you
can still specify the size of the initial time step. Different initial time step sizes can be specified for
dopants and point defects, respectively, by using the parameters INIT.TIME and PDINIT.TIME. For
example, the command
METHOD INIT.TIME=0.001 PDINIT.TIME=0.001
would set the initial time step to 1 millisecond for both dopants and point defects. Default values are
INIT.TIME=0.1 seconds and PDINIT.TIME=1.0E-5 seconds.
Note: There is no guarantee that the program will actually use these values. For this initial time step, the only purpose of
these parameters is to make it feasible for you to give the program a hint about an appropriate initial time step size.
3.1.5: The Fully Coupled Model
The Fully Coupled Diffusion Model is identical to the Two Dimensional Model. Be familar with that
model before reading any further. The one important difference is that the diffusion of the defects is
now influenced by the diffusion of the dopants by the addition of the joint pair fluxes to the flux terms
in the governing equation of the defects. Therefore, there is a true two-way interaction between the
diffusion of dopants and the diffusion of point defects, which gives this model its name. The fully
coupled model is slightly more CPU-intensive than the two dimensional model, but encompasses the
capability of reproducing certain important aspects of semiconductor processing such as the Emitter
Push Effect in the case of phosphorus diffusion.
From a physical viewpoint, however, this original fully coupled model suffers from the shortcoming of
not explicitly representing pairs, and the consequential lack of a subdivision of defects and dopants
into paired and non-paired fractions. Therefore, this model cannot reproduce the saturation of the
dopant diffusivity that is believed to occur at very high damage concentration due to a total pairing of
dopants. In other words, the model relies on the dilute approximation (i.e., the assumption that the
concentration of pairs is much smaller than both the dopant and the defect concentrations). To use the
Fully Coupled Model, specify parameter FULL.CPL in the METHOD statement.
3-16
Silvaco
SSUPREM4 Models
The Fully Coupled Model establishes a two-way coupling between the diffusion of dopants and point
defects respectively by adding the joint dopant-defect pair fluxes to the flux terms of the defect
equations, which then become:
∂ C +
---
∂t V
∂ C +
---
∂t I


= –∇ ⋅  JV +
c

AV
∑J


c  = –∇ Þ  JI +
AI 

∑J
∑C
A ,c
∑C
A ,c
A ,c
A ,c

–R
c
AV

c  – R B + R T – R { 311 }
AI 
3-54
3-55
where summations run over all dopants and pair charge states. The rest of the Fully Coupled Model
Equations are identical to those in the Two Dimensional Model described in the previous section. The
effect of the correction terms only displays itself at very high dopant or high implant damage
conditions or both, where the Fermi level enhancement and point defect supersaturation will increase
the dopant diffusivities significantly.
High Concentration Extension to the Fully-Coupled Model
This extension to the fully coupled model takes into account additional higher order defect-dopant/
defect pairing the extra point defect recombination mechanisms. This model was developed at Stanford
University [14] to include higher order dopant-defect interactions in the cases, where the number of
dopant-defect pairs are significant. This is the case for high dopant concentration in silicon. It is
activated by the following command:
METHOD HIGH.CONC FULL.CPL
It is an extension of the basic fully coupled model and may only be used in conjunction with the
METHOD FULL.CPL command. This model includes two extra bulk recombination reactions and two
extra Si/SiO2 interface recombination reactions.
In the bulk, extra terms for point defect recombination apply at high concentrations, where
statistically, a high level of dopant-defect pairing is prevalent
D PI + D V
= IIFACTOR ⋅  --------------------- DI + DV 
⋅ Kr
3-56
D I + D PV
= IVFACTOR ⋅  --------------------- DI + DV 
⋅ Kr
3-57
PI – V
Kr
I – PV
Kr
The extra model parameters calibrate the ratio of effective capture cross sections of dopant-defect/
defect to defect/defect recombination mechanisms. The IIFACTOR and IVFACTOR parameters can be
set in the INTERSTITAL statement as follows:
INTERSTITIAL SILICON IVFACTOR=<n> IIFACTOR=<n>
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ATHENA User’s Manual
RTA Diffusion Modelling
SSUPREM4 has the capability to model rapid thermal annealing (RTA) processes within the framework
of existing diffusion models (i.e., the two dimensional model and the fully coupled model). Since RTA
is a short time thermal cycle involving steep temperature ramping to high temperatures, Transient
enhanced diffusion (TED) will dominate whenever a significant amount of lattice damage is prevalent.
Because the amount of dopant diffusion is intimately coupled to the evolution of the point defect
populations, you can calibrate these models to RTA conditions by tuning the point defect related
parameters. The ratio of interstitial damage in the form of {311} clusters to that in the form of free
interstitials and the characteristic time for dissolution of interstitial clusters are important
parameters to include when setting up SSPUREM4 for an RTA scenario.
Table 3-6 shows an approximate time for completion of about 95% of the TED at various temperatures.
Table 3-6. The approximate duration of TED at various annealing temperatures
Annealing Temperature (C)
Time for completion of 95% of TED
600
390 hours
700
3.3 hours
750
30 minutes
800
3.7 minutes
850
43 seconds
900
8.3 seconds
950
1.9 seconds
1000
0.48 seconds
1050
0.13 seconds
3.1.6: Electrical Deactivation and Clustering Models
When dopants are present at high concentrations, the electrically active (mobile) concentration, Cact,
may be less than the corresponding chemical concentration, Cchem.
In order for an impurity to become electrically active in a semiconductor material, it must be
incorporated into a substitutional lattice site, which then will contribute with a carrier to either the
valence band (an acceptor impurity) or the conduction band (a donor impurity). Above certain dopant
concentrations, however, it is impossible to incorporate more dopants into substitutional lattice sites.
The excess dopants are said to be non-active.
The threshold where the deactivation occurs is often called the solid solubility limit, since impurities
can exist in different phases in the crystal. But for this section, we’ll call it deactivation threshold.
Therefore, it isn’t well-defined which phase transition the solid solubility limit might refer to. For
example, excess dopants could be participating in small clusters or larger precipitates. Deactivation
threshold would be a more proper designation for this limit and will be used throughout the rest of this
th
section. The notation, C act will be used for the deactivation threshold. Therefore, for all the models
described in this section, the following points are assumed for each dopant type:
•
3-18
Dopants in excess of the deactivation threshold are considered electrically inactive (i.e., they do not
contribute to the carrier populations).
Silvaco
SSUPREM4 Models
•
Additionally, dopants in excess of the deactivation threshold are considered to be immobile (i.e.,
they cannot diffuse).
Electrical Activation Model
The Electrical Activation Model is used to calculate which level of dopant concentration the
deactivation occurs. For this purpose, two different Electrical Activation Models are used for all
diffusion models:
• An AsV Clustering Model for arsenic or similar models for other impurities.
• A Semi-empirical Activation Model, based on Table B-14 in Appendix B: “Default Coefficients”,
for all other dopants.
These models can be activated in the IMPURITY statement by parameters CLUSTER.ACT and
SOL.SOLUB respectively. By default, the CLUSTER.ACT model is used only for As in silicon and
polysilicon.
The AsV Clustering Model used in SSUPREM4 is based on the simple reaction:
+
=
As + V
⇔ AsV –
3-58
Assuming that Equation 3-58 is always in equilibrium, the following equation describes the
relationship between the chemical and the active arsenic concentration.
2 C 

n
V
C chem = C act + C clust = C act  1 + C TN  ---- ⋅ -----------∗ -
n 
C


V
i
3-59
Since there is a cyclic dependency between the active arsenic concentration, Cact, and the carrier
concentration, n, an initial guess for the value of n has to be made at the start of the simulation. In
∗
addition, C V ⁄ C V is (by definition) set to unity when running the Fermi Diffusion Model (see Section
3.1.2: “The Fermi Model”).
The clustering coefficient, CTN, is temperature dependent according to the following equation.
CTN.E
C TN = CTN.0 exp  – -----------------

kT 
⋅ ni
3-60
Here, the CTN.0 and CTN.E parameters can be defined in the IMPURITY statement.
You can specify CLUSTER.ACT, CTN.0 and CTN.E parameters for other acceptors in the IMPURITY
statement. But be aware the model isn’t elaborated for other impurities and these parameters are
unknown. The model can also be empirically used for acceptors (e.g., indium). The following equation
is based on acceptor-interstitial clusters with empirical parameters CTP.0 and CTP.E.

p 2C 
C chem = C act  1 + C TP  ---- -------I- 
 n  C∗

i I 
.
3-61
The Semi-empirical Activation Model, based on Table B-14 in Appendix B: “Default Coefficients”,
which is used for all other dopants except arsenic, uses a two-step scheme to calculate the active
dopant concentration.
1.
The program interpolates into a table of experimental (e.g., temperature and deactivation
threshold) data pairs and finds a concentration independent deactivation threshold,
th
Cact
, that
corresponds to the current simulation temperature. You can set these pairs in the IMPURITY
statement by assigning values to the parameters, SS.TEMP and SS.CONC. The temperature should
be specified in Celsius.
Silvaco
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ATHENA User’s Manual
2. A logarithmic concentration dependency is incorporated by setting the final deactivation threshold
to the value:


 th
 C act
th
C
act = 




th
⁄ C act – b
th
⋅ 1 + ( 1 – b ) ln -------------------------------; C act > C act
1–b
C
C
act
act
;
C
3-62
th
act
≤ C act
where the parameter b must be in the range of [0.8, 1.0]. Parameter b can be specified as ACT.FACTOR
in the IMPURITY statement. The effect of Equation 3-62 is to produce a rounding in the top of the
active profile that slightly follows the form of the chemical profile.
Transient Activation Model
The Transient Activation Model assumes that dopants, after an implant, are inactive. A certain time is
required before the dopants become active. After an ion is implanted into silicon, this model assumes
that all dopants are inactive and may not be activated immediately but become gradually active
instead. The Transient Activation Model simulates this behavior and applies it to activating the
implant dopants.
The following equation for the active concentration CA is solved.
eq
CC – CA
∂ (C
Chem – C A ) = --------------------∂t
τA
3-63
CC is the chemical concentration of the dopant, and CAeq is the equilibrium active concentration
calculated either from solid solubility or clustering model (for arsenic) as defined in the previous
section. The parameter τΑ is the time constant for activation, which is a function of temperature, and
is calculated using the following Arrhenius expression.
------------------------- 
τ A = TRACT.0 ⋅ exp  – TRACT.E

kT
3-64
The initial condition at time t=0 for Equation 3-63 is specified by
CA
= min ( C A , TRACT.MIN ⋅ n i )
eq
t=0
3-65
where ni is the intrinsic carrier concentration. Therefore, implantation activation will occur
immediately up to a level of TRACT.MIN ⋅ ni, after the active concentration is calculated according to
Equations 3-59 and 3-62.
To activate the transient activation model, set the CLUST.TRANS parameter in the METHOD statement
and specify the TRACT.0, TRACT.E, and TRACT.MIN parameters in the IMPURITY statement.
The defaults for B, P, As and Sb are TRACT.0=8e-16sec, TRACT.E=-4.2, and TRACT.MIN=1.0
(TRACT.MIN for Phosphorus is 2.0).
3-20
Silvaco
SSUPREM4 Models
3.1.7: Grain-based Polysilicon Diffusion Model
The mechanism for impurity diffusion in polysilicon is different than that of crystalline silicon.
Polysilicon has a micro-structure of small (compared to the interesting device regions) crystalline
regions called grains. These grains are separated by grain boundaries which occupy a certain spatial
volume and are connected to form a complex network. The texture and morphology of the grain
structure depends on the deposition conditions and on subsequent thermal treatment (during which
recrystallization can occur). Impurities inside the grain will diffuse differently than those in the grain
boundaries. Dopant will also transport through grain and grain boundary interfaces.
A model for impurity diffusion in polysilicon outlined in [15], [16] and [17] is incorporated in
SSUPREM4. To use polysilicon diffusion, specify the POLY.DIFF parameter in the METHOD statement.
Most of parameters, which control the model, have a prefix PD and are specified in the IMPURITY
statement. In this model, the concentration of each impurity Ci is split into two components, namely
the concentration within grain interior Cig and concentration in the grain boundary Cigb. The impurity
diffusion within grain interior is simulated by the standard model used for crystalline silicon (see
Equations 3-2 to 3-7):
g
∂ Ci
g
g
g g
------------ = ∇  Di ∇ Ci – ZD i C i 1--- ∇n – G i

n 
∂t
3-66
g
where diffusivity of impurity i within grains Di is calculated exactly as in Equations 3-10 and 3-11.
The diffusion in the grain boundary is assumed to be constant and very rapid:
gb
gb gb
∂ Ci
--------------- = ∇2 D i C i  + G i


∂t
3-67
where Digb is diffusivity of impurity i along the grain boundaries:
gb
--------------------------- 
Di
= PD.DIX.0 ⋅ exp  – – PD.DIX.E


kT
3-68
The PD.DIX.0 and PD.DIX.E parameters are specified in the IMPURITY statement. The last term G
in Equations 3-66 and 3-67 controls impurity segregation between grain interior and grain boundaries:
 Cg

i – C gb τ – 1
G i =  ----------i 
p
 seg

3-69
where pseg is segregation coefficient and τ is the rate of segregation specified as PD.TAU in the
IMPURITY statement. Initial conditions for Equations 3-66 and 3-67 are determined by setting the
PD.CRATIO parameter in the IMPURITY statement. This parameter specifies the initial ratio between
impurity concentration in the grain boundary Cigb and total concentration Cigb + Cig.
The grain boundary segregation is calculated according the model suggested in [17]:
Qs
Q
1 - -------p seg = ------------ A exp  – ------0

kT 
L g ( t ) N Si
Silvaco
3-70
3-21
ATHENA User’s Manual
where Qs is the density of segregation sites at the grain boundary specified by the PD.SEGSITES
parameter in the IMPURITY statement, NSi is the atomic density of crystalline silicon (2.5 1022 atoms/
cm3), A is the entropy factor specified by the PD.EFACT parameter in the IMPURITY statement, Q0 is
the segregation activation energy specified by the PD.SEG.E parameter in the IMPURITY statement,
and Lg(t) is the time-dependent grain size calculated according to the grain growth model suggested in
[16]:
L (t) =
g
PD.GROWTH.0
2
PD.GROWTH.E
L 0 + ------------------------------------------ ⋅ exp  – – ------------------------------------------- 


kT
kT
⋅t
3-71
where L0 is the initial polysilicon grain size, which should be specified by GR.SIZE parameter in the
DEPOSIT POLYSILICON statement (GR.SIZE.F parameter allows to have linearly graded grain size
within deposited polysilicon layer), the grain growth parameters PD.GROWTH.0 and PD.GROWTH.E are
specified in the IMPURITY statement, and t is the elapsed diffusion time.
The segregation boundary condition at the polysilicon/silicon boundary is also modified when
POLY.DIFF model is used. The default segregation coefficient M12 in Equation 3-12 is increased by a
factor, which depends on the impurity concentration in the grain boundaries:
gb


Ci
∗ = M 12  1 + PD.SEG.GBSI ⋅ ------------------------
M12
3-72

gb
g
Ci + C 

where M*12 is modified segregation coefficient and the PD.SEG.GBSI parameter is specified in the
IMPURITY statement.
3-22
Silvaco
SSUPREM4 Models
3.2: Advanced Diffusion Models
The ultimate goal of TCAD simulation is to compute the electrical characteristics of a given device by
using only process-related data as input parameters. Since the electrical characteristics of the device
are heavily dependent on the distribution of the electrically active impurity (dopants), resulting from
the entire thermal processing sequence, it is important that the diffusion models used in the process
simulation are as accurate as possible. This is particularly important for deep sub-micron processes.
Therefore for these emerging technologies, 2D or even 3D phenomena are expected to be of growing
importance, whereas there is presently no accurate technique to measure multi-dimensional dopant
profiles. Consequently, the active dopant 2D distributions can only be obtained by simulation based on
models that are as reliable as possible. It has become clear that the "abnormal" behaviors of dopant
diffusion in silicon are caused by non-equilibrium point defects. These are induced by the diffusion
process itself (emitter push effect caused by high concentration of phosphorus diffusion), or injected
into the substrate by external treatments, such as oxidation or silicidation. Otherwise, they result
from the ion implantation used to introduce the dopants into the silicon substrate. With the necessary
decrease of the thermal budget due to the shrinkage of the device dimensions, these transient
phenomena become key issues for accurate dopant diffusion simulation.
Figure 3-1: The model consists of three parts: the classical dopant diffusion model, the interstitials clusters
model and the model of mixed dopant clustering.
The new model of dopant diffusion implemented in ATHENA is called PLS and was developed in
collaboration with CNRS-Phase (Strasbourg, France), CEA-LETI (Grenoble, France) and SILVACO.
This model is up to date with actual physical models and contains only physical parameters [18]. It
consists of three parts: the classical dopant diffusion (CDD) model, the interstitials clusters (IC) model
and the model of mixed dopant-defect clustering (DDC). This section describes the three parts of the
model and how the new model differs from the fully coupled model.
The main physical points taken into account in the models are the following:
• Dopant diffusion of all species is assisted by both vacancies (V) and self-interstitials (I). These
point-defects exist in various charge states and their relative concentrations depend on the local
Fermi level position (i.e. on the local dopant concentration).
• Both I and V have strong binding energies with the dopant atoms and consequently the diffusing
species are dopant-defect pairs (the isolated substitutional dopants are immobile). These impuritydefect pairs in their various charge states are not assumed to be in local equilibrium with the free
substitutional dopant atoms and the free defects. In the PLS model, at high dopant concentrations,
Silvaco
3-23
ATHENA User’s Manual
the concentrations of these pairs are not considered to be negligible with respect to the substitutional
(active) dopant concentration. Therefore, the pair concentrations are explicitly taken into account to
compute the total dopant concentration and the Fermi level position (i.e., carrier concentration).
Consequently, a partial self-compensation takes place at high doping concentrations, which
contributes to the differences between total and active concentrations and affects the variations of
the extrinsic diffusivities as a function of the total doping.
• The flux of each diffusing species (dopant-defect pairs and free defects) includes the drift terms
caused by the built-in electric field, due to the dopant gradients.
• Both I and V are not considered to be in local equilibrium but can be annihilated by bimolecular
recombination. This feature of the CDD model performs annihilations between not only the free
defects but also between the impurity defects pairs, which play the role of recombination centers.
Therefore, the I-V recombination rate is strongly enhanced at high dopant concentration.
• It is now well established that transient enhanced diffusion (TED) is strongly correlated with the
evolution of the self-interstitial supersaturation governed by the nucleation and evolution during the
high temperature anneal of a variety of extended defect structures, such as the interstitials clusters.
Thus, the predictive process modeling of the deep submicron MOSFET technologies requires the
development of accurate diffusion models which take into account the full set of interactions between
dopants and the point or extended defects (clusters). The PLS model, coupled with the BCA
implantation, allows you to calculate the evolution of the clusters. Therefore, it is unneccessary to
artificially add {311} or other clusters because the model automatically generates them and
calculates their evolutions according to the Ostwald ripening theory.
• At concentrations near the solid solubility limit, a dynamic clustering model is considered.
Immobile complexes (AsnV or BnIm) are formed, which result in decrease of the effective diffusivity
and increase of the inactive dopant concentration. These complexes are not assumed to be in local
equilibrium with the other species.
• When the dopant concentration exceeds a few 1020cm-3, the dopant-vacancy pairs can no longer be
considered as isolated entities because the vacancies can interact with more than one dopant atom.
3.2.1: Classical Model of Dopant Diffusion (CDD)
The basic idea of the model is isolated substitutional dopant atoms (As) are immobile. The dopant
diffusion occurs only through the migration of dopant--self-interstitial (AI) and of dopant--vacancy
(AV) pairs. Moreover, in this enhanced model, local equilibrium is not assumed between the pairs and
their components (unlike the original CNET model [5]). All possible charge states of the free defects
and of the pairs have been considered and their relatives concentrations depending on the local Fermi
level position.
To turn on the CDD model, specify PLS parameter in the METHOD statement. All physical
parameters of the model can be modified in the *.mod files. To specify the location of these files, use
the B.MOD, P.MOD, AS.MOD, IC.MOD, and VI.MOD parameters in the DIFFUSE statement. By default
all these files are located in the $SILVACO/lib/athena/<version_number>/common/pls
directory.
Charge States
Point Defects
The result of diffusion studies in metals and ionic crystals have led to the establishment of several
basic atomic diffusion mechanisms. These mechanisms dominate the interpretation of silicon diffusion
experiments with the exception that in silicon there is a very wide energy range available to the Fermi
level. Therefore, a given lattice defect can appear in a variety of ionized states. The fundamental
principles of thermodynamic predict that such defects will exist in equilibrium at all temperatures
above 0° K, because the presence of such defects minimizes the free energy of the crystal. The entities
(0)
Veq
3-24
(0)
and Ieq
are the equilibrium defect concentrations for vacancies and silicon self-interstitials in
Silvaco
SSUPREM4 Models
their neutral charge state. The weight factors γ and δ account for the different charge states for
distribution of point defects under extrinsic conditions. Each γ and δ is assumed to be temperature
dependent through Arrhenius expressions.
For point defects (V or I), five various charge states are considered:
(s)
( s )  n i s 0
(s) n s 0
---- I , V = δ  ----i V
 n
 n
3-73
where s is one of the charge states -2, -1, 0,+1, or +2. All parameters γ and δ are specified in the charge
state statements of the defect.mod file.
I
(s)
= γ
With this consideration, the equilibrium concentrations Veq and Ieq are estimated as
I
eq
0
= I eq
∑
γ
eq
( s )  n i s
---- , V = V 0
eq
 n
∑
δ
( s )  n i s
--- n
.
3-74
Under intrinsic conditions (i.e., n=p=ni), the equilibrium concentration can be simply written as:
eq
0
I i = I eq
∑γ
(s)
eq
0
, Vi = V
eq
∑δ
(s)
.
3-75
Equilibrium concentration for vacancies and silicon self-interstitials are defined as a simple Arrhenius
functions:
eq
Ii =
E
I
KI exp  – -----f- , V i
kT
0
I
V
where E f and E f
eq
V
 Ef 
0
= K V exp  – --------
 kT 
3-76
represent respectively the formation energy for I and V, and
0
0
K I , K V are
coefficients. These parameters are specified in the defect.mod file.
Dopant-defect Pairs
Using the same assumption as for point defects, the dopant-defect pairs are defined by the charge
states of -1, 0, +1.
For boron pairs we have
BI
(s)
s
(0)
p -
=  ----------BI ,
 p( s ) 
BI
(s)
p BI =
K
– 1-
 s---------- 2 
γ
BI
------------------ ⋅ n i,
⋅ ------------+ 3-
 s-----------s+1
K
BI
BV
(s)
p  s (0)
=  ------------BV ,
(s)
p BV 
+ 1( s-----------)
2
(s)
p BV =
 -------------
 2 
K
γ
 2 
– 1-
 s---------- 2 
+ 1-
 s----------- 2 
 -------------
 2 
------------ 2 
δ
BV
------------------ ⋅ ---------------- ⋅ ni,
 s + 3
s+1
K
BV
3-77
δ
3-78
The BV pairs exist, however, with positive (+1) and neutral (0) charge states only. Moreover, it is well
established BI pairs exhibit a negative-U behavior and neutral state is unstable. Therefore, the three
charge states BI+, BI0 and BI- are considered.
Silvaco
3-25
ATHENA User’s Manual
For donor impurities, the three charge states for dopant-interstitial pairs are also considered. Though
only AV- and AV0 are known to exist (E-centers).
K
– 1-
 s---------- 2 
+ 1
 s----------- 2 
AI
- ⋅ γ------------- ⋅ ni,
n AI = ----------------– 3-
 s----------s–1
 n  s (0)
(s)
- AI ,
AI
=  ------------ n( sAI) 
(s)
K
AI
 n  s (0)
(s)
- AV ,
AV
=  -------------(s)
 n AV 
 ------------
 2 
K
γ
 2 
– 1
 s---------- 2 
+ 1-
 s----------- 2 
AV
- ⋅ δ------------- ⋅ ni,
n AV = -----------------– 3-
 s----------– 1-
K  s---------- 2 
 2 
δ
AV
(s)
3-79
3-80
The KAI(s) and KAV(s) parameters for both donors and acceptors represent the pairing coefficients for the
dopant-interstitial and dopant-vacancy pairs and are defined by following formula:
K
AI
(s)
E AI ( s )
0
- ,
= KAI( s ) exp  – ----------- kT 
K
AV
(s)
=K
0
AV
(s)
 E AV( s )
exp  – -------------
 kT 
3-81
Fully Coupled Equations
The point defects, dopant-defect pairs and active dopant evolve according to the following continuity
equations:
tot
∂----------I - = – ∇ ⋅ J + GR + GR + GR
AV – I,
I
IV
AI
∂t
tot
∂------------V - = – ∇ ⋅ J + GR + GR + GR
AI – V,
V
IV
AV
∂t
tot
∂--------------AI - = – ∇ ⋅ J – GR + GR
AI – V,
AI
AI
∂t
3-82
tot
∂ AV - = – ∇ ⋅ J – GR + GR
----------------AV
AV – I,
AV
∂t
∂ As
--------- = GR AI + GR AV – GR AV – I – GR AI – V
∂t
Here, Xtot is the total concentration of the species X, and [As] is active dopant concentration in
substitutional position. J represents the flux of species X, and GRX is a generation-recombination term
corresponding to the reactions that contain X.
Flux Equations
Point Defects
As the migration rate of a given species may depend on its charge state, two distributions must take
into account in the flux equation. The first one is the Fickian term and the second is the Nerstian term.
Thus, the flux can be written for a given species X with the charge state s:
J
X
3-26
s
s
s p
= – D s  ∆ X – sX ∆
-------
X
p
.
3-83
Silvaco
SSUPREM4 Models
For point defects, the PLS model makes the assumption that the diffusivity is independent of the
charge state at high temperature. This implies that for vacancy and silicon self-interstitial at any
charge state s the following is always true.
DI = D s ,
DV = D
I
3-84
s
V
Moreover, it is assumed that diffusivities at high temperature follow the simple Arrhenius law:
m
m
0
EI 
- ,
D I = DI exp  – ------ kT 
m
0
EV 
D V = D exp  – ------- kT 
V
3-85
m
where E I
and E V represent respectively the migration energy for self-interstitials and vacancies.
0
0
m
m
Parameters D I , D V , E I
and E V are defined in the defect.mod file.
2
Finally, taking into account that np = n i and
I
(s)
= I
tot
∑
s n
γ  ----
s
–1
s
,
ni
V
(s)
= V
tot
∑
s n
δ  ----
s
ni
s
–1
,
3-86
the flux equations for Itot and Vtot are defined as follows:
J
I
J
=
tot
∑J
s
V
tot
=
I
s
∑J
s
V
= – D I DI
s
tot
∑
sγ
( s )  n i s
--- n
tot s
– I --------------------------------------n-∆
n
s
n
(s) i
γ  ----
n
s
3-87
∑
= – D V DV
tot
∑
sδ
( s )  n i s
--- n
tot s
∆ n– V ---------------------------------- -----n
s
n
(s) i
δ  ----
n
s
3-88
∑
Dopant--Defects Pairs
V
I
The diffusion of dopant--defect pairs implies on the fact that diffusivities D A and D A are calculated
from the basic parameters for the pairs defined by Equation 3-77 through 3-81 as follows:
I
D A = f I D Ai =
∑D
AI
s AI
eq
,
V
D A = ( 1 – f I )D Ai =
∑D
AV
s AV
eq
,
3-89
s
s
where fI is the interstitialcy component under intrinsic conditions, and DAi is the intrinsic diffusivity
of the impurity A. The fI and DAi parameters are defined for each dopant in the corresponding
dopant.mod file.
Silvaco
3-27
ATHENA User’s Manual
It should be emphasized that several relationships exist between this various parameters. Therefore,
you can decrease the number of free fitting parameters. From physical point of view, it can be safely
assumed the ratio between the diffusivities of the various charge states must be equal. Consequently,
we have
D –
D 0
s
AI
AI
------------ = ----------------- = ( ρ AI ) ,
D 0
D +
AI
D –
D 0
s
AV
AV
------------- = ------------------ = ( ρ AV ) ,
D 0
D +
AI
AV
3-90
AV
where s=1 for donors and s= -1 for acceptors. These diffusivities are free parameters when the various
coupling parameters in Equation 3-81 are known. Therefore, you can calculate them through the
experimentally known intrinsic diffusivities DAi and the interstitialcy component fI. The
ρ AI and
ρ AV parameters are defined as an Arrhenius functions.
Finally, the flux equations, for instance, for boron--point defect pairs are defined as follows:
∑ (ρ
BI
s
) K
BI
s
p- s 1 ( s 1 )
 ---γ
n 
i
s
J tot =
J s = – D 0 ------------------------------------------------------------s1 ( s1 )
BI
BI
BI
p
K s  ----- γ
s
BI  n 
i
s

p s1 ( s1 ) 
sK s  ----- γ


BI  n 


i
tot
tot
p- ,
s
 ∆ BI – BI ------------------------------------------------∆
-----

p s1 ( s1 ) p 

K s  ----- γ


BI  n 
i


s
∑
∑
×
3-91
∑
∑
p- s 1 ( s 1 )
 ---δ
BV n 
i
s
J tot =
J s = – D 0 ---------------------------------------------------------------s1 ( s1 )
BV
BV
BV
p
K s  ----- δ
s
BV  n 
i
s

p s1 ( s1 ) 
sK s  ----- δ


BV  n 


i
tot
tot
∆ p- ,
s
 ∆ BV – BV -------------------------------------------------- -----

p s1 ( s 1 ) p 

K s  ----- δ


BV  n 
i


s
∑ (ρ
BV
∑
∑
s
) K
s
×
3-92
∑
∑
where s1=s+1.
The equations for pairs formed by donor impurities are completely symmetrical to the equations
above.
3-28
Silvaco
SSUPREM4 Models
Generation-Recombination Terms
The generation-recombination terms GRX in Equation 3-82 describe the evolution of particular
reactions. For example, GRAV represents the formation of the dopant-vacancy:
f
A
kAV
+ V ⇔ AV
s
3-93
r
kAV
Formation of Pairs
In the model, the formation of dopant-defect pairs is taken into account by simulating the following
reactions:
3-94
f
kAI
+ I 0 ⇔ AI –
–
As
r
kAI
f
–
As
+ V+
kAV
⇔ AV 0
3-95
r
kAV
where kf and kr are the reaction kinetic constants for each reaction. They are define as
f
eff
k AI = 4 π R D I ,
f
eff
k AV = 4 π R D V ,
r
k AI = k
f
AI
0
⁄ KAI0
k AV = k AV ⁄ K
r
f
AV
3-96
3-97
0
where KAI0, KAV0 are defined by Equation 3-81, and Reff is the silicon lattice constant. Thus, the
generation-recombination terms in Equation 3-82 are as follows:
– 0
r
f
0
GR AI = k AI A s I – k AI AI ,
3-98
– +
f
r
+
GR AV = k AV A s V – k AV AV
3-99
Frenckel Pair Recombination
During annealing, many of the interstitials and vacancies recombine either at the surface or in the
bulk. The driving force for this reaction is to change both interstitial concentration Itot and vacancy
tot
tot
concentration Vtot toward their equilibrium concentrations I eq and V eq . Moreover, it is clearly
shown that defect recombination strongly depends on the impurity concentration.
Silvaco
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ATHENA User’s Manual
The following reaction is also considered.
f
V
α
β
kVI
+ V ⇔ 〈 0〉
3-100
r
kVI
The recombination rate can be written as follows:
tot tot eq eq
GR IV = k BM  I eq V eq – I V

.

3-101


(s)
( s ) ni s
k BM = k a  ( γ + δ )  ---- – 1
 n


 s

3-102
Here:
∑
and
k a = 4 π a 0 ( D I + D V ),
3-103
where a0=2.35°A is the distance between two separated silicon atoms in crystal.
Bimolecular Recombination
As an alternative to the direct recombination of point defects in reaction of Equation 3-100, it is also
possible for I and V to recombine through reactions such as
f
f
AV
0
+ I+
kAV – I
+
⇔ As
,
kAI – V
AI
0
r
+ V+
+
⇔ As
r
k AV – I
k AI – V
.
3-104
In these cases, the annihilation of the Frenckel pairs implies a dissociation of a dopant-defect pairs.
Recombination at the Surface
Understanding of the mechanisms that determine the interaction of interstitials and vacancies with
the interfaces is getting more important, because the implantation energies of dopants and the
temperatures for the thermal treatments become lower and the devices are fabricated closer to the
surface. It has been also demonstrated that the fundamentals of the point defect properties are
critically important in accurate prediction of device behavior. For example, the reverse short channel
effect.
The recombination flux of silicon self-interstitials at a nonoxidizing interface Γ is given by the formula:
JI
Γ
D tot tot
= -----I  I – I eq  ,

LI 
JV
Γ
D
tot
tot
= ------V-  V – V eq  ,

LV 
3-105
where LV and LI are called the recombination length at the surface. These parameters can be used for
adjusting the recombination rate at the surface and are specified in the defect.mod file.
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SSUPREM4 Models
In the case of dopant implantation, an exodiffusion may occur during the thermal treatment.
Therefore, you can write the dopant flux at the surface as:
JAI
Γ
= σ AI AI
tot
,
JAV
Γ
= σ AV AV
tot
3-106
where σAI and σAV are the exodiffusion coefficients for each dopant-defect pair and are defined in
dopand.mod files. These parameters are defined by the following Arrhenius functions:
E σ AI
0
- ,
σ AI = σ AI exp  – ----------
E σ AV
0
-
σ AV = σ AV exp  – -----------
kT
kT
.
3-107
3.2.2: Solid Solubility Model
The model for precipitation is assumed to be a constant solid solubility cut-off. This means that all
solute atoms above the solid solubility level will form a precipitate almost instantaneously. This model
is activated by adding the SS parameter to the METHOD PLS statement.
The rate equation for the solid solubility model can be formulated as follows [23]:
 D λ ( A – A ( T ) ) for A > A ( T ),
s
s
ss

3-108

0
for
A
A
(
T
),
<

s
ss

where Apr is the concentration of the precipitate and λ is the effective length of capture. The solid
solubility Ass(T) is defined using Arrhenius expressions in the corresponding dopant.mod file.
A pr
-------- = D λ A pr ( A s – A ss ( T ) ) +
∂t
3.2.3: Interstitials Clusters Model (IC)
Point defects in crystalline materials inherently have high free energy. Free interstitials in silicon are
thermodynamically unstable because of their unpaired electron orbitals and induced lattice strain. At
high concentrations, the interstitials clusters are formed to reduce free energy. Many of interstitial
cluster species have been observed for many years (e.g., {311} defects and dislocation loops). The
interstitial cluster configurations are believed to occur mainly in ion-implanted silicon. The formation
and dissolution of interstitial clusters are simulated to correctly predict TED.
To activate the interstitial clusters models, use the following statement:
METHOD PLS IC
During a typical rapid thermal annealing, various type of clusters (small clusters, {311} defects, perfect
and faulted loops) evolve according to a competitive growth mechanism named Ostwald ripening. The
driving force for this evolution is the reduction of the formation energy per interstitial of these clusters
as they grow in size and change their crystallographic structures.
In IC model, a cluster containing n interstitials (In) evolve to a cluster of size n+1 by interaction with a
free interstitial according to the following reactions:
f
I
0
k2
r
k2
Silvaco
f
+ I ⇔ I2 ,
0
0
I2
0
k3
+ I 0 ⇔ I 3 0,
r
k3
f
…
0
In – 1
kn
+ I ⇔ I n0 ,
0
r
kn
3-109
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where according to [19]:
I
∆g
Ef – E f ( n )
D
f
r
k n = 4 π R eff D I exp  – --------n- , k n = 6 -----I θ n exp  – ------------------------- kT 


2
kT
λ
3-110
Here, Reff represents the effective capture radius. The elementary jump length λ is equal to the
I
inter-atomic distance a0=2.35°A. θn is the number of dissociating sites, E f is the self interstitial
formation energy defined in Equation 3-76, and Ef(n) is the formation energy per interstitial for
clusters of size n. The number of reactions taken into account is specified in the ic.mod file.
The value of effective energy barrier ∆gn in Equation 3-110 can be represented as the sum of two
components:

 I tot 


 I eq 

- + E f ( n ) ,0 .
∆ g n = max  – k B T ln  ----------tot
3-111
The first of the two terms represents the change in free energy associated to the change in chemical
potential when an interstitial jumps from the supersaturated phase to the cluster. The second term is
the formation energy per interstitials. This parameter is a function of the size and of the
crystallographic structure of the cluster. The values of the formation energy per interstitial are
specified in the ic.mod file. The first nine parameters corresponding to the formation energy per
interstitial for clusters of size 2 through size 10 are defined in [20]. For larger clusters, the energy of
formation per interstitial is calculated by the following empirical formula:
1 - + E { 311 } ( ∞ )
E f ( n ) = A log  1 + -------------------f

C
(n + B)
.
3-112
{ 311 }
The empirical parameters of the model A, B, C and E f
are specified in the ic.mod file. Thus, the
system of coupled equations for the IC model can be written as:
N
tot
∂ I - = – ∇ · J + GR + GR + 2GR
----------I
IV
AI
IC ( 2 ) +
∂t
∑
GR IC ( n ),
n=3
tot
∂------------V - = – ∇ J + GR + GR ,
· V
IV
AV
∂t
tot
∂ AI - = – ∇ · J – GR + GR
,
--------------AI
AI
AI– V
∂t
3-113
tot
∂ AV - = – ∇ · J – GR + GR
,
----------------AV
AV
AV – I
∂t
∂A
--------s- = GR AI + GR AV – GR AV – I
∂t
∂ In
-------- = GR IC ( n ) – GR IC ( n + 1 ),
∂t
3-32
– GR AI– V ,
n = 2 ,3 ,… ,N,
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SSUPREM4 Models
where the generation-recombination term:
f tot
r
GR IC ( n ) = k n I I n – 1 – k n I n .
3-114
It is important to notice that the IC model is completely independent of the dopants involved in the
process.
3.2.4: Vacancy Cluster Model (VC)
In the VC model, a cluster containing m vacancies (Vm) evolves to a cluster of size m+1 by interaction
with a free vacancy according to the following reactions:
f
0
V +V
0
k2
⇔
r
k2
f
0
V2
0
V2
,
+V
0
k3
⇔
0
V3
r
k3
…
,
0
Vm – 1
+V
0
f
km
⇔ V m0 ,
r
3-115
km
where:
f
km
= 4 π R eff D V ,
V
E f – E f ( m )
D
- , m = 2, … , M .
= 6 ------V- θ m exp  – -------------------------

kT
2
r
km
3-116
λ
Here, Reff represents the effective capture radius and the elementary jump length λ is equal to the
V
inter-atomic distance. θm is the number of dissociating sites. E f is the vacancy formation energy
defined in Equation 3-76, and Ef(m) is the formation energy per vacancy for clusters of size m.
To take into account the interactions VC with interstitials, the following reactions are added:
f
0
V2 + I
(0)
f
k2
⇔ V 2 ( 0 ),
r
k2
0
V3 + I0
kI4
0
⇔
V3 ,
r
k V3
…
f
k Im + 1
0
0
Vm + I
⇔ V0m – 1
3-117
r
k Vm
Therefore, the VC model consists of Equations 3-113 and 3-118.
∂V
---------m∂t
= GR VC ( m ) – GR VC ( m + 1 )
3-118
According to the following reactions, Equations 3-115 and 3-117, there are two kinds of summands in
the generation-recombination part.
f
0
f
0
GR VC ( m ) = k m V V m – 1 + k Im + 1 I V m
r
r 0
0
GR VC ( m + 1 ) = k m V m + k m – 1 V m – 1
3-119
The equations for vacanies and intersititials will also contain the additional terms from
Equation 3-119.
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3.2.5: Electrical Deactivation and Clustering Models (DDC)
At high doses of dopant, the electrically active concentration may be less than corresponding chemical
concentration. The impurity atom becomes activated inside semiconductor only if it is incorporated
into a substitutional lattice site. In this case, the activated atom will contribute with a carrier to either
the valence band (an acceptor impurity), or the conduction band (a donor impurity). It has been
observed that, even below solid solubility, a significant dopant concentration can stay inactive. This
effect can be explained by the formation of immobile dopant-defect clusters, which is described by the
DDC model. This is the third part of the PLS model. The model strongly depends on the nature of the
dopant and therefore is presented separately for each type of dopant below. To activate the DDC
model, add the DDC parameter to the METHOD PLS statement.
Boron
In the case of boron, these clusters are named boron interstitial clusters (BIC). The BIC species BnIm
consists of n atoms of boron and m atoms of silicon self-interstitials. In absence of any direct
experimental data concerning the exact composition of these clusters, BIC structure and charge states
are chosen according to recent ab-initio theoretical calculation [18]. Various possible path are
considered for these clusters: a given cluster can grow or dissolve by the addition or release of a silicon
self interstitial or a boron-interstitial pair (Figure 3-2).
Figure 3-2: BIC reaction paths [5]
By default, the DDC model is based on the formation and dissociation of four BIC’s species: BI2, B2I,
B3I2, and B4I3. Thus, the following reaction are added.
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f
k BI
BI
+
f
2
+ I 0 ⇔ BI 2
r
k BI
+
,
B2 I
+
kB
kB
3-120
2I
f
3 I2
+
+ BI ⇔
r
kB
2I
0
⇔
B2 I ,
r
2
f
0
kB
+
–
B s + BI
B3 I2
+
,
B3 I2
+ BI
kB
–
4I3
⇔
B4 I3
r
kB
3I2
0
.
3-121
4 I3
By default, the model assumes that dopants just after implantation are inactive. As this model does
not assume any local equilibrium between each species, the activation of the dopant will gradually
evolve with time.
The kinetic constants kf and kr for each reactions are defined as:
f
kB
n Im
r
kB
= 4 π R eff D BI ,
D I
E (B I )
kT
B
b
n m 
- θ exp  – ---------------------= 6 -------2 n


n Im
λ
3-122
Reff and Eb(BnIm) are respectively the effective capture radius and the binding energy for each BoronInterstitial Cluster and can be specified and modified in the boron.mod file.
Phosphorus
For phosphorus, the similar situation can be considered [22]. Therefore, phosphorus atoms can form
clusters with self-interstitials. These clusters have been experimentally observed and are called
phosphorus interstitials clusters (PIC).
The following reactions are taken into consideration.
k
f
f
0
– P2 I
–
Ps + I ⇔ P2 I ,
r
kP
0
PI + I
2I
k PI
⇔r
0
k PI
PI 2 ,
2
0
3-123
2
These and additional reactions and their parameters can be specified in the phosphorus.mod file.
Arsenic
The case of arsenic is a little bit different. Arsenic migrates through the vacancy and interstitial
mechanisms with roughly the same proportion. It is well known that arsenic can form clusters with
vacancies of type AsnV. Therefore, the DDC model needs to take into account the following reactions:
f
f
k As V
2
+
–
As s + AsV ⇔ AsV 0 ,
r
k As V
2
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0
0
k As
3V
0
0
As 2 V + AsV ⇔
A s3 V + V ,
r
k As V
3-124
3
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f
k As
0
0
4V
0
A s4 V + V
As 3 V + AsV ⇔
r
k As V
0
3-125
4
The system of equations for DDC model is
tot
∂ I - = – ∇ · J + GR + GR + GR
----------I
IV
AI
AV – I + GR AIC ,
∂t
tot
∂------------V - = – ∇ J + GR + GR + GR
· V
IV
AV
AI – V + GR AVC ,
∂t
tot
∂--------------AI
- = – ∇ · J AI – GR AI + GR AI – V + GR AIC ,
∂t
tot
∂ AV - = – ∇ · J – GR + GR
+ GR AVC ,
----------------AV
AV
AV – I
∂t
∂A
--------s- = – ∇ · J AV + GR AV – GR AI – V
∂t
3-126
– GR AV – I + GR AIC + GR AVC ,
∂-----------AIC- = GR ,
AIC
∂t
∂ AVC- = GR ,
-------------AVC
∂t
where GRAVC, GRAIC are generation-recombination terms caused by reactions (Equations 3-120 and
3-125).
3.2.6: Typical Examples
The following will show each part of the PLS model validated using specific experimental results.
The CDD model is tested using a simple predeposition step. The interstitial cluster part of the model is
validated using the Cowern’s experiment [20], and the mixed cluster part of the model is then analyzed
using the Pelaz experiment [24]. To illustrate the improvements given by the PLS model, we perform
simulations within a very broad range of experimental conditions from a standard implantation and
diffusion step to a "state of the art" RTA
Predeposition
Boron
As a first indication that the PLS model is able to handle the complex couplings between boron and the
free point defects, we show in Figure 3-3 the result of the conventional predeposition steps simulation
(diffusion with a constant surface concentration).
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SSUPREM4 Models
Figure 3-3: Simulation of Boron predeposition using the CDD model at various temperature, time annealing and
surface concentration. (Crosses, pluses, and squares are experimental data from [25])
Although not corresponding to the modern deep sub-micron technologies, this simulation represents
the high dopant concentration features that reveal the complex couplings between dopant and point
defects. Therefore, it is considered as a meaningful basic test for any advanced diffusion models.
Although this model has been developed for advanced silicon technologies, it still can be used as the
standard diffusion model for any diffusion step. For example in the case of buried layer formation, the
TED phenomena become irrelevant. Therefore, you can use only CDD part of the PLS model while
ignoring IC and DDC models.
Phosphorus
To illustrate the improvements that result from the CDD model, we show simulations of phosphorus
predeposition profiles at high and intermediate concentrations. The simulation results are compared
to the SIMS data of Yoshida and Matsumoto. This experiment represents high dopant concentration
features that reveal the complex couplings between dopants and point defects. Therefore, it is
considered as a meaningful test for advanced diffusion models.
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Figure 3-4: Simulation of phosphorus predeposition at 900°C during 1 hour with various surface concentration.
(Squares, pluses, and crosses are experimental data from [26])
As our simulations prove, the PLS model accurately reproduces the experimental profiles features.
Particularly, the simulated profiles exhibit the enhanced tail with more or less pronounced inflexion in
the surface region. This inflexion is the result of the strong coupling between the defect gradients and
the dopant.
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Cowern’s Experiment
To validate the IC model, we first try to compare our model prediction with the experimental data
obtained by Cowern et al. [20]. Briefly described, this experiment consists of observing the diffusivity
of two boron marker layers after a silicon implantation at 40 keV to a dose of 2 ⋅ 1013 atoms/cm2
(simulated in the left hand side from Figure 3-5). From these observations, Cowern et al. have
estimated the diffusion enhancement and the evolution of supersaturation with time. On the right
hand side of Figure 3-5, the PLS simulation of the supersaturation evolution is shown.
Figure 3-5: Simulation of the Cowern experiment and extraction of the evolution of the supersaturation during the
annealing. (Experimental data are from [20])
Figure 3-5 shows the free interstitial supersaturation behavior with time. This quantity is simply
calculated using the ratio between local effective interstitial concentration and its equilibrium value.
From the experimental point of view, this quantity can be related to the boron diffusion enhancement
with respect to its thermal equilibrium diffusion.
The supersaturation evolution curve exhibits three parts:
• The first step characterized by a high supersaturation value corresponds to a large acceleration of
the dopant diffusion and can be explained by the presence of small clusters.
• The second step exhibits a plateau slightly decreasing with time. It is explained by the competitive
growth between <311> defects known as the Ostwald ripening phenomena.
• The third step characterized by the supersaturation collapse is explained by the entire dissolution
of the IC population, due to the recombination at the surface.
It is clear that the CDD model alone (dashed lines in Figure 3-5) cannot reproduce these three steps of
the transient enhanced diffusion, since the curves are monotonically decreasing.
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Pelaz Experiment
In this experiment, a boron marker is deposited at a depth of 0.15 µm. To observe the boron diffusion,
Pelaz et al. have performed a silicon implant to generate a high interstitial concentration at the
surface. Unlike the Cowern experiment, the boron concentration is high enough to allow the formation
of BICs. Thus, this experiment exhibits a particular effects of in the boron diffusion: an immobilization
and disactivation of the dopant at high concentrations even under the solid solubility limit.
Figure 3-6 demonstrates simulations of this particular experiment, using various parts of the PLS
model.
Figure 3-6: Simulation of the Pelaz experiment using various parts of the PLS model. (Experimental Data are
extracted from [24])
The results obtained with the full PLS model correspond to the experimental data. As expected, the
boron at the highest concentration stay immobile and are still inactive due to the formation of mixed
BICs. Moreover, it is clear that only the full model can explain this behavior. Therefore, CDD and IC
models cannot simulate this particular phenomenon without DDC model involved.
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SSUPREM4 Models
Implantation Diffusion Experiment
The analysis above proves validity of each part and the entire PLS diffusion model. In addition, we
present several simulations relevant to specific processes important in the modern VLSI technologies.
Experiment with boron implanted at 20 keV
Boron implantation at 20 keV is widely used in silicon technologies. Since the experiment setup
involves low temperature, such as 800°C, the effects of boron immobilization and disactivation at high
concentration take place. Therefore, you must use three parts of the PLS model.
Figure 3-7: Simulation of 35 minutes boron diffusion at 800°C after an implantation at 20 keV
with a dose of 5 ⋅ 1014 cm-2. (Experimental data are extracted from [27])
As shown in Figure 3-7, PLS model results in an excellent fit with the experimental annealed curves.
The comparison of chemical and electrically active boron concentration shows that even below the solid
solubility, most of the dopant stay inactive due to the formation of mixed dopant-defect clusters. By
comparing results obtained with only CDD or IC model with the full PLS (IC + DDC), it can be
concluded that this type of clusters also consume free interstitials which leads to reduction of the
boron diffusion. This fact justifies one more time that all three parts of the model: CDD, interstitial
clusters and mixed dopant-defect clusters are needed in simulation of post-implant diffusion.
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Experiment with boron implanted at 2 keV
A most aggressive technology simulation has been carried out with a 2 keV boron implant with a dose
of 1014 cm-2 followed by a RTA at 1000°C during 10 seconds. This type of simulation is difficult because
it needs to take into account a large number of phenomena including strong defect recombination at
the surface, and the fact that TED duration is function of the implant setup and subsequent diffusion
duration. Despite of these difficulties, Figure 3-8 shows a very good fit with experimental annealed
data which proves the excellent quality of the model.
Nevertheless, as presented in the literature, the TED effect decreases at very low implant energy and
high temperature annealing. This explain why the simulations done using CDD and IC models and
only CDD model sometimes give reasonable agreement with experiments.
Figure 3-8: Simulation of boron diffusion at 1000°C during 10 s after an implantation at 2 keV
with a dose of 1 ⋅ 1014cm-2. (Experimental data are from [28])
Experiment with arsenic implanted at 2 keV
The PLS model is not only design for the boron diffusion but also for other common dopant, such as
phosphorus or arsenic.
An Arsenic implantation has been performed with a energy of 2 keV at a dose of 1015 at/cm-2 and
followed by a spike RTA at 950°C with a ramp up estimated at 100°C/s. In this typical process example
for ultra shallow junction, dopant is implanted at such a high dose that its concentration reaches the
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SSUPREM4 Models
solid solubility limit. In this case, most of the dopant at concentration higher that this limits will
precipitate in the early stage of the annealing.
Moreover, all other specific characteristics in arsenic diffusion is taken into account. In other words:
•
Arsenic migrate both through interstitial and vacancy mechanisms with roughly the same
proportion.
•
Arsenic atoms form with vacancy any clusters, As2V or As4V.
The initial interstitial profile generated by the arsenic implant is modeled though a simple "plus n"
model.
Figure 3-9: Simulation of Arsenic diffusion after an implantation at 2 keV with a dose of 1 ⋅ 1014 cm-2 and a spike
anneal at 950°C with a temperature ramp rate estimated at 100°C/s. (Experimental data are from [29])
The result obtain with the full PLS model is in good agreement with experimental data. As expected,
most of the arsenic at concentration above the solid solubility limit precipitate quickly and
consequently immobilize the dopant.
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3.3: Oxidation Models
The fabrication of integrated circuit microelectronic structures and devices vitally depends on the
thermal oxidation process for the formation of gate dielectrics, device isolation regions, spacer regions,
and ion implantation mask regions. Particularly, the precise control of silicon dioxide thickness as
device geometries continue to scale to sub-micron dimensions.
In SSUPREM4 silicon thermal oxidation is modeled when a DIFFUSION statement contains a DRYO2,
WETO2, F.O2, or F.H2O parameter. Oxidation takes place when there is an interface between silicon
(or polysilicon) and silicon dioxide or a silicon (polysilicon) surface is exposed to an oxidizing ambient.
SSUPREM4 simulates polysilicon oxidation in a very similar manner as silicon (almost all oxidation
parameters for polysilicon are the same as for silicon). SSUPREM4 also allows oxidation completely
through a silicon (polysilicon) layer. This is very important in processes (e.g., poly buffered LOCOS) in
which polysilicon regions are completely consumed during oxidation.
Because exposed silicon surfaces usually have a thin native oxide layer, SSUPREM4 automatically
deposits a thin native oxide layer on all exposed silicon (polysilicon) surfaces at the beginning of
oxidation steps. The INITIAL parameter in the OXIDE statement determines the layer’s thickness,
which has a default value of 20 Å.
The two-dimensional oxidation models in SSUPREM4 are based on the well-known linear-parabolic
theory of Deal and Grove [30]. Numerical aspects of the model implementation can be found in [31].
Silicon oxidation is modeled by considering the following three processes:
(1) Oxidant (e.g., H2O or O2) is transported from the ambient gas into the SiO2 layer at the gas/SiO2
interface.
(2) Oxidant is transported across the SiO2 layer until reaching the Si/SiO2 interface.
(3) Oxidant, arriving at the Si/SiO2 interface, reacts with silicon to form a new layer of SiO2.
The transport of oxidant across the gas/SiO2 interface is given by
*
F1 = h ( C – C0 ) n0
3-127
where:
• h is the gas-phase mass-transport coefficient.
• C* is the equilibrium oxidant concentration in SiO2.
• C0 is the oxidant concentration in SiO2 at the gas/SiO2 interface.
• n0 is a unit vector normal to the gas/SiO2 interface pointing toward the silicon layer.
The equilibrium oxidant concentration in SiO2 is linearly related to the partial pressure of the oxidant,
P, in the gas by Henry’s law:
*
C = K⋅P
where K is a constant.
3-128
Diffusion of oxidant molecules in the SiO2 is driven by a concentration gradient and is given by Fick’s
law as
F 2 = – D eff ∇ C
3-129
where Deff is the effective oxidant (H2O or O2) diffusivity in the growing SiO2 layer. C is the oxidant
concentration in the oxide.
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The reaction at the Silicon (or Polysilicon)/SiO2 interface between silicon and the oxidant is expressed
as
F 3 = kC n
i i
3-130
where:
• k is the apparent surface reaction rate constant.
• Ci is the oxidant concentration at the Silicon (or Polysilicon)/SiO2 interface.
• ni is a unit vector normal to the Si/SiO2 pointing toward the silicon layer.
Under steady state conditions, the three fluxes are equal.
F = F1 = F2 = F3
3-131
By dividing the flux by N1, the number of oxidant molecules incorporated in a unit volume of SiO2, and
considering one dimensional growth, the growth rate of the oxide layer is given by
dx
F--------0 = ----dt
N1
3-132
where x0 is the oxide thickness. From Equation 3-127 and Equations 3-129–3-131, Equation 3-132 can
be expressed as
dx 0
B -------- = -----------------A + 2x 0
dt
3-133
where:
A = 2D eff  1--- + 1---
 k h
3-134
*
B = 2Deff C
------N1
3-135
Equation 3-133 is modified for thin oxides (less than 500 Å) as follows:
dx 0
B -+R
-------- = -----------------dt
A + 2x 0
3-136
where R is calculated according to [32]:
x0
THINOX ⋅ E

R = THINOX ⋅ 0 exp  --------------------------------- exp  ------------------------------- THINOX ⋅ L


kT
⋅ P THINOX ⋅ P
3-137
where P is partial pressure. THINOX.0, THINOX.E, THINOX.L, and THINOX.P parameters are
specified in the OXIDE statement.
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3.3.1: Numerical Oxidation Models
In the previous section, an introduction to one-dimensional oxidation modeling was presented. This
section describes the two-dimensional numerical oxidation models implemented in SSUPREM4. The
numerical oxidation models build on the Deal-Grove oxidation theory and provide the capability to
simulate arbitrary two-dimensional structures.
The numerical oxidation models require solving the oxidant diffusion equation at incremental time
steps at discrete grid points in the growing SiO2 layer. The oxidant diffusion equation is given by
∂ C- = ∇ ⋅ F
-----∂t
3-138
where:
• C is the oxidant concentration in SiO2.
• t is the oxidation time.
• F is the oxidant flux.
Equation 3-138 is solved by substituting Equation 3-129 for F and defining appropriate boundary
conditions at material interfaces with SiO2. At the gas/SiO2 interface, Equation 3-127 describes the
interface transport flux of oxidant molecules, accounting for the boundary condition at that interface.
The boundary condition at the Silicon (or Polysilicon)/SiO2 interface is described by Equation 3-130.
The flux at boundaries between SiO2 and other materials in the simulation structure is set to zero. By
solving Equation 3-138, the oxidant concentration is determined at each grid point in the SiO2 layer.
The SiO2 growth rate or Si/SiO2 interface velocity, Vs, is determined at each point along the interface
by combining Equations 3-130 and 3-132 resulting in the following.
kC i n i
V s = ------------N1
3-139
At each time step, Equation 3-139 is solved. The incremental oxide thickness grown is calculated by
multiplying Equation 3-139 by the time step. During the oxidation reaction silicon atoms bond with
the oxidant to form the SiO2 compound. Thus, silicon material is removed during the oxidation
process. The ratio of the silicon thickness consumed to form a given thickness of SiO2 is specified using
the ALPHA parameter in the OXIDE statement.
Equation 3-138 is sufficient to describe the motion of the Si/SiO2 interface if the oxide flow is in the
same direction as the growth (for planar oxidation structures). In most structures of interest, the oxide
flow is two dimensional. Therefore, additional equations have to be solved. Both the Compress and
Viscous models calculate the two-dimensional flow of oxide elements by solving a simplified
hydrodynamic creeping flow equation.
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3.3.2: Compress Model
In addition to solving Equations 3-138 and 3-139, a simplification of the hydrodynamic flow equation is
solved to obtain the flow of oxide elements [34]. The Compress Model is activated by specifying
COMPRESS in the METHOD statement prior to a DIFFUSE statement. The Compress Model is the default
oxidation model in SSUPREM4. Neglecting the acceleration and gravitational terms in the
hydrodynamic flow equation, the creeping-flow equation is given by
2
µ∇ V = ∇ P
3-140
where P is the hydrostatic pressure, V is velocity of oxide elements and µ is the oxide viscosity.
The oxide viscosity is calculated from the following equation:
YOUNG.M µ = --------------------------------------------( 2 + 2 ⋅ POISS.R )
3-141
where YOUNG.M is Young’s modulus, which is specified in the MATERIAL statement, and POISS.R is
Poisson’s ratio, which is specified in the MATERIAL statement.
The oxide flow is treated as an incompressible fluid. By doing this, it implies the density of the oxide is
constant with respect to time. Applying this fact to the mass continuity equation, the incompressibility
condition is given as
∇⋅V=0
3-142
The incompressibility condition in Equation 3-142 is implemented by allowing a slight compressibility
of the flowing oxide. Thus, Equation 3-142 is modified to give the following equation:
– ( 2 ⋅ POISS.R )- P
∇ ⋅ V = 1-------------------------------------------µ
3-143
The solution of Equation 3-143 at each time step gives the velocity field of the flowing oxide elements.
The Compress Model is recommended for simulations of planar and non-planar structures, where
stress effects play a minor role in determining the oxide shape. When stress effects are important, you
can use the Viscous oxidation model.
Figure 3-10 shows a two-dimensional cross section of the structure resulting from a LOCOS oxidation
using the Compress Model.
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Figure 3-10: Resulting Structure from a LOCOS Oxidation step using the Compress Model
3.3.3: Viscous Model
The Viscous Model solves the same flow equations as described in the previous section. This model is
activated by specifying the VISCOUS parameter in the METHOD statement prior to the DIFFUSE
statement. The Viscous Model calculates stresses in the growing oxide and creates almost the same
shape for the silicon/oxide interface as does the Compress model.
The stresses in the oxide are calculated as follows:
– VISC.E
2 ⋅ VISC.0 ⋅ exp  ---------------------- ∂ v
 kT   x ∂ v y
σ xx + σ yy = ----------------------------------------------------------------------  -------- + --------
∂x
∂y
1 – 2 ⋅ POISS.R
3-48
3-144
∂v
– VISC.E ∂ v
σ xx – σ yy = 2 ⋅ VISC.0 ⋅ exp  ----------------------  --------x – --------y
kT
∂x ∂y
3-145
∂v
– VISC.E ∂ v
σ xy = VISC.0 ⋅ exp  ----------------------  --------x + --------y
kT
∂x
∂y
3-146
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where vx and vy are the x and y components of flow velocity v respectively. VISC.0 and VISC.E are the
pre-exponential and activation energy, respectively for viscosity, are specified on the MATERIAL
statement.
The stress calculated by the Viscous oxidation model replace stress that may have been previously
generated by the STRESS.HIST parameter in the STRESS statement.
The stress-dependent nonlinear model based on Eyring’s work [33] allows a description of the real
shape of LOCOS profiles with kinks on the interface. The model is turned on by specifying the
STRESS.DEP parameter the OXIDE statement. Using Equation 3-140 and Equations 3-143–3-146, the
non-linear solver first finds a linear solution for flow velocities and stresses and then uses the stresses
obtained to calculate the reduction factors for oxidant diffusivity, Deff, oxide viscosity, µ, and the
interface reaction rate constant k as follows:
V (σ
(i)
(i – 1)
D eff = D eff
+σ
)
d xx
yy -
⋅ exp  ------------------------------------
kT
τV
 --------c-
(i)
( i – 1 )  2kT
µ = µ
-------------------------τ Vc
sin h  ---------
 2kT
k
(i)
= k
(i – 1)
3-147
3-148
σ V +σ V
r r
t -t
⋅ exp  – -----------------------------
kT
3-149
where i is the iteration. Vd, Vc, Vr, and Vt are the activation volumes (in Å3), specified in the OXIDE
statement.
τ is the total shear stress:
2
2
τ = 1--- ( σ xx – σ yy ) + 4 σ xy
2
3-150
σr is the normal component of the total stress:
2
2
σ r = σ xx n x + σ yy n y + 2 σ xy n x n
y
3-151
σt is the tangential component of the total stress:
2
2
σ t = σ xx n y + σ yy n x + 2 σ xy n x n
y
3-152
where nx and ny are the x and y components of the unit vector normal respectively.
The reduced parameters feed back to the next iteration. This process continues until the accuracy
criterion is met. Fast convergence of this process is not guaranteed. Oxidation calculations by the
stress-dependent model usually take much more CPU time than the Compress Model.
Figure 3-11 shows the resulting structure from a LOCOS oxidation step using the stress dependent
Viscous Model.
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Figure 3-11: Resulting Structure from a LOCOS Oxidation step using the Stress-Dependent Viscous Model
3.3.4: Linear Rate Constant
For short oxidation times and low oxidation temperatures the oxide growth is linearly related to the
oxidation time. The interface processes (oxidant transport across the gas/SiO2 interface and oxidant
reaction at the Si/SiO2 interface) are the determining factor in describing the growth kinetics. In this
regime, the oxide thickness can be approximated as
x0
--- t
≅  B

A
3-153
where (B/A) is called the linear rate constant and is obtained by dividing Equation 3-135 and Equation
3-134, resulting in the following equation:
*
C -1
B
--- = -------- + 1---
 A
N 1  h k
3-154
The equilibrium oxidant concentration in the oxide, C*, is defined by Equation 3-128. K in Equation 3128 is specified by the HENRY.COEF parameter in the OXIDE statement. The gas-phase mass-transport
coefficient, h, is given by the following Arrhenius relation:


h = TRN.0 ⋅ exp  – TRN.E
-----------------
 kb T 
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where the TRN.0 and TRN.E parameters are specified in the OXIDE statement. The interface reaction
rate constant, k, is determined from Equation 3-154 and experimentally determined values of (B/A).
The linear rate constant is composed of several dependencies including orientation, pressure, chlorine
additions, and doping effects.
B
--- =  B
---  B
---  B
---  B
---  B
---
 A
 A i  A ori  A P  A Cl  A doping
3-156
(B/A)i is given by:

 LIN.L.E
 LIN.L.0 exp  – -------------------- T < L.BREAK

kb T 


B
--- = 
 A i
 LIN.H.E

 LIN.H.0 exp  – ---------------------- ( T ≥ L.BREAK )
kb T 



3-157
which is the linear rate constant determined for oxidations on lightly-doped substrates annealed at
atmospheric pressure with no chlorine content in the ambient. The parameters appearing in Equation
3-157 are specified in the OXIDE statement. The remaining factors in Equation 3-156 are described in
the following sections.
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Orientation Dependence
The silicon substrate orientation is known to affect the oxidation kinetics [34, 35]. The influence of
orientation on the linear rate constant is modeled as (B/A)ori in Equation 3-156. The orientation
dependencies for <100> and <110> orientations are modeled by appropriate reduction factors, and
(B/A)ori for <111> substrates is unity.
Figure 3-12 shows the silicon dioxide thickness dependence as a function of the substrate orientation
for several oxidation temperatures.
Figure 3-12: Silicon Dioxide Thickness versus Time for Different Substrate Orientations and Temperatures
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Pressure Dependence
High pressure silicon oxidation allows one to grow relatively thick SiO2 films while keeping the
temperature low so that dopant redistribution is reduced [36]. The pressure dependence in the linear
rate constant is given by
L.PDEP
B
--- = P
 A P
3-158
where L.PDEP is specified on the OXIDE statement for each oxidant and P is the partial pressure of the
oxidizing gas.
Figure 3-13 shows the silicon dioxide thickness versus time with PRESSURE as a parameter.
Figure 3-13: Silicon Dioxide Thickness versus Time with Pressure as a Parameter
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Chlorine Dependence
The addition of chlorine to the oxidation system results in better passivation and higher oxide
dielectric strength [30, 35]. For a dry oxygen ambient, chlorine introduction gives rise to a higher
oxidation rate. It has been suggested [35] that chlorine reacts with O2 to produce H2O and Cl2 as
products. The oxidation rate is higher in H2O ambients than in O2 ambients because equilibrium
concentration of H2O in the oxide is higher. A look-up table approach is implemented to model the
increase in the linear rate constant in Equation 3-156 though the (B/A)Cl term. The table gives an
enhancement factor to the linear rate constant as a function of chlorine percentage and temperature.
The default values for chlorine dependence are included in Appendix B: “Default Coefficients”.
The effects of adding chlorine to the oxidizing ambient is shown in Figure 3-14, where the silicon
dioxide thickness increases as more chlorine is added to the ambient.
Figure 3-14: Silicon Dioxide Thickness Versus Oxidation Time with HCl Percentage and Temperature as
Parameters
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Doping Dependence
It is well known that SiO2 formation on highly-doped n-type and p-type substrates can be enhanced
compared to SiO2 formation on lightly-doped substrates [37]. The dependence of silicon dioxide growth
kinetics on doping concentration is manifested as part of the linear rate constant, where the physical
significance of the high doping levels has been explained primarily as an electrical effect [37], [38].
This factor in the linear rate constant is given by

– BAF.KE  V∗
B
---
- – 1
= 1 + BAF.K0 ⋅ exp  -------------------------  ------ A doping
 k T  V ∗ 
b
i
3-159
where V* is the equilibrium vacancy concentration in silicon at the Si/SiO2 interface. Vi* is the
equilibrium vacancy concentration in intrinsic silicon. BAF.K0 and BAF.KE are specified on the OXIDE
statement.
The equilibrium vacancy concentration, composed of vacancy defects in different charged states,
depends on the Fermi level location [8], [39] and is given by
n +
n 2

n 2 
n  –  --- i φ +  ----i φ ++ +  ---φ +   φ = 
 1 +  ---
 n
n 
n
n


i
i
V∗ = V i∗  ------------------------------------------------------------------------------------------------------------------ 
–
=
1 + φ + + φ ++ + φ + φ






3-160
where n is the electron concentration and ni is the intrinsic carrier concentration, and
φ+ =


---------------------
BAF.EBK exp  – BAF.PE
kb T 



-------------------------
φ ++ = BAF.EBK exp  – BAF.PPE


3-162
–
 BAF.NE
BAF.EBK exp  – ---------------------
kb T 

3-163
=
 BAF.NNE
= BAF.EBK exp  – --------------------------
kb T 

3-164
φ =
φ
kb T
3-161
where φ+, φ++, φ−, and φ= are fractions of the vacancy concentration which are positively, double
positively, negatively, and double negatively charged respectively.
Figure 3-15 shows a plot of V*/Vi* at 950°C for common silicon dopants. Notice that for n-type dopants
(V*/Vi*) increases as the doping concentration increases, but V*/Vi* remains essentially constant for
the p-type dopant. The increase in V*/Vi* for n-type dopants increases the linear rate constant. This
ultimately leads to thicker oxides when oxidizing highly-doped n-type substrates due to a higher
availability of unoccupied silicon lattice sites (vacancies) for oxidant molecules to be incorporated.
The oxide thickness trend is shown in Figure 3-16, where the SiO2 thickness is plotted versus doping
concentration for common silicon dopants.
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Figure 3-15:
∗
∗
V ⁄ V i Ratio versus Doping Concentration
Figure 3-16: Simulated Silicon Dioxide Thickness vs. Doping Concentration for Common Silicon Dopants
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3.3.5: Parabolic Rate Constant
For long oxidation times and high temperatures the oxide growth is parabolically related to the
oxidation time. The diffusion of oxidant in the oxide is the determining factor in describing the growth
kinetics. For these times and temperatures, the oxide thickness can be approximated as:
2
x0
≅ Bt
3-165
where B is called the parabolic rate constant and is given by Equation 3-135. When using this
equation, the oxidant diffusivity, Deff, is determined from specified values for C*, N1, and
experimentally-determined values of B. The parabolic rate constant has been determined to have
dependencies on the ambient pressure and the chlorine content during oxidation and is given by
B = B i ⋅ B P ⋅ B HCl
3-166
where:



 PAR.L.0 exp  – PAR.L.E
----------------------- T < P.BREAK

k
T


b

Bi = 
3-167
 PAR.H.E

 PAR.H.0 exp  – ------------------------ T ≥ P.BREAK
kb T 



Bi is determined as a function of temperature and time for lightly-doped substrates annealed at
atmospheric pressure with no chlorine content in the ambient. The parameters in Equation 3-167 are
specified for the appropriate oxidant species using the OXIDE statement. The pressure dependence and
chlorine dependence are described in the following sections.
Pressure Dependence
The effects of pressure on the kinetics of the silicon oxidation process have been studied by Razouk et
al. [36] for pyrogenic steam and Lie et al. [39] for dry oxygen. The parabolic rate varies with pressure
because of its dependence on the oxidant equilibrium concentration in the oxide, C*, which is directly
proportional to the partial pressure of the oxidizing gas. The following relation is used to model this
dependency.
BP = P
P.PDEP
3-168
Here, P is the partial pressure of the oxidizing gas in atmospheres and P.PDEP is specified on the
OXIDE statement.
See Figure 3-13 for a plot of SiO2 thickness as a function of time and pressure.
Chlorine Dependence
It has been observed that additions of chlorine during thermal oxidation also affect the parabolic rate
constant. One possible explanation is that as chlorine enters the oxide film, it tends to cause the SiO2
lattice to become strained, which increases the oxidant diffusivity [35].
Chlorine concentration dependence on the parabolic oxidation rate is modeled in a similar manner to
that of the linear rate constant. Given an HCl percentage, a look-up table is used to determine an
enhancement factor for the parabolic rate constant. Figure 3-14 shows the SiO2 thickness dependency
on HCl percentage.
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3.3.6: Mixed Ambient Oxidation
In practice, an oxidizing ambient may be a gas mixture consisting of more than one oxidant and other
impurities. The total oxidation rate will be the combined effect of all these species. To simulate
oxidation under a multi-gas ambient, SSUPREM4 simultaneously calculates the diffusion and
oxidation of several ambient gases.
The capability is invoked by specifying the gas flow parameters: F.O2, F.H2, F.H2O, F.N2, and
F.HCL on the DIFFUSE statement. From the gas flow, the partial pressure of each gas is calculated as:
Fj
P= P
------------j
total
Fj
∑
3-169
where Pj and Fj are partial pressure and gas flow rate for the jth gas respectively, and Ptotal is the total
pressure of the gas mixture (specified by the PRESSURE parameter on the DIFFUSE statement).
If only one oxidant gas is specified in the gas flow (i.e., only O2 or H2O with other gases), oxidation is
then modeled as previously described. Equation 3-169 determines the pressure of the oxidant gas. If
both F.H2 and F.O2 are specified, the reaction of H2 and O2 to form H2O is assumed to occur. The
partial pressure of H2O is then calculated before solving the oxidation equations.
For ambients containing more than one oxidant (e.g., O2 and H2O), the partial pressure of each oxidant
is used to calculate C* for each species. From C*, k and Deff for each oxidant species are calculated in a
similar manner as that described in the pairs sections, respectively.
Equation 3-138 is solved for each oxidant to obtain each oxidant’s concentration distribution in the
growing SiO2. The contributions of each oxidizing species to the Si/SiO2 interface velocity is calculated
with the following equation:
Vs =
∑
j
k j C ij n ij
-------------------N 1j
3-170
where Equation 3-139 has been used and j corresponds to the jth oxidant gas.
The flow equations are also calculated for a mixed ambient where both O2 and H2O exist and
COMPRESS or VISCOUS has been specified on the METHOD statement. The stress dependence of Deff and
k is a function of the composition of dry or wet oxide which depends on oxidation history. Mixed
ambient oxidation simulations take longer to solve than simple ambient equations.
3.3.7: Analytical Oxidation Model
You can use the analytical oxidation models to simulate a limited set of simple structures. Possible
structures include a silicon substrate with an oxide layer deposited (or grown) on it. Since you can only
specify the mask at the left part of a simulated structure, oxidation will only occur to the right of the
mask edge. Analytical methods do not account for any real material layer located to the right of the
specified mask edge. As the oxide layer thickens, the material is elevated, but growth rate and oxide
shape are not affected. In all analytical models, the initial silicon surface must be planar.
The ERFG model simulates the bird’s beak oxide shape under nitride masks of different thicknesses
[40]. The ERFG model consists of two models: ERF1 and ERF2. The ERF1 model describes the oxide
growth under a thin nitride layer, where the stress from the nitride mask layer is negligible. ERF2
model describes the oxide growth when nitride layer thicknesses are large enough to cause stress in
the oxide, which can result in the oxide layer being pinched. When ERFG is specified, either the ERF1
or ERF2 model will be automatically selected based on the structure under consideration. Both models
are based on the error-function shape of the oxide/silicon and oxide/ambient or oxide/nitride interfaces:
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Z = A erfc ( By + C ) + D
3-171
The A, B, C, and D parameters are complex functions of several geometric parameters:
• initial thickness of oxide lox and nitride ln,
• current thickness Eox of oxide given by the Deal-Grove Model (Equation 3-132),
• the length of lateral oxidation under the nitride layer Lbb,
• and the lifting of the mask during oxidation H.
These functions are specified in the OXIDE statement. All defaults are taken from [40].
3.3.8: Recommendations for Successful Oxidation Simulations
Achieving successful oxidation simulations can be a frustrating task for a novice user of process
simulation software. This section highlights some of the most common barriers encountered using
process simulation to model oxidation steps, and describes how to overcome those barriers with the
proper methods for simulating these oxidation steps.
One of the most common errors made in simulating oxidation steps is improperly gridding of the oxide
structure. Improper gridding can result in jagged oxide shapes and errors in resolving impurity
distributions. As the oxide layer is growing, grid points are added at predefined spacings. As silicon is
being consumed, dopants are transported across the Si/SiO2 interface. It is important to obtain a well
gridded oxide to properly account for dopant redistribution during the oxidation step.
Growing Thin Oxides
A typical application where thin oxide growth is important is during a gate oxidation step of a
MOSFET which has a highly-doped polysilicon gate. By default, SSUPREM4 uses a grid spacing of 0.1
microns in the growing oxide layer. Thus, one grid layer will be added in the growing oxide every 0.1
microns (or 1000 angstroms). This grid spacing is appropriate for field oxidations, and hence the
reason it is the default grid spacing in the growing oxide layer. Using the default grid spacing in the
oxide for typical gate oxidations in today’s MOS technology results in no grid being added in the
interior of the SiO2 layer. With no grid present in the oxide to resolve the dopant diffusion in the oxide
during subsequent processing, the polysilicon dopant can penetrate into the underlying silicon
substrate. This simulation artifact can cause threshold voltages to be very different than expected.
To rectify this simulation artifact, you can control the number of grid layers added during the
oxidation with the GRID.OXIDE and GRIDINIT.OXIDE parameters in the METHOD statement. You
should place this statement before the gate oxidation diffusion step. Setting these parameters to a
value, which results in three or four grid layers in the gate oxide (e.g., 15 angstroms for a 60 angstrom
gate oxide thickness), can alleviate this problem. We suggest you to set back these parameters to the
default values after the gate oxidation step.
Figure 3-17 shows a cross section of an NMOSFET with a highly-doped phosphorus polysilicon gate.
The default grid spacing in the oxide is used in Figure 3-17(b), while the grid spacing is adjusted
properly for Figure 3-17(a). By comparing these two figures, it is obvious that phosphorus has
penetrated through the gate oxide for Figure 3-17(b) but does not penetrate through the gate oxide in
Figure 3-17(a).
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Figure 3-17: (a) MOSFET Structure with Proper Gridding in Gate Oxide, (b) MOSFET Structure with Default Grid
Spacing in Gate Oxide
Implantation Through Thermally-Grown Oxides and Dopant Loss During Subsequent Annealing
Frequently, dopants are implanted through thermally grown oxide layers. It is important to have a
proper grid spacing in the oxide through which the dopant is implanted for two reasons. First, this will
aid in determining the proper dopant profile in the oxide layer and the underlying silicon. Secondly,
proper gridding is required to resolved the dopant diffusion in the oxide during subsequent processing
steps.
During annealing, the dopant will diffuse in SiO2 and silicon and eventually evaporate into the
ambient at the gas/SiO2 interface. If proper gridding is not supplied in the growing oxide layer, the
amount of dopant evaporating can be underestimated, yielding a larger dose retained in the silicon
substrate. The mechanism is similar to what was described in the earlier sections. There may not be
any grid points in the interior of the growing SiO2 layer. The problem is again remedied by specifying
more grid layers to be added as the SiO2 layer grows.
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Figure 3-18 shows a comparison of the resulting arsenic profiles in silicon using the default grid
spacing and a corrected grid spacing in the growing SiO2 layer. For this experiment, a silicon dioxide
layer was thermally grown. Arsenic was ion implanted through the SiO2/Silicon structure. A
subsequent annealing step followed which results in the profiles shown in Figure 3-18.
Figure 3-18: Comparison of Arsenic Profiles in Silicon with Default Grid Spacing and Improved Grid Spacing in
the Growing SiO2 layer.
Oxidation Enhanced Diffusion (OED) / Oxidation Retarded Diffusion (ORD)
During silicon thermal oxidation, some of the dopant in silicon gets incorporated into the growing SiO2
layer and some remains in silicon where it diffuses. As oxidation proceeds, silicon lattice atoms become
interstitial (interstitials are injected into silicon at the Si/SiO2 interface) as oxygen molecules are
incorporated into the lattice to form SiO2. Due to the injection of interstitial defects during oxidation,
you can enhance dopant diffusivities. To properly simulate this effect, you must include the creation
and movement of point defects, vacancies and interstitials in the simulation. By specifying TWO.DIM in
the METHOD statement before the oxidation step, non-equilibrium point defect concentrations
(including injection and recombination at the Si/SiO2 interface) are included in the simulation. For
more information on point defect diffusion kinetics, see Section 3.1: “Diffusion Models”.
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Note: Figure 3-19 compares the boron concentration profiles after an oxidation step when point defects remain at their
equilibrium values (FERMI) and when point defects are allowed to obtain non-equilibrium values (TWO.DIM). It is evident from
Figure 3-19(a) that boron diffusion is enhanced for the TWO.DIM case. The corresponding interstitial concentrations are shown
in Figure 3-19(b). The interstitial concentration is above the equilibrium interstitial concentration for the TWO.DIM case (thus,
allowing oxidation enhanced diffusion to be observed) but remains at equilibrium for the FERMI case.
Figure 3-19: (a) Boron Concentration Versus Depth (b) Corresponding Interstitial Concentration Versus Depth
You can also have a diffusion retardation effect during thermal oxidation. For dopants diffusing
primarily through a vacancy mechanism, you can reduce their diffusivities during oxidation because of
the recombination of vacancies with injected interstitials at the SiO2/Silicon interface. Figure 3-20
shows an example of this phenomenon.
Figure 3-20(a) shows the resulting antimony concentration profiles after an oxidation step where the
FERMI and TWO.DIM models were used. In contrast to boron (Figure 3-19(a)), the resulting antimony
concentration profile is shallower for the TWO.DIM case when compared to the FERMI case.
Figure 3-20(b) shows the reduced vacancy concentration, displaying the results from the TWO.DIM and
FERMI models.
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Figure 3-20: (a) Antimony Concentration Versus Depth (b) Corresponding Vacancy Concentration Versus Depth
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3.4: Silicidation Model
Silicide modeling capability is implemented in SSUPREM4. Silicides are formed when a metal reacts
with silicon or polysilicon to create an intermediate phase. The conductivity of silicides is typically
orders of magnitude greater than that of highly doped n+ and p+ regions. Modern CMOS technologies
use silicides to reduce contact and interconnect resistances. Also, the use of SALICIDE technology
(self-aligned silicides) is a practical way to reduce poly gate resistance and source and drain sheet
resistance.
Silicidation process is invoked by depositing refractory metal layers on the exposed silicon/poly surface
and then specifying a thermal cycle in the DIFFUSE statement. There are four standard refractory
metals in ATHENA: Titanium, Tungsten, Platinum, and Cobalt. Corresponding silicides are called
TISIX, WSIX, PTSIX, and COSIX. User-defined metal and corresponding silicide can be also specified
using parameters MTTYPE and /MTTYPE in the SILICIDE statement.
The modeling and understanding of silicide growth is nowhere near as developed as for oxidation. But,
you can consider simulation of silicidation process similar to that of oxidation. It starts with insertion
of a thin (0.002 microns) initial layer of silicide on the boundary between silicon (or polysilicon) and
corresponding metal. During each time step, growth velocities are calculated for each point at both
metal-silicide and silicon (or polysilicon)-silicide interfaces. The growth velocity at the ith interface
point is calculated as follows:
dx i
n in
------- = k i C i -------dt
N 1i
3-172
where ki is the interface reaction rate coefficient, N1i is the number of silicon or metal molecules per
unit silicide material, and Ci is the silicon or metal concentration. nin is the interface normal vector
which points towards the silicon-poly or metal side. Similarly to oxidation, this equation can be solved
by applying an initial boundary condition xi = x0 at t = 0. The solution is
2
xi
xi
- = t+τ
------- + ----------B
B⁄A
3-173
B = ( 2D i C i ) ⁄ N 1i and B ⁄ A = ( k i C i ) ⁄ N 1i are equivalent to Deal-Grove
coefficients of classical oxidation model. The silicide growth data indicates that for most silicides the
rate limiting step is diffusion of silicon. This simplifies the Equation 3-174 to
where parameters
2
xi
= Bt
3-174
The silicide growth rates parameters are extracted from experimental data for TiSi2 [41], [42] and
CoSi2 [43]. For two other standard silicides PTSIX and WSIX as well as for user-defined Silicides the
TiSi2 growth rates are used. The silicide growth rates can be modified by varying parameters D.0 and
D.E for silicon (or interstitial) diffusivity in silicide Di, which are specified in the INTERSTITIAL
statement. Defaults are D.0=1.96 and D.E=1.81 for all silicides.
Silicide formation usually leads to a large volume decrease. The ratio between consumed volumes of
silicon and metal and resultant volume of silicide are specified by ALPHA parameters in the SILICIDE
statement. The default values for the ALPHA parameter are taken from [44].
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Silvaco
SSUPREM4 Models
The 2D movement of growth interfaces and volume change cause the viscous flow of the silicide layer.
This silicide flow is modeled analogously to the compress model of oxidation, where the equations
solved are:
2
µ∇ V = ∇ P
3-175
1 – 2v
∇ ⋅ V = –  --------------- P
µ
3-176
E
µ = --------------------
3-177
2(1 + v)
where:
• V is the velocity.
• P is the pressure.
• µ is the viscosity.
• v is Poisson’s ratio.
• E is Young’s modulus.
The parameters v and E are specified using the POISS.R and YOUNG.M parameters in the MATERIAL
statement.
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3.5: Ion Implantation Models
ATHENA uses analytical and statistical techniques to model ion implantation. By default, the analytic
models are used. Analytical models are based on the reconstruction of implant profiles from the
calculated or measured distribution moments. The statistical technique uses the physically based
Monte Carlo calculation of ion trajectories to calculate the final distribution of stopped particles.
3.5.1: Analytic Implant Models
ATHENA uses spatial moments to calculate ion implantation distributions. This calculation method is
based on range concepts from “Range Concepts and Heavy Ion Ranges” [45] in which an ionimplantation profile is constructed from a previously prepared (calculated or measured) set of
moments. A 2D-distribution could be essentially considered a convolution of a longitudinal (along the
implant direction) 1D-distribution and a transverse (perpendicular to implant direction) 1Ddistribution.
In the rest of this section, we will first describe three 1D implant models and the method used to
calculate 1D profiles in multi-layered structures. Then, two models of transverse (lateral) distribution
and a method of construction of 2D implant profiles will be outlined. Finally, three methods of implant
parameter specification will be described.
Gaussian Implant Model
There are several ways to construct 1D profiles. The simplest way is using the Gaussian distribution,
which is specified by the GAUSS parameter in the IMPLANT statement:
2
–( x – Rp )
φ - exp -------------------------C ( x ) = --------------------2
2 π∆ R ρ
2∆Rp
3-178
where φ is the ion dose per square centimeter specified by the DOSE parameter. Rp is the projected
range. ∆ Rp is the projected range straggling or standard deviation.
Pearson Implant Model
Generally, the Gaussian distribution is inadequate because real profiles are asymmetrical in most
cases. The simplest and most widely approved method for calculation of asymmetrical ionimplantation profiles is the Pearson distribution, particularly the Pearson IV function. ATHENA uses
this function to obtain longitudinal implantation profiles.
The Pearson function refers to a family of distribution curves that result as a consequence of solving
the following differential equation:
df
( x ) = ----------------------------------------( x – a )f ( x ) -----------dx
2
b0 + b1 x + b2 x
3-179
in which f(x) is the frequency function. The constants a, b0, b1 and b2 are related to the moments of f(x)
by:
∆ Rp γ ( β + 3 )
a = – -------------------------------A
3-180
2
2
∆R p (4β – 3γ )
b 0 = – ----------------------------------------A
b1 = a
3-181
3-66
3-182
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SSUPREM4 Models
b
2
2 β – γ – 6-------------------------=
–
2
A
where A = 10 β - 12 γ
3-183
2
- 18,
γ and β are the skewness and kurtosis respectively.
These Pearson distribution parameters are directly related to the four moments ( µ , µ , µ , µ ) of the
1 2 3 4
distribution f(x):
R
= µ
1
p
∆ Rp =
µ3
γ = ---------
µ2
3
Rp
µ4
β = ---------
3-184
4
Rp
µ i is given by:
∞
µ1 =
∫ xf ( x ) dx
3-185
–∞
∞
µi =
i
∫ ( x – R p ) f ( x ) dx
i = 2, 3, 4
3-186
–∞
The forms of the solution of the Pearson Differential Equation depend upon the nature of the roots in
the equation b0+b1x+b2x2=0. There are various shapes of the Pearson curves. You can find the
complete classification of various Pearson curves found in “Atomic and Ion Collision in Solids and at
Surfaces” [46]. Obviously, only bell-shaped curves are applicable to ion implantation profiles. It is
readily shown by Ashworth, Oven, and Mundin [47] that f(x) has a maximum when b0+b1x+b2x2 < 0.
You can reformulate this as the following relation between β and
1 ⁄ 2
 2
6
4
2
9  ( 6 γ + 5 ) + [ ( 9 γ ) ⁄ 16 + 8 γ + 25 ( γ + 1 ) ] 

β > -------------------------------------------------------------------------------------------------------------------------------2
50 – γ
with the additional constraint that
γ:
3-187
2
γ <50.
Only Pearson type IV has a single maximum at x = a+Rp and monotonic decay to zero on both sides of
the distribution. Therefore, Pearson type IV is usually used for ion implantation profiles; it is the
solution of Equation 3-178 when the following conditions are satisfied:
3⁄2
2
2
39 γ + 48 + 6 ( γ + 4 )
β = ---------------------------------------------------------------2
32 – γ
Silvaco
and
2
0 < γ < 32
3-188
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ATHENA User’s Manual
This gives the following formula for Pearson IV distribution:
f(x) = K b + b (x – R ) + b (x – R )
0
1
p
2
p
2
1-------2b 2
b1
------ + 2a
 2b ( x – R ) + b 
b2
2
p
2
exp – ----------------------------------atan  -------------------------------------------


2
2
 4b b – b

4b 1 b 2 – b 1
1
1 2
3-189
where K is defined by the constraint:
∞
∫ f ( x ) dx = 1 .
3-190
–∞
2
In the narrow area of β – γ plane where Pearson IV type criterion (Equation 3-188) is not satisfied
while bell-shaped profile criterion (Equation 3-187) holds ATHENA, by default, uses other than type IV
Pearson functions. These functions are bell-shaped but they are not specified over the whole ( [ – ∞, ∞ ] )
interval. Usually, this doesn’t affect the quality of calculated profiles because the limits of these
functions are situated far from their maximums. If you want to use only Pearson-IV distribution, set
the ANY.PEARSON parameter to FALSE. In all cases when
β and γ do not satisfy one of the mentioned
β up to the value that satisfies the criterion used. In the
standard Pearson model, the longitudinal dopant concentration is proportional to the ion dose φ :
criteria, ATHENA will automatically increase
C(x) = φf(x)
3-191
This single Pearson approach (method) has been proved to give an adequate solution for many ion/
substrate/energy/dose combinations. But, there are many cases when the channeling effects make the
Single Pearson Method inadequate.
Dual Pearson Model
To extend applicability of the analytical approach toward profiles heavily affected by channeling, Al
Tasch [48] suggests the dual (or Double) Pearson Method. With this method, the implant concentration
is calculated as a linear combination of two Pearson functions:
C ( x ) = φ1 f1 ( x ) + φ2 f2 ( x )
3-192
where the dose is represented by each Pearson function f1,2(x). f1(x) and f2(x) are both normalized, each
with its own set of moments. The first Pearson function represents the random scattering part (around
the peak of the profile) and the second function represents the channeling tail region. Equation 3-191
can be restated as:
C ( x ) = φ [ ℜ f 1 ( x ) + ( 1 – ℜ )f 2 ( x ) ]
3-193
where φ = φ 1 + φ 2 is the total implantation dose and ℜ = φ 1 ⁄ φ .
To use dual Pearson distribution, supply nine parameters— four moments for each Pearson function
with the dose ratio ℜ . The dual Pearson model will be used only when all nine parameters are present
(see the “Specification of Implant Parameters in the Moments Statement” on page 3-76) and the
AMORPHOUS parameter is not specified in the IMPLANT statement (the default is CRYSTAL). Otherwise,
the single Pearson formula will be used.
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SSUPREM4 Models
SIMS-Verified Dual Pearson (SVDP) Model
By default, ATHENA uses SIMS-Verified Dual Pearson (SVDP) implant models. These are based on the
tables from the University of Texas at Austin. These tables contain dual Pearson moments for B, BF2,
P, and As extracted from high quality implantation experiments are also conducted by the University
of Texas at Austin. Table 3-7 show these implantation tables contain dose, energy, tilt, rotation angle,
and screen oxide thickness dependence.
Table 3-7. Range of Validity of the SVDP Model in ATHENA
Ions
Energy (keV)
Dose (cm-2)
Tilt Angle(°)
Rotation Angle(°)
Screen Oxide (Å)
B
1  100a
1013  8×1015
0  10
0  360
native oxide  500b
BF2
1  80c
1013  8×1015
0  10
0  360
native oxide
P
12  200d
1013  8×1015
0  10
0  360
native oxide
As
1  200e
1013  8×1015
0  10
0  360
native oxide
a
Experimentally verified for 5-80keV. For energy range, 1-5keV, an interpolation between 5keV and 0.5keV calculated with UT-MARLOWE, is
used; an extrapolation is used for energy range 80± 100keV.
b Only for 15-80keV.
c Experimentally verified for 5-65keV. For energy ranges, 1-5keV and 65-80keV, the same procedures is used for boron.
d Experimentally verified for 15-80keV. Numerical extrapolation is outside this energy range.
e Experimentally verified for 5-180keV. Interpolation between 5keV and UT-MARLOWE calculated profile at 0.5keV.
If you choose a simulation outside the parameter ranges, described in Table 3-7, ATHENA will not use
the Dual Pearson Implant SVDP Models but will use the standard tables instead. When using the
Dual Pearson model, remember the following:
• For implant energies below 15keV, for boron, BF2 and arsenic, the simulation predicts the
dopant profiles for implants into a bare silicon surface (i.e., silicon wafer subjected to an HF etch
less than two hours before implantation). Low energy implant profiles at such low implant energies are found to be extremely sensitive to the presence of a thin (0.5-1.5nm) native oxide layer or
disordered silicon layer on the wafer surface [49]. Remember this fact when using the model for
the simulation of low energy ion implantation and when performing implantations.
• For implant energies between 10keV and 15keV, the simulations are performed for boron, BF2,
and arsenic by using an interpolation between the Dual Pearson Model parameters at 15keV, and
the Dual Pearson Model parameters at 10keV. The parameters at 15keV correspond to implantation through a native oxide layer (0.5-1.5nm), while the parameters at 10keV correspond to
implantation into a bare silicon surface (i.e., silicon wafer subjected to an HF etch less than two
hours before implantation).
• For implant energies below 5keV, the models for boron, BF2, and arsenic have not been verified
experimentally. The simulations in this range of implant energy are performed using an interpolation between experimentally verified Dual Pearson parameters at 5keV and parameters based
on UT-MARLOWE estimates at 0.5keV.
• The SIMS measurements upon which these profiles are based have a concentration sensitivity
–2
15
16
to 2 × 10 cm
, increasing with dose from the implant. The prolimit in the order of 5 × 10
files have been extended below these limits, following the trends that occur within the sensitivity
limits of the SIMS.
• The screen oxide thickness range has been verified from 1.5 to 40nm (only for boron and 1580keV energy range). But the oxide range has been extended to 50nm.
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Screen Oxide Thickness Parameter (S.OXIDE)
To specify screen oxide, use the S.OXIDE (µm) parameterin the IMPLANT statement. This thickness is
specified independently of any actual surface oxide in the structure. It is, however, possible to
automate the extraction of the surface oxide thickness for use with the IMPLANT statement. An
example is supplied demonstrating this.
S.OXIDE is another parameter for dual Pearson moments selection from the implant tables. It’s up to
you to select its value accordingly. The effect of this parameter is that it represents ion implantation
through a thin (0÷50nm) surface oxide layer. The present algorithm in ATHENA when encountering a
multi-layered structure (see Section 3.5.2: “Multi-Layer Implants”). For example, oxide/silicon
switches to multi-material scaling technique for evaluating the depth profile. This technique will
combine two profiles — single Pearson for the oxide and dual Pearson for silicon with S.OXIDE
preferably set to the thickness of the oxide.
There are two reasons why this separation between the surface oxide is present in the structure before
the IMPLANT statement and the S.OXIDE parameter. The first reason is because the flexibility of using
this parameter for different thin surface layers other than oxide (with appropriate scaling of their
thickness for stopping). The second reason the currently restricted availability of moments with screen
oxide in the tables (0÷50nm, 15÷80keV and for boron only). If you need a more precise dependence of
the implantation profiles on the surface screen oxide, use a single layer of silicon with S.OXIDE set to
an appropriate value.
3.5.2: Multi-Layer Implants
To apply any of the described analytical distribution functions for structures that are comprised from
several different material layers, use a scaling method that’s mentioned in this section. This is because
stopping powers and range parameters are different in different materials. This section will describe
the implant scaling methods available in ATHENA.
DOSE.MATCH
The Dose-Matching Method was historically the first and is the most widely used [50] method. The
Dose-Matching Method is selected by the DOSE.MATCH parameter (default) in the IMPLANT statement.
With this method, the segment of the profile within ith layer is calculated by:
C i ( x ) = φ f ( x – x t + x eff )
3-194
where f(x) is the distribution function specified for this implant (Gaussian, Pearson, or Dual Pearson)
with moments corresponding to the ith layer; xt is the distance from the surface to the top of the ith
layer:
k≤i–1
xt =
∑
tk
3-195
k=1
xt is the thickness of the kth layer; xeff is the effective thickness evaluated from:
x eff
∫
k≤i–1
C i ( x ) dx =
0
where
∑
Φk
3-196
k=1
φ k is the portion of the total implant dose, which is consumed in the kth layer. Obviously, for the
first layer xeff = 0 and xt = 0.
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Silvaco
SSUPREM4 Models
RP.SCALE and MAX.SCALE
The other two methods for analytical calculation of implantation profiles in the layered structures are
projected range depth scaling (set by RP.EFF or RP.SCAL in the IMPLANT statement) and maximal
depth scaling (set by the MAX.SCALE parameter). These two methods differ from the dose-matching
method in the way the effective depth xeff is calculated and in the normalization of the partial profiles
in the layers. Like in the dose-matching method, the distribution in the first layer is calculated directly
from the moments corresponding to the first layer without any corrections. For subsequent layers, the
implant distribution is calculated by the formulae:
C ( x ) = Nf ( x – x + x )
i
t
eff
3-197
and
 i–1



N= φ–
Φ k ⁄ φ i


 k=1 
∑
where N is the normalization factor,
3-198
φ is the total implantation dose, and xeff is the effective depth
calculated as follows. In the case of projected range scaling, xeff for the ith layer is:
i–1
∑
x eff =
k=1
where
tk k + 1
--------R
k p
Rp
3-199
k
R p is the projected range of the specified ion in the material of the kth layer. For the case of the
maximal range scaling, xeff is calculated as:
i–1
x eff =
∑
tk
k=1 
k+1
+ 3∆R p
---------------------------------R

k
k  p
Rp + 3 ∆ Rp
3-200
k=1
k
where ∆ R p is the projected range straggling in the kth layer. In this approximation, the estimated
maximum ion range R p + 3 ∆ R p is taken as the measure of the ion penetration into the corresponding
material.
MOM.SCALE
In all three models described above, the range parameters in each layer are considered independent of
the presence of other layers. But obviously, the distribution of ions stopped in the deeper layers may
depend on the thickness and stopping characteristics of the upper layers because each ion trajectory
passes through these upper layers. The Moment Correction Method set by the MOM.SCALE parameter
of the IMPLANT statement partially accounts for this effect. In the SCALE.MOM, method the projected
range and range straggling in the layer are normalized according to the probability for the ion to
penetrating into the layer. The only available measure of the probability is the portion of the dose
accumulated in the specific layer. Therefore, the corrected projected range Rpc and range straggling
∆ R pc in the ith layer are calculated as follows:
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ATHENA User’s Manual
i–1
i
R
= φ Rp +
pc
i
k
∑
φ k Rp
3-201
k=1
i–1
R
pc
i
= φ i Rp +
k
∑
φ k Rp
3-202
k=1
where
i–1
φi = φ –
∑
φk
3-203
k=1
You can use the SCALE.MOM parameter together with any of three depth matching methods.
3.5.3: Creating Two-Dimensional Implant Profiles
Convolution Method
ATHENA calculates 2D implant profiles using a convolution method described as follows. First, it
calculates the implantation direction within the simulation plane using the TILT
θ and ROTATION ϕ
θ is the angle between the ion beam direction
and y-axis, ϕ is the angle between ion beam direction and the simulation plane. For example, ϕ = 0°
and θ > 0° correspond to an ion beam parallel to the simulation plane and directed toward the lowerright corner of the simulation area. The case of ϕ = 90° and θ > 0° correspond to an ion beam in the
angle parameters specified in the IMPLANT statement.
plane perpendicular to the simulation plane and directed from behind the simulation plane. The
effective implantation angle in the simulation plane could be found from
tan ( α ) = tan ( θ ) cos ( ϕ )
3-204
When the FULLROTAT parameter is specified in the IMPLANT statement ATHENA calculates
superposition of 24 implants with rotation angles equal to (15n)° and doses equal to
ϕ /24.
The implantation front (perpendicular to the α direction) is divided into a number of slices Ns (usually
> 100) of width a. The implant concentration in each grid point, i, with coordinates (xi, yi) is calculated
by the summation of contributions from each slice, k:
C ( x i, y i ) =
∑
C k ( x i, y i )
3-205
1 ≤ k ≤ Ns
The contribution from each slice Ck is calculated by integration of the point source 2D frequency
function F2D(x,y) (with the starting point at the intersection of the normal n to the central of the slice
with the structure surface) over slice width:
a⁄2
C k ( x i, y i ) = φ
∫
f 2D ( d i, t i ) dt
3-206
–a ⁄ 2
3-72
Silvaco
SSUPREM4 Models
where di is the depth along implant direction (i.e., distance between the starting point and the
projection of the point i on the vector n) and ti is the transversal distance (i.e., distance between the
point i and the vector n). See Figure 3-21.
Figure 3-21: Integration Geometry for the Convolution Method
Depth-Independent Lateral Distribution
The simplest type of the 2D frequency function is a product of longitudinal function fl(x), which can be
a Gaussian (Equation 3-178), Pearson (Equation 3-191), Dual-Pearson (Equation 3-193), and depthindependent transversal function ft(y). See Equation 3-207.
f 2D ( x, y ) = f l ( x )f t ( y )
3-207
This approximation is used in ATHENA by default. Obviously, the function ft(y) must be symmetrical
and have a bell shape.
Gaussian Lateral Distribution Function
The traditional selection for this function is a Gaussian. ATHENA uses the Gaussian approximation
unless the transversal kurtosis
β y (KURTT in the MOMENTS statement) is specified to be different from
its default value of 3.0. In this case, Equation 3-206 can be easily integrated into the following
equation:
ti – a ⁄ 2
ti + a ⁄ 2
C ( x i, y i ) = 1--- φ f l ( d i ) erfc ------------------ – erfc -------------------2
2∆Y
2∆Y
where
∆Y is the transversal (lateral) standard deviation defined from:
∞
∆Y =
3-208
∫ ∫ f2D ( x, y )y
2
dx dy
3-209
–∞
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ATHENA User’s Manual
Specification of Lateral Standard Deviation
You can specify Lateral Standard Deviation (LSTD.DEV or LDRP) together with other moments in the
MOMENTS statement (see the“Specification of Implant Parameters in the Moments Statement” on page
3-76). You can also control it with the LAT.RATIO1 parameter in the IMPLANT statement.
LAT.RATIO1 is the ratio between
∆Y and ∆R p which is equal to 1.0 by default. This means that if
the lateral standard deviation and LAT.RATIO1 are not specified it will be equal to projected range
straggling
∆R p . In the case of dual Pearson model for longitudinal profile, corresponding parameters,
SLSTD.DEV or SLDRP and LAT.RATIO2 are used. The only difference is that the default for
LAT.RATIO2 is 0.2. This is because the channelled portion of a 2D profile is obviously very narrow.
Parabolic Approximation of Depth-Dependent Lateral Distribution
It has been shown [51], [52], [53] and [54] that in general, the transversal function ft(y) is not
independent of depth because there is considerable correlation between transversal and longitudinal
motion of the implanted ions. This correlation could be taken into account by using a transversal
function with the depth-dependent lateral standard deviation
σ y ( x ) . As it was shown in [52] and [54],
if the spatial moments up to fourth order are used, the best approximation for
σ y ( x ) is the parabolic
function:
2
σ y ( x ) = c0 + c1 ( x – Rp ) + c2 ( x – Rp )
2
3-210
In order to find the coefficients of the function two additional spatial moments should be used. These
are mixed skewness:
∞
γ xy =
∫ ∫ f2D ( x, y ) ( x – Rp )y
2
dx dy
3-211
2 2
y dx dy
3-212
–∞
and mixed kurtosis:
∞
β xy =
∫ ∫ f2D ( x, y ) ( x – Rp )
–∞
The c0, c1, and c2 parameters can be found by substituting Equation 3-207 into Equations 3-209, 3-211,
and 3-212 and taking into account in Equations 3-180—3-186, while integrating over x. This results in
the system of equations where you can find the following relations.
3-74
2
c0 = ∆ Y ( 1 – B )
3-213
2
∆Y ( γ – γB )
c 1 = ---------∆ R p xy
3-214
2
∆Y -B
c 2 = ------------2
∆R p
3-215
Silvaco
SSUPREM4 Models
where:
β xy – 1 – γγ xy
B = ---------------------------------2
β–1–γ
3-216
This parabolic approximation for depth-dependent ft will be used if the FULL.LAT parameter is used in
the IMPLANT statement and when mixed spatial moments:
γ xy (SKEWXY
parameter) and
β xy
(KURTXY parameter) are non-zeros. In the case of the Dual Pearson longitudinal function, the mixed
spatial moments for the second Pearson, SSKEWXY and SKURTXY, can be also specified. The values of
spatial moments are not yet included in the default moments tables and should be specified in the
MOMENTS statement (see the “Specification of Implant Parameters in the Moments Statement” on page
3-76).
Non-Gaussian Lateral Distribution Functions
Detailed Monte Carlo simulations [55] and [56] also show that in most cases, transversal distribution
function, ft, is not Gaussian. In other words, the transversal kurtosis
β y is calculated as
∞
βy =
∫∫ f2D ( x, y )y
4
dx dy
3-217
–∞
and is not always equal to 3.0 and also depends on depth. Several non-Gaussian transversal
distribution functions were examined in [46]. Their conclusions were as follows. The symmetrical
Pearson functions (type II for β y ≤ 3 and type VII when β y > 3) are acceptable, providing an
agreement with amorphous Monte Carlo simulations and have computational advantage because they
can be integrated over x in a closed form through incomplete beta functions [57].
Another good alternative for transversal distribution function is the Modified Gaussian Function
(MGF) suggested in [55]. It is shown in [57] that it also can be integrated in the close form through the
incomplete gamma function. Selection of transversal distribution function is subjective because it is
based on comparison with the lateral cross-section of the 2D Monte Carlo distributions, which cause
accuracy to diminish further away from its maximum. The analysis of [56] based on the BCA
simulation (see Section 3.5.4: “Monte Carlo Implants”) showed that when β y ≤ 2.5 ÷ 2.8 , which
usually happens for random part of the 2D distribution or for amorphous implants, the Pearson type II
function slightly underestimates concentrations obtained in the BCA calculations while the MGF
slightly overestimates these concentrations. Therefore, it was decided to use in ATHENA an average
between the Pearson type II and the MGF for all β < 3 . When β = 3 both functions reduce to
y
y
standard Gaussian. Finally, in the case of higher values of lateral kurtosis it was found [56] that the
MGF appears to be a better approximation, so it is used in ATHENA.
It is very difficult to find β y ( x ) as was done for σ y ( x ) already mentioned, because the spatial moments
of fifth and sixth order would be needed to build analytical functions for β ( x ) . Therefore, ATHENA
y
uses constant β y (the KURTT and SKURTT parameters for the first and second Pearson functions,
correspondingly) when you specify the FULL.LAT model in the IMPLANT statement. The generic
approximations [56] for σ ( x ) (instead of Equation 3-210) and for β ( x ) will be implemented in future
y
y
when more complete tables of lateral parameters will be generated using Monte Carlo simulations.
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Specification of Implant Parameters in the Moments Statement
As mentioned previously, the analytical ion implantation simulations strongly depend on the input
parameters (moments). ATHENA provides several ways of implant parameter specification. They are:
look-up tables, user-defined look-up tables, and the MOMENTS statement.
Two types of look-up tables are currently provided with ATHENA. The files containing the tables are in
ASCII format and can be found in the <install>/lib/athena/<>version>/common/implant-tables
directory. The first type are standard tables (std-tables file) containing parameters for most ionmaterial combinations used in ATHENA. These are longitudinal parameters for the single Pearson
distribution in the energy interval 10keV to 1MeV. The energy interval is extended to 1keV÷8MeV for
B, P, and As in silicon, silicon oxide, polysilicon, and silicon nitride. These tables also include a limited
set of parameters for the dual-Pearson function (only for B and BF2 in the energy interval 10÷100keV,
tilt angle 7°, rotation angle 30°, and native oxide as well as with simple interpolation of the dose ratio
parameter ℜ between different doses). Parameters for the FULL.LAT model are provided only for B
implants in silicon. They are based on the spatial moment calculations in amorphous silicon as in [58],
[59]. The auxiliary file userimp in the <install>/lib/athena/<version>/common directory provides a
template for specifying implant parameters in the format of standard tables. The second type of lookup tables are SVDP tables described in the “Dual Pearson Model” on page 3-68. The format of these
tables is much more flexible than the format of the standard tables. It also allows parameters for
lateral distribution to be added easily.
The SVDP tables are used by default. If no moments are found, ATHENA will search through standard
tables. If it cannot find parameters for a specified energy/ion/material combination, a warning message
is issued, which will tell you a very small projected range and straggling will be used in simulation for
this combination. The message will also suggest that you use the Monte Carlo method in order to find
the right moments. This is the sequence of ATHENA actions in the case when no MOMENTS statement
precede the current IMPLANT statement. The MOMENTS statement serves to control the moment
parameters/tables to be used in subsequent IMPLANT statements. If you specify the STD_TABLES
parameter, ATHENA will skip searching through SVDP tables and proceed directly to the standard
tables. If you specify the USER_STDT or USER_SVDPT parameter, then the user-defined file specified
with the USER.TABLE=<filename> parameter will be used as the first choice. Of course, if the
moments are not found in the specified file, ATHENA will proceed to the standard tables. Finally, the
set of MOMENTS statement can be used to specify all spatial moments for any ion/material/energy/dose
combination. ATHENA will use parameters from this set before proceeding to a standard search
sequence. If the moments for certain implant conditions are unavailable, then you can use the Monte
Carlo simulation for these conditions.
Using PRINT.MOM for Extraction of Spatial Moments
The PRINT.MOM parameter in the IMPLANT statement prints the calculated (or extracted from the
tables) moments into output and also saves the moments in the standard structure file. The last
capability allows you to use the extract (EXTRACT statement) and substitution functions of DECKBUILD
for automatic generation of the MOMENTS statement. If spatial (lateral and mixed) moments need to be
found from Monte Carlo calculation, use the IMPCT.POINT parameter because it forces all trajectories
to be started in one point. This not only allows the spatial moments to be found, but also the building
of a Monte Carlo calculated source-point 2D distribution function, which can be useful for comparison
purposes.
3.5.4: Monte Carlo Implants
The analytical models described in the previous section give very good results when applied to ion
implantation into simple planar structures (bare silicon or silicon covered with thin layer of other
material). But for structures containing many non-planar layers (material regions) and for the cases,
which have not been studied yet experimentally requires more sophisticated simulation models. The
most flexible and universal approach to simulate ion implantation in non-standard conditions is the
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Monte Carlo Technique. This approach allows calculation of implantation profiles in an arbitrary
structure with accuracy comparable to the accuracy of analytical models for a single layer structure.
ATHENA contains two models for Monte-Carlo simulation of ion implantation: Amorphous Material
Model and Crystalline Material Model. Both of them are based on the Binary Collision Approximation
(BCA) and apply different approximations to the material structure and ion propagation through it.
Nature of the Physical problem
A beam of fast ions (energy range, approximately 50 eV/amu to 100 keV/amu) entering crystalline or
amorphous solid is slowed down and scattered due to nuclear collisions and electronic interaction.
Along its path, an individual projectile may create fast recoil atoms that can initiate collision cascades
of moving target atoms. These can either leave the surface (be sputtered) or deposited on a site
different from their original one. Together with the projectiles being deposited in the substrate, this
results in local compositional changes, damage creation and finally amorphization of the target.
Depending on the crystal orientation or the direction of the beam or both, the implanted projectiles
and the damage created by them has different spatial distribution. With even more higher fluency,
these phenomena will cause collisional mixing in a layered substances, changes of the surface
composition due to preferential sputtering, and the establishment of a stationary range profile of the
implanted ions.
Method of Solution
The paths of the individual moving particles and their collisions are modeled by means of the binary
collision approximation for a crystalline, polycrystalline and amorphous substance, using a screened
Coulomb potential for the nuclear collisions and a combination of local and non-local free-electron-gas
approximation for the electronic energy loss. For each nuclear collision, the impact parameter and the
Azimuthal Deflection Angle are determined according to the crystal structure using its translational
symmetry. For amorphous materials, the impact parameter and the azimuthal deflection angle are
determined from random numbers. A proper scaling is chosen so that each incident projectile (pseudoprojectile) represents an interval of implantation dose. Subsequent to the termination of each pseudoprojectile and its associated collision cascades, the local concentrations of the implanted species,
created vacancies and interstitials are calculated according to the density of the matrix.
Nuclear Stopping
As mentioned before, during their passage through matter ions interact not only with the atoms from
the lattice but also with the electrons. Figure 3-22 shows the scattering geometry of two particles in
the Laboratory Co-ordinate System. In the computational model, it is assumed that ions from one
deflection point to the next move along straight-line segments, these being the asymptotes of their
paths. At each collision, ion loses energy through quasielastic scattering by a lattice atom and by an
essentially separate electron energy loss part.
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Figure 3-22: The trajectories of the ion (projectile) and the lattice atom (recoil).
The scattering angles of the projectile and the recoil are as follows:
tan ϑ 1 = Af sin θ ⁄ ( 1 + Af cos θ )
3-218
tan ϑ 2 = f sin θ ⁄ ( 1 + f cos θ )
3-219
where:
f =
1 – Q ⁄ Er
3-220
Q is the energy lost by electron excitation.
A = M 2 ⁄ M 1 is the ratio of the mass of the target (scattering) atom to that of the projectile
(implanted ion).
θ is the barycentric scattering angle calculated as follows:
θ = π – 2p
∞
1
- dr
∫R --------------2
3-221
r g(r)
where:
g(r) =
3-78
2
( r -)
---------1 – p------ – V
2
Er
r
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SSUPREM4 Models
where:
• p is the impact parameter,
E = AE ⁄ ( 1 + A ) is the relative kinetic energy,
r
0
•
• E
0
is the incident energy of the projectile,
• r is interatomic separation,
• V ( r ) is the interatomic potential,
• R is defined from equation
g( R) = 0 .
In ATHENA, the intersections of the incoming and outgoing asymptotes are evaluated with the hard
core approximation of the time integral:
x 1 = p tan ( θ ⁄ 2 )
3-222
x2 = 0
3-223
Interatomic Potential
ATHENA uses two-body screened Coulomb potentials with a screening function, which is a numerical
fit to the solution given by Firsov [60]. It also preserves the same analytic form as for the isolated
atom:
2
Z1 Z2 e
r
V ( r ) = ------------------- χ  ------
a 
r
0
3-224
where Z1 and Z2 are the atomic numbers of the two atoms and
a 0 = 0.8853a B Z
a 0 is the screening length defined by
–1 ⁄ 3
3-225
where Z is an ‘average’ atomic number of the two atoms calculated as
Z
–1 ⁄ 3
0.23
0.23
=  Z1
+ Z2


–1
M .
The main drawback of these two-body potentials is their relatively slow decay as r
3-226
→ ∞ . The
screening parameter, a 0 , is often regarded as an adjustable parameter for each two-body combination,
which can be matched either to self-consistent field calculations or to experimental data. ATHENA uses
the screening function in the form
4
χ =
∑ ai exp ( –bi x )
3-227
i=1
where a i and b i are taken from [61].
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Electronic Stopping
Electronic stopping used in the simulation consists of two essentially separate mechanisms for
inelastic energy losses: local and non-local. These two types of electronic stopping are quite different in
nature and behavior -- they have different energy and spatial dependencies [62]. The local inelastic
energy losses are based on the model proposed by Firsov [63]. In this model, the estimation of the
electronic energy loss per collision is based on an assumption of a quasi-classical picture of the
electrons (i.e., the average energy of excitation of electron shells, and electron distribution and motion
according to the Thomas-Fermi model of the atom).
In this quasi-classical picture, the transfer of energy, ∆ E , from the ion, to the atom, is due to the
passage of electrons from one particle to the other. Thus, resulting in a change of the momentum of the
ion (proportional to its velocity , υ , and a rising of a retarding force acting on the ion). When ions move
away from the atom (despite being trapped by ions) electrons will return to the atom. There is no
transfer of momentum calculated back, because the electrons fail in higher energy levels. The energy
loss in the Firsov's Model is calculated as follows:
5⁄3
0.05973 × ( Z 1 + Z 2 )
E ⁄ M1
– ∆ E = ------------------------------------------------------------------------------eV
5
1⁄3
( 1 + 0.31 ( Z 1 + Z 2 ) R 0 )
3-228
where:
°
R 0 is their distance of closest approach in A , which is approximately equal to the impact
•
parameter in case of small-angle collisions.
•
E is the energy of the moving atom (the ion) in eV.
•
M 1 is its mass in a.m.u.
In a binary collision, the scattering angles are affected by the inelastic energy loss ∆ E (see Equation 3228) through the parameter f .
The non-local electronic energy losses are based on the model proposed by Brandt and Kitagawa [64].
dE
Their stopping power, S = – -------- , of the medium for an ion is in the first approximation proportional to
dx
a mean-square effective ion charge. They derive the effective stopping power charge of a projectile,
Z∗1 from a given ionization state, q. If a fractional effective charge of an ion with the given ionization
state, q is defined as
Z∗
Z1
S
q
1 - = -----------ζ ½ -------
1⁄2
3-229
Sq = 1
where S q = 1 is the stopping power for bare nucleus. Brandt and Kitagawa theories produces the
following simple expression for the fractional effective charge of an ion:
2
ζ ≈ q + C ( k F ) ( 1 – q ) ln ( 1 + ( 2 Λ v F a 0 v 0 ) )
3-230
where:
•
3-80
q = ( Z 1 – N ) ⁄ Z 1 is the fractional ionization,
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•
N is the number of electrons still bond to the projectile nucleus,
•
a
•
k
0
F
and r
are Bohr's radius and velocity,
0
and v
F
are Fermi wave vector and velocity.
For the screening radius
becomes:
Λ , Brandt and Kitagawa assume exponential electron distribution, which
2⁄3
0.48N
Λ = ------------------------------------------
3-231
Z 1 ( 1 – N ⁄ ( 7N 1 ) )
The only undefined quantity, C, is of about 0.5 and somewhat depends on the target. The degree of
ionization, q, can be expressed as
 – 0.92v r
-
q = 1 – exp  -----------------2⁄3
 v0 Z1 
3-232
where v r ≡ 〈 v 1 – v e 〉 is the relative velocity between the projectile and the target electrons, which
are calculated as follows:
2
 2v 1  1  v 1
3v
- – ------ ----v r = -------F- 1 +  ---------4
 3v2  15  v F
for
v1 < vF
3-233
F
2
vF 
v r = v 1  1 + -------2

5v 
for
v1
≥ vF
1
3-234
Damage Accumulation Model
The present model includes dynamic processes of the transformation from crystalline to amorphous
state as ion implantation proceeds. Each pseudo-projectile in the simulation represents a portion of the
real dose
Φ , where N
is the number of projectiles.
Φ∆Φ = ---
3-235
N
The deposited energy is accounted for each grid point of the target and accumulated with the number
of projectiles. As the implantation proceeds, deposited energy increases and the crystalline structure
gradually turns into an amorphous structure. This is quantified by the Amorphization Probability
Function as follows:
∆E( r)
f ( r ) = 1 – exp --------------Ec
Here,
∆E(r)
is the energy deposited per unit volume at the grid point r, and
3-236
E c is the critical energy
density, which represents the deposition energy per unit volume needed to amorphize the structure in
the relevant volume.
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It is defined as:
E 0 ( T – T ) – 2

∞
E c ( T ) = E c0  1 – exp ---------------------------- 
2k
TT
B

∞ 
3-237
where E is activation energy, k B is Boltzmann's constant, and T ∞ is the temperature at and above
which the infinite dose is required for crystalline to amorphous transition.
Some experimental values for E c ( E c0 ) are given by F. L Vook [65]. In the BCA module, the value
f(r)=0.6 corresponds to a fully amorphized state and any additional energy deposited at point r does
not contribute to the amorphization process.
Implantation Geometry
Figure 3-23 shows the orientation of the ion beam, relative to the crystallographic orientation of the
substrate. There three major planes regarding ion implantation in crystalline materials, mainly:
• the implantation plane α,
• the surface plane Σ,
• and the simulation plane β.
The implantation plane is where the initial beam of incoming ions lays in. It equivocally defines the
direction of the incoming beam -- tilt and rotation. If the orientation of the surface plane is [100],
which is the only substrate orientation available currently in the Binary Collision approximation
implantation module (BCA or CRYSTAL parameters), the offset of the rotation angle is the direction
<101> on this plane. This means that the tilt angle, ϑ, specified by the TILT parameter in the
IMPLANT statement will be the polar angle in laying this plane, while the rotation angle, ϕ, specified
by the rotation parameter will be the difference of azimuths of the line where the implantation plane,
α, crosses the surface plane, Σ, and the direction <101>. See Figure 3-23.
Note: Presently, the surface orientation (the ORIENT parameter in the INITIALIZE statement) does not have any affect in the
crystal Monte-Carlo module and the surface orientation is always {100}.
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Figure 3-23: Implantation geometry
The simulation (projection) plane is where all data regarding the simulation is projected on, which is
what finally goes into ATHENA’s structure. The orientation of the simulation plane is specified by the
ROT.SUB parameter in the INITIALIZE statement. By default, the simulation plane is oriented along
equivalent <101> direction (ROT.SUB=-45o).
In summary, the laboratory coordinate system used in the BCA implant simulation is right-hand-sided
-Y is depth, X is the other co-ordinate and Z is from the observer. The azimuth angle is measured in the
X-Z plane. ROT.SUB is relative to X. Simulation plane is X’-Y.
The simulation plane (where TONYPLOT displays results and ATHENA calculates) is always parallel to
the major flat, which is specified by ROT.SUB (-90o < ROT.SUB < 90o).
The implant calculation in bulk is 3D. Ray-tracing for BCA (i.e., calculation of ion impacts, scattering
from walls and re-implantation) is 2.5D. In other words, structure is infinitely extended in the third
dimension (along Z). All simulation results (doping, damage) are projected on the simulation plane and
appropriately scaled.
ROTATION is measured from the major flat and in ATHENA’s case from the simulation plane because it
is coupled with the wafer’s major flat.
For silicon (and other crystalline materials), you can think of TILT/ROTATION as always relative to the
simulation plane giving the same shadowing effects while ROT.SUB defines which direction the
simulation plane will slice the crystal structure through (in the laboratory coordinate system).
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Specifying different ROT.SUB will have an effect on channeling. But remember, that ion propagation is
three dimensional and there are some channeling patterns that remain the same or become stronger/
weaker because of favorable/unfavorable initial impact conditions (TILT/ROTATION/ROT.SUB
combination).
If other substrate material is used, say 4H-SiC, the simulation plane (X 'Y plane in Figure 3-23) in
ATHENA coincides with 4H-SiC ( 1100 ) crystal plane in Figure 3-24. This is specified by ROT.SUB=0.
Figure 3-24: 4H-SiC( 1100 ) Crystal Plane
If you want to specify the ( 1120 ) crystallographic plane as being the simulation X 'Y-plane in ATHENA,
then set it to ROT.SUB=90. MC Implant in ATHENA requires that ROT.SUB should be always less than
90. Therefore, you need to use other equivalent crystallographic planes, for example ( 2110 ), which
could be specified by ROT.SUB=30.
Amorphous Material Monte Carlo
In the doping of semiconductors, the rest distribution of the implantations is of principal importance.
The penetration of ions into amorphous targets is most simply described by using a Statistical
Transport Model, which is the solution of Transport Equations or Monte Carlo Simulation. Among the
two approaches, Monte Carlo is more convenient for multiple components and two or three
dimensional targets, which is partly possible because the Monte Carlo method treats an explicit
sequence of collisions, so the target composition can change on arbitrary boundaries in space and time.
The rest of the distribution is built up from a vast number of ion trajectories and the statistical
precision of which depends directly on this number: ∝ N . As the ion penetrates a solid, it
undergoes a sequence of collisions with the target atoms until it comes to rest. A simplified model of
this interactions is a sequence of instantaneous binary nuclear collisions separated by straight line
segments (free flight path lengths) over which the ion experiences continuous (non-local) electronic
energy loss. The collisions are separated (i.e., the state of an ion after a collision depends solely on the
state of the ion before the collision).
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The model assumes that the arrangement of the target atoms is totally randomized after each collision
(i.e., the target has no structure and no memory). As a result, a sequence of collisions is described by
randomly selecting the location of the next collision partner relative to the pre-flight location and
velocity direction of the ion. This means that this model cannot simulate the anomalous tail
penetration observed for implanted ions into aligned single crystal targets. The model adequately
describes the ion penetration into multilayer non-planar structures.
Crystalline Material Monte Carlo
The crystalline model used in ATHENA is based on the program CRYSTAL described elsewhere, [66]. In
order to calculate the rest distribution of the projectiles, ATHENA simulates atomic collisions in
crystalline targets using the Binary Collision Approximation (BCA). The algorithm follows out the
sequence of an energetic atomic projectiles (ions) launched from an external beam into a target. The
targets may have many material regions, each with its own crystal structure, (crystalline or
amorphous) with many kinds of atoms. The slowing-down of the projectiles is followed until they either
leave the target or their energy falls below some predefined cut-off energy.
The crystal model is invoked with the MONTE parameter in the IMPLANT statement. ATHENA will then
choose which model to use depending on the predefined crystal structure of the material. Specifying
CRYSTALLINE has no affect on the implantation and the BCA parameter is just a synonym for MONTE.
You can manipulate the implantation module to consider all materials amorphous by adding the
AMORPHOUS parameter in the IMPLANT statement. At that moment, the materials with predefined
crystal structure are Si, Ge, GaAs, SiGe, InP as well as three types of silicon carbides (3C-SiC, 4H-SiC,
and 6H-SiC) and two types of superconductors (Ba2YCu3O7 and Ba2NdCu3O7). All remaining
materials in ATHENA are considered amorphous.
Statistical Sampling
In order to reduce calculation time and improve statistical quality of simulated profiles, ATHENA
implements a three-dimensional rare event algorithm. An implantation profile can differ significantly
in concentration values across implantation depth. Low concentrations in the profile are due to low
probability of implanted species (rare events) to reach that point in space. Therefore, the number of
cascades simulated to get good statistics profile depends on the desired number of orders of magnitude
of accuracy. Even in real experiments, depending on device size, implant distributions below some
threshold concentration value could exhibit significant statistical noise.
The algorithm uses trajectory splitting to achieve increased occurrence of the rare target events by
generating several independent sub-trajectories from less rare events. The original idea [67], [68], and
[69] was first developed into a refined simulation technique by Villién-Altamirano et al., [70]. They call
their version of this approach, Restart. The basic idea is to identify subspaces from where it is more
likely to reach the target subspace where the rare event occurs. Each time these subspaces are
reached, current events sequence are split in a number of replicas all continuing from the splitting
state. The number of rare events will then increase, depending on the number of restart thresholds
defined and the number of replicas generated.
The trajectory splitting algorithm naturally fits into the problem of Monte Carlo simulation of
stopping and ranges (i.e., ion implantation). A similar method was first used by Phillips and Price to
simulate hot electron transport [71]. Yang et al. were the first ones to apply the rare event algorithm
was applied to simulation of transport phenomena of ions in matter [72]. Then, Beardmore et al.
significantly refined this algorithm [73].
A brief but comprehensive review of trajectory splitting methods used in modelling of ion implantation
is given in [74].
With the rare event trajectory splitting technique, the speed-up is due to changes in the statistical
behavior so that rare events are provoked to occur more often. The rare event algorithm in ATHENA
achieves this by identifying subspaces from where it is more likely to observe given collision event,
followed by making replicas of the cascade sequences that reach these subspaces.
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Figure 3-25 illustrates the trajectory splitting and restart of events (replicas) as a new threshold is
reached. When applying splitting to collision cascades (or any other specific system), the two things
that need to be determined are when to split and how many sub-trajectories to create when splitting.
There are different criteria that can be used to obtain the threshold states when splitting need to
occur. For example, Bohmayr et al. use a trajectory split method based on checking the local dopant
concentration at certain points [75]. Beardmore et al. rare event algorithm uses the integrated dose as
a criterion when to split [73].
ATHENA uses the same criterion to determine the splitting depths. Dose integration is carried out
along the radius vectors of ions' co-ordinates thus, roughly taking into consideration the threedimensionality of the ion distribution.
Figure 3-25: Restarting Collision Events by splitting at “m” thresholds
Due to the discrete nature of collision cascades, the number of sub-trajectories created at each split
depth should be an integer number greater or equal to two. Suppose Ti is the event at each threshold
state (i.e., this is the event of ion passing through a split depth). Suppose also the probability of an ion
being in state Ti-1 to reach the state Ti is pi=P(Ti|Ti-1). Then, the recommended number of replications
at each threshold (a split depth) is Ri=1/P. This relation gives the link between the number of
replications at each split and the criterion to identify the threshold states (i.e., the split depths).
If Ri=2, then the number of ions passing through split depth will be twice smaller the number of
particles passing through split depth. In ATHENA, the criterion to determine the split depths is the
integrated dose along the radius vectors of stopped particles, di (i.e., split depths d1, d2, d3, and so on
will be at doses 0.5φ, 0.75, 0.875φ, and so on, where φ is the total retained implant dose).
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In ATHENA, trajectory splitting is turned on with the SAMPLING command in the IMPLANT statement.
For more information this statement, see Chapter 6: “Statements”, Section 6.28: “IMPLANT”.
Theoretically, sampling estimators are unbiased and consistent. In practice, however, the estimate is
obtained as the average of finite number of samples, as opposed to the theoretical expectation, which is
obtained from the whole ensemble of sample paths, including even the very unlikely ones. Overbiasing
can occur if the only goal in mind is to increase the probability of the event that needs to be analyzed
further as is the case of trajectory splitting ion implantation simulations. The result of overbiasing is
usually the underestimation of the probability to be evaluated (dopant concentration in case of ion
implantation). In fact, it has been reported in [76] that when the splitting parameters are not
consistent with the system's large deviations behavior, the probability in question may be
underestimated by several orders of magnitude. This situation is almost present in ion implant
simulators when treating multi-layered targets and two-dimensional layouts. Therefore, use splitting
with caution.
In conclusion, you should bare in mind that:
• increasing the probability of occurrence of the event to be analyzed is not always enough to
guarantee variance reduction.
• trajectory splitting should be used carefully.
• complex implantation geometries could lead to large deviations behavior of the system, thus
overbiasing and underestimating the relevant statistics.
3.5.5: Ion Implantation Damage
Ion implantation induced crystal damage can play an important role in the various mechanisms
related to diffusion and oxidation. ATHENA includes several different types of damage formation,
which can be used in a subsequent diffusion calculation. Implantation induced damage results from
cascades of atomic collisions. If these collisions cascades are dense, it may result in the crystal lattice
becoming locally amorphized. Accurate simulation of collision cascades with simultaneous estimation
of generating various types of point defects, clusters, and spatial defects can be done only in elaborated
Binary Collision Approximation (BCA) or Molecular Dynamics (MD) simulators. Such simulations are
usually time consuming and impractical within general-purpose process simulators. Generally, the
amount of damage and distribution of defects associated with it depend on the energy, species, and
dose of implanted ions.
ATHENA includes several simple models that link various types of defect distributions with ion
implantation distributions calculated using any of the models described in previous sections.
The following types of defects can be estimated:
• Interstitial profiles
• Vacancy profiles
• {311} Clusters
• Dislocation Loops
You can describe the damage types to the simulator during the analytical ion implantation process
simulation step by scaling their distribution densities to the implanted profile.
Plus 1 Model
The first damage model is related to free point defects. Here, interstitials are scaled to the as
implanted dopant profile with the scaling parameter DAM.FACTOR=<n>. This model is invoked with
the UNIT.DAM flag on the IMPLANT line.
For example:
IMPLANT PHOS DOSE=5E14 ENERGY=45 UNIT.DAM DAM.FACTOR=0.001
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This model is known as the Plus 1 model. In the case of low implantation doses, the value for
DAM.FACTOR has been suggested to be equal to unity. Although perhaps valid at low doses, the related
and subsequent diffusion mode METHOD FULL.CPL is not required in most cases. Therefore, this
combination is an impractical approach. Recent research on RTA diffusion models (e.g., Stanford’s
{311} Cluster model) has introduced other forms of damage. Thus, lowering the dependency of free
point defects being initially set at a Plus 1 scaled profile.
The DAM.FACTOR parameter, when used with the {311} Cluster model, should have a far lower value in
the order of 0.001. Note that this is an extremely sensitive parameter when studying shallow junction
formation so use it carefully.
{311}Cluster Model
The {311} Cluster model introduces a bulk injection source of interstitials in addition to any other free
point defects sources. Clusters are introduced during ion implantation, scaled to the dopant, and
within two user-defined concentration thresholds. For example, you can scale clusters to 1.4 times the
dopant concentration but only exists between the dopant concentrations of 1e19 and 1e17 cm-3. This
allows a scalable approach, where clusters will follow implanted dopant as energies and doses vary
(see Figure 3-26). The following syntax to both switch on and control the cluster model damage scaling.
METHOD FULL.CPL CLUSTER.DAM
CLUSTER CLUST.FACT=1.4 MIN.CLUST=1e17 MAX.CLUST=1e19 PHOS
See “RTA Diffusion Modelling” on page 3-18 on how to use the {311} clusters during RTA.
Figure 3-26: Cluster Damage Control
Dislocation Loops Model
Dislocation loops can also be scaled to the as-implanted dopant profile. Loops are introduced as a
simple static band to act as an interstitial sink. Here, interstitials will be recombined at an enhanced
rate according to
Rate = damalpha   C I – C ∗I  


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Here, CI is interstitial concentration and C
∗
is equilibrium interstitial concentration.
I
Loops are placed in a band scaled to dopant concentration with the following command before
implantation.
DISLOC.LOOP MIN.LOOP=1e16 MAX.LOOP=1e18 PHOSPHORUS
The recombination rate within the loop band is controlled as follows:
INTERSTITIAL SILICON DAMALPHA=1e8
C-Interpreter Model
The C-Interpreter capabilities shown in Appendix A: “C-Interpreter” allows you to extend control over
the damage formation models described. The template for the implant damage model function is also
shown in Appendix A. The function is introduced by setting the DAM.MOD parameter in the IMPLANT
statement. The user-defined damage model introduced in the function will be used only within the
current IMPLANT statement. All subsequent implants will use the default damage models.
3.5.6: Stopping Powers in Amorphous Materials and Range Validation
Stopping powers in amorphous materials have been validated against available experiments. Figure 327 shows a validation of boron and phosphorus ranges in amorphous silicon where compiled
experimental data are taken from [61].
Figure 3-27: Comparison of Monte Carlo simulated project ranges (lines) and measured ranges (dots) for Boron
and Phosphorus in Silicon. Experiments are from [61].
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The solid lines were calculated with ATHENA’s Monte-Carlo Module. The spread of the experimental
points in Figure 3-27 is typical and cannot be avoided. For example, systematic errors due to the depth
calibrations and memory effects in SIMS measurements if accounted improperly would yield less
accurate (usually longer) ranges. Therefore, the Monte-Carlo module in ATHENA is calibrated to give
overall agreement with the available experimental data. The figure also demonstrates that there can
be a possible disagreement with individual set of measurements. Similar stopping powers validations
were performed for other important materials. The accuracy of the calculated ranges in ATHENA is
within 10% for majority of ion/material combinations, which is close to the best possible achievements
of today’s theory of stopping and ranges.
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3.6: Deposition Models
A deposition step is simulated by the DEPOSIT statement where the material and the thickness
(THICKNESS parameter) of the layer to be deposited must be specified. The deposited layer is
constructed by a simple algorithm that describes conformal deposition. In this algorithm, the whole
layer is divided into a number of sublayers with thicknesses equal to grid spacings calculated
according to the grid control algorithm (see Section 3.6.2: “Grid Control During Deposit”). Each
sublayer is deposited and triangulated separately.
More complete physically based models for deposition are available in the ELITE module as described
in Chapter 4: “ELITE Models”.
3.6.1: Deposition of Doped Layers
You can add the uniform or graded concentration of impurities or defects or both to each node of the
deposited material by using the C.BORON, F.BORON, C.INTERST parameters in the DEPOSIT
statement.
3.6.2: Grid Control During Deposit
You can control the grid inside deposited layer. The grid distribution along normal direction is
controlled by a number of divisions (the user-defined parameter, DIVISIONS) in a uniform vertical
grid. If non-uniform vertical grid is used, then specify the DY and YDY parameters in the DEPOSIT
statement.
DY specifies nominal spacing and YDY specifies the position where to apply the nominal spacing. The
spacings further from the nominal position YDY increase or decrease according to geometrical series.
The coefficients of the geometrical series are calculated so that total number of the spacings will be
equal to the DIVISIONS parameter.
When the conformal deposition algorithm fails to deposit next sublayer (which happens when
deposition occurs on the structure with narrow trenches or undercuts or both), the current spacing
divides into two and thinner layer is checked. This spacing division algorithm is applied recursively
because in these situations, the number of sublayers (divisions) actually deposited can be higher than
the number specified in DIVISIONS.
3.6.3: Epitaxy Simulation
SSUPREM4 models high temperature deposition of single crystal silicon through the EPITAXY
statement. This statement combines deposit and diffusion steps and parameters. See Chapter 6:
“Statements”, Section 6.18: “EPITAXY” for more information.
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3.7: Etching Models
Although etching is an integral process step in silicon technology, SSUPREM4 lacks a complete physical
description of etching steps. To circumvent this problem, SSUPREM4 considers etching simulation as a
purely geometrical problem. Etching is simulated as a low-temperature process. Impurity
redistribution is ignored during the etching process.
Etch steps are simulated using the ETCH statement in which the material to be etched and the
geometrical shape of the etch region are specified. It is not necessary that material to be etched be
exposed or at the top surface of the structure. There are five different ways to define an etch region:
1. A polygonal region may be defined by specifying the x and y coordinate of each vertex in the polygon. Etching will confined to that polygon only.
2. A region to the left or right of a line segment may be defined by specifying the x and y coordinates
of the end points of the line segment. Etching will then proceed from the left or right of the line
segment to the edge of the structure.
3. A region between the top boundary of the structure and a line obtained by translating exposed portion of the top boundary down in the y-direction may be defined by specifying the DRY parameter
in the ETCH statement. The THICKNESS parameter will determine the distance to etch in the ydirection.
4. An extension of the DRY etch produces the etch region with slopped sidewalls and undercuts under
the mask. The UNDERCUT parameter specifies the top boundary’s extension of the etch region
under the mask. The ANGLE parameter defines the slopes of sidewalls of the region. The bottom
line of the etch region is defined by vertical translation of the top boundary with undercut taken
into account.
The ANGLE less than 90° results in trenches narrowing to the bottom. The ANGLE greater than 90°
produces retrograde sidewalls. The UNDERCUT length is measured along the boundary line between
etched material and masking layer.
In a special case when the etched material layer is sandwiched between two other layers, the
THICKNESS parameter is ignored and UNDERCUT is applied to both the upper and lower boundaries
of the etched material layer.
5. All regions of a particular material may be etched by specifying the ALL parameter of the ETCH
statement.
When a region is defined in one of the first three ways. By default, all materials in the defined region
will be etched. Specifying a material in the ETCH statement limits etching to only that material within
the defined region. For a complete description of physically based etch models, see Chapter 4: “ELITE
Models”. ELITE is a complete 2D topography simulator included in the ATHENA framework.
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3.8: Compound Semiconductor Simulation
ATHENA allows you to simulate basic technological processes in compound semiconductors. The set of
standard compound materials includes: GaAs, AlGaAs, InGaAs, and InP. Additional user-defined
materials can be also specified. The following chemical elements are typical dopants in these
compound semiconductors: Si, C, Se, Be, Mg, Ge, and Zn.
3.8.1: Diffusion Models
The default diffusion model in compound semiconductors is the same as the Fermi Model with electric
field effect used for silicon in SSUPREM4 (see Section 3.1.2: “The Fermi Model”). All diffusivity
parameters from Table 3-2 can be specified for each dopant in all compound materials. But, only
reasonably calibrated set of diffusion parameters exist for GaAs, [77]. You should perform calibration
or all other materials.
Note: More advanced diffusion models TWO.DIM and FULL.CPL can be potentially specified for compound semiconductors.
The point defects kinetics, however, is largely unknown which means that extensive research and calibration is needed
It was determined in [77], that n-type dopants, Si, Se, and Ge in GaAs, diffuse through the Ga Vacancy
Mechanism, while p-type dopants, Be, Mg, Zn, and C, diffuse through the Ga interstitial mechanism.
This means that for donors in GaAs the diffusivity is calculated as follows:
x
– n
=
n 2
D donor = D AV + D AV ---+ D AV  ----


n
ni
i
3-239
To look up these diffusivity terms, see Table 3-2.
The intrinsic carrier concentration ni is calculated by Equation 3-9 with the parameters NI.0, NI.E,
and NI.POW taken from [78]. The experimental data cited in [77] show that diffusivity of Si and Se in
GaAs can be considered as concentration independent and therefore only the first term of this
equation is non-zero for these impurities. It appears that diffusion of Ge in GaAs is proportional to the
second power of (n/ni).
The diffusivity for acceptors is the following:
x
– p
=
D acceptor = D AI + D AI ---+ D AI
ni
p
 ---n 
i
2
3-240
Different terms are dominant for different acceptors. Carbon diffusivity is considered as concentration
independent. Be and Mg diffusivities are proportional to p/ni, while diffusivity of Zn is proportional to
(p/ni)2.
It’s important to know that some dopants in compound semiconductors are amphoteric and can be
either donor or acceptors under certain conditions. This means, you can use the DONOR and ACCEPTOR
parameters in the IMPURITY statement to specify the type of dopant.
Boundary and interface condition for impurities in compound semiconductors are specified using the
transport velocity parameters TRN.0 and TRN.E and the segregation coefficients SEG.0 and SEG.E.
The impurity activation in compound semiconductors is calculated using solid solubility model with
default value for solid solubility limit for all impurities set at 1019 cm-3.
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3.8.2: Implantation Models
Ion implantation models for compound semiconductors are essentially the same as those for silicon.
The Pearson analytical approximation uses look-up tables derived from experiments [79] and
calculations [59]. These tables correspond to amorphous approximation and ignore effects of material
crystalline structure.
When accuracy of simulated as-implant profiles is important and ion implant channeling is
pronounced, use the Monte Carlo BCA implant model. The Monte Carlo model takes into account both
crystalline structure and composition of compound materials. The actual composition and density of
the default ternary compounds, InGaAs and AlGaAs, as well as the user-defined materials must be
specified in the MATERIAL statement.
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3.9: SiGe/SiGeC Simulation
Several experiments (e.g., [80], [81], and [82]) revealed that boron diffusion in Si1-xGex or
Si1-xGexCy alloys may differ from diffusion in pure Si substrates. To simulate effects of Ge
concentration fraction, x, and carbon concentration fraction, y, on boron diffusion several models were
introduced in SSUPREM4. To activate these models, set the MODEL.SIGEC parameter in the METHOD
statement.
3.9.1: Deposition of SiGe/SiGeC Epitaxial Layer
In this model, Si1-xGex or Si1-xGexCy alloys are considered as heavily doped with Ge or Ge and C.
Usually, layers with either constant or graded germanium content are formed by a special epitaxy
process.
You can simulate the formation of the Si1-xGexCy layer with a constant Ge and C content using the
DEPOSIT statement with a C.GERMANIUM parameter set equal to y*NSi, where NSi is the atomic
density of undoped silicon equal to 5.0 1022 cm-3. For layers with graded germanium content, use an
additional parameter, F.GERMANIUM, in the DEPOSIT statement. The following statement:
DEPOSIT SILICON THICK=0.1 DIN=10 C.GERMANIUM=1e20 F.GERMANIUM=5e21
C.CARBON=1e19
will create the 0.1µm layer of Si1-xGexCy with constant carbon concentration of 1.0 1019 cm-3 and with
germanium concentration varying from 1.0 1020 cm-3 at the bottom of the layer to 5.0 1022 cm-3 at the
top of the layer. This corresponds to Ge content x varied from 0.2% to 10%.
3.9.2: Boron Diffusion in SiGe/SiGeC
The special model takes empirically into account experimental facts that boron diffusivity apparently
decreases with germanium and carbon content. The total boron diffusivity (see Equation 3-10)
decreases exponentially with the Ge content, x, and carbon content, y.
 x Þ EAFACT ⋅ SiGe + y ⋅ EAFACT ⋅ SIGE
D B [ Si 1 – x – y Ge x C y ] = D B [ Si ] exp  – -------------------------------------------------------------------------------------------------------------
N Si kT


3-241
Another effect taken into account in this model is variation of intrinsic carrier concentration ni with x
and y. It is presumed that ni increased with x and decreased with y.

x ⋅ NIFACT ⋅ SIGE- ⁄ 
y ⋅ NIFACT ⋅ SIC
n i [ Si 1 – x – y Ge x C y ] = n i [ Si ]  1 – ------------------------------------------------  1 + ---------------------------------------------
N Si
N Si

 

3-242
The user-defined calibration parameters (EAFACT and NIFACT) for the above equations are specified in
the MATERIAL statement for silicon.
As an alternative to Equations 3-241 and 3-242, you can use different dependencies for diffusivity and
intrinsic carrier concentration through C-Interpreter function specified by SIGECDF.MOD and
SIGECNI.MOD parameters in the METHOD statement.
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3.9.3: Boron Transient Diffusion Suppression by Carbon Incorporation Models
There are experimental indications [82] that interstitials diffuse slowly and tend to disappear or get
trapped more intensively in SiGe layers with substitutional carbon. These effects result in suppressing
of the boron transient diffusion when carbon is incorporated into SiGe layer. The following equations
shows the diffusivity of interstitials, DI, is controlled by the DCARBON.E parameter.
D I [ Si
1–x–y
 y ( DCARBON ⋅ E )
Ge C ] = D I [ Si ] ⋅ exp  – ----------------------------------------------
x y
N Si kT


3-243
This model also introduces an additional sink for interstitials in the layers with high carbon
concentration. Intensity of the sink is proportional to the carbon concentration and is controlled by the
recombination parameters, KCARBON.0 and KCARBON.E, specified in the “INTERSTITIAL SILICON”
statement.
This means that the following recombination term will appear on the right-hand side of the interstitial
transport equation Equation 3-24.
---------------------------------
R CARBON = KCARBON ⋅ 0 exp  – KCARBONE


kT
3-96
y ( C – C∗ )
⋅ --------I
I
N
3-244
Si
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3.10: Stress Models
ATHENA allows you to calculate stresses generated during semiconductor processing. There are three
ways to calculate stresses. The first way is to calculate the stresses during viscous oxidation or viscous
material reflow (see Chapter 4: “ELITE Models”, Section 4.5: “Reflow Model”). The second way is to
calculate the stresses due to thin film intrinsic stress or thermal mismatch using the STRESS
statement at a certain moment of the processing sequence usually after thin film deposition or etching
or both. The third way is to follow stress history by specifying the STRESS.HIST parameter in the
METHOD statement.
In the cases of the second and third methods, ATHENA performs a finite element analysis of the
material structure solving the similar set of equations as in case of viscous oxidation (Equations 3-1443-146). The only difference are the thermal expansion and intrinsic terms added to the right-hand side
of Equation 3-144.
T1
4  1 + POISS · R


 – VISC · E
– ------------------------------------------- VISC · 0 ⋅ exp  ------------------------ LCTE + INTRIN · SIG
i
1 – 2 ⋅ POISS · R
 KT 
∫
3-245
T2
The linear coefficient of the material thermal expansion LCTE can be specified as a function of
temperature T in the MATERIAL statement. The film intrinsic stress parameter, INTRIN.SIG, is
specified in the MATERIAL statement. T1 and T2 are initial and final temperatures.
If the STRESS.HIST method is specified, ATHENA then calculates stresses when the simulation
structure changes after etching, deposition, epitaxy, and diffusion processes. The temperature
(including ramp) specified for current process step is used in the calculation. The room temperature is
used if the temperature isn’t specified in the ETCH or DEPOSIT statement. The final stresses from the
previous step is used as a initial condition for the subsequent step.
If the temperature is changed between the end of one step and the start of another, the stress
calculation with corresponding temperature ramp is automatically inserted. If stresses are calculated
using the STRESS statement or during oxidation with VISCOUS model or during REFLOW simulation,
then stresses previously calculated by the STRESS.HIST model are ignored and new stresses are
computed.
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Chapter 4:
ELITE Models
4.1: Overview
The ELITE module of ATHENA allows the use of sophisticated models for deposition and etch processes.
These processes are modeled by defining a machine and invoking the machine to perform either
deposit or etch. ELITE also includes a model for material reflow. ELITE can also be licensed with
modules for Monte Carlo deposition, Monte Carlo etching, and Chemical Mechanical Polishing (CMP).
In ELITE, a number of default machines are defined so that specifying any process reasonably close to
the standard is especially simple. Process modifications or additions are easily implemented by
changing or adding individual machines without affecting the remainder of the simulator.
For all models except Monte Carlo deposition and Monte Carlo Etching, ELITE uses a string algorithm
to describe topographical changes that occur during deposition and etching processes. This chapter
describes the models and techniques used in ELITE and the command language used to access model
parameters.
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4.2: String Algorithm
The ELITE simulation regime consists of a set of triangles that hold information on the materials that
are being simulated. The string algorithm treats each of these interfaces as a set of segments that
move in response to a particular process calculation.
As microfabrication technology becomes more complex, modeling each step of the manufacturing
process is increasingly important for predicting the performance of the technology. Etching is a step
that is universal in microfabrication. It may take place as the dissolution of a photoresist by an organic
solvent, the etching of an oxide by an alkali, or the plasma etching of an electron resist. Whatever its
physical details, the etching process can in many cases be modeled as a surface etching phenomenon.
Etching simulation starts from an initial profile that moves through a medium in which the speed of
etching propagation can be a function of position and other variables that determine the final profile.
Two major assumptions limit the generality of the string algorithm in ELITE. First, the pattern to be
etched is uniform in one dimension, so the problem can be solved using only two dimensions. For most
microfabrication problems, the important cases involve the cross-sections of lines, so this model is
directly applicable. In certain other cases, such as round holes, the symmetry of some cross-sections is
such that the algorithm is still valid. The second major assumption is that the etch rate is a scalar
function of position, and is independent of the direction of local etch front motion and the history of the
front. In some real situations, this does not hold. PMMA, for instance, has been found to have a gel
region at the resist-solvent interface during development, so the etch rate is a function of the history of
the adjacent regions as well as of the exposure. Another case where the second assumption does not
hold is in the so-called “preferential etching” where etching proceeds more quickly along certain
crystal directions, making the etch anisotropic.
The algorithm described here is known as a “string algorithm” [83]. The etch front is simulated by a
series of points joined by straight line segments, forming a string. During each time increment, each
point advances perpendicularly to the local etch front as in Figure 4-1. A major portion of the
algorithm adjusts the number of segments to keep them approximately equal in length. Other
subroutines input the data and output the etch front.
Choosing suitable criteria for segment length was a major problem in developing the algorithm. It
seemed that segments must be short enough so that any curve that developed would be well defined,
i.e., there should be some maximum angle between adjacent segments, perhaps 0.1 radians. This
criterion, however, led to a proliferation of segments in regions where the front was either expanding
or contracting. The algorithms in ELITE attempt to maintain approximately equal segment lengths.
This results in position errors of about one-half segment length. The error can be reduced by
decreasing the average segment length with a proportional increase in computation time.
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Figure 4-1: String Model approximation to the Etch Front
For the most cases of interest, the etch rate varies with position. This leads to some errors in the
position and in the direction of each point on the string. Errors in position arise from the use of a
rather simple integration algorithm. The local rate at the start of each time step is assumed to be
constant throughout the step. This can easily lead to position errors as large as the distance covered in
one step. Consider, for example, an etch front in a photoresist approaching an unetchable substrate. A
point, which is barely outside the substrate at the start of the time step, will advance into the
substrate at the rate associated with the resist. Thin layers of alternating fast and slow etch rates
could spawn errors in position. With too large a time step, a point could jump over a slow region.
Errors in direction arise from non-uniform rates along the string and from certain boundary
conditions. During each step perpendicularity to the front, which is defined below, is assumed to be
constant in direction. If two adjacent points have greatly differing rates, however, the quickly moving
point cannot start turning towards the slower point until the end of the time step. This mechanism
tends to introduce relatively small errors in position because the error is roughly proportional to the
cosine of the angle error.
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4.3: Deposition Models
ELITE provides a set of deposition models that correspond to different physical deposition techniques.
Most of the models were first developed at UC Berkeley [84], [85], [86], and [87] and were originally
implemented in the topography simulator SAMPLE [88]. Any one of these models can be selected to
define a “machine” for simulating processes on the structure. In addition, ELITE provides a conformal
deposition capability that can be used to define initial structures.
In most integrated-circuit processes, at least one layer of interconnect is formed by depositing and
patterning an Al or Al alloy film. The trend toward lower temperature processing, combined with the
very steep edge profiles produced by anisotropic dry etching processes, results in sharp step profiles,
which are difficult to cover with a uniform film of metal.
4.3.1: Conformal Deposition
You can perform conformal deposition by specifying a material to deposit, a thickness, and a number of
vertical grid spacings on the DEPOSIT statement. The conformal deposition model produces unity step
coverage.
4.3.2: CVD Deposition
To use this model, specify the CVD parameter in the RATE.DEPO statement as well as the material type,
the deposition rate DEP.RATE, and step coverage, STEP.COV.
The local deposition rate R(x,y) for the CVD model is given by
R ( x, y ) = DEP.RATE [ ( 1 – STEP.COV ) cos θ + STEP.COV ]
4-1
where θ is the angle between the surface segment and the horizontal.
4.3.3: Unidirectional Deposition
To specify this model, specify the UNIDIRECT parameter in the RATE.DEPO statement.
As shown in Figure 4-2, the region of the substrate not shadowed sees the arrival of the vapor streams
in one direction only. The growth rate of the deposited film in the shadowed region is equal to zero.
According to these assumptions, growth rate on the substrate R(x,y) can be expressed as:
R (x,y) = 0 , if point (x,y) is shadowed
R (x,y) = C sin ω i + C sin ω j
4-2
4-3
where:
•
ω is the angle between the y-axis and the direction of the vapor stream.
•
i and j are the unit vectors in the x and y direction respectively.
•
C is the growth rate of an unshadowed surface normal to the vapor stream.
•
Angle ω is specified as ANGLE1 on the RATE.DEPO command.
The following is a short description of the cosine law deposition. This is a simple model that accounts
for metallization, due to evaporation. The cosine law deposition model is based on the following
assumptions:
4-4
•
The mean free path of atoms or particles is much larger than the distance between the source and
the substrate.
•
The source to substrate distance is large compared to the surface topography.
•
The film grows in the direction toward the vapor flux.
•
Shadowing effects must be included.
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The magnitude of the film growth rate follows the cosine distribution law, which says that deposited
film thickness grows at a rate proportional to cos(ω), where ω is the angle between the vapor steam
and the normal surface.
The sticking coefficient can be used as a tuning parameter. It is assumed to be 1.0 for deposition on the
cold substrates (at 300 K).
ω
Figure 4-2: Step Profile with a Unidirectional Source
4.3.4: Dual Directional Deposition
This model is invoked by specifying the DUALDIRECT parameter in the RATE.DEPO statement. In this
type of source, each point in the unshadowed region views the vapor streams arriving from two
different directions, and assumes the diffusion length of deposited material large compared to the
features (see Figure 4-3). Growth rate is given as:
R ( x, y ) = 0, if point ( x, y ) is shadowed
4-4
R ( x, y ) = C sin ω 1 i + C sin ω 1 j or R ( x, y ) = C sin ω 2 i + C sin ω 2 j
4-5
if point (x,y) is partially shadowed.
R ( x, y ) = C ( cos ω 1 + cos ω 2 )i + C ( sin ω 1 + sin ω 2 )j
4-6
if point (x,y) is unshadowed, where ω1 and ω2 are the incident angles. ω1 and ω2 are specified on the
RATE.DEPO command by ANGLE1 and ANGLE2, respectively.
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ω2
ω1
Figure 4-3: Step Profile with Dual Source
4.3.5: Hemispheric Deposition
To use this model, specify the HEMISPHERIC parameter in the RATE.DEPO statement
The flux of vapor is continuously distributed in a range of directions (see Figure 4-4). The growth rate
can be calculated as:
R ( x, y ) = C ( cos ω 1 – cos ω 2 )i + C ( sin ω 1 – sin ω 2 )j
4-7
where ω1 and ω2 are the lower and upper bounds, respectively, of the incident angles of the vapor
streams set by parameters ANGLE1 and ANGLE2, respectively.
To avoid step-coverage problems, planar sputtering is often used to achieve better film profiles. The
ideal sputtering source is modeled by means of a hemispheric vapor source with atoms impinging on
the substrate from all angles.
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ω2
ω1
Figure 4-4: Step Profile with a Hemispherical Vapor Source
4.3.6: Planetary Deposition
To use this model, specify the PLANETARY parameter in the RATE.DEPO statement.
Figure 4-5 illustrates the planetary evaporation system. By inspecting this system, you can be
convinced that the rotation of the planet along the system central axis has no effect on the deposition
rate. For simplicity’s sake, you can calculate the growth rate by holding the planet stationary and by
rotating only the source along the axis of the planet (see Figure 4-5). The growth rate is derived
according to the following equations:
2
R x (x,y) =
2
2
[ R – r – rL tan ∆ + LW ] [ – L sec ( ∆ ) ] [ L tan ∆ sin β – L cos β ] tan δdδ
∫ --------------------------------------------------------------------------------------------------------------------------------------------------------------2
2
2
2
2
2
2
2
[ R – r + L – 2rL tan ∆ ] ( R + W ) [ R – ( r + L tan ∆ ) ]
2
2
4-8
2
[ R – r – rL tan ∆ + LW ] [ – L sec ( ∆ ) ] [ L tan ∆ sin β – L cos β ]
R x (x,y) = ∫ ---------------------------------------------------------------------------------------------------------------------------------------------------- dδ
2
2
2
2
2
2
2
2
[ R – r + L – 2rL tan ∆ ] ( R + W ) [ R – ( r + L tan ∆ ) ]
4-9
where:
•
δ is the incident angle of the vapor stream.
•
β is the tilt angle of the planet plane.
•
∆ = δ − β.
•
r is the distance between the position of the wafer and the planet axis.
•
R, L, and W are the parameters dependent on the system dimensions.
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β
γ
Figure 4-5: Illustration of Planetary Evaporator
Using the planetary model of ELITE, you can observe asymmetries both in edge coverage and the depth
of cracks produced by the particular location and orientation of a specimen in a planetary system.
Figure 4-6 shows the following planetary model parameters:
γ = ANGLE2,
β = ANGLE3,
r = DIST.PL, P.AXIS, C.AXIS, and ANGLE1
ANGLE1 is used to calculate DIST.PL = P.AXIS * tan(ANGLE1).
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γ
Figure 4-6: Geometric of Source to Substrate in a Conical Evaporator
4.3.7: Conical Deposition
To use this model, specify the CONICAL parameter in the RATE.DEPO statement.
The Conical model is a simplified version of the Planetary model with β and r = 0, the substrate always
sees a symmetrical cone source. In this type of configuration, the integral of the above two equations
can be evaluated analytically and expressed in the following simple closed form:
2
2
2

– R ( R + LW )
L
L
R x ( x, y ) = -------------------------------------------------------  1 –  --- tan δ max – 1 –  --- tan δ min 
R

R

2
2
2
2 2

R + W ⋅ (R + L ) 
4-10
If expression under either square root in this formula is less than 0 it is set to exact 0.

2

(
+
LW
)
L
L
R
R z ( x, y ) = -------------------------------------------------------  asin  --- tan δ max –
R
2
2
2
2 2
R + W ⋅ (R + L ) 

Silvaco

 L2
2 
asin  -----2- tan δ min  
R


4-11
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ATHENA User’s Manual
In the Conical model, the parameter, ANGLE1=γ, and other parameters are C.AXIS and P.AXIS as
shown in Figure 4-6.
4.3.8: Monte Carlo Deposition
There are two models that are invoked by specifying the MONTE1 or MONTE2 parameters in the
RATE.DEPO statement. The parameters SIGMA.DEP, DEP.RATE, and ANGLE1. MONTE1 invokes the Monte
Carlo based deposition model, which you can use to model low-pressure chemical vapor deposition
(LPCVD) [89], [90].
Since the radicals are incident on the substrate with non zero thermal velocities, they may be reemitted from the surface before they react. Therefore, the probability of their sticking is considered.
You can define the sticking coefficient using STICK parameter in the RATE.DEPO statement.
Ψ
Figure 4-7: Deposition and Relaxation Model used in Ballistic Deposition model (MONTE2)
4-10
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ELITE Models
The model uses an analytical approach to calculate a surface diffusion through a normalized gaussian
distribution nd:
2


x
nd = exp  – ------------------------------
 SIGMA.DEP 2
4-12
where x is the point of contact with the surface as shown in Figure 4-7.
MONTE2 invokes a ballistic deposition model, which simulates film growth by the random irreversible
deposition of hard two-dimensional discs launched with linear trajectories from a random point at the
top of the simulation area towards the structure surface.
At the point of contact with the growing film, the incident discs are relaxed to the nearest cradle point
with the highest coordination number (contacting the largest number of neighbor discs) within a
radius equal to SIGMA.DEP, which is four disc diameters by default.
The profile was initialized using a series of discs. In order to inhibit unrealistic “epitaxial” growth from
a closest-packed surface [91] and [92], the initial series of discs was spaced with centers approximately
1.3 diameters apart.
This relaxation process simulates limited surface diffusion that occurs in films to reduce the surface
energy associated with areas of high curvature.
A prediction of the trends in local film density can be achieved. Plot with discs can be obtained using
the parameter OUTFILE=<filename> in the DEPOSIT statement. Figure 4-7 shows the vapor flux
distribution arriving can be defined using the ANGLE1 parameter describing the angle measured
between the vertical from the source and the wafer normal.
To use multiple steps for both MONTE1 and MONTE2 models, set the DIVISION parameter in the DEPOSIT
statement. The number of incoming particles can be defined by the N.PARTICLE parameter in the
DEPOSIT statement.
4.3.9: Custom Deposition Models
ELITE implements two slightly different custom deposition models. In both models, the angle is d.
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4.4: Etch Models
ELITE provides a set of etch models that correspond to different physical etching techniques [93], [94],
and [95]. Any one of these models can be selected to define a machine that can then be invoked to
perform processing on the structure. In addition, ELITE provides a primitive etching capability that
can be used to define initial structures.
4.4.1: Isotropic Etch Model
To use the model, specify the WET.ETCH parameter in the RATE.ETCH statement. In wet etching and
simple plasma etching, the substrate is immersed in a fluid (liquid or gas), which chemically reacts
with the exposed surface. In wet etching, the liquid attacks the surface and removes soluble products.
This reaction produces volatile by-products, which are removed by a vacuum pump. Physical reactions
do not take place. A barrel plasma reactor achieves such conditions, usually at low powers and
moderate pressures. Due to the chemical reaction, isotropic profiles develop with mask undercutting
and circular cross-sections.
riso bisects the angle
between line segments.
r = riso
Figure 4-8: Segment Point in Case of Isotropic
4.4.2: RIE Model
In the Reactive Ion Etching (RIE) model, the etching process is divided into the two adjustable
components isotropic etching and anisotropic etching. Each of these components is characterized by
empirical etch rates (riso and rdir).
The ratio:
r dir
A = -----------------------r riso + r dir
4-13
defines the measure of anisotropy.
The isotropic component riso models chemically reactive etching which results in profiles with
undercut and circular cross-sections. For A=0, the process is completely isotropic. Under isotropic
conditions, the string-points are advanced at the constant rate riso, in the direction of the
perpendicular bisector of the adjacent segments (see Figure 4-8).
4-12
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ELITE Models
The anisotropic etch rate component rdir is proportional to the cosine of the angle between the flux
direction and the surface normal (the perpendicular bisector of adjacent segments). For A=1, the
process is anisotropic yielding vertical sidewalls (see Figure 4-9).
Figure 4-10 illustrates the regions of significance for each component in the RIE model. The shadowing
effect is accounted for by the riso component in the shadowed area.
α
r = rdir + cos α
rdir
r = rdir
Figure 4-9: Point Advance due to Directional Influence
α
α
Figure 4-10: Regions of Significance of rdir and risc
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4.4.3: Dopant Enhanced Etching
Dopant enhanced etching is a feature included in ELITE and allows the etch rate at any point on the
surface to be changed depending on the value of any solution variable present. The etch rate at any
point is then given by the formula
ER enh = ( 1 + enh )ERM
4-14
where ERenh is the enhancement or retardation due the presence of particular dopant. All impurities
as well as interstitials, vacancies, and stress solutions Sxx, Sxy, and Syy can be specified in the model.
This enhancement is calculated using the formula
enh = 0.5 ENH · MAX ( tanh ( ENH · SCALE ( S – ENH · MINC ) + 1 ) )
4-15
where ENH.MAX is the maximum value of enhancement or retardation, ENH.MINC gives the solution
value below which enhancement decays and ENH.SCALE gives the spread of the enhancement over
solution values. In other words, how quickly does the enhancement or retardation factor reach its
maximum. S is the dopant value. The positive value of ENH.MAX corresponds to enhancement, while
negative value corresponds to retardation.
For exponentially varying solutions, e.g., oxidation stress and dopant concentrations, both S and
ENH.MINC are taken to be log base 10 of their respective value. Parameters of the model are specified in
the RATE.DOPE statement.
4.4.4: Plasma Etch Model
The plasma etch model in ATHENA is based on a Monte Carlo simulation of the ion transport from the
neutral plasma or bulk, denoted by its glow, through the dark sheath surrounding the electrodes and
walls and isolating the plasma. Ions enter the sheath from the plasma and are then accelerated
through the sheath due the electrical potential drop between the plasma and the electrodes. The
Monte Carlo simulation follows a large number ions in their transport through the sheath including
collisions with other gaseous species present in the etch chamber. The number of collisions
encountered by a particular ion depends on both the ion mean free path, a calculated quantity, and the
sheath thickness, an user-specified quantity. To reduce the computation time, ion trajectories are
calculated independently and inter-ion interactions are not considered in this version of the code.
In the current version of ATHENA, the simulated Monte Carlo distributions are used to calculate an
ion flux incident on the substrate surface. This flux is then used to calculate an etch rate by
integrating this flux over the window of visibility at each point on the surface. The window of visibility
is, for point on a flat surface, simply from 0 to 2 π . But for more complicated structures (e.g., trenches),
points on the surface are shadowed and the “window of visibility” is reduced. Currently, only a simple
linear surface kinetic model for etching is supported.
See Chapter 7: “SSUPREM4 Models” for a description of the RATE.ETCH parameters required for
plasma etch simulation.
4.4.5: Monte Carlo Etching Model
The shrinking critical dimensions of modern technology place a heavy requirement on optimizing the
etching of narrow mask opening. In addition, the aspect ratio of etches has been increased, requiring
deeper etches along with the small kc/s. The simulation of these process requires more advanced
techniques than the analytical rate-based etching models described above. A more complete treatment
involving calculation of the plasma distribution and direct interaction of plasma particles with
substrate materials is required.
4-14
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ELITE Models
The Monte Carlo etch module is implemented into ATHENA/ELITE. The main application of the module
is simulation of plasma or ion assisted etching. The module can take into account the redeposition of
the polymer material generated as a mixture of incoming ions with etched (sputtered) molecules of
substrate material. Also, the module has interface to the C-Interpreter, which allows simulation of
several other processes such as wet etch and deposition, ion milling and sputtering deposition of
various materials. The Monte Carlo etch module was successfully used by Toshiba researchers for
simulations of reactive ion etching of narrow deep trenches in oxide [96].
Simulation of Incoming Ions and Neutrals
Direct modeling of the plasma sheath is not included into this release and will be added later. It is
assumed that ions and neutrals fluxes leaving plasma sheath are represented by bimaxwell velocity
distribution function along the direction determined by user specified incident angle:
υ ||
υ
f( υ || , υ ⊥) ∼ I ⋅ exp  – ------------ – -----⊥-
 T ||
T ⊥
4-16
where:
υ ||
is the ion velocity component parallel to the incident direction.
υ ⊥ is the ion velocity component perpendicular to the incident direction.
I ion (or neutral) current density specified by parameters, MC.ION.CU1 or MC.ION.CU2 in the RATE.ETCH
statement.
T ||
is the dimensionless parallel temperature specified by parameters, MC.NORM.T1 or MC.NORM.T2.
T ⊥ is the dimensionless lateral temperature specified by parameters,
MC.LAT.T1 or MC.LAT.T2.
The incident angles are specified by the MC.ANGLE1 and MC.ANGLE2 parameters.
Calculation of Ion and Neutral Fluxes
During each time step, the simulation consists of the three stages. These stages are as follows:
1. Calculation of ion, neutral, and polymer fluxes
2. Calculation of etch, polymer ejection and redeposition rates
3. Surface movement
On the first stage, the fluxes of incoming and reflected ions and neutrals are calculated on the each
segment of the surface. Computation of the ion fluxes is done by tracing the user-defined number of
particles (Figure 4-11, model a). Each particle is generated at random positions on top of the
simulation area, with normal and lateral velocities randomly determined from the bimaxwell
distribution function (Equation 4-1). Then, each particle trajectory is traced until the ion is either
absorbed by the surface or back scattered out of the simulation area.
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Figure 4-11: Diagram of Plasma Flux algorithm: (a) including zoom-in of ion reflection models (a & b)
The interaction of the ion with material surface is governed by two factors. The first is the reflection
coefficient Prefl, which is specified by the MC.ALB1 and MC.ALB2 parameters for two types of plasma
particles. The second is MC.PLM.ALB for polymer particles and roughness of the surface R, which is
specified by the MC.RFLCTDIF parameter. Both factors depend on the surface material and the type of
ion. Reflection coefficient is the probability of the particle to be reflected from the surface. Roughness
determines how the ion is reflected. If R = 0 the reflection is specular (Figure 4-11, model b). If R = 1,
the reflection is random with uniform angular distribution (Figure 4-11, model c). In general, the
velocity v refl of the ion after a collision with a surface segment could be presented as follows:
v refl = 0(ion is absorbed) , if x > P refl
4-17
v refl = v sp ⋅ ( 1 – R ) + v rand ⋅ R, if
4-18
x > P refl
where:
•
4-16
v sp is the ion velocity after specular reflection.
Silvaco
ELITE Models
•
v rand is the ion velocity after random reflection.
•
x is a random number.
v sp = v rand = v i , where v i is the velocity of incident ion.
•
Each absorbed ion is used to compute the incoming flux
F i at the surface segment. The following
characteristics describe the flux.
N norm = N abs ⋅ I ⁄ N traj
4-19
where:
N norm is the normalized number of absorbed particles,
•
•
N abs is the number of absorbed particles,
•
N traj is the number of trajectories specified by the MC.PARTS1 and MC.PARTS2 parameter for each
type of plasma particles, and by the MC.POLYMPT parameter for polymer particles,
•
normalized normal
v ⊥abs and tangential v || abs velocity components of the absorbed particle
before the encounter with the surface:
I
v ⊥abs = ----------- ⋅
N traj
∑ v⊥
N abs
I
v || abs = ----------- ⋅
N traj
•
v
4-20
∑ v||
4-21
N abs
normalized kinetic energy of absorbed particles:
2
abs
I
= ----------- ⋅
N traj
∑v
2
4-22
N abs
Calculation of Polymer Fluxes
After ion and neutral fluxes are determined, the fluxes of the polymer particles are calculated as
follows. As the result of ion flux interaction with the surface segment, the polymer particles are
generated. The angular distribution of the polymer particles is uniform and the current density of
these particles is determined by the etch model (see “Linear Etch Model” on page 4-18) and the sum of
the fluxes from incoming ions, neutrals, and from polymer particles ejected from other surface
segments. Obviously, the latter flux needs to be pre-calculated.
This flux is computed as follows. First, the configuration (or geometrical) factors, are calculated. These
factors are the fractions of the number of particles ejected from one segment and absorbed by the other
one. These are calculated using the same trajectory tracing algorithms, which are described above for
the incident ions and neutrals with the only one difference: starting points are not at the upper
boundary of the simulation area but at the surface segments. Then, an iteration process is initialized.
At the first iteration, only the incoming ion and neutral fluxes are used for calculation of the ejection
rates from each surface segment. Knowing the current densities of ejected particles and the
configuration factors, the polymer fluxes are calculated. At subsequent iterations, the polymer fluxes
calculated at the previous iteration are used to update the etch and ejection rates. The iterations are
repeated until etch and ejection rates converge.
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Calculation of Rates
The second stage involves calculation of the etching rates as well as ejection and redeposition rates of
the polymer particles. During each time step, the two processes simultaneously take place on each
surface segment. The first is redeposition of the polymer with the rate equal to the polymer flux. The
second is etching by incoming ions and neutrals. The combination of these two processes can be treated
as deposition of a virtual polymer layer with subsequent etching of the two-layer structure. If the etch
rate of polymer by incoming ions and neutrals is less than the polymer deposition rate, the result is the
redeposition of a polymer layer on the surface. If the etch rate of polymer by incoming ions and
neutrals is larger than the polymer deposition rate, the result is actual etch of the underlying
material.
Linear Etch Model
In the case of the linear model, the etch rate ER(m) of each material m is calculated as
ER ( m ) =
∑ EP ( m, i ) ⋅ vabs
4-23
n
where n is the number of plasma ion types specified by the parameter ION.TYPES (n could be equal to
1 or 2), EP(m,i) is the etch parameter for material m, and ion type i specified by parameters MC.ETCH1
and MC.ETCH2, v abs is the ion velocity as calculated in Equation 4-22.
If calculated, ER(polymer) is less than the polymer flux (redeposition rate), PF the actual etch rate,
and ER is negative which corresponds to redeposition.
ER = ER ( polymer ) – PF < 0
4-24
The corresponding ejection rate EJR is equal to the etch rate of polymer.
EJR = ER ( polymer )
4-25
When calculated ER(polymer) is larger than polymer flux, the actual etch rate is positive.
EP ( m, i ) ER = ER ( m ) – PF ⋅ ∑ -------------------------------------EP ( polymer, i )
4-26
n
The corresponding ejection rate is calculated as follows.
EJR = PF + ER
4-18
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ELITE Models
C-Interpreter
You can use the C-Interpreter to introduce different etch and ejection models. The following
parameters are passed to the C-Interpreter file and can be used for implementing the models: number
of ion types, the four characteristics of ion fluxes for each ion type (Equations 4-19-4-22), PF, and
surface material, m. Returned parameters are ER and EJR.
For example, you can simulate the wet etching by setting the etch rate to a constant positive value
depending only on the surface material. In this case, the trajectory tracing part of the model is not
needed. The number of trajectories can be set to one.
Uniform deposition can be simulated by the setting of a negative constant etch rate and by specifying
the redeposited material other than polymer in the ETCH statement. If the fluxes are not used, as in the
wet etching simulation, the void formed will eventually be filled with the deposited material, because
inside the C-Interpreter there is no way to determine if the current surface segment belongs to the
void or not. This obstacle can be overcome by simulating ion fluxes and by setting the etch rate to zero
if the flux on the surface segment is less than some small threshold value.
Surface Movement
A sophisticated string algorithm is used to move all segments, according to the rates (positive or
negative) calculated at each time step. If the rate is negative, the surface moves outside and the area is
filled with redeposited material (by default, polymer). If the rate is positive, the surface moves inwards
and the area is filled with vacuum.
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4.5: Reflow Model
A two-dimensional viscous reflow capability is included in ELITE. The vitreous silica (e.g., oxide,
BPSG,) are modeled as the viscous incompressible fluids, which are dynamically deformed under the
driving force of surface tension. The finite-element method is used to solve the creeping flow equations
for the chosen materials. With a 7-node triangle element as the basic discretization unit, arbitrarily
shaped 2D regions and surface curvatures are automatically described. Using the built-in user defined
material capability, you can simulate multiple material combinations. The flow equation solver can be
coupled with impurity diffusion to simulate the impurity redistribution and oxide growth.
The reflow is invoked by setting the reflow flag in the DIFFUSE statement and by setting the REFLOW
flag in the MATERIAL statement to choose a specific material. Physical parameters that are specific for
various materials, such as viscosity and surface tension, are also given in MATERIAL statement. Reflow
will proceed according to the time and temperature given in the DIFFUSE statement. The finite element
solver are invoked by specifying the VISCOUS parametrs and various numerical control parameters in
the METHOD statement.
The viscous creep flow equations solved are as follows (see [97]):
2
µ∇ V = ∇P
4-28
1 – 2ν
∇ ⋅ V = –  --------------- P
µ
4-29
E µ = -------------------2(1 + υ)
4-30
where V is the velocity, P the pressure, µ the viscosity, ν the Poisson’s ratio, and E the Young’s modulus.
The parameters v and E can be specified as POISS.R and YOUNG.M in the MATERIAL statement.
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ELITE Models
4.6: Chemical Mechanical Polish (CMP)
Chemical Mechanical Polish (CMP) is a module in ATHENA. To run CMP, you need to have the license
to use ELITE. CMP is used to model wafer planarization using polishing pad and chemical slurry
characteristics. CMP is also used to circumvent two major problems. First, the depth of focus of high
numerical aperture lithography systems. Second, metal thinning that can occur over non-planar
topographies
The CMP module that is incorporated into ATHENA has two distinct models. The first is the Hard
Polish or Buzz Saw Model [98]. The second is the Soft Polish Model based on the work of J.Warnock
[99]. To access these models, use the ATHENA statements: RATE.POLISH and POLISH. These statements
are similar to those used for the ELITE deposition, RATE.DEPO and DEPOSIT, and the ELITE etching,
RATE.ETCH and ETCH. The RATE.POLISH statement sets up the parameters for a particular machine,
while the POLISH statement executes the actual polishing step using the machine.
4.6.1: Hard Polish Model
The Hard Polish Model [98] simulates the grinding down of the topography based on a rate calculated
as a function of the pattern factor Pf of the surface. The higher the pattern factor, the lower the
polishing rate. Use the following formula.
R ( x, y ) = MAX.HARD ⋅ ( 1 – Pf ) + MIN.HARD ⋅ Pf
4-31
The hard polish model parameters are MAX.HARD and MIN.HARD. Pf = 1 corresponds to a flat surface. Pf
is calculated from the topography by the formula:

Pf =  ∑ ( x i – x i – 1 )
 i

 ⁄ X total
y > Y max – ∆Y
4-32
where (xi,yi) are points on the polished material surface, y denotes both yi and yi-1, Ymax is the highest
point of the structure and ∆Y is the rate effective height calculated by the previous rate multiplied by
the current time step value. For Figure 4-12, a pattern factor will be as follows:
∆ X1 + ∆ X2
Pf = -------------------------X total
4-33
The rate for points at height Ymax are equal to the R calculated in Equation 4-31. Points below Ymax
have a rate cause the structure to polish to the y coordinate Ymax − ∆Y. Therefore, the structure
becomes more planar as shown in Figure 4-13.
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Figure 4-12: Illustration of the Hard Polish Model: Structure before Planarization
Figure 4-13: Illustration of Hard Polish Model: Structure after Planarization
A total amount of ∆Y is always removed at each time step in the above fashion.
You can mix the hard polish model with the soft polish model and isotropic etch component by
specifying the ISOTROPIC parameter of the RATE.POLISH statement.
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ELITE Models
4.6.2: Soft Polish Model
The soft polish model is based on the work of J.Warnock [99]. It has four parameters: SOFT, LENGTH.FAC,
HEIGHT.FAC, and KINETIC.FAC. SOFT is the polish rate on a flat surface. LENGTH.FAC is the horizontal
deformation scale in microns. It is a measure of the polishing pad’s flexibility. It describes the distance
at which shadowing will be felt by a “tall” feature. HEIGHT.FAC is the vertical deformation scale in
(microns). This measures how much the polishing pad will deform with respect to the height of the
feature. KINETIC.FAC increase the vertical polish rate as the surface becomes more vertical.
The following formula gives the polishing rate.
Ki Ai
P i = ---------Si
4-34
Ki is the kinetic factor or horizontal component of the polish removal rate at point i. Ai is the
accelerating factor of point i and is large for points that are higher and shadow other points. Si is the
shadow factor and decreases the polish rate as a function of the points that are above point i. For a flat
surface, Ki Ai/Si = 1. Following the work of Warnock, these three factors are calculated using the
following set of equations.
The shadow factor is the one for flat surfaces. But it is generally calculated basedon one or two points
that shadow point i and is given by the equations below.
∆ zi
S i = exp  ------------------------------------
HEIGHT.FAC
4-35
∆zi >= 0.0, so Si > 1. ∆zi is obtained by integration over the surrounding topography.
i right
∆ zi =
ri

∑ zi ⁄ cosh  ------------------------------------LENGTH.FAC
4-36
i left
In these equations, ileft and iright refer to the two points that can possibly shadow point i. The effect of
these shadow points depends on the two parameters LENGTH.FAC and HEIGHT.FAC as shown in the
equations. The variable zi is the vertical distance between the point i and the point ileft/iright. The
variable ri is the horizontal distance between the point i and the point ileft/iright.
The acceleration factor, Ai, is given by the equations below. Ai is calculated for the two points that
shadow point i. In this manner, multiple shadowing effects are taken into account through the term
Aileft/Airight. This is the acceleration factor for the point(s) that shadow. If point i shadows some other
point j in the system, it will increase Ai by a similar factor. This increase is then passed on to Aileft.
A ileft = A ileft + A i ⋅ B i ⋅ ( 1 – 1 ⁄ S i )
4-37
A iright = A iright + A i ⋅ B i ⋅ ( 1 – 1 ⁄ S i )
4-38
The constant Bileft/Biright is a weighing factor based on the amount of shadowing at point i due to
shadow point ileft/iright.
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The kinetic factor is based on the following equation.
K i = 1 + KINETIC.FAC ⋅ tan α i
4-39
This shows the effect of the parameter, KINETIC.FAC, on the polishing rate. The angle αi is the local
angle that is tangent to the polished surface. The maximum allowable angle αi is 89.9544° (1.57
radians) will avoid calculation errors.
Figure 4-14 demonstrates three regions where each of the components of the polishing rate would be
large.
Figure 4-14: Soft Polishing Model: Areas where different components dominate
4-24
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Chapter 5:
OPTOLITH Models
5.1: Overview
The OPTOLITH module of ATHENA allows the use of sophisticated models for imaging, photoresist
exposure, photoresist bake, and photoresist development. OPTOLITH includes a library of photoresists
with default characterizations for development and optical properties. These default characterizations
can easily be tuned to adjust for variations that very typically occur from one facility to another. This
chapter describes the models and capabilities of OPTOLITH.
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5.2: The Imaging Module
OPTOLITH includes an imaging module that utilizes the Fourier series approach.
The theoretical resolution (RES) and Depth Of Focus (DOF) of a microlithographic exposure system
are approximated by:
λ
RES = k 1 ⋅ -------NA
5-1
and
λ
DOF = k 2 ⋅ --------------2( NA )
5-2
where λ is the wavelength of the exposing radiation, NA is the Numerical Aperture of the imaging
system, and k1 and k2 are process dependent constants. Typical values for k1 are 0.5 for a research
environment and 0.8 for a production process; the value usually assigned to k2 is 0.5.
We shall discuss the basic assumptions upon which the model rests. Next, we shall derive the principal
equations used for calculation of the image irradiance distribution for objects illuminated by partially
coherent light.
The treatment presented here assumes the radiation incident on the object to be quasimonochromatic, which means that the spectral bandwidth is sufficiently narrow so that wavelengthdependent effects in the optics or in diffraction angles are negligible. The source is of a finite spatial
extent so that the advantages of spatial incoherence are realized in imaging.
The mask is completely general in that phase and transmission are variable, but it must be composed
of rectangular features.
The calculation of the diffraction phenomena is based upon the scalar Kirchhoff diffraction theory.
Since the dimensions of the mask are almost the same as the illumination wavelength, we can ignore
any polarization taking place as the radiation propagates through the mask.
We assume scalar diffraction, which means neglecting the vector nature of the radiation. This is
acceptable if all convergence angles are small.
According to Watrasiewicz [100], who experimentally investigated the limiting numerical aperture,
the breakdown of the scalar theory occurs at angles of convergence greater than 30°, which
corresponds to a numerical aperture of 0.5. Similar results were published by Richards and Wolf [101],
who used theoretical calculations to investigate the electromagnetic field near the focus produced by
an aplanatic system working at a high convergence angle. They also found appreciable departures
from scalar theory for convergence angles larger than 30°. Since the convergence angles are calculated
in air, we can assume that the accuracy of this model is even better inside the photoresist, where
angles are reduced in accordance with Snell’s law.
Consequently, it can be stated that the scalar diffraction theory gives a reliable limit for imaging
system numerical apertures of 0.5.
The approach used for calculating the image irradiance distribution is based on the work of Hopkins
[102] and [103], which showed the partially coherent illumination of the object structure can be
simulated by the incoherently illuminated exit pupil of the condenser. The exit pupil serves as an
effective source, which produces the same degree of coherence in the illuminated object plane as the
actual condenser system. The degree of coherence in the object plane is therefore determined by the
shape and angular size of the effective source. The condenser system is assumed to be diffraction
limited, that is, free of aberrations. Residual aberrations of the illuminator do have an appreciable
influence on the final image for Koehler type illumination systems as shown by Tsujiuchi [104].
5-2
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OPTOLITH Models
Figure 5-1 shows a schematic diagram of a generalized optical system. The actual source and the
condenser system are replaced by the equivalent effective source having an irradiance distribution of g
(x0, z0). The effective source for the object plane U is taken to lie in the exit pupil reference sphere of
the condenser lens. This means that directing from arbitrary points (x0, z0) on the effective source,
plane waves propagate towards the object plane U having irradiance values of γ (x0, z0).
source
(condensor)
Imaging system
reticle plane
X
P
h0
α
α0
h
Image plane
U′
X
P′
h′
α′
P0
E
E′
U
X
Figure 5-1: Schematic Diagram of a Generalized Optical System
The reduced coordinates [103] on the object plane are defined as follows:
2π
u = ------ ⋅ n ⋅ sin α ⋅ ξ
5-3
2π
v = ------ ⋅ n ⋅ sin α ⋅ η
5-4
λ
λ
where ξ and η are the Cartesian coordinates of the object plane, 2π/λ is the absolute value of the wave
vector, and n-sinα is equal to the numerical aperture (NA) of the imaging system. Primed quantities
indicate the corresponding coordinates and angles in the image space of the projection system. The
fractional coordinates on the object pupil spheres are defined as follows:
x = --ξh
5-5
z = η
--h
5-6
where h is the radius of the pupil. The fractional coordinates of the exit pupil of the condenser are
given by
x 0 = --x-
σ
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ATHENA User’s Manual
z 0 = --z-
5-8
σ
In these equations:
n 0 ⋅ sin α 0
σ = ----------------------n ⋅ sin α
5-9
where α0 and α are angular semi-apertures of the condenser and the objective respectively. n0 and n are
the refractive indices in the image space of the illuminator and the object space of the imaging system,
usually both are set to one. The ratio σ is the radius of the effective source referred to the aperture of
the objective and governs the degree of spatial coherence in the object plane. The limits
σ → 0 and
σ → ∞ correspond respectively to coherent and incoherent illumination.
The object is taken to be infinitely thin. Therefore, a complex amplitude transmission function can
describe the object, which gives the change in magnitude and phase produced on the radiation passing
through it. The object has the complex transmission A(u,v). Its real part is given by
ℜ ( A ( u, v ) ) = { 1 in transparent areas
0 in opaque areas
5-10
The complex amplitude of the Fraunhofer diffraction pattern on the entrance pupil reference sphere at
E of the imaging system is given, apart from a constant factor, by
1
a ( x, z ) = ------ ∫ ∫ A ( u, v ) ⋅ exp ( – i ( ux + vz ) ) dudv
2π
5-11
which is the inverse Fourier transform of the complex amplitude transmission of the object. If not
stated otherwise, integration ranges from to – ∞ to + ∞.
If the object is illuminated by an element dx0, dz0 of the effective source at (x0, z0) with its amplitude
proportional to γ ( x 0, z 0 ) , the object spectrum a(x,z) is then shifted by a corresponding amount. In this
instance, the complex amplitude distribution on the entrance pupil sphere of the objective is
γ ( x 0, z 0 ) ⋅ a ( x – x 0, z – z 0 )
5-12
The complex amplitude on the exit pupil reference sphere at E’ will be given by
a ′ ( x, z ) =
γ ( x 0, z 0 ) ⋅ a ( x – x 0, z – z 0 )f ( x, z )
5-13
In this equation, f(x,z) denotes the pupil function of the optical system. If the system has an annular
aperture, where the central circular obstruction has the fractional radius ε, the pupil function has the
form:

2
2
2
 0
x +z <ε

f ( x, z ) =  τ ( x, z ) ⋅ exp ( i ⋅ k ⋅ W ( x, z ) ) x 2 + z 2 ≤ 1

2
2
 1
x +z ≥1

5-4
5-14
Silvaco
OPTOLITH Models
t(x,y) is the pupil transmission, which is usually set to one, and W(x,z) denotes the wave-front
aberration. For an entirely circular aperture, ε becomes zero. Note that the approach taken here is
somewhat similar to the one used in the investigations on phase contrast microscopy [105].
The function W(x,z) gives the optical path difference between the real wave-front and the exit pupil
reference sphere. Commonly, the wave-front aberration is expanded into a power series [103], giving
W ( x, z ) =
∑
2
2
2
2 n
W l, m, n ( χ + ζ ) + ( x χ + z ζ ) + ( x + z )
5-15
l, m, n
for a particular position (x,z) in the exit pupil. χ and ξ denote the fractional coordinates of the image
field. The values of l, m, and n describe the order of aberrations, while the coefficients W(l,m,n)
determine the magnitude of the aberrations.
The aberration coefficients up to the ninth order of aberration are specified in the ABERRATION
statement.
For third order aberrations l, m, and n take the values:
l=0
l=0
l=0
l=1
l=1
l=0
,
,
,
,
,
,
m=0
m=1
m=2
m=0
m=1
m=0
,
,
,
,
,
,
n=2
n=1
n=0
n=1
n=0
n=1
:
:
:
:
:
:
spherical aberration
coma
astigmatism
field curvature
distortion
defocus
where isoplanatism is assumed for the particular section of the image field for which the irradiance
distribution is calculated. The coefficient W001 can be determined from
2
( n ′ ⋅ sin α′ )
W 001 = δ ⋅ -----------------------------2⋅λ
5-16
where δ refers to the distance of the defocused image plane to Gaussian image plane.
The resulting amplitude in the image plane due to a wave coming from the point x0, z0 of the effective
source is
1
A ′ ( x 0, z 0 ;u ′, v ′ ) = ------ ⋅ γ ( x 0, z 0 ) ⋅ ∫ a ′ ( x – x 0, z – z 0 ) ⋅ exp ( i ( u ′ x + v ′ z ) )dxdz
2π
5-17
where (u′,v′) refers to a point in the image plane. The irradiance distribution associated with the
illuminating wave of the effective source will then be represented by
2
dI ′ ( x 0, z 0, ;u ′, v ′ ) = A ′ ( x 0, z 0, ;u ′, v ′ ) dx 0 dz 0
5-18
Since, by definition, the effective source is equivalent to a self-luminous source, the total irradiance at
(u′,v′) can be obtained by integrating over the entire source Σ.
I ′ ( u ′, v ′ ) =
∫ ∫ A ′ ( x0, z0 ;u ′, v ′ )
2
dx 0 dz 0
5-19
Σ
where Σ indicates the area of the effective source for which γ(x0,z0) has non-zero values.
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For this purpose, Equation 5-19 is put into the form:
I ′ ( u ′, v ′ ) =
∫ ∫ γ ( x0, z0 ) ⋅
2
Φ ( x 0, z 0 ;u ′, v ′ ) dx 0 dz 0
5-20
1
Φ ( x 0, y 0 ;u ′, v ′ ) = ------ ⋅ ∫ ∫ a ′ ( x – x 0, y – y 0 ) ⋅ f ( x, y ) ⋅ exp ( i ( u ′ x + v ′ y ) )dxdy
2π
5-21
Σ
where:
Φ ( x 0, z 0 ; u′, v′ ) is proportional to the intensity at the point (u′,v′) due to a wave of unit irradiance
passing through (x0, z0) of the effective source.
In the case of an annular shaped source, x0, z0 has the form:

2
2
2
 0 for x 0 + z 0 < ε 0

γ ( x 0, z 0 ) =  1 for x 2 + z 2 ≤ 1
0
0

 0 for x 2 + z 2 > 1
0
0

5-22
where ε0 is the fractional radius of the centered circular obstruction in the exit pupil of the condenser
lens. For a circular exit pupil, ε0 becomes zero.
Equation 5-20 is the principle relation of a generalized Abbe theory, where the image formation under
partially coherent illumination of the object is accounted for by a combination of coherent imaging
processes for perpendicular and obliquely incident illuminating plane waves on the object. Since only
the image irradiance is of interest, it can be determined without using of coherence theory [103]. For
the computation, the whole source is divided into a number of luminous point sources considering the
imaging due to each source as an independent coherent image formation process. The contributions
from each point source do not interfere, so the net image irradiance is the sum of the irradiance from
each source point.
The normalization used throughout this investigation is that the mask is illuminated with unit
irradiance so that the ideal image has unit irradiance, where unit magnification is assumed.
Therefore, the brightness of the source decreases as its size increases. Equation 5-20 is the principle
equation of the algorithm, which is used for studying the influence of annular apertures.
The object spectrum (see Equation 5-11) is calculated analytically, and the coherent image (see
Equation 5-18) is calculated using a Fourier Series approach.
The shape of a single mask feature must be rectangular. This is because the Fourier transform for a
rectangular feature is calculated based on an analytical formula.
Since the Fourier transform is linear, you can compose arbitrary shaped mask features from the
rectangular components. The object spectra of the single mask features (components) are simply added
up. The treatment can then be considered as appropriate, and no numerical discretization errors in the
size and placement of the mask features can occur.
Note: You may use MASKVIEWS to create or import masks of any arbitrary shape. The mask layout will be sliced (divided) on
rectangular elements when it is imported into OPTOLITH. OPTOLITH can import masks containing any number of mask
elements.
5-6
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OPTOLITH Models
5.3: Optical System
Figure 5-2 shows the optical system used by OPTOLITH. The meshes in the Fourier and Image planes
are totally independent. There is no mesh in the object or reticle plane.
α’
source
condensor reticle
α
projection
lens
aperture
stop
projection
lens
image plane
Figure 5-2: The Generated Optical System
5.3.1: Discretization Errors
The size of the window in the reticle plane is determined by the number of mesh points in the projector
pupil, the numerical aperture, and by the chosen wavelength:
CW = NP ⋅ lambda ⁄ NA
5-23
where:
•
CW is a computational or sampling window (mask or image cell) in the object or reticle plane.
•
NP is the number of mesh points in the projector pupil.
•
NA is the numerical aperture of the stepper.
•
lambda is the chosen wavelength.
For an i-line stepper with NA = 0.54, the size of the sampling window is the square whose side length
is equal to 6.8 µm (10 · 0.365/0.54). No mask feature should exceed this dimension.
You can increase the size of the sampling window for this particular stepper to any size by increasing
the number of mesh points in the projector pupil. This will be done automatically to accommodate the
mask and image windows that were specified.
Mask features cannot be placed outside of the sampling window. As mentioned earlier, the image mesh
is totally independent of the mesh in the Fourier plane. This allows you to arbitrarily specify the
number and distance of image points.
5.3.2: Mesh
The size of the computational window is determined by Equation 5-23) and the position of the mask
points. By positioning this window so that the mask cell in the object plane is covered, multiple image
cells can be calculated.
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5.3.3: Computation Time
To increase computation, first use a very coarse mesh for screening-type simulations and then refine
the mesh as you approach specific points of interest. Computation time is linearly dependent on the
number of source points, which is determined by the coherence factor.
5-8
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OPTOLITH Models
5.4: The Exposure Module
The Exposure Module computes the intensity distribution in the photoresist through the numerical
solution of the Helmholtz equation (Equation 5-24).
2
2 2
∇ E+k n E = 0
5-24
Here, E is the electric field, n(x,y) is the complex refractive index of media, and k is the wave number.
The specific solution of this general equation is determined by a set of boundary conditions. Generally,
the target (substrate coated with the resist film) consists of an arbitrary number of different materials
with n in Equation 5-24 and interfaces between material regions. Also, material refractive index can
depend on the absorbed dose (i.e., n can vary with the exposure time).
According to the electromagnetic theory, any field distribution can be represented by unique set of
plane waves. Generally, such a set has an infinite number of terms. But, the main contributions are
the incident wave and reflections from interfaces. Therefore, the calculation of the field inside the
complex structure can be divided into several subsequent calculations of the plane wave propagation
through the structure. The final field distribution is the sum of distributions obtained for all separate
plane waves. The simulation algorithm is outlined as below.
1. Simulation of the incident field propagation through the target (resist + substrate)
2. For each segment of each interface:
•
compute the direction of the reflection,
•
align the coordinate system and simulation domain with the direction of the reflection,
•
obtain the field distribution over the segment,
•
recursion of the propagation simulation procedure for the field generated over the surface
segment.
3. Summation of the distributions obtained with all recursive steps.
The reflection from each segment of interface is computed, using the preliminary obtained field on the
segment as the initial (incident) field. The recursion depth can be specified as a simulation parameter.
The Beam Propagation Method (BPM) [106] is used to simulate the field propagation. The BPM can be
used for different types of radiation (e.g., UV, EUV, X-ray) as well as for multi exposure processes and
multilayer and non-linear resists.
There are three reason why we choose this method. The first reason is because the diffraction of the
field along the propagation is automatically taken into account. The second reason is because it
includes a capability to simulate non-linear effect of the intensity distribution on the local optical
properties of the resist material. The third reason is because it provides a good “accuracy to run time”
ratio.
The BPM is used to solve the Helmholtz equation for electromagnetic field inside the structure. During
the simulation, the field distribution is formed as the superposition of incident light with all the
reflections from all elements of the resist-substrate interface and secondary reflection(s) from the
upper resist surface. [106] shows the formal descriptions of the BPM.Papers [107], [108], and [109] also
describe some applications using BPM.
In this model, the Helmholtz equation (Equation 5-24) for the electric field, E, in the media with
complex refractive index, n(x,y), is solved in two main stages. The first stage, the diffraction over a
small spatial step along the propagation is calculated. Thus, obtaining the new field amplitude
distribution without absorption taken into account. Then, the actual field distribution is computed as a
product of this amplitude distribution and the distribution of the complex absorption over the step. Let
the wave propagate along the y-axis.
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We find the solution as a quasi-plane wave E=A(x,y)exp(inky) with a slowly varied amplitude A. A is
then modified with y, which is slower than phase term inky. In this case, the Fourier image of current
distribution A in the plane y=y0 is defined as follows.
FA ( kx ) =
∫ A ( x, y0 ) exp ( –ikx x ) dx
5-25
After propagating over a small step, ∆y, each component of FA obtains additional phase shift
corresponding to the value of k y = k − k x . Thus, the amplitude distribution at new y (without
accounting for absorption) can be written as follows.
2
A ( x, y 0 + ∆y ) =
2
∫ FA ( kx ) exp ( iky ∆y ) exp ( ikx x ) dkx
5-26
Since actual material optical properties differ from the properties of vacuum, the field at the new
plane is computed simply as follows.
E ( x, y 0 + ∆y ) = A ( x, y ) exp { ik [ n ( x, x ) – 1 ]∆y }
5-27
The algorithm is repeated recursively step-by-step over all simulation domains. The same calculations
are then applied to reflections from all interface segments. The current intensity distribution is
calculated from the field distribution as
I ( x, y ) = E ( x, y )
2
5-28
During the exposure, the resist structure is modified. So, the dissolution inhibitor is converted to the
photo reaction product. The initial normalized concentration of photoactive compound (PAC) is defined
by local intensity magnitude as:
M PAC = exp [ – CI ( x, y ) ]
5-29
where I(x,y,) is the current intensity distribution, and C is Dill’s C-parameter. Accordingly, the optical
properties of the resist (complex refraction index n, which includes both refractive and absorption
indices) are modified too. The capability to take into account is the effect of dose (intensity) on the
refraction index n, which is implemented into the module and the following approach is realized. Nonlinear dependence of n on dose is defined through the PAC concentration as
= n un exp osed + ∆n [ 1 – M PAC ( x, y ) ]
5-30
Here, nunexposed is the complex refraction index of the unexposed resist. ∆n=nexposed -nunexposed is the
difference between values of n for completely exposed and unexposed resists.
Current intensity distribution is calculated after each simulation of direct propagation and all the
reflections from interfaces with BPM. Then, current MPAC and n(x,y) are calculated using
(Equation 5-29) and (Equation 5-30) respectively for each point of the resist volume. The new values of
n(x,y) are used during next recursion of the field and intensity simulations. Thus, the resulting
intensity distribution is obtained as an accumulation of intermediate results.
You can specify the optical properties of the simulated material in the OPTICAL statement. You can
specify the refraction and absorption indices for unexposed resist (and/or for any other material) using
5-10
Silvaco
OPTOLITH Models
the REFRAC.REAL and REFRAC.IMAG parameters respectively. To specify the difference of the
refraction index for the completely exposed resist from the unexposed one, use the DELTA.REAL and
DELTA.IMAG parameters. If this difference isn’t specified, the effect of intensity on the resist refraction
index will not be taken into account during the simulation. The number of recursions to obtain the
intensity distribution in both cases with and without taking into account dose-to-n effect is specified in
the EXPOSE statement as NUM.REFL. The maximum dose that corresponds to completely exposed resist
is specified with DOSE parameter.
The examples below show how to use the OPTICAL and EXPOSE statement to specify parameters for
the exposure module.
Example1: Resist exposure with accounting dose effect
OPTICAL NAME.RESIST=CURREN_RESIST I.LINE REFRAC.REAL=1.4 REFRAC.IMAG=0.02
DELTA.REAL=-0.2 DELTA.IMAG=0.01
EXPOSE DOSE=200 NUM.REFL=5
Example2: Resist exposure without accounting dose effect
OPTICAL NAME.RESIST=CURREN_RESIST I.LINE REFRAC.REAL=1.4 REFRAC.IMAG=0.02
EXPOSE DOSE=200 NUM.REFL=5
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5.5: Photoresist Bake Module
Post Exposure Baking (PEB) of the photoresist has been demonstrated to dramatically reduce
standing wave fringes of the developed resist image resulting from optical interference of
monochromatic illumination. This effect is generally accepted to be a result of bulk diffusion of the
PAC and photo reaction products.
The simple physical model, which is adopted here to describe the PEB, is that just one chemical
constituent of the resist diffuses. This constituent is generally assumed to be PAC or the dissolution
inhibitor, which diffuses according to the diffusion equation with the diffusion constant D being
independent of time, concentration and location.
dM
-------- = ∇ ⋅ ( D ∇ M )
dt
5-31
M is the PAC concentration and t is the PEB time. For a more general discussion, see [110]. M is
calculated by solving the two dimensional diffusion (Equation 5-31).
The diffusion length can be related to the bake time t and the diffusion coefficient D.
2tD = σ
2
5-32
For a PEB of 60 seconds at 125ºC, a diffusion length in the range of 0.04 < σ < 0.06 microns would be
appropriate.
PEB can also be specified with parameters temperature and time. The diffusivity D is given by the
equation:
D = D o exp ( – D E ⁄ kT )
5-33
You can specify the D0 and DE parameters in the RATE.DEVELOP command.
“Reflective” boundary conditions at the air/resist interface and at the resist/substrate interface must
be incorporated to ensure that the total amount of dissolution inhibitor in the resist is conserved.
M(x,y,t) is extended into regions outside the resist by reflection at the planar interfaces.
A post development bake is also available. It models a physically based reflow of the photoresist.
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OPTOLITH Models
5.6: The Development Module
The development model is based on the knowledge of the PAC distribution or dissolution inhibitor in
the resist layer after exposure and post-exposure bake. In classical Novolac resists, the dissolution
inhibitor and the PAC are usually part of the same molecule. In chemically amplified resists, the
reaction kinetics are more complicated. The inhibitor concentration still, however, is considered to be
the key quantity for the development process.
In positive tone Novolac resists, to determine the inhibitor concentration from exposure simulations,
use Dill’s model as previously described. This model applies when the resist material undergoes a
transition between two chemical states during the exposure step. The actual development process is
treated as a surface limited etching process, which is dependent on the particular resist-developer
chemistry and on the local concentration of the dissolution inhibitor at the surface of the resist that
has been decomposed to a degree during the exposure step. If the resist developer chemistry is held
constant, the dissolution rate is assumed to be a function of the inhibitor concentration only.
The rate function r(x,y) is determined experimentally and usually fitted by an empirical function to
experimental development rate data as a function of the remaining PAC concentration M(x,y).
You can use one of the following models to simulate the development process for the specific resistdeveloper combination.
•
Dill
•
Kim
•
Mack
•
Trefonas
•
Hirai
Each model assumes a specific rate function type to describe the rate-inhibitor concentration relation.
These models are described in the following sections.
5.6.1: Dill’s Development Model
The Dill model [111] uses the parameters E1, E2, and E3. Surface induction effects are not considered.
The bulk development is given by:
2
R ( x, y ) = exp ( E 1 + E 2 ⋅ M ( x, y ) + E 3 ⋅ M ( x, y ) )
5-34
and for M(x,y) ≤ 0.4:
R ( x, y ) = exp ( E 1 + E 2 ⋅ 0.4 + E 3 ⋅ 0.16 )
5-35
5.6.2: Kim’s Development Model
The Kim model [112] describes the development rate through the function
d(y)
R Induction = 1 – ( 1 – ( R 5 – ( R 5 – R 6 )M ( x , y, z ) ) ) ⋅ exp – ---------R4
1
R Bulk ( x, y ) = -------------------------------------------------------– M ′ ( x, y )- + M
′ ( x, y -)
1---------------------------------------------R1
R2
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M ′ ( x, y ) = M ( x, y ) ⋅ exp ( – R 3 ( 1 – M ( x, y ) ) )
5-38
R ( x, y ) = R Induction ⋅ R Bulk
5-39
R ( x, y ) = R Induction ⋅ R Bulk
5-40
where RBulk is the bulk development rate and RInduction is the surface induction factor. The limiting
development rate values are R1 and R2 respectively for completely exposed and unexposed resist. The
function RInduction(x,y) is an empirical relationship describing the reduced dissolution rate at the
surface of a resist layer and is a function of the normal distance from the original surface of the resist
d(y) and the amount of remaining PAC, M(x,y). The parameter R4 is the characteristic length along
this path for the induction effect. The parameters R5 and R6 are respectively the ratio of the surface
rate to the bulk rate for a completely exposed resist, and the ratio of surface rate to bulk rate for an
unexposed resist.
5.6.3: Mack’s Development Model
The Mack model [113] describes the development rate through the function
n
a + 1 ) ( 1 – M ( x, y ) ) - + R
R ( x, y ) = R max ⋅ (---------------------------------------------------min
n
a + ( 1 – M ( x, y ) )
5-41
n+1
n
a = ------------- ⋅ ( 1 – M th )
n–1
5-42
where the parameter n is a selectivity parameter describing the sensitivity of the developer to the
exposed photoresist. The Mth parameter is the threshold PAC concentration. The Rmax parameter is
the development rate of a completely exposed resist. The parameter Rmin is the development rate of
totally unexposed resist.
5.6.4: Trefonas’ Development Model
The Trefonas development rate model [114] requires only two parameters.
R ( x, y ) = R 0 ⋅ ( 1 – M ( x, y ) )
q
5-43
where R0 is the development rate for unexposed photoresist and q is sensitivity.
5.6.5: Hirai’s Development Model
The development rate model by Hirai [115] is very similar to the one by Trefonas. The rate function of
the Hirai model is given by
α
R ( x, y ) = R 0 ⋅ ( 1 – M ( x, y ) ) + R C
5-44
where R0 is the development rate for fully exposed photoresist, RC is the rate for unexposed resist
material and α is a reaction constant.
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OPTOLITH Models
5.7: Proximity Printing
Alongside with the “standard” projection imaging simulation, OPTOLITH includes an additional
module for simulation of proximity printing. The proximity 1×1 printing (i.e., the imaging without any
reduction lens) is used to print relatively big features of a micron scale. This method is still practical
and in some cases could be cost effective. Internally, projection and proximity printing modules use
different simulation techniques. A common syntax and user interface, however, allow you to switch
easily from one module to another. Some specifics of the proximity lithography and a brief theory used
in the proximity printing module are described below.
5.7.1: General Description of Proximity Lithography
Proximity lithography is used to print images of masks without expensive projection systems. It has
internal resolution limits but still applicable for relatively large objects. Figure 5-3 shows the optical
scheme of proximity lithography.
Figure 5-3: Scheme of proximity optical system.
Light illuminating the mask creates a diffraction image in resist film, placed on some distance (gap)
from the mask. Due to diffraction effects in the gap, the image in the resist film is a distorted mask
image. Distortion depends on the gap size and on the radiation wavelength and size of printed
features. The reliability and longevity of the mask also depends on the gap. Therefore, identification of
the optimal printing conditions is a very important technology design task.
5.7.2: Theory of Proximity Printing
A formal description of diffraction on a gap can be found in any classical book on physical optics. The
Fresnel diffraction is applicable here. Usually, the Fresnel diffraction integral is obtained by applying
Huygens diffraction approximation. It can be derived from the “first principles” by applying specific
limitation to common wave equation. The goal is to obtain distribution of the light intensity over the
resist surface. The real resist exposure with the light absorption into resist, reflections from materials
interfaces, and following photo-chemical resist modifications are considered the same way as for the
projection printing.
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The common wave equation is
2
2
2
2
∂ E- + ∂-------E- + ∂-------E- + k 2 E = 0
∇ E + k E = ------2
2
2
∂x
∂y
∂z
5-45
where E is the electromagnetic field and k is the wave-vector.
Because the normal incidence on the mask is considered and propagation of light from the mask to
resist surface is to be calculated, it is convenient to represent
E ( r ) = A ( r ) exp ( ikz )
5-46
where A is amplitude of electromagnetic field and z is direction along the light propagation.
Substitution from Equation 5-46 into Equation 5-45 gives
2
2
2
A
∂--------A- + ∂-------A- ∂-------A- 2ik ∂-----+
+
= 0
2
2
2
∂z
∂x
∂y
∂y
5-47
Obviously, A is modified with z weakly. Therefore, you can neglect the third term in Equation 5-47. As
the result, Equation 5-47 can be rewritten as
2
2
A
∂--------A- + ∂-------A- + 2ik ∂-----= 0
2
2
∂z
∂x
∂y
5-48
Now Equation 5-48 looks as a diffusion equation with complex diffusion coefficient, where z replaces
diffusion time. It means that the propagation along the z-direction can be formally considered as a
“diffusion” of complex amplitude A in the x,y-plane with a complex “diffusion coefficient”.
The known δ-solution of traditional diffusion equation
2
2
∂ f- + ------∂ f- – ----1- + 2ik ∂----f = 0
------2
2
2
∂t
∂x
∂y ϒ
5-49
is as follows
 x 2 + y 2
1--f 0 = exp  – -----------------
t
 4 ϒ2 t 
5-50
The substitution in Equation 5-48 results in:
2
2
1
x +y
A 0 = --- exp  – ik -----------------

z
2z 
5-51
The solution for given “initial conditions” (i.e., amplitude A immediately after (thin) mask should be
equal to the mask transparency T(x,y)) can now be expressed as a convolution of Ao with T:
2
2
 ( x – Xm ) + ( y – Ym ) 
1
A ( x, y, z ) --- ∫ T ( X m, Y m ) exp  – ik ---------------------------------------------------- dX m dY m
z
2z


5-52
This expression exactly corresponds to the Fresnel diffraction.
5-16
Silvaco
OPTOLITH Models
5.7.3: Simulation Method
The Beam Propagation Method (BPM) is very efficient for tasks where a “one-way” propagation of
electromagnetic field is considered. Common description of BPM can be found in [116], [117]. A
simplified approach applicable to proximity printing conditions (i.e., a gap space filled with
homogeneous matter, so refractive index does not depend on coordinates in the gap) is described here.
The initial distribution of amplitude A in x and y (in the plane perpendicular to the propagation
direction z) can be obtained easily as a complex mask transparency function:
A 0 = A ( x, y, z = 0 )
5-53
Then by applying the 2D Fourier transform over x and y, you can obtain the “angular” distribution:
A ( k x, k y, k z = 0 ) =
∫ A ( x , y, z =
0 ) exp [ i ( k x x + k y y ) ] dx dy
5-54
In this angular-spectrum domain, the relation between A and its z-derivative from Equation 5-48 is
given by the following expression [118]:
∂A
------ ( k x, k y, z ) = i k 2 – k 2x – k 2y A ( k x, k y, z )
∂z
5-55
It means that for each particular “direction”, a specific phase shift has to be applied to get the value of
A at a new z-position:
A ( k x, k y, z + ∆ z ) = A ( k x, k y, z ) exp ( ik z ∆ z )
5-56
In this equation, the z-component of the wave vector is derived by:
kz =
2
2
2
k – kx – ky
5-57
Now the inverse Fourier transform will produce the distribution of the field amplitude over x, y plane
at z=∆z (i.e., at the gap distance from the mask).
Finally, the required intensity distribution is the square of the module of the field amplitude A.
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ATHENA User’s Manual
This page is intentionally left blank.
5-18
Silvaco
Chapter 6:
Statements
6.1: Overview
ATHENA executes a file that describes the process, meshing, and models to be used in a simulation.
The contents of the file are statements, each of which prompts an action or sets a characteristic of the
simulation. This chapter is a reference to the command language that can be used to control ATHENA.
Throughout this manual, we will refer to commands, statements, and parameters. A line in an input
file is referred to as a statement (or statement line).
An ATHENA statement is specified in the general format
<COMMAND>
<PARAMETERS>=<VALUE>
where <COMMAND> is the command name, <PARAMETER> is the parameter name, and <VALUE> is the
parameter value. Four types of parameters are used in ATHENA — Real, Integer, Logical, and
Character. The space character is used to separate parameters from a command or from other
parameters.
Table 6-1. Types of Parameters
Value
Required
Example
Yes
OUTFILE=MOS.STR
Any whole number
Yes
DIVISIONS=10
Boolean
A true or false condition
No
OXIDE or OXIDE=f
Real
Any real number
Yes
C.BORON=1.5e14
Type
Description
Character
An alphabetic,
numeric string
Integer
alphanumeric,
or
Any parameter that does not have a logical value must be specified in the form PARAM=VAL, where
PARAM is the name of the parameter and VAL is the value of the parameter. Boolean parameters must
be separated from other parameters or commands with a space.
For example, in the statement line:
DEPOSIT NITRIDE THICK=0.35
the NITRIDE parameter has a Boolean value (true) and the THICK parameter has a value of 0.35(real).
Many parameters are provided default values. If a parameter is not specified, its default value will be
used. Table 6-1 explains the different types of parameters which may be used when preparing an
ATHENA input deck. The command language of ATHENA is not case sensitive and can be entered using
either upper case or lower case letters.
6.1.1: Abbreviations
It is not always necessary to input the entire statement or parameter name. ATHENA only requires
that you input enough letters to distinguish that command or parameter from other commands or
parameters. For example, DEPO can be used to indicate the DEPOSIT command.
Silvaco
6-1
Overview
ATHENA User’s Manual
6.1.2: Continuation Lines
Since it may be necessary for a statement line to contain more than 256 characters, ATHENA allows
you to specify continuation lines. If a statement line ends with a backslash (\), the next line will be
interpreted as a continuation of the previous line.
6.1.3: Comments
Comments are indicated by the COMMENT statement or a number sign (#). All characters on a line
which follow a comment indicator (COMMENT or #) will not be processed by ATHENA. The comment
symbol $ is not supported anymore. The $ should be avoided for use as a character in strings since it is
used as part of shell capabilities included in DECKBUILD.
6.1.4: General Syntax Description
An ATHENA statement is a sequence of words starting with a statement name and followed by some or
all of the statement’s parameters. This manual describes the syntax for each statement in the
following way:
STATEMENT NAME
DESCRIPTION OF PARAMETER 1
DESCRIPTION OF PARAMETER 2 . . .
Parameters are described in the following form:
PARAM=<n>... a real valued parameter
PARAM=<c>... a string valued parameter
PARAM ... a Boolean parameter
Boolean parameters are those that recognize the Boolean values TRUE and FALSE as valid values. In
ATHENA, Boolean parameter values are automatically set to true if the name of the Boolean
parameter appears by itself in a statement. A Boolean parameter can be set to false using the syntax:
PARAM=FALSE or PARAM=F.
A mutually exclusive choice among parameters is indicated by parentheses around the parameters
and vertical bars between each parameter (PAR1|PAR2). Only one parameter in such a group may be
specified at a time. Specifying more than one parameter in a mutually exclusive group is an invalid
operation and will generally prompt a warning or error message.
Parameters that are optional to a statement are enclosed by brackets [ ]. Most parameters are
assigned default values and so defining them is optional. All parameters and parameter values,
however, should be checked in the context of the actual process that will be simulated before relying on
the results of any simulation.
String-valued parameters can be specified as a single word, e.g., INFILE=FILE1, or as a sequence of
words surrounded by double quotes, e.g., MATERIAL="Nickel Silicide". Real-valued parameters
can be specified as expressions involving numbers, numerical constants, the operators +, -, *, /, and
the functions listed in Table 6-2. If an expression contains spaces, then enclose it in parentheses.
6-2
Silvaco
Overview
Table 6-2. Functions
Function
Description
abs5
Absolute value
active
Active portion of the specified dopant
erf
Error function
erfc
Complimentary error function
exp
Exponential
gradx
Computes the approximate gradient in the x direction
grady
Computes the approximate gradient in the y direction
log
Logarithm
log10
Logarithm base 10
mat1@mat2
Returns the y value of the interface between mat1 and mat2 along a
vertical slice at the given location
mat1|mat2
Returns the x value of the interface between mat1 and mat2 along a
horizontal slice at the given location
scales
Scales the value given by the maximum value
sqrt
Square root
xfn
Takes y and z and finds a matching x
yfn
Takes x and z and finds a matching y
zfn
Takes x and y and finds a matching z
Examples:
PAR1=<n>
PAR1 is a required numeric valued option.
PAR1=( 4.0 * EXP( -2.0 / (8.62E-5 * 1173.0) ) )
PAR1 is a required numeric valued option, assigned a real number expression.
[PAR2=<c>]
PAR2 is an optional character variable.
For further examples of expressions, see SET and EXTRACT in VWF INTERACTIVE TOOLS USER’S MANUAL,
VOL. I.
6.1.5: Command Line Parsing
ATHENA supports expressions on the command line. For example:
DIFFUSE TIME=10/60 TEMP=1000
Be careful when using parentheses as the precedence of arithmetic operators, as in programming
languages, is not guaranteed in all cases.
Silvaco
6-3
ATHENA Statements List
ATHENA User’s Manual
6.2: ATHENA Statements List
This chapter contains a complete description (in alphabetical order) of every statement used by any of
the ATHENA products. The following documentation is provided for each statement:
•
The statement name
•
A list of all of the parameters of the statement and their type
•
A description of each parameter or group of similar parameters
•
An example of the correct usage of each statement
The ATHENA command language encompassed by this document describes each of the modules of
ATHENA, namely: ELITE, OPTOLITH, SSUPREM4 and their submodules. Depending on which of the
ATHENA modules have been purchased, some of the capabilities described may not be available as part
of the ATHENA installation.
Note: You can print a summary of statement names and parameters by using the HELP statement.
The following list classify ATHENA statements and provide their brief description and use.
6.2.1: Structure and Grid Initialization Statements
These statements define the dimensions, boundary conditions, grid density, and material type of the
initial structure. Typically, only LINE and INITIALIZE statements are required.
•
BASE.MESH specifies parameters of the base mesh used for initial grid generation.
•
BOUNDARY specifies which lines in a rectangular grid are exposed to gas.
•
INITIALIZE sets up the initial grid and specifies background doping concentrations and material type.
•
LINE specifies the positioning of x and y grid lines for a rectangular mesh.
•
REGION specifies corresponding sections of the rectangular mesh and material.
6.2.2: Structure and Mesh Manipulation Statements
These statements manipulate the geometry or attributes of the structure or create output files.
6-4
•
ADAPT.MESH enables the adaptive meshing algorithm.
•
ADAPT.PAR specifies adaptive meshing parameters.
•
BASE.PAR defines adjacent mesh characteristics of an automated base mesh.
•
ELECTRODE names electrode regions.
•
GRID.MODEL defines a template file containing adaptive meshing commands.
•
PROFILE causes ATHENA to read in an ASCII file of depth and doping data.
•
RELAX loosens the grid within a user-specified area.
•
STRETCH allows changes in structure geometry by stretching at a horizontal or vertical line.
•
STRUCTURE writes the mesh and solution information into a file. This is the main output
statement for generating program data to be plotted.
Silvaco
ATHENA Statements List
6.2.3: Simulation Statements
These statements apply physically based models for processing operations to the structure.
•
BAKE performs post-exposure or post-development photoresist bake.
•
DEPOSIT deposits a material layer.
•
DEVELOP performs photoresist development.
•
DIFFUSE performs a time/temperature step on the wafer and calculates oxidation and diffusion
of impurities.
•
EPITAXY performs high temperature silicon epitaxial growth.
•
ETCH performs a geometric or machine type etch on the structure.
•
EXPOSE models photoresist exposure.
•
IMAGE calculates a 2D or 1D aerial image.
•
IMPLANT models ion implantation.
•
POLISH simulates chemical mechanical polishing in the ELITE module.
•
STRESS computes the thermal elastic stresses.
•
STRIP removes photoresist or another user specified material.
6.2.4: Model Statements
These statements are used to change model parameters and coefficients. The parameters are described
in the statement descriptions. When starting-up, ATHENA executes the model statements in the file
named athenamod located in the $SILVACO/lib/athena subdirectory corresponding to the version
number and system type of ATHENA that you are running. This file contains the default parameters
for most model statements.
•
ABERRATION defines aberration parameters of the optical projection system.
•
CLUSTER specifies parameters of {311} cluster model.
•
ILLUMINATION describes the photolithographic illuminating system.
•
ILLUM.FILTER defines filters used in the illumination source for photolithography.
•
IMPURITY sets the coefficients of impurity kinetics.
•
INTERSTITIAL sets the coefficients of interstitial kinetics.
•
LAYOUT describes the mask reticle for imaging.
•
MATERIAL sets the coefficients of various materials.
•
METHOD sets the numerical options or models for solving the equations.
•
MOMENTS specifies moments for Pearson implant model.
•
OPTICAL specifies the coefficients of reflection and refraction.
•
OXIDE specifies oxidation coefficients.
•
PROJECTION defines the photolithographic projection system.
•
PUPIL.FILTER defines filters in the pupil plane.
•
RATE.DEPO specifies deposition rates for machine type deposits.
•
RATE.DEVELOP specifies development rates and other photoresist parameters.
•
RATE.ETCH specifies the etch rate for machine etches.
•
RATE.POLISH specifies polishing parameters for definition of a polishing machine.
•
SILICIDE sets the coefficients for silicidation reactions.
•
TRAP sets the coefficients of trap kinetics.
•
VACANCY sets the coefficients of vacancy kinetics.
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6-5
ATHENA Statements List
ATHENA User’s Manual
6.2.5: Special DECKBUILD Statements
These statements invoke special operations when running under DECKBUILD. For more information on
these statements, see the VWF INTERACTIVE TOOLS manual.
•
AUTOELECTRODE defines layout-based electrodes.
•
EXTRACT extracts parameters.
•
GO indicates interfacing between simulators.
•
MASK performs photoresist deposition and etching through the MASKVIEWS interface.
•
SET sets the value of a user-defined variable.
•
SYSTEM allows execution of any UNIX C-shell command within an input file.
•
TONYPLOT creates a plot using TONYPLOT.
6.2.6: Post-processing Statements
Starting from version 4.0, all internal plotting capabilities of former SUPREM-IV have been
depreciated. Enhanced superior capabilities are available through TONYPLOT and other VWF
INTERACTIVE TOOLS. Only the following two post-processing statements remain.
•
PRINT.1D is used to print the values (data points and profile information).
•
SELECT allows a variable to be chosen as the z coordinate for the PRINT.ID command to follow.
6.2.7: Execution Control Statements
These statements control some execution capabilities. Some of them are useful only in a batch mode
when ATHENA is run outside DECKBUILD.
•
COMMENT is used to document the input file.
•
CPULOG instructs ATHENA to output CPU statistics.
•
FOREACH/END specifies the command looping facility.
•
HELP prints summary of statement names and parameters.
•
OPTION specifies the level of run-time output.
•
PRINTF parses a string or expression and places result into standard output.
•
QUIT terminates execution of ATHENA.
•
SETMODE sets execution mode parameters.
•
SOURCE causes ATHENA to read statements from the specified file.
•
UNSETMODE sets execution mode parameters to false.
6.2.8: Obsolete Statements
The following statements existed in earlier versions of ATHENA. Their capabilities were substituted
either by superior capabiliites of VWF INTERACTIVE TOOLs or included in other more advanced or generic
statements.
6-6
•
ANTIMONY is substituted by the I.ANTIMONY parameter in the IMPURITY statement.
•
ARSENIC is substituted by the I.ARSENIC parameter in the IMPURITY statement.
•
BORON is substituted by the I.BORON parameter in the IMPURITY statement.
•
COLOR - all plotting capabilities are now provided by TONYPLOT.
•
CONTOUR - all plotting capabilities are now provided by TONYPLOT.
•
ECHO is a synonym of the PRINTF statement
•
DEFINE is substituted by the SET capability in DECKBUILD.
•
INDIUM is substituted by the I.INDIUM parameter in the IMPURITY statement
Silvaco
ATHENA Statements List
•
LABEL - all plotting capabilities are now provided by TONYPLOT
•
PAUSE is substituted by the Pause button in DECKBUILD.
•
PHOSPHORUS is substituted by I.PHOSPHOR parameter in the IMPURITY statement
•
PLOT.1D - all plotting capabilities are now provided by TONYPLOT
•
PLOT.2D - all plotting capabilities are now provided by TONYPLOT.
•
PLOT.3D - all plotting capabilities are now provided by TONYPLOT.
•
UNDEFINE is substituted by the SET capability in DECKBUILD.
•
VIEWPORT - all plotting capabilities are now provided by TONYPLOT.
6.2.9: Standard and User-Defined Materials
Different materials can be specified as parameters in various statements. Both standard and userdefined materials are available in ATHENA. The generic name MATERIAL appeared in a statement
syntax description signifies that you can only specify one of standard material names from the list
below or user-defined material. The generic name MATERIALS appeared in a statement syntax
description signifies that you can specify one or several standard and user-defined materials.
The following shows the standard material names currently available in ATHENA.
Semiconductors
SILICON, POLYSILICON, GAAS, ALGAAS, INGAAS, SIGE, INP, GERMANIUM, SIC_6H, SIC_4H,
SIC_3C
Note: Since ATHENA parser doesn’t recognize parameter names that begin with numerals, non-standard names are used for
Silicon Carbides: SIC_6H, SIC_4H, and SIC_3C. Standard names: 6H-SiC, 4h-SiC, and 3C-SiC are used
for these materials outside ATHENA (e.g. TonyPlot and ATLAS).
Insulators
OXIDE, OXYNITRIDE, NITRIDE, PHOTORESIST
Metals
ALUMINUM, TUNGSTEN, TITANIUM, PLATINUM, COBALT
Silicides
WSIX (Tungsten Silicide), TISIX (Titanium Silicide), PTSIX (Platinum Silicide), COSIX (Cobalt
Silicide)
Special Materials
GAS is used only in the IMPURITY, INTERSTITIAL and VACANCY statements to specify some
parameters (i.e., segregation) at exposed boundaries.
BARRIER is a fictitious material. It can be specified only in DEPOSIT and ETCH statements and serve
as a masking material.
Silvaco
6-7
ATHENA Statements List
ATHENA User’s Manual
User-defined Materials
User-defined materials can be specified by MATERIAL = <c>, where <c> could be a single word
MATERIAL=OXIDE1 or any string in double quotes as MATERIAL=”MY INSULATOR”. The userdefined material with the names exactly corresponding to SILVACO standard material names are
saved in SILVACO Structure Files as those standard materials and will be recognized as such by other
tools, e.g. DEVEDIT and ATLAS. The following are the lists of those SILVACO standard materials that
can be used in ATHENA as previously described.
•
Semiconductors: “Fictive GaAs”, AlInAs, AlAs, "Alpha Si 1", "Alpha Si 2", "Alpha Si 3","Alpha
Si 4", "AlxGa1_xAs_x_0.25", "AlxGa1_xAs_x_0.5", "AlxGa1_xAs_x_0.75", "InxGa1_xAs_x_0.50
Unstr", "InxGa1_xAs_x_0.33 Str GaAs", "InxGa1_xAs_x_0.75 Str InP", "AlxIn1_xAs_x_0.50",
Diamond, AlP, AlSb, GaSb, GaP, InSb, InAs, ZnS, ZnSe, ZnTe, CdS, CdSe, CdTe, HgS, HgTe,
PbSe, PbTe, SnTe, ScN, GaN, AlN, InN, BeTe, InGaP, GaSbP, GaSbAs, InAlAs, InAsP, GaAsP,
HgCdTe, CdZnTe, InGaAsP, AlGaAsP, AlGaAsSb, SiN, Si, CuInGaSe, InGaN, AlGaN, InAlGaN,
InGaNAs, InGaNP, AlGaNAs, AlGaNP, AlInNAs, AlInNP, InAlGaAs, InAlGaP, InAlAsP, Pentacene, Alq3, TPD, PPV, and Organic.
•
Insulators: Sapphire, Vacuum, TEOS, BSG, BPSG, PMMA, SOG, Polyimide, "Cooling package
material", Ambient, Air, Insulator, Polymer, and ITO.
•
Metals and Silicides: Gold, Silver, AlSi, Palladium, Molibdinum, Lead, Iron, Tantalum, AlSiTi,
AlSiCu, TiW, Copper, Tin, Nickel, WSix, NiSix, TaSix, PdSix, MoSix, ZrSix, AlSix, Conductor,
Contact, Ba2YCu3O7 and Ba2NdCu3O7
The generic name /MATERIAL specifies the second material in those statements, which specify
parameters related to the boundary between two materials.
6.2.10: Standard Impurities
Different impurities can be specified as parameters in various statements. The generic name
IMPURITY appeared in a statement syntax description signifies that you can only specify one of
impurity names from the list below. The generic name IMPURITIES appeared in a statement syntax
description signifies that you can specify one or more impurity names from the list below in the
statement simultaneously. The impurity names below can appear as is or as a part of a parameter
name, e.g. I.BORON, C.BORON and F.BORON. The following is the list of standard impurity names
currently available in ATHENA:
ALUMINUM, ANTIMONY, ARSENIC, BERYLLIUM, BORON, CARBON, CHROMIUM, FLUORINE,
GALLIUM, GERMANIUM, GOLD, HELIUM, HYDROGEN, INDIUM, MAGNESIUM, NITROGEN, OXYGEN,
PHOSPHORUS, SELENIUM,
SILICON, and ZINC
6-8
Silvaco
ABERRATION
6.3: ABERRATION
ABERRATION defines aberration parameters of the optical projection system.
Syntax
ABERRATION
[X.FIELD=<n>][Z.FIELD=<n>] [SPHERICAL=<n>] [COMA=<n>]
[ASTIGMATISM=<n>] [CURVATURE=<n>] [DISTORTION=<n>]
[FIFTH|SEVENTH|NINTH]
C1=<n>][C2=<n>][C3=<n>][C4=<n>][C5=<n>]
[C6=<n>][C7=<n>][C8=<n>][C9=<n>][C10=<n>][C11=<n>]
[C12=<n>][C13=<n>][C14=<n>][C15=<n>][C16=<n>][C17=<n>]
[C18=<n>][C19=<n>][C20=<n>]
Description
This statement specifies the aberration coefficients in the power series expansion of the wave
aberration function. Each coefficient is entered in fractions of a wavelength in the range 0 ≤ C ≤ 0.5.
X.FIELD and Z.FIELD define or change the position in the image field for which the irradiance
distribution is to be computed. Note that the position is expressed in fractional field coordinates, so
that the values for the x and z directions vary between -1.0 and 1.0.
SPHERICAL specifies 0C40, the amount of third order spherical aberration present in the power
series expansion of the wave aberration function of the optical projector.
COMA specifies 1C31, which is the amount of third order coma present in the power series expansion
of the optical projector.
ASTIGMATISM specifies 2C22, which is the amount of third order astigmatism present in the power
series expansion of the optical projector.
CURVATURE specifies 2C20, which is the amount of third order field curvature present in the power
series expansion of the optical projector.
DISTORTION specifies 3C11, which is the amount of third order distortion present in the power
series expansion of the optical projector.
FIFTH, SEVENTH, and NINTH specify the aberration order. Coefficients for only one aberration
order can be specified on a single statement.
C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12, C13, C14, C15, C16, C17, C18, C19, and C20
are described in Table 6-3. Coefficients for fifth, seventh, and ninth order aberrations must be entered
in separate ABERRATION commands for each order. Each of these parameters represents a particular
aberration coefficient depending on the order specified by parameters FIFTH, SEVENTH, or NINTH.
Table 6-3. Aberration Coefficients
Silvaco
Parameter
Fifth
Seventh
Ninth
C1
4C20
6C20
8C20
C2
2C40
4C40
6C40
C3
0C60
2C60
4C60
C4
5C11
0C80
2C80
6-9
ABERRATION
ATHENA User’s Manual
Table 6-3. Aberration Coefficients
Parameter
Fifth
Seventh
Ninth
C5
3C31
7C11
0C100
C6
1C51
5C31
9C11
C7
4C22
3C51
7C31
C8
2C42
1C71
5C51
C9
3C33
6C22
3C71
C10
4C42
1C91
C11
2C62
8C22
C12
5C33
6C42
C13
3C53
4C62
C14
4C44
2C82
C15
7C33
C16
5C53
C17
3C73
C18
6C44
C19
4C64
C20
5C55
Examples
If high order aberrations are to be studied, they must be entered on a separate command line for each
order.
ABERRATION X.FIELD=.5 SPHERICAL=.25
ABERRATION FIFTH C1=.25 C2=.5
ABERRATION SEVENTH C1=.3 C4=.4
For more examples, see IMAGE, ILLUMINATION, PROJECTION, ILLUM.FILTER, PUPIL.FILTER,
LAYOUT.
6-10
Silvaco
ADAPT.MESH
6.4: ADAPT.MESH
ADAPT.MESH enables the adaptive meshing algorithm.
Syntax
ADAPT.MESH
[SMOOTH] [SMTH.COUNT=<n>] [ADAPT] [ADAPT.COUNT=<n>] [ADD.I.LINE=<n>]
[SENSITIVITY] [MATERIAL] [/MATERIAL]
Description
This statement runs the adaptive meshing algorithm or the smoothing algorithm in standalone mode.
SMOOTH flag to do mesh smoothing.
SMTH.COUNT specifies the number of smooth loops during the smooth operation. The default is 1.
ADAPT flag to do stand alone mesh adapting. Specifies that a stand alone adaptive meshing step
should be performed to refine or relax the current mesh based on the material/impurity specification
given on ADAPT.PAR command The default is False.
ADAPT.COUNT specifies the number of adapting loops during the stand alone adaptive meshing
operation The default is 1.
ADD.I.LINE depth of the shadow interface mesh line in microns. Add the mesh line at the interface
between two materials as defined by the booleans MATERIAL and /MATERIAL. The line is added in
MATERIAL at a distance ADD.I.LINE from /MATERIAL.
SENSITIVITY specifies sensitivity of adaptation algorithm. The lower value leads to grid with more
triangles. The default is 1.0.
MATERIAL one of standard materials or user specified material (see Section 6.2.9: “Standard and
User-Defined Materials” for the list of materials).
/MATERIAL one of standard materials or user specified material (see Section 6.2.9: “Standard and
User-Defined Materials” for the list of materials).
Examples
The following statement will add a set of lines close to the silicon/silicon dioxide interface. For this to
work, the existing grid spacing at the interface must be greater than 0.005 microns. Note that since
the lines are added only between existing mesh lines and the interface the lines must be specified in
this order (i.e., getting closer to the surface)
ADAPT.MESH SILICON /OXIDE ADD.I.LINE=0.005
ADAPT.MESH SILICON /OXIDE ADD.I.LINE=0.001
ADAPT.MESH SILICON /OXIDE ADD.I.LINE=0.0005
ADAPT.MESH SILICON /OXIDE ADD.I.LINE=0.0001
For more examples, see ADAPT.PAR.
Silvaco
6-11
ADAPT.PAR
ATHENA User’s Manual
6.5: ADAPT.PAR
ADAPT.PAR specifies adaptive meshing parameters.
Syntax
ADAPT.PAR
[MATERIALS] [I.IMPURITIES] [I.INTERST] [I.VACANCY] [DISABLE]
[MAX.ERR=<n>] [MIN.ERR=<n>] [CONC.MIN=<n>] [AREA.MIN=<n>] [AREA.MAX=<n>]
[EDGE.MIN=<n>] [EDGE.MAX=<n>] [MIN.ADD=<n>]
[MAX.POINT=<n>] [MAX.LOOP=<n>] [IMPL.SMOOTH] [DIFF.SMOOTH] [IMPL.SUB]
[DOSE.ERR=<n>] [DOSE.MIN=<n>] [DIFF.LENGTH=<n>] [ANISOTROPIC]
Description
ADAPT.PAR specifies parameters used during adaptive meshing enabled by the ADAPT.MESH
statement.
MATERIALS specify standard materials or user specified material regions in which mesh adaptation
takes place (see Section 6.2.9: “Standard and User-Defined Materials” for the list of materials). One or
several materials can be specified at a time.
I.IMPURITIES specify the impurities to be used for the grid adaptation (see Section 6.2.10:
“Standard Impurities” for the list of impurity names that can be used, e.g. I.BORON). You can specify
one or several impurities at a time.
I.INTERST specifies that interstitials to be used for the grid adaptation.
I.VACANCY specifies that vacancies to be used for the grid adaptation.
DISABLE specifies that the materials/impurities combinations given are disabled to be effective on
mesh adapting or smoothing. Default is false.
MAX.ERR specifies the maximum error allowable before adding points to the mesh, (unitless). Error
calculated above this value cause points to be added.
MIN.ERR specifies the minimum error below which points can be deleted from the mesh, (unitless).
Error calculated below this value will remove points. Both MAX.ERR and MIN.ERR are calculated using
the Bank-Weiser error estimator.
CONC.MIN specifies the minimum impurity concentration below which adapting will stop. Units are
cm-3. Default is 1.0 1014cm-3.
AREA.MIN specifies the minimum triangle area below which adding points will stop. Units are cm2.
Default is 1.0 10-15
AREA.MAX specifies the maximum triangle area below which deleting points will stop. Units are
cm2. Default is 1.0 10-11.
EDGE.MIN specifies the minimum edge length below which adding points will stop. Units are cm.
Default is 1.0 10-6.
EDGE.MAX specifies the maximum edge length below which deleting points will stop. Units are cm.
Default is 1.0 10-5.
MIN.ADD percent criteria to turn off implant adapt loop. MIN.ADD stops point addition in IMPLANT
when the number of points added in the current loop is less than MIN.ADD * (total number of points).
The default value for MIN.ADD = 0.05.
MAX.POINT specifies the maximum number of points above which adapting will stop. Default is
20000.
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ADAPT.PAR
MAX.LOOP specifies the maximum loop count above which adapting will stop. This is only effective
with implant. Default is 10.
IMPL.SMOOTH specifies which annealing algorithm to use after each adaption step. Currently,
IMPL.SMOOTH=0 corresponds to no annealing during IMPLANT. IMPL.SMOOTH=1 corresponds to
Laplacian smoothing and dose conservation interpolation algorithm. The default is IMPL.SMOOTH=1.
DIFF.SMOOTH specifies which annealing algorithm to use after each adaption step. Currently,
DIFF.SMOOTH=0 corresponds to no annealing during DIFFUSE. DIFF.SMOOTH = 1 corresponds to
Laplacian smoothing and dose conservation interpolation algorithm. The default is DIFF.SMOOTH=0.
IMPL.SUB flag to do grid subtracting in implant adapt. IMPL.SUB is a boolean flag that stops point
removal during IMPLANT adaptive meshing. The default value for IMPL.SUB=false signifies that
points are not being removed.
DOSE.ERR specifies dose error for the refinement/unrefinement.
DOSE.MIN specifies minimum of dose level for grid refinement during adaptation.
DIFF.LENGTH used to limit the activity of adaptation of grid during the simulation of dopant
diffusion. This parameter will allow the mesh to adapt only after a given diffusion length for a given
dopant and will override any other adaptation triggers based upon gradient error estimates. This is a
useful control to limit the number of time steps. Units are microns.
ANISOTROPIC is the flag used to maintain the mesh to be anisotropic. The flag is material
dependent.
Examples
The following is an example of setting the adaptive meshing parameters during diffusion for Boron.
IMPLANT BORON DOSE=1E15 ENERGY=60
ADAPT.PAR DIFF.LEN=0.1 SILICON I.BORON
DIFFUSE TEMP=1000 TIME=100 NITROGEN
For more examples, see ADAPT.MESH.
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BAKE
ATHENA User’s Manual
6.6: BAKE
BAKE performs post-exposure or post-development photoresist bake.
Syntax
BAKE
[DIFF.LENGTH=<n>] [TEMERATURE=<n>] [REFLOW]
[TIME] [SECONDS|MINUTES|HOURS]
[DUMP=<n>] [DUMP.PREFIX=<c>]
Description
This command runs a bake process using the diffusion length as the parameter that incorporates the
bake temperature and bake time.
DIFF.LENGTH specifies the diffusion length for the post exposure bake. Default is 0.05 micrometers
TEMPERATURE specifies the temperature of the bake process in oC.
REFLOW specifies that material flow should be calculated during the bake process. Default is
False.
TIME specifies the amount of time for the bake step in specified units. Default is MINUTES.
HOURS, MINUTES, and SECONDS specify the units of the TIME parameter.
DUMP and DUMP.PREFIX specify that a structure file be output at every DUMPth time step. The
files are readable with the STRUCTURE statement or can be displayed using TONYPLOT. The names will
be of the form DUMP.PREFIX<time>.str, where <time> is the current total time of the simulation.
Examples
The BAKE command is entered with the user-specified diffusion length for post exposure bake:
BAKE DIFF.LENGTH=0.05
BAKE can also be entered with time and temperature parameters for post exposure bake:
BAKE TIME=45 TEMP=120
For photoresist reflow (post development bake), the above command is entered with the REFLOW
parameter:
BAKE REFLOW TIME=45 TEMP=120
For more examples, see DIFFUSE and RATE.DEVELOP.
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BASE.MESH
6.7: BASE.MESH
BASE.MESH specifies parameters of the base mesh used for initial grid generation.
Syntax
BASE.MESH
[SURF.LY=<N>] [SURF.DY=<N>] [ACTIVE.LY=<N>]
[ACTIVE.DY=<N>] [EPI.LY=<N>] [EPI.DY=<N>]
[SUB.LY=<N>] [SUB.DY=<N>] [BACK.LY=<N>] [BACK.DY=<N>]
Description
This command specifies parameters of the base mesh used for initial grid generation.
SURF.LY specifies the location of surface. The default is y=0.0 µm.
SURF.DY specifies the local grid spacing in y-direction at SURF.LY.
ACTIVE.LY, EPI.LY, SUB.LY specify another three base line location at some critical region of the
device structure to be fabricated.
ACTIVE.DY, EPI.DY, SUB.DY specify the local grid spacing at the ACTIVE.LY, EPI.LY, SUB.LY. The
units are all in microns.
BACK.LY and BACK.DY are the location of bottom in the structure to be fabricated and the BACK.DY
is the local grid spacing in the BACK.LY location.
Examples
The following example assigns the initial base line for the substrate materials. It places the base line
at y=1.0, y=2.0, y=10.0 with a local grid spacing of 0.01 µm, 0.5 µm, 1.0 µm and 10 µm separately. The
device dimension in the y-direction is specified as y.main=0. y=max=100. This depth, however, is
only for reference. The real depth and width of the device structure will be assigned in the
INITIALIZE command.
BASE.MESH SURF.LY=0.0 SURF.DY=0.01\
ACTIVE.LY=1.0 ACTIVE.DY=0.5 EPI.LY=2.0 EPI.DY=1.0\
SUB.LY=10.0 SUB.DY=10.0 BACK.LY=500 BACK.DY=100
For more examples, see BASE.MESH and INITIALIZE.
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BASE.PAR
ATHENA User’s Manual
6.8: BASE.PAR
BASE.PAR runs the base mesh for generating the initial grid.
Syntax
BASE.PAR
[MATERIAL] [GRAD.SPACE] [RATIO.BOX]
Description
MATERIAL one of standard materials or user specified material (see Section 6.2.9: “Standard and
User-Defined Materials” for the list of materials).
GRAD.SPACE specifies the gradient of the adjacent grid spacing in the y-direction of this material.
Default is 1.5.
RATIO.BOX specifies the approximate aspect ratio of triangle element after base mesh generation in
this material. Default is 2.0.
Examples
The following example generates a good quality base mesh for each related material region.
BASE.PAR OXIDE
GRAD.SPACE=5
RATIO.BOX=2
BASE.PAR SILICON
GRAD.SPACE=1.5
RATIO.BOX=2
BASE.PAR POLYSILICON GRAD.SPACE=5
RATIO.BOX=2
BASE.PAR OXIDE
GRAD.SPACE=5
RATIO.BOX=2
BASE.PAR SILICON
GRAD.SPACE=1.5
RATIO.BOX=2
BASE.PAR POLYSILICON GRAD.SPACE=5
RATIO.BOX=2
For more examples, see BASE.MESH.
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BOUNDARY
6.9: BOUNDARY
BOUNDARY specifies boundary conditions for the initial material.
Note: For most typical boundary conditions, ATHENA has defaults that eliminate the need for BOUNDARY statements. The
BOUNDARY statement can be used to modify the treatment of the surfaces for special purpose simulations.
Syntax
BOUNDARY
[REFLECTING|EXPOSED|BACKSIDE]
[XLO=<c>] [YLO=<c>)] [XHI=<c>] [YHI=<c>]
Description
EXPOSED surfaces correspond to the top of the wafer. Only exposed surface have deposition or
oxidation on top of them. A surface created by etching will also be exposed unless the ETCH
NO.EXPOSE syntax is used.
REFLECTING surfaces correspond to the sides of the device and are also applicable to the backside
as long as defects are not being simulated. All surfaces default to REFLECTING.
BACKSIDE surfaces are physically identical to the reflecting surface with special meaning only when
backside electrode is specified in the ELECTRODE statement
XLO, YLO, XHI, and YHI set the left, right, top, and bottom bounds of the rectangle being specified.
The value string should be one of the tags specified in one of preceding line statements.
Examples
The following lines define the top of the mesh to be an exposed surface and the bottom to be the
backside.
BOUNDARY EXPOSED XLO=LEFT XHI=RIGHT YLO=SURF YHI=SURF
BOUNDARY BACKSIDE XLO=LEFT XHI=RIGHT YLO=BACK YHI=BACK
For more examples, see REGION and INITIALIZE.
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CLUSTER
ATHENA User’s Manual
6.10: CLUSTER
CLUSTER specifies parameters of {311} cluster model.
Syntax
CLUSTER
[I.IMPURITY] [MATERIAL]
[CLUST.FACT=<n>] [MIN.CLUST=<n>] [MAX.CLUST=<n>]
[TAU.311.0=<n>] [TAU.311.E=<n>]
Description
This command specifies the scaling of {311} clusters during a subsequent IMPLANT step and the time
constant for the dissolution of clusters into free interstitials.
Note: This command will only work if you switch on the {311} cluster model with the METHOD CLUSTER.DAM command.
I.IMPURITY specifies an impurities to be used for the {311} cluster scaling (see Section 6.2.10:
“Standard Impurities” for the list of impurity names that can be used, e.g. I.BORON).
MATERIAL specifies a material in which the scaling takes place (see Section 6.2.9: “Standard and
User-Defined Materials” for the list of materials). Default is SILICON.
MIN.CLUST and MAX.CLUST define two values of implanted dopant concentration. Clusters will be
placed between these two dopant concentration levels only. These parameters are used to control the
scaled position of clusters during ion implantation. Typically, MIN.CLUST is the background doping
level. MAX.CLUST is the dopant concentration required to amorphize the substrate
CLUST.FACT specifies the ratio between the concentration of clustered interstitials and the
implanted dopant concentration.
TAU.311.0=<n> and TAU.311.E=<n> specify the time constant in seconds for the dissolution of
clusters into free interstitials. TAU.311.0 is the pre-exponential linear coefficient and TAU.311.E is
the exponential coefficient used to control temperature dependence.
Examples
The following command introduces clusters during ion implantation. The clusters will have an
effective interstitial concentration of 1.4 times the concentration of implanted boron. The clusters will
lie in the region where Boron is between 1015 and 1019 cm-3.
METHOD CLUSTER.DAM
CLUSTER I.BORON SILICON MIN.CLUS=1e15 MAX.CLUST=1e19 CLUST.FACT=1.4
IMPLANT DOSE=1e14 ENERGY=50 BORON
The example goes on to define the cluster dissolution time and a short thermal cycle. Results for each
timestep of the diffusion cycle will be stored in files RTA_*
CLUSTER I.BORON SILICON TAU.311.0=10 TAU.311.E=0.24
DIFFUSE TEMP=1000 TIME=10/60 NITRO DUMP=1 DUMP.PREF=RTA_
For more examples, see METHOD, DISLOC.LOOP, INTERSTITIAL, and VACANCY.
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COMMENT
6.11: COMMENT
COMMENT is used to specify character strings for documenting the input deck and ATHENA output.
Syntax
COMMENT
#
or
$
Description
The COMMENT statement, # or $ are used to document the input file. You can insert them in the
beginning of any line of the input deck.
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CPULOG
ATHENA User’s Manual
6.12: CPULOG
CPULOG instructs ATHENA to output CPU statistics.
Syntax
CPULOG
[LOG] [CPUFILE = <c>]
Description
The CPULOG statement logs the CPU time used in various internal operations. The CPU time
information appears in the standard output or in the DeckBuild Text Subwindow unless it is redirected into CPUFILE.
LOG enables logging of CPU usage when true, and disables CPU logging when false. The default is
true.
CPUFILE specifies a name of the file to which CPU log is written. The default is the standard output.
Examples
The following example enables ATHENA to gather CPU statistics and store it in the file timeusage.out.
CPULOG LOG CPUGFILE=timeusage.out
Note: The accuracy of time statistics depends on the computer and operating system. It is usually around 0.01 sec.
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DEPOSIT
6.13: DEPOSIT
DEPOSIT deposits a layer of specified material. DEPOSITION is a synonym for this statement.
Note: Unless the ELITE module is used, all deposition steps in ATHENA are 100% conformal. This means deposition on all
surfaces with a step coverage of 1.0.
Syntax
DEPOSIT
MATERIAL [NAME.RESIST=<c>] THICKNESS=<n>
[SI_TO_POLY] [TEMPERATURE=<n>]
[DIVISIONS=<n>] [DY=<n>][YDY=<n>] [MIN.DY=<n>] [MIN.SPACE=<n>]
[C.IMPURITIES=<n>] [F.IMPURITIES=<n.] [C.INTERST=<n>] [F.INTERST=<n>]
[C.VACANCY=<n>] [F.VACANCY=<n>] [C.FRACTION=<n>] [F.FRACTION=<n>]
[MACHINE=<c>] [TIME=<n>] [HOURS|MINUTES|SECONDS]
[N.PARTICLE=<n>] [OUTFILE=<c>] [SUBSTEPS=<n>][VOID]
Description
This statement is used to simulate deposition of specified material on the exposed surface of the
current structure.
MATERIAL specifies the material to be deposited (see Section 6.2.9: “Standard and User-Defined
Materials” for the list of materials).
NAME.RESIST specifies the type of photoresist to be deposited.
THICKNESS specifies the deposited layer thickness in microns.
SI_TO_POLY specifies that crystalline silicon will be deposited only over crystalline silicon, while
polysilicon will be deposited elsewhere.
TEMPERATURE specifies deposition temperature used by STRESS.HIST model. The temperature
is also used for surface diffusion simulation during ELITE deposition.
Grid Control Parameters
DIVISIONS specifies the number of vertical grid spacings in the layer. In some cases, it is important
to control the number of grid points in a conformally deposited layer since this also controls the
accuracy of subsequent processes. SPACES is an alias for DIVISIONS. The default is 1.
Note: The default for DIVISIONS is 1. This typically needs to be increased for all deposition steps. If DIVISIONS is set
too low to maintain grid integrity in a non-planar deposition, ATHENA will attempt to recover by increasing DIVISIONS
automatically. ATHENA will echo the number of DIVISIONS finally used to the run-time output.
DY specifies the nominal spacing in the layer. Units are microns.
YDY specifies the depth where the nominal spacing will be applied. YDY is calculated relative to the
top of the newly deposited layer. Units are microns.
MIN.DY specifies the minimum spacing in microns allowed between grid lines in the y direction in the
new material. The default is 0.001 microns (10 Angstroms).
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DEPOSIT
ATHENA User’s Manual
MIN.SPACE specifies a minimum spacing between points on the surface of each sub-layer. Increasing
this parameter will reduce the number of points on arced deposited surfaces. Units are microns.
ARC.SPACE is a synonym for this parameter.
Parameters Specific to Depositing Doped Layers
C.IMPURITIES specify the concentration of the impurity in the deposited layer in cm-3. You can
specify more than one of these parameters to define materials doped with multiple impurities.
F.IMPURITIES can only be specified together with the corresponding C.IMPURITY (e.g., F.BORON
and C.BORON). This parameter generates the linearly graded concentration of the specified impurity
in the deposited layer, where C.IMPURITY specifies concentration at the bottom of the layer and
F.IMPURITY specifies concentration at the top of the layer. Units are cm-3.
C.INTERST specifies the concentration of interstitials in deposited layer. Units are cm-3.
F.INTERST can only be specified together with C.INTERST. This parameter generates the linearly
graded interstitial concentration in the deposited layer, where C.INTERST specifies concentration at
the bottom of the layer and F.INTERST specifies concentration at the top of the layer.
C.VACANCY specifies the concentration of vacancies in deposited layer. Units are cm-3.
F.VACANCY can only be specified together with C.VACANCY. This parameter generates the linearly
graded vacancy concentration in the deposited layer, where C.VACANCY specifies concentration at the
bottom of the layer and F.VACANCY specifies concentration at the top of the layer. Units are cm-3.
C.FRACTION specifies the fractional component of the first element of a ternary compound to be
deposited (i.e., Al is the first component for AlGaAs). The fractional component of the second
component (i.e., Ga is the second component for AlGaAs) is 1 - C.FRACTION. This parameter is valid
for standard ternary materials AlGaAs and InGaAs or user-defined ternary materials with the
following standard names: AlInAs, InGaP, GaSbP, GaSbAs, InAlAs, InAsP, GaAsP, HgCdTe, InGaN, and
AlGaN.
F.FRACTION can only be specified together with C.FRACTION. This parameter generates the
deposited layers with linearly graded fractional component, where C.FRACTION specifies the
fractional component of the first element at the bottom of the layer and F.FRACTION specifies the
fractional component of the first element at the top of the layer. This parameter is valid for standard
ternary materials AlGaAs and InGaAs or user-defined ternary materials with the following standard
names: AlInAs, InGaP, GaSbP, GaSbAs, InAlAs, InAsP, GaAsP, HgCdTe, InGaN, and AlGaN.
GR.SIZE specifies grain size in deposited polysilicon layer. This parameter is recognized only when
POLY.DIFF model is specified in the METHOD statement. Units are microns.
F.GR.SIZE can only be specified together with GR.SIZE. This parameter deposits polysilicon layer
with grains linearly graded with their sizes, where GR.SIZE specifies grain size at the bottom of the
layer and F.GRAIN.SIZE specifies grain size at the top of the layer. Units are microns.
Parameters Specific to ELITE Depositions
MACHINE specifies the name of the machine to be run for ELITE deposits. The machine name must
be specified in a previous RATE.ETCH statement.
TIME sets the time in specified units the etch machine will be running.
HOURS, MINUTES, and SECONDS specifies the units of the TIME parameter. Default is MINUTES.
N.PARTICLE specifies the number of particle trajectories to calculate for the Monte Carlo deposit
model.
OUTFILE specifies the name of the file to be written with Monte Carlo particle positions.
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DEPOSIT
SUBSTEPS specifies the number of timesteps made for each division of the deposit in the ELITE
module.
VOID specifies that the voids formed during deposition are to remain unfilled with deposit material.
Conformal Deposition Example
The following statement deposits a conformal layer of silicon dioxide, 1000 Angstroms thick, on the
surface of the simulation structure. It will contain 4 vertical grid points.
DEPOSIT OXIDE THICK=0.1 DIVISIONS=4
Example Depositing Doped User-defined Material
The following deposits a layer of a user defined material BPSG doped with boron and phosphorus.
DEPOSIT MATERIAL=BPSG THICKNESS=0.1 DIV=6 C.BORON=1e20 C.PHOS=1e20
Grid Control Example
The following statement deposits a conformal layer of silicon nitride with a thickness of 0.3µm. The
grid spacing at the bottom of the layer is 0.01µm and the layer will include 10 vertical sublayers.
DEPOSIT NITRIDE THICK=0.3 DY=0.1 YDY=0.3 DIVISIONS=10
ELITE Machine Deposition Example
The following statements define a machine named MOCVD and use it to deposit tungsten with a
thickness of 0.1µm on planar areas and step coverage of 0.75.
RATE.DEPO MACHINE=MOCVD DEP.RATE=.1 u.m STEP.COV=.75 TUNGSTEN
DEPOSIT MACHINE=MOCVD TIME=1 MINUTE
For more examples, see RATE.DEPO.
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DEVELOP
ATHENA User’s Manual
6.14: DEVELOP
DEVELOP runs the development module in OPTOLITH.
Syntax
DEVELOP
[MACK|DILL|TREFONAS|HIRAI|KIM|EIB]
[TIME=<n>] [STEPS=<n>] [SUBSTEPS=<n>]
[DUMP=<n>] [DUMP.PREFIX=<c>]
Description
This command runs the development module and enables the use of the option to select a development
model.
MACK, DILL, TREFONAS, HIRAI, KIM and EIB specify the development model to be used.
TIME, STEPS, and SUBSTEPS are related parameters that control the string algorithm in
development. TIME is the total development time in seconds. STEPS gives the number of times ETCH is
to be performed. SUBSTEPS controls string movement. Each substep or string movement has a time
duration of TIME/STEP*SUBSTEPS.
DUMP determines whether a structure is saved after each step of the development is completed.
DUMP.PREFIX specifies the prefix name for the structure file to be saved. The number of steps will
be equal to the number of output files. The files are readable with the STRUCTURE statement or can
be displayed using TONYPLOT. The names of the files will be of the form DUMP.PREFIX***.***.str,
where ** is the current development time.
Examples
The following example dumps out five structure files to show the evolution of development using the
KIM development model.
DEVELOP KIM DUMP=1 TIME=60 STEPS=5
For more examples, see RATE.DEVELOP.
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DIFFUSE
6.15: DIFFUSE
DIFFUSE runs a time temperature step on the wafer and calculates oxidation, silicidation and
diffusion of impurities. DIFFUSION is a synonym for this statement.
Syntax
DIFFUSE
TIME=<n> [HOURS|MINUTES|SECONDS]
TEMPERATURE=<n> [T.FINAL=<n>|T.RATE=<n>]
[DRYO2|WETO2|NITROGEN|INERT] [HCL.PC=<n>] [PRESSURE=<n>]
[F.02=<n>|F.H2=<n>|F.H20=<n>|F.N2=<n>|F.HCL=<n>]
[C.IMPURITIES=<n>]
[DUMP][DUMP.PREFIX=<c>] [TSAVE=<n>] [TSAVE.MULT=<n>]
[B.MOD=<c>] [p.MOD=<c>] [AS.MOD=<c>] [IC.MOD=<c>] [VI.MOD=<c>]
[NO.DIFF] [REFLOW]
Description
This command specifies diffusion and/or oxidation/silicidation steps. Any impurities present in the
wafer are diffused if they have non-zero diffusivities. The oxidation and diffusion control parameters
are contained in the associated METHOD, OXIDE, and SILICIDE statements. Default coefficients are in
the ATHENAMOD file available from the DeckBuild Commands menu under Models. To change model
coefficients, refer to the appropriate IMPURITY statement for information.
Parameters to Define the Diffusion Step
TIME specifies the amount of time for the diffusion step in specified units.
HOURS, MINUTES, and SECONDS specify the units of the TIME parameter. Default is MINUTES.
TEMPERATURE specifies the ambient temperature in oC. This temperature should fall within the
range between 700 and 1200oC. Outside of this range, the diffusion coefficients may be inaccurate and
numerical difficulties may occur during simulation. For ramped thermal step, a synonym T.START
can be used.
T.FINAL specifies the final temperature for ramped thermal steps. Synonym is T.STOP.
T.RATE specifies the ramp rate in oC/minute for ramped thermal steps.
Parameters to Define the Diffusion Ambient
DRYO2, WETO2, INERY and NITROGEN specify the type of ambient during the diffusion step.
DRYO2 specifies that ambient is dry oxygen, WETO2 specifies that ambient is wet oxygen, NITROGEN
specifies that ambient is inert. INERT is a synonym for NITROGEN.
HCL.PC specifies the percentage of HCl in the oxidant gas stream.
PRESSURE specifies the partial pressure of the active species in atmospheres. Units are
atmospheres. The default is 1.
F.02, F.H2, F.H20, F.N2, and F.HCL specifies the relative flow rate of the components of oxygen,
hydrogen, water, nitrogen, and HCl in the ambient. If these parameters are used, the DRYO2, WETO2,
NITROGEN set or HCL.PC should not be specified.
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6-25
DIFFUSE
ATHENA User’s Manual
C.IMPURITIES specifies concentration of the impurities in the ambient gas. (see Section 6.2.10:
“Standard Impurities” for the list of impurity names that can be used, e.g. I.BORON). Units are
atoms/cm3. You can define multiple impurity parameters for ambients with multiple impurities. You
can only use boron, phosphorus and arsenic if you specify the advanced diffusion model (PLS) in the
METHOD statement.
Parameters Related to File Output
DUMP and DUMP.PREFIX specify that a structure file be output at every DUMPth time step. The
files are readable with the STRUCTURE statement or can be displayed using TONYPLOT. The names will
be of the form DUMP.PREFIX<time>.str, where <time> is the current total time of the simulation in
minutes.
TSAVE and TSAVE.MULT specify that intermediate structure files be output when the advanced
PLS diffusion model is used. The structure files named DUMP.PREFIX<time>.str will be output
at time = TSAVE * TSAVE.MULTk, k=0,1,2,... where time is in seconds. The default value for the
parameter DUMP.PREFIX is “at”. The parameter TSAVE.MULT should be greater than 1.0.
Parameters Related to the Model Files for Advanced Diffusion Models
B.MOD, P.MOD, AS.MOD, IC.MOD, and VI.MOD specify direct paths to boron.mod,
phosphorus.mod, arsenic.mod, i.mod, and defect.mod files correspondingly. By default,
these files are in $SILVACO/lib/athena/<version_number>/common/pls directory. You can modify
your own *.mod files inside directories specified by these parameters.
Miscellaneous Parameters
NO.DIFF specifies that impurity diffusion be neglected during the calculation. This can be used to
observe oxidation or silicidation geometry without unnecessary timesteps related to impurity diffusion
REFLOW specifies that a surface tension based reflow of the material is to be performed during the
diffusion step.
Predeposition Example
The following statement specifies a 1000°, 30 minute boron pre-deposition.
DIFFUSE TIME=30 TEMP=1000 C.BORON=1.0E20
Oxidation Example
The following statement instructs the simulator to grow oxide for 30 minutes in a dry oxygen ambient.
DIFFUSE TIME=30 TEMP=1000 DRYO2
Gas Flow Example
The following command performs diffusion with a mixed ambient with relative components of oxygen,
hydrogen, and HC1 of 10, 10, and 0.1 respectively.
DIFFUSE TIME=10 TEMP=1000
F.02=10 F.H2=10 F.HCl=.1
Hydrogen and Oxygen are combined in a ratio 2:1 to form the ambient WETO2. Any excess hydrogen
is considered inert. Any excess oxygen is considered as the ambient DRYO2. Since the total pressure of
the gas flow is defined (or defaults to one atmosphere) the partial pressure of WETO2 will be reduced
if any excess hydrogen or oxygen is present.
File Output Example
The following commands perform diffusion in dry oxygen ambient for 30 minutes at 1000 oC. After
every second timestep a structure file is written with a name prefix TEST. Following the diffusion, the
TONYPLOT statement plots each timestep output file in a manner suitable for creating a diffusion movie.
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Silvaco
DIFFUSE
A SYSTEM command is used to execute a UNIX command prior to the diffusion step to remove all
TEST*.str files from previous runs.
SYSTEM rm -rf TEST*.str
DIFFUSE TIME=30 TEMP=1000 DRYO2 DUMP=2 DUMP.PREFIX=TEST
TONYPLOT -st TEST*.str
Advanced Diffusion Model Example
The following command performs the boron pre-deposition at 950°C for 1 hour. The boron
concentration in the ambient gas is 1020cm-3. As a result, the output files predep1.str,
predep10.str, predep100.str, and predep1000.str will be saved.
METHOD PLS
DIFFUSE TIME=1 HOUR TEMP=950 C.BORON=1E20 TSAVE=1 TSAVE.MULT=10
DUMP.PREFIX=predep
For more examples, see IMPURITY, INTERSTITAL, MATERIAL, METHOD, OXIDE, TRAP, and
VACANCY.
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DISLOC.LOOP
ATHENA User’s Manual
6.16: DISLOC.LOOP
DISLOC.LOOP defines the scaling parameters and position of dislocation loops.
Syntax
DISLOC.LOOP
MATERIAL I.IMPURITY MIN.LOOP.CO =<n> MAX.LOOP.CO=<n>
Description
This command specifies the scaling of dislocation loops during a subsequent IMPLANT step. Dislocation
loops are used as interstitial sinks whose recombination rate can be determined with the
INTERSTITIAL DAMALPHA=<n> command.
Note: This command will only work if you switch on the dislocation loop model with the METHOD I.LOOP.SINK
command.
MATERIAL specifies material for which dislocation loops parameters are set (see Section 6.2.9:
“Standard and User-Defined Materials” for the list of materials). Default is SILICON.
I.IMPURITY specifies an impurities to be used for the dislocation loop scaling (see Section 6.2.10:
“Standard Impurities” for the list of impurity names which can be used, e.g. I.BORON).
MIN.LOOP.CO and MAX.LOOP.CO define the upper and lower bounds of the dopant concentrations
where the loops are placed.
Dislocation Loop Generation Example
The following example switches on the loop model and then places loops in the position where indium
concentrations lie between 1e16 and 1e15 cm-3.
METHOD I.LOOP.SINK
DISLOC.LOOP MIN.LOOP.CO=1e15 MAX.LOOP.CO=1e16 I.INDIUM SILICON
IMPLANT INDIUM DOSE=1e15 ENERGY=45
For more examples, see METHOD, CLUSTER, INTERSTITIAL, VACANCY, DIFFUSE, and IMPLANT.
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ELECTRODE
6.17: ELECTRODE
ELECTRODE defines electrodes and names for ATLAS or other device simulation.
Syntax
ELECTRODE
NAME=<c> [X=<n> | Y=<n> | BACKSIDE | LEFT | RIGHT]
Description
This statement defines a whole material region as an electrode.
NAME gives a name to the electrode that can be plotted or referenced in TONYPLOT or ATLAS.
X specifies the horizontal location or x-coordinate of the region, which will be defined as an electrode.
Y specifies the vertical location or y-coordinate of the electrode being defined. If no value of Y is
specified, the top of the structure is assumed.
BACKSIDE specifies that a flat (zero height) electrode will be placed on the bottom of the simulation
structure. This is the one exception to whole regions being defined as electrodes. If a metal region is
present on the bottom of the structure, this parameter will not be used and the XY coordinates used
instead. BOTTOM is a synonym for this parameter.
LEFT specifies that the top left region of the structure will be defined as an electrode.
RIGHT specifies that the top right region of the structure will be defined as an electrode.
Note: The ELECTRODE statement recognizes the regions made of polysilicon, standard metals (see.Section 6.2.9:
“Standard and User-Defined Materials” for the list of standard metals) or user-defined materials with the following standard
names: Gold, Silver, AlSi, Palladium, Molybdenum, Lead, Iron, Tantalum, AlSiTi, AlSiCu, TiW, Copper, Tin, Nickel, NiSix, TaSix,
PaSix, MoSix, ZrSix, AlSix, Conductor, Contact.
Note: ATLAS contains syntax that makes use of the common electrical names for highly preferred terminals. These are
anode, cathode, emitter, base, collector, gate, source, drain, bulk and substrate.
Metal Region Electrode Definition Example
The following gives the name source to the metal or polysilicon region at location x=1 micron on the
top of the current structure.
ELECTRODE X=1.0 NAME=SOURCE
Substrate Definition Example
The following gives the name well to a flat electrode along the bottom edge of the current structure
There is no metal required at this location.
ELECTRODE BACKSIDE NAME=WELL
For more examples, see STRUCTURE.
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EPITAXY
ATHENA User’s Manual
6.18: EPITAXY
EPITAXY specifies an epitaxial deposition process step.
Syntax
EPITAXY
TIME=<n> [HOURS|MINUTES|SECONDS]
TEMPERATURE=<n> [T.FINAL=<n> | T.RATE=<n>]
[THICKNESS=<n> | GROWTH.RATE=<n>]
[C.IMPURITIES=<n>] [F.IMPURITIES=<n.] [C.INTERST=<n>] [F.INTERST=<n>]
[C.VACANCY=<n>] [F.VACANCY=<n>]
[DIVISIONS=<n>][DY=<n>][MIN.DY=<n>][YDY=<n>][SI_TO_POLY]
Description
This statement simulates the epitaxial deposition of silicon. This model is limited to silicon on silicon
applications and should not be used when other materials are present. The model is inherently 1D and
isn’t suitable for selective epitaxial deposition processes.
Parameters to Define the Epitaxial Step
TIME specifies the amount of time for the epitaxial step in specified units.
HOURS, MINUTES, and SECONDS specify the units of the TIME parameter. Default is MINUTES.
TEMPERATURE specifies the ambient temperature, in oC. This temperature should fall within the
range between 700 and 1200oC. Outside of this range, the diffusion coefficients may be inaccurate and
numerical difficulties may occur during simulation. For ramped thermal step, a synonym T.START
can be used.
T.FINAL specifies the final temperature for ramped thermal steps. Synonym is T.STOP.
T.RATE specifies the ramp rate in oC/minute for ramped thermal steps.
THICKNESS specifies thickness of epitaxially grown layer. Units are microns.
GROWTH.RATE specifies epitaxial growth rate. It is applicable only when THICKNESS is not
specified. Units are µm/minute.
Doping Related Parameters
C.IMPURITIES specify the concentration of the impurity in the epitaxially grown layer in cm-3. You
can specify more than one of these parameters to define materials doped with multiple impurities.
F.IMPURITIES can be specified only together with the corresponding C.IMPURITY (e.g. F.BORON
and C.BORON). This parameter generates the linearly graded concentration of the specified impurity
in the epitaxially grown layer, where C.IMPURITY specifies concentration at the bottom of the layer
and F.IMPURITY specifies concentration at the top of the layer.
C.INTERST specifies the concentration of interstitials in the epitaxially grown layer in cm-3.
F.INTERST can be specified only together with C.INTERST. This parameter generates the linearly
graded interstitial concentration in the epitaxially grown layer, where C.INTERST specifies
concentration at the bottom of the layer and F.INTERST specifies concentration at the top of the
layer.
C.VACANCY specifies the concentration of vacancies in the epitaxially grown layer in cm-3.
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EPITAXY
F.VACANCY can be specified only together with C.VACANCY. This parameter generates the linearly
graded vacancy concentration in the deposited layer, where C.VACANCY specifies concentration at the
bottom of the layer and F.VACANCY specifies concentration at the top of the layer.
Gridding Parameters
DIVISIONS controls the number of vertical grid points in the resulting epitaxial layer. This is an
optional parameter since it will be generated automatically by default and is related to the surface
grid spacing of the original simulation structure before epitaxial process. SPACES is an alias for this
parameter. The default is 10.
DY specifies the nominal spacing in microns in the epitaxial layer.
YDY specifies the depth where the nominal spacing will be applied. YDY is calculated relative to the
top of the newly grown epitaxial layer.
MIN.DY specifies the minimum spacing allowed between grid lines in the y direction in the new
material. The default is 0.001 microns (10 Angstroms).
SI_TO_POLY specifies that the crystalline silicon layer will be grown only over Silicon, while
Polysilicon will be grown elsewhere.
Deposition Rate Example
The following statement will simulate the growth of boron doped silicon on top of silicon at a rate of 0.5
µm per minute. The deposit thickness is time x rate=5 µm.
EPITAXY TIME=10 TEMP=1150 C.BORON=5E14 GROWTH.RATE=0.5
Time and Temperature Example
The following statement will deposit 6µm of epitaxial silicon on top of silicon over 10 minutes.
Phosphorus is out-diffused during the processing. The number of vertical grid points in the completed
epitaxial layer is set with the DIVISIONS parameter. The syntax is similar to the DEPOSIT statement.
EPITAXY THICK=6 TIME=10 TEMP=1180 C.PHOS=1.5E14 DIVISIONS=20
Non-uniform Grid Control Example
The following statement performs epitaxial process with a non-uniform vertical grid spacing. The
vertical grid spacing will be 0.5 µm at a distance of 5 µm below the final surface. The epitaxial layer
will be subdivided into 40 sublayers:
EPITAXY THICK=10 TIME=30 TEMP=1100 DY=.5 YDY=5.0 DIVISIONS=40
For more examples, see DEPOSIT and DIFFUSE.
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ETCH
ATHENA User’s Manual
6.19: ETCH
ETCH simulates an etch process.
Syntax
ETCH
[MATERIAL] [NAME.RESIST]
[ALL|DRY] [THICKNESS=<n>] [ANGLE=<n>] [UNDERCUT=<n>]
[LEFT|RIGHT|ABOVE|BELOW] [P1.X=<n>] [P1.Y=<n>] [P2.X=<n>] [P2.Y=<n>]
[START|CONTINUE|DONE] [X=<n>][Y=<n>]
[INFILE=<c>] [TOP.LAYER] [NOEXPOSE]
[MACHINE=<c>] [TIME=<n>] [HOURS|MINUTES|SECONDS]
[DT.FACT=<n>] [DT.MAX=<n>] [DX.MULT=<n>]
[MC.REDEPO] [MC.SMOOTH = <n>] [MC.DT.FACT = <n>] {MC.MODFNAME = <c>]
Description
ATHENA provides two different etch simulation methods. The first is geometrical etching available
within any ATHENA module. The second is physical etching available only in ELITE.
Parameters used for Geometrical Etching
MATERIAL specify the material to be etched (see Section 6.2.9: “Standard and User-Defined
Materials” for the list of materials). If a material is specified, only that material is etched even if other
materials lie within the etch region. If no material is specified, all materials in the etch region are
removed.
NAME.RESIST specify the type of photoresist to be etched.
ALL specifies that all of the specified materials are removed.
DRY indicates that the resulting surface will replicate the exposed surface and will simply be lowered
by a fixed depth of THICKNESS microns below the exposed surface. If ANGLE or UNDERCUT or both is
specified, the shape of DRY etched region is modified accordingly. TRAPEZOI is a synonym for this
parameter.
THICKNESS specifies the thickness to be etched for the dry etch type. Units are microns.
ANGLE specifies sidewall slopes in degrees (90° corresponding to vertical slope is the default).
UNDERCUT specifies the distance in microns that ETCH extends under a mask when dry etch is
performed (the default is 0).
LEFT, RIGHT, ABOVE, and BELOW provide a quick means of etching with a trapezoidal cross
section. The etch region will be to the specified side (left/right/above/below) of the line specified by the
coordinates given in P1.X, P1.Y and P2.X, P2.Y.
P1.X, P1.Y, P2.X, and P2.Y allow you to specify a line for left/right/above/below etching. The P1
parameters are always required if left/right/above/below are used. The P2 parameters are
required when the etch angle is non-vertical. Units are microns.
START, CONTINUE, and DONE specify an arbitrarily complex region to be etched. You can combine
several lines to specify the several points that make up the region. See the examples.
X and Y specify a point in the start/continue/done mode of etch region specification. Units are
microns.
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ETCH
INFILE specifies that the etch profile will be taken from the filename specified by the INFILE
parameter. The specified file must have the following format:
X1
Y1
X2
Y2
X3
Y3
...
Xn
Yn
This will etch the region enclosed by the boundary coordinates within the file. You can define any
number of coordinates within the file. This command is often useful for inputting data from digitized
experimental profiles or external programs. The closing line is automatically drawn from the final
coordinate point to the initial point.
TOP.LAYER specifies that only the top layer of the etched material should be etched.
NOEXPOSE specifies that the new surface is not exposed for subsequent oxidation or deposition after
geometrical etch. Use this parameter to remove a part of the structure from the bottom or side of
simulation.
Parameters used only with physical etching in the ELITE module
MACHINE specifies the name of the etch machine that is to be run.
TIME specifies the time the etch machine is to be run.
HOURS, MINUTES, and SECONDS specify the units of the TIME parameter.
Parameters used only with RIE, WET.ETCH, and PLASMA models
DT.FACT is used with ELITE type etch calculations. By default, the movement of a string node is
limited to less than or equal to one quarter of the median segment length. This is a good compromise
between simulation speed and the danger of loop formation. The optimization factor DT.FACT must
not exceed 0.5. You can, however, decrease it if necessary for more accuracy.
DT.MAX is used to limit timesteps size. By default, the upper limit for the maximum timestep is one
tenth of the total etch time specified. This is a good compromise between calculation accuracy and
calculation time. But sometimes, it is useful to adapt this value to the specific simulation problem.
Allowing the time steps to become greater gives a higher simulation speed but the accuracy may suffer.
For smaller time steps, the simulation speed will decrease but the accuracy may be greater.
DX.MULT is the accuracy multiplier for ELITE etches. The discretization size used for the etch
calculation will be multiplied by DX.MULT. For improved accuracy at the cost of extra simulation time,
decrease the value of DX.MULT.
Parameters used only with MC.PLASMA model
MC.REDEPO specifies that redeposition of polymer should be simulated. Default is true.
MC.SMOOTH specifies level of smoothing of the surface.
MC.DT.FACT specifies time step control for Monte Carlo etching and redeposition.
MC.MODFNAME specifies name of the C-Interpreter file with user-defined Monte Carlo etching and
redeposition models.
Simple Geometrical Etch Example
The following command etches all the nitride to the left of a vertical line located at x=0.5:
ETCH NITRIDE LEFT P1.X=0.5
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ETCH
ATHENA User’s Manual
Arbitrary Geometrical Shape Etch Example
The following set of commands etch the oxide in the square defined at (0,0), (1,0), (1,1), and (0,1):
ETCH OXIDE START X=0.0 Y=0.0
ETCH CONTINUE X=1.0 Y=0.0
ETCH CONTINUE X=1.0 Y=1.0
ETCH DONE X=0.0 Y=1.0
Be careful when using this style of syntax that the list of coordinates forms a regular polygon. The
closing line from the last coordinate pair to the initial point is automatically added.
Anisotropic Geometrical Etch Example
The following command finds the exposed surface and lowers it straight down 0.1 microns. This line
will be the new surface.
ETCH DRY THICK=0.1
Physical Etch Example
The following sequence defines an etch machine named PLASMA1 that performs reactive ion etching of
silicon. The machine is applied to etch the current structure for 10 minutes.
RATE.ETCH MACHINE=PLASMA1 SILICON U.M RIE ISOTROPIC=0.1 DIRECT=0.9
ETCH MACHINE=PLASMA1 TIME=10 MINUTES
Note: The program can be sensitive to grid placement. It often helps to prepare the initial grid by having a vertical grid line
exactly at the etch coordinate for geometric etches.
For example, see RATE.ETCH.
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EXPOSE
6.20: EXPOSE
EXPOSE runs the exposure module of OPTOLITH.
Syntax
EXPOSE
[INFILE=<c>] [PERPENDICUL|PARALLEL] [X.CROSS|Z.CROSS]
[CROSS.VALUE=<n>] [DOSE=<n>] [X.ORIGIN=<n>
[FLATNESS=<n>] [NUM.REFL=<n>]
[FRONT.REFL=<n>] [BACK.REFL=<n>] [ALL.MATS=<n>]
[MULT.EXPOSE] [POWER.MIN=<n>]
Description
This command defines the parameters associated with and performs two dimensional exposure.
INFILE is the name of an input file that contains a user aerial image cross section data file. This file
has the form:
<wavelength in microns>
<number of data pairs>
<x location in structure>
<relative image intensity>
PERPENDICUL and PARALLEL specify TE mode or TM mode respectively. PERPENDICUL is the
default.
X.CROSS and Z.CROSS specify that the cross section is parallel to the x-axis (z=constant) and
parallel to the z-axis (x=constant), respectively. X.CROSS is the default.
CROSS.VALUE specifies the x or z coordinates of the cross section of the aerial image. The default
will be centered in the image window. Units are microns.
DOSE specifies the exposure dose in mJ/cm2.
X.ORIGIN locates the beam relative to the structure. This allows the aerial image to be shifted if
necessary. Units are microns. The default is 0.0.
FLATNESS specifies the accuracy of the change in surface topography in degrees. A value of zero
specifies that all grid points will be calculated. The default value is 0.25. In any case, maintain the
limits 0 ≤ FLATNESS ≤ 1.
NUM.REFL specifies the number of reflections to be considered.
FRONT.REFL specifies that front surface reflection should be considered in the calculation. The
default is no front reflection.
BACK.REFL specifies the back surface reflection. The default is no back reflection.
ALL.MATS specifies that intensity be displayed in all materials. The default is photoresist only.
MULT.EXPOSE is used to make multiple exposures. MULT.EXPOSE is specified on the second EXPOSE
command for addition of exposures. If MULT.EXPOSE is not specified, previous exposures will be
erased.
POWER.MIN sets the minimum power accounted for in multiple reflections. POWER.MIN is used in a
multiplicative format. In other words, if power attenuation due to 10 reflections is less than
POWER.MIN it will not be counted for calculation.
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EXPOSE
ATHENA User’s Manual
Examples
The following statement loads a cross section of an aerial image that you can input. It then runs the
exposure module. The number of reflections increases calculation time when it is set to a value greater
than one.
EXPOSE INFILE=CROSS.SECT NUM.REFL=3
The following command runs the exposure module for the Z.CROSS section of a two dimensional aerial
image that has been previously generated. The x value of the cross section is 0.1.
EXPOSE Z.CROSS CROSS.VAL=0.1
Note: The DEFOCUS parameter on the IMAGE statement must be used to do defocus exposure calculations. The image
command must be used in conjunction with the EXPOSE command for a defocussed bulk image.
For more examples, see INITIALIZE and IMAGE.
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EXTRACT
6.21: EXTRACT
The EXTRACT command is used to analyze the current structure or a previously saved file. It can
extract important parameters such as material thickness, junction depth and peak doping levels. It
also includes electrical extractions such as sheet resistance, threshold voltage and CV curves.
Note: The EXTRACT statement is supported under DECKBUILD and is fully documented in the VWF INTERACTIVE
TOOLS MANUAL USER’S MANUAL, VOL. I.
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FOREACH
ATHENA User’s Manual
6.22: FOREACH
FOREACH specifies the command looping facility.
Syntax
FOREACH(NAME)(LIST)
(COMMANDS)
END
Description
This command is used to specify input loops. FOR is equivalent to FOREACH. When the loop executes,
NAME will consecutively take on each value in LIST and exit the loop after assuming the last value.
COMMANDS will be executed once for each value in LIST. NAME is set to a value in LIST using the shell
define function.
LIST is a set of strings separated by commas or spaces. The values in LIST can be delimited by either
commas or spaces. LIST can also take the following numerical operator form:
START TO END STEP VAL
where START is a numerical start value, END is the last value, and VAL is the amount to increment at
each iteration.
Examples
The following statement will increment val from 1.0 to 10.0 in steps of 0.5. This loop will be executed
19 times.
FOREACH VAL ( 1.0 TO 10.0 STEP 0.5 )
ECHO VAL
END
Note: Command line continuation using the backslash character “\” indicator is not supported in the FOREACH statement.
Note: This statement is not supported within the VWF Automation Tools. The Automation Tools contain a separate and more
powerful capabilities for defining input parameter variations.
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GO
6.23: GO
GO starts the simulator. Each ATHENA input file should begin with a GO statement.
Note: The GO command is executed by DECKBUILD and documented in the VWF Interactive Tools User’s Manual, Vol. I.
Examples
Two useful features of the GO command are shown here.
This command initializes ATHENA with a specified version number
go athena simflags=”-V 4.3.0.R”
This command initializes ATHENA with a model file <install>/lib/athena/<version>/common/
athenamod.97a
go athena simflags=”-modfile 97a”
Note: If DECKBUILD encounters a GO statement and there is no change in the version or model file, ATHENA will continue
running.
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HELP
ATHENA User’s Manual
6.24: HELP
HELP prints summary of statement names and parameters syntax.
HELP [<command>]
or
? [<command>]
Description
HELP lists the parameters of the specified statement and provides a short description of each. If there
is no statement name given, HELP will show an introductory help message and will list all statements.
Examples
The following will print a list of valid ATHENA commands to the standard output.
HELP
The following will print a description of the DIFFUSE command and its parameters.
HELP DIFFUSE
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ILLUM.FILTER
6.25: ILLUM.FILTER
ILLUM.FILTER specifies the illumination source shape and illumination source filtering in OPTOLITH.
Syntax
ILLUM.FILTER
[CIRCLE|SQUARE|GAUSSIAN|ANTIGAUSS|SHRINC]
[GAMMA=<n>] [RADIUS=<n>] [ANGLE=<n>] [SIGMA=<n>]
[IN.RADIUS=<n>] [OUT.RADIUS=<n>] [PHASE=<n>]
[TRANSMIT=<n>] [CLEAR.FIL]
Description
This statement specifies the illumination source options as well as illumination source filtering.
CIRCLE, SQUARE, GAUSSIAN, ANTIGAUSS, and SHRINC define or change the shape of the exit
pupil of the illumination system. SHRINC can be used to define the illumination system only, not
annular filters.
GAMMA defines or changes the GAMMA value for GAUSSIAN or ANTIGAUSS source transmittance.
GAMMA is a parameter that defines the truncation of the GAUSSIAN by the pupil. In the limit of
GAMMA→0, the source will be uniform.
RADIUS specifies the radius of a single source if you define the SHRINC illuminator concept. This
parameter must be entered in fractions of unity.
ANGLE specifies the angular location for the SHRINC illuminator.
SIGMA defines or changes the filling factor for the combination of the illumination and projection
systems. The value of SIGMA is expected to vary, but it will not be reset. Also, specifies the radius of a
single source if you specify the SHRINC illuminator concept. This parameter must be entered in
fractions of unity (assuming a unit pupil radius).
IN.RADIUS and OUT.RADIUS define or change the intensity transmittance and phase
transmittance of an annular zone inside the exit pupil of the illumination system. This qualifier is
used to simulate spatial filtering techniques. IN.RADIUS and OUT.RADIUS are used to define an
annular zone in the exit pupil having the pupil transmittance equal to TRANSMIT and producing the
phase angle equal to PHASE. Radius values are specified in fractions of unity, and phase is specified in
degrees. Note that the annular zones should not overlap. The outer radius of an inner zone must be
smaller than the inner radius of an outer zone.
PHASE specifies the phase shift in degrees produced by the illumination source filter (-180o ≤ PHASE
≤ 180o).
TRANSMIT specifies the intensity transmittance produced by the illumination filter (0 ≤ TRANSMIT
≤ 1).
CLEAR.FIL resets the illumination source filter list.
Example
The following example defines a SHRINC illumination source, where the quadruple circular
illumination sources are located at 45° to the x-axis with the center at a radius of 0.2 from the origin
and a circle radius of SIGMA=0.2.
ILLUM.FILTER SHRINC RADIUS=.2 SIGMA=.2 ANGLE=45
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ILLUMINATION
ATHENA User’s Manual
6.26: ILLUMINATION
ILLUMINATION specifies the basic illumination parameters in OPTOLITH.
Syntax
ILLUMINATION
[I.LINE|G.LINE|H.LINE|KRF.LASER|DUV.LINE|ARF.LASER|F2.LASER|LAMBDA=<n>]
[X.TILT=<n>][Z.TILT=<n>]
[INTENSITY=<n>]
Description
I.LINE, G.LINE, H.LINE, KRF.LASER (alias DUV.LINE), ARF.LASER, and F2.LASER specify
that the standard wavelengths of the illumination to be used. The corresponding wavelengths are
0.365, 0.436, 0.407, 0.268, 0.193, and 0.157 microns.
LAMBDA defines or changes the source wavelength. Only monochromatic sources are assumed for
simulation, that is only one wavelength can be specified. The units are microns.
X.TILT and Z.TILT specify the tilt of the illumination system with respect to the optical axis of the
projection system. All values are to be entered in degrees.
INTENSITY defines or changes the absolute value (usually set to one) of the complex amplitude, that
is the intensity in the mask or reticle plane.
Examples
The following statement defines i.line illumination with X and Z tilt of 0.1° and an intensity of 1.
ILLUMINATION I.LINE X.TILT=0.1 Z.TILT=0.1 INTENSITY=1
For more examples, see IMAGE, PROJECTION, ILLUM.FILTER, PUPIL.FILTER, ABERRATION,
LAYOUT.
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IMAGE
6.27: IMAGE
IMAGE calculates a one or two dimensional aerial image.
Syntax
IMAGE
[INFILE=<c>] [DEMAG=<n>] [GAP=<n>]
[OPAQUE|CLEAR] [DEFOCUS=<n>][CENTER]
[WIN.X.LOW=<n>] [WIN.X.HIGH=<n>] [WIN.Z.LOW=<n>] [WIN.Z.HIGH=<n>]
[DX=<n>] [DZ=<n>] [X.POINTS=<n>] [Z.POINTS=<n>] [N.PUPIL=<n>]
[MULT.IMAGE] [X.CROSS|Z.CROSS] [ONE.DIM]
Description
This statement calculates a 2D aerial image and sets parameters that control the accuracy, input, and
output of the imaging module. The IMAGE statement accepts layout information created by MASKVIEWS.
INFILE is the name of the mask data file from MASKVIEWS. It contains coordinates of rectangular
mask features as well as the transmittance and phase of each feature. This file name usually ends
with the extension.sec.
Note: For more information on the alternative method of loading MASKVIEWS layout information for image calculations, see
the LAYOUT statement.
DEMAG specifies demagnification factor. If specified, all elements of layout as well as all parameter of
image window and grid will decrease.
GAP specifies the mask-to-wafer gap for the case of contact printing. The units are microns.
OPAQUE and CLEAR specify the type of mask to be used. The background will be opaque if you
select OPAQUE, while the mask features will be clear. The background will be clear if you select CLEAR
and the mask features will be opaque.
DEFOCUS is a user specified defocus parameter. If < 0, above the resist. If > 0, below the resist
surface.
CENTER specfies that layout loaded using the INFILE parameter will be shifted so its center is in
the point (0,0)-- the origin of coordinates for the computational window.
WIN.X.LOW, WIN.X.HIGH, WIN.Z.LOW, and WIN.Z.HIGH set the minimum and maximum x and z
values that define the image window. If unspecified, default values from the mask file will be used. The
units are microns.
DX specifies the mesh resolution for the image window in x. If DX is not specified, X.POINTS and
Z.POINTS will be used. The units are microns.
DZ specifies the mesh resolution for the image window in z. The default is DZ=DX. The units are
microns.
X.POINTS and Z.POINTS are the number of x and z coordinate points in the image window,
respectively. These parameters are used only if DX is not specified. Default value is 10 for both
coordinates.
N.PUPIL defines or changes the number of mesh points in the projector’s exit pupil used in imaging
simulations. The value of N.PUPIL sets the number of mesh points along the exit pupil’s radius.
Larger values provide better accuracy. The default setting should be adequate for accuracy. N.PUPIL
also sets the size of the mask or image cell for imaging simulations. Finally, N.PUPIL affects the
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discretization of the source. This means that if a very fine source discretization is required, N.PUPIL
should be set to a larger value. Note that computation time grows linearly with the number of pupil
mesh points and source points used in the simulation.
MULT.IMAGE specifies that the preceding and current images will be added. You can add any
number of images as long as the IMAGE command contains this boolean.
X.CROSS and Z.CROSS specify if the one dimensional image is parallel to the x-axis or z-axis
respectively.
ONE.DIM use a one dimensional image module that images a line drawn across a 2D layout. This is
the best method when the image will be used for subsequent EXPOSE statements.
Example
This statement loads a mask named MASK.SEC and specifies x resolution in the image window of
DX=0.1 micrometers. It then runs the imaging module.
IMAGE INFILE=MASK.SEC DX=0.1
For more information, see ILLUMINATION, PROJECTION, ILLUM.FILTER, PUPIL.FILTER,
ABERRATION, LAYOUT, and EXPOSE.
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IMPLANT
6.28: IMPLANT
IMPLANT specifies an ion implantation process step.
Syntax
IMPLANT
[GAUSS|PEARSON|FULL.LAT|MONTECARLO|BCA] [CRYSTAL|AMORPHOUS]
IMPURITY ENERGY=<n> DOSE=<n> [FULL.DOSE]
[TILT=<n>] [ROTATION=<n>] [FULLROTATION]
[PLUS.ONE] [DAM.FACTOR=<n>] [DAM.MOD=<c>] [PRINT.MOM]
[X.DISCR=<n>] [LAT.RATIO1] [LAT.RATIO2] [S.OXIDE=<n>]
[MATCH.DOSE|RP.SCALE|MAX.SCALE][SCALE.MOM] [ANY.PEARSON]
[N.ION=<n>] [MCSEED=<n>] [TEMPERATURE=<n>] [DIVERGENCE=<n>]
[IONBEAMWIDTH=<n>]
[IMPACT.POINT=<n>] [SMOOTH=<n>] [SAMPLING] [DAMAGE] [MISCUT.TH][MISCUT.PH]
[TRAJ.FILE=<n>] [N.TRAJ=<n>]
[Z1 = <n>] [M1 = <n>]
Description
This statement simulates ion implantation using different analytical and Monte Carlo models.
Model Selection Parameters
GAUSS, PEARSON, FULL.LAT, MONTECARLO, and BCA specify the implant model that is being
used. GAUSS selects a Gaussian distribution. PEARSON selects the Pearson-IV distribution or where
available dual Pearson-IV distributions. FULL.LAT is the same as PEARSON with lateral component of
the 2D distribution calculated using all available moments instead of just a lateral standard deviation.
MONTECARLO (synonym is BCA) activates the Monte Carlo Implant Module, which based on the Binary
Collision Approximation.
CRYSTAL and AMORPHOUS specify whether or not the silicon lattice structure is to be taken into
account during implant steps. The statements are mutually exclusive and CRYSTAL is true by default.
For implants through thick screen materials, you often need to specify AMORPHOUS to avoid incorrect
channeling profiles.
•
For analytical implant models, these parameters select which set of tables are used for
silicon implant ranges. The CRYSTAL model uses the SVDP tables where available and is
the default.
•
For MONTECARLO or BCA models these parameters control whether the crystalline lattice
structure is considered or not.
Parameters Applicable for All Implant Models
IMPURITY specifies the impurity to be implanted (see Section 6.2.10: “Standard Impurities” for the
list of impurities). BF2 is also available.
ENERGY specifies the implant energy in keV.
DOSE specifies the dose of the implant. Dose is calculated in a plane normal to the implant direction.
The units are in cm-2.
FULL.DOSE specifies that the implanted dose is adjusted to compensate for the tilt angle. This type
of dose specification is often used for high tilt implants.
Adjusted Dose
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= DOSE/cos(TILT)
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TILT specifies the tilt with respect to the vertical of the implantation ion beam. The units are degrees.
The default is 7°.
ROTATION specifies the angle of rotation of the implant relative to the plane of the simulation. The
units are degrees.The default is 30°.
FULLROTATION specifies that the implant be performed at all rotation angles.
PLUS.ONE (synonyms are UNIT.DAMAGE and D.PLUS), and DAM.FACTOR (synonym is
D.SCALE) specify the implant damage calculation. UNIT.DAMAGE specifies that the interstitial profile
should be a scaled version of the doping profile from the implant. DAM.FACTOR specifies the scaling
factor to be used for the UNIT.DAMAGE model. At a depth, the interstitial concentration from the
UNIT.DAMAGE model will equal to the implanted ion concentration multiplied by DAM.FACTOR.
PRINT.MOM prints out moments for all ion/material combinations used in the analytical model. In
the case of Monte Carlo simulation, it prints out moments calculated from the coordinates of ion in the
standard structure file and can extracte them by the EXTRACT function.
DAM.MOD specifies the name of the C-Interpreter file, which can be used to modify defect
concentration models.
Parameters Applicable Only for Analytical Implant Models
X.DISCR specifies the width of slices along the direction of the ion beam used to calculate the
implanted profile. The value used is scaled relative to the lateral straggling of the current implant. By
default, a slice width of between 0.1 and 0.2 of the average lateral straggle will be used. This
parameter allows you to override the internal selection of discretization along the implant front. If the
value of X.DISCR decreases, simulation accuracy and simulation time will increase.
LAT.RATIO1 specifies a factor by which all lateral standard deviations for the first Pearson
distribution would be multiplied. Default is 1.0.
LAT.RATIO2 specifies a factor by which all lateral standard deviations for the second Pearson
distribution would be multiplied. Default is 0.2.
Note: The LAT.RATIO* parameters provide simple scaling of the default lateral standard deviation. Use the MOMENTS
statement for more complete lateral standard deviation modifications.
S.OXIDE specifies screen oxide parameter for the SVDP implant model. Default is 0.001 microns.
The screen oxide thickness is not determined from the structure and must be user-specified. See
Chapter 3: “SSUPREM4 Models”, Section 3.5: “Ion Implantation Models” for more details and the online examples on how to set this parameter automatically.
MATCH.DOSE, RP.SCALE (synonym is RP.EFF), and MAX.SCALE specify the method for implant
calculations in multi-material structures (see Chapter 3: “SSUPREM4 Models”, Section 3.5.2: “MultiLayer Implants”). Default is MATCH.DOSE.
SCALE.MOM specifies that moment scaling to be used with selected multilayer implant model.
ANY.PEARSON specifies no restrictions on the combinations of allowed skewness and kurtosis. This
is true by default as required for the SVDP models. See Chapter 3: “SSUPREM4 Models”, Section 3.5:
“Ion Implantation Models” for details on potential problems with this setting. ATHENA versions
earlier than 4.0 had this parameter set to false by default.
Parameters Applicable Only for Monte Carlo/BCA Implant Models
N.ION specifies the number of ion trajectories to be calculated for the Monte Carlo method. When the
SAMPLING is not specified, the default is N.ION is 1,000 for 1D structures and 10,000 for 2D
structures.
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IMPLANT
MCSEED specifies a seed for the random number generator used for the Monte Carlo calculation.
TEMPERATURE specifies the temperature of the substrate during implantation.
DIVERGENCE specifies the implant beamwidth in degrees. When the BEAMWIDTH angle is specified
the TILT angle is varied between TILT +/- DIVERGENCE/2.0. Each ion will have an angle somewhere in
this range decided by a random number generator. Distribution of the ions is uniform across the
defined angular distribution. Correct specification of DIVERGENCE is generally required for accurate
zero degree implant ranges. Default is 1 degree.
IMPACT.POINT specifies (only in the Monte Carlo method) that the ion beam enters the surface in
the point with lateral coordinate x=(left+IMPACT.POINT*L), where left is the x-coordinate of
the left boundary of the structure and L is the length of the structure. This parameter would be used
for calculation of the point-source 2D distribution and spacial moments using Monte Carlo method.
IONBEAMWIDTH specifies the ion beam width in nanometers. It can only be used with the
IMPACT.POINT parameter.
SMOOTH specifies that a special Gaussian convolution smoothing to be applied to the Monte Carlo
results. SMOOTH multiplied by estimated standard deviation of the whole profile serves as the standard
deviation for the Gaussian formula.
SAMPLING specifies that statistical sampling to be used in the Monte Carlo method.
DAMAGE specifies that damage formation should be calculated during Monte Carlo implant.
MISCUT.TH and MISCUT.PH specify the wafer's miscut. The explanation of these parameters is as
follows. Let’s consider the internal coordinate system of the crystal structure, xyz, to be right-hand
oriented, where y is the inward direction relatively to the surface. You can then define the misorienting
of the surface by tilting the wafer by MISCUT.TH degrees in the xy-plane and rotating it counterclockwise in the xz-plane by MISCUT.PH degrees if MISCUT.PH is positive and clockwise if
MISCUT.PH is negative. Remember that ROT.SUB, MISCUT.TH and MISCUT.PH are measured
from the internal co-ordinate system, compared to the ROTATION parameter, which is measured from
the wafer's major flat defined by ROT.SUB. The simulation plane shown in Chapter 3: “SSUPREM4
Models”, Figure 3-23 is defined by the ROT.SUB parameter. In the case of silicon carbide, the
simulation XY-plane for 4H-SiC is ( 1100 ). In other words, if specified by ROT.SUB=0 in the
INITIALIZE statement, then:
•
a miscut of 8° towards the 〈 1120〉 direction (i.e., in the
MISCUT.TH=8 and MISCUT.PH=60.
{ 1010 } plane) is specified by
•
a miscut of 8° towards the 〈 1010〉 direction (i.e., in the
MISCUT.TH=8 and MISCUT.PH=90.
{ 1120 } plane) is specified by
TRAJ.FILE specifies the name of the file in which ion trajectories calculated with the Monte Carlo
(BCA) method are to be saved.
Note: This parameter switches off statistical sampling if it’s specified by the SAMPLING parameter.
Note: When TRAJ.FILE parameter is specified, the Monte Carlo implant simulation will be performed on a single
processor, even if the multiple processors are available and parallel capability is specified by the -P parameter in the GO
ATHENA statement.
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N.TRAJ specifies the number of ion trajectories to be saved in the TRAJ.FILE. The default is
minimum of N.ION and 2000.
Z1 specifies the atomic number of an "inert" ion used only for damage or amorphization of substrate.
No new impurity will be introduced into the structure except "damage", which will affect subsequent
Monte Carlo implants.
M1 specifies the atomic weight of the "inert" ion with atomic weight of Z1. If M2 is not specified, the
atomic weight of the main isotope will be used.
Analytical Implant Example
This example specifies that a 100keV implant of phosphorus to be done with a dose of 1.0 e14 and with
a tilt angle of 15° to the surface normal. The Pearson model is to be used to calculate the doping profile.
IMPLANT PHOSPH DOSE=1E14 ENERGY=100 TILT=15
SVDP Boron Implant Example
This example shows the syntax for a zero tilt and 50keV boron implant through 5nm of screen oxide.
The oxide is defined by S.OXIDE and this definition is independent of any actual oxide in the structure
itself.
IMPLANT BORON DOSE=1E13 ENERGY=50 TILT=0 S.OXIDE=0.005
Monte Carlo Implant Example
This example specifies a 300keV boron implant at zero degrees tilt and rotation. Accurate modeling of
such implants is only possible in the BCA model. Since ion channeling is highly dependent on the tilt
angle.
IMPLANT BORON DOSE=1E13 ENERGY=300 BCA TILT=0 ROTATION=0
Implant Damage Example
This example implants phosphorus and invokes the unit damage model. The UNIT.DAMAGE model
creates an interstitial profile scaled to the implant doping profile. DAM.FACTOR is used here to specify
that the interstitial concentration will be ten times less than the doping throughout the depth of the
implant profile.
IMPLANT PHOSPHORUS DOSE=1E14 ENERGY=50 UNIT.DAMAGE DAM.FACTOR=0.1
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IMPURITY
6.29: IMPURITY
IMPURITY specifies impurity parameters.
Note: This statement supersedes the older syntax using separate statements for each impurity type. The ARSENIC,
ANTIMONY, BORON, INDIUM and PHOSPHORUS statements should no longer be used.
Syntax
IMPURITY
I.IMPURITY [DONOR|ACCEPTOR|NEUTRAL] MATERIAL
[AT.NUMBER=<n>][AT.MASS=<n>]
[DIX.0=<n>] [DIX.E=<n>] [DIP.0=<n>] [DIP.E=<n>]
[DIPP.0=<n>] [DIPP.E=<n>] [DIM.0=<n>] [DIM.E=<n>]
[DIMM.0=<n>] [DIMM.E=<n>] [DVX.0=<n>] [DVX.E=<n>]
[DVM.0=<n>] [DVM.E=<n>] [DVMM.0=<n>] [DVMM.E=<n>]
[DVP.0=<n>] [DVP.E=<n>] [DVPP.0=<n>] [DVPP.E=<n>]
[SOL.SOLUB|CLUSTER.ACT]
[CTN.0=<n>] [CTN.E=<n>] [CTP.0=<n>][CTP.E=<n>]
[SS.CLEAR][SS.TEMP=<n>][SS.CONC=<n>]
[ACT.FACTOR=<n>] [TRACT.0=<n>] [TRACT.E=<n>] [TRACT.MIN=<n>]
[/MATERIAL] [SEG.0=<n>][SEG.E=<n>][TRN.0=<n>][TRN.E=<n>]
[TRNDL.0=<n>][TRNDL.E=<n>]
[PD.DIX.0=<<n>>] [PD.DIX.E=<n>] [PD.EFACT=<n>] [PD.SEG.E=<n>]
[PD.TAU=<n>][PD.SEGSITES=<n>] [PD.GROWTH.0=<n>] [PD.GROWTH.E=<n>]
[PD.CRATIO=<n>][PD.SEG.GBSI=<n>]
Description
This statement allows to specify coefficients of impurity diffusion, transport, segregation, and so on.
Generic Parameters
I.IMPURITY is the name of impurity which parameters to be specified (see Section 6.2.10: “Standard
Impurities” for the list of impurities).
DONOR, ACCEPTOR and NEUTRAL specify the type of the impurity in the given material. Default
is NEUTRAL.
MATERIAL specify the material in which the impurity parameters apply as well as MATERIAL1 for
the segregation and transport parameters on the boundary between two materials (see Section 6.2.9:
“Standard and User-Defined Materials” for the list of materials).
AT.NUMBER and AT.MASS specify the atomic number and atomic mass of the impurity respectively.
This parameters are used in Monte Carlo/BCA implant calculations.
Diffusion Parameters
The units for all pre-exponential diffusion constants are cm2/sec, while the units for activation
energies are eV.
DIX.0 and DIX.E specify the diffusion coefficient for the impurity diffusing with neutral interstitials.
DIX.0 is the pre-exponential constant and DIX.E is the activation energy.
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DIP.0 and DIP.E specify the diffusion coefficient for the impurity diffusing with single positive
interstitials. DIP.0 is the pre-exponential constant. DIP.E is the activation energy.
DIPP.0 and DIPP.E specify the diffusion coefficients for the impurity diffusing with double positive
interstitials.
DIM.0 and DIM.E specify the diffusion coefficient for the impurity diffusing with single negative
interstitials. DIM.0 is the pre-exponential constant. DIM.E is the activation.
DIMM.0 and DIMM.E specify the impurity diffusing with doubly negative interstitials. DIMM.0 is the
pre-exponential constant. DIMM.E is the activation energy.
DVX.0 and DVX.E specify the impurity diffusing with neutral vacancies. DVX.0 is the pre-exponential
constant. DVX.E is the activation energy.
DVM.0 and DVM.E specify the impurity diffusing with single-negative vacancies. DVM.0 is the
pre-exponential constant. DVM.E is the activation energy.
DVMM.0 and DVMM.E specify the impurity diffusing with double-negative vacancies. DVMM.0 is the
pre-exponential constant. DVMM.E is the activation energy.
DVP.0 and DVP.E specify the impurity diffusing with single-positive vacancies. DVP.0 is the preexponential constant. DVP.E is the activation energy.
DVPP.0 and DVPP.E specify the impurity diffusing with double-positive vacancies. DVPP.0 is the
pre-exponential constant. DVPP.E is the activation energy.
FI.0 and FI.E are the fractional interstitialcy parameters that determine whether the impurity
diffuses through interaction with interstitials or vacancies. Once the expression for total FI is
evaluated from these coefficients, the value of total FI can vary between 0 and 1. FI equal to 1
corresponds to a pure interstitial-based diffusion, while value of 0 corresponds to a pure vacancy
mechanism.
Activation Model Parameters
SOL.SOLUB specifies that solid solubility model and solid solubility tables will be used for
calculation of active concentration of the specified impurity in the specified material. This is default
for all cases except Arsenic in Si and Poly.
CLUSTER.ACT specifies that cluster activation will be used. It is default only for AS in Si and Poly.
SS.CLEAR, SS.TEMP, and SS.CONC are the parameters for solid solubility data. SS.CLEAR clears
the currently stored solid solubility data for the specified impurity in the specified material. SS.TEMP
and SS.CONC add a single temperature and an associated solid solubility concentration point to those
already stored for the impurity. Units for SS.TEMP are oC. Units for SS.CONC are cm-3.
CTN.0 and CTN.E specify the vacancy clustering coefficients for the impurity. CTN.0 is the preexponential coefficient and CTN.E is the activation energy. By default, these parameters are only used
for Arsenic.
CTP.0 and CTP.E specify the vacancy clustering coefficients.
ACT.FACTOR specifies parameter for concentration dependent solid solubility activation model. The
value of ACT.FACTOR must be between 0.8 and 1.0.
TRACT.0, TRACT.E, and TRACT.MIN specify parameters of the transient activation model. Units
for TRACT.0 and TRAT.MIN are seconds. Units for TRACT.E are eV.
Interface Transport Parameters
/MATERIAL specify MATERIAL2 for the segregation and transport parameters on the boundary
between two materials (see Section 6.2.9: “Standard and User-Defined Materials” for the list of
materials).
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IMPURITY
SEG.0 and SEG.E allow the computation of the equilibrium segregation concentrations. SEG.0 is the
unitless pre-exponential constant. SEG.E is the activation energy in eV.
TRN.0 and TRN.E allow the specification of the transport velocity across the interface given. TRN.0 is
the pre-exponential constant (units are cm/sec). TRN.E is the activation energy (units are eV).
TRNDL.0 and TRNDL.E specify parameters of the Interface Trap Model, describing dose loss at
silicon/oxide interface. Units for TRNDL.0 are cm/sec; units for TRNDL.E are eV.
Polysilicon Diffusion Model Parameters
PD.DIX.0 and PD.DIX.E specify impurity diffusivity along grain boundaries. PD.DIX.0 is the preexponential factor of grain boundary diffusivity (units are cm2/sec). PD.DIX.E is the activation energy
for grain boundary diffusivity (units are eV).
PD.EFACT specifies entropy factor of grain boundary segregation coefficient.
PD.SEG.E specifies the activation energy of grain boundary segregation coefficient. Units are eV.
PD.TAU specifies the grain boundary time constant. Units are seconds.
PD.SEGSITES specifies density of segregation sites at grain boundary. Units are sites/cm2.
PD.GROWTH.0 specifies the grain growth rate pre-exponential coefficient. Units are eV*cm2/sec.
PD.GROWTH.E specifies the grain growth rate activation energy. Units are eV.
PD.CRATIO specifies initial ratio between impurity concentration in grain boundaries and total
concentration.
PD.SEG.GBSI specifies the factor which controls segregation between polysilicon grain boundaries
and Silicon.
Examples
The following statement changes the neutral interstitial diffusivity component of phosphorous in
silicon.
IMPURITY I.PHOSPHORUS SILICON DIX.0=3.85 DIX.E=3.85
The following statement changes the segregation parameters at the silicon-silicon dioxide interface.
The concentration of phosphorous in silicon will be 30 times the concentration of phosphorous in oxide
at equilibrium.
IMPURITY I.PHOSPHORUS SILICON /OXIDE SEG.0=30.0 SEG.E=0.0
The following syntax sets the temperature dependent impurity activation of Indium in Silicon.
IMPURITY I.INDIUM SILICON SS.TEMP=800 SS.CONC=<VAL1> SS.CLEAR
IMPURITY I.INDIUM SILICON SS.TEMP=900 SS.CONC=<VAL2>
IMPURITY I.INDIUM SILICON SS.TEMP=950 SS.CONC=<VAL3>
Note: The transport and segregation coefficients, TRN.0, TRN.E, SEG.0, and SEG.E, are known to be inaccurate for
some values of concentration, material combinations, and temperature ranges. If the simulation is inaccurate, consider these
coefficients for calibration.
For more examples, see DIFFUSE, METHOD, INTERSITITIAL, and VACANCY.
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INITIALIZE
ATHENA User’s Manual
6.30: INITIALIZE
INITIALIZE specifies the initial starting material and background doping levels. LOADFILE is a
synonym for this statement.
Syntax
INITIALIZE
[MATERIAL] [ORIENTATION=<n>] [ROT.SUB=<n>] [C.FRACTION=<n>]
[C.IMPURITIES=<n>|RESISTIVITY=<n>][C.INTERST=<n>][C.VACANCY=<n>]
[BORON|PHOSPHORUS|ARSENIC|ANTIMONY] [NO.IMPURITY]
[ONE.D|TWO.D|AUTO] [X.LOCAT=<n>] [CYLINDRICAL]
[INFILE=<c>] [STRUCTURE|INTENSITY]
[SPACE.MULT=<n>] [INTERVAL.R=<n>] [LINE.DATA] [SCALE=<n>] [FLIP.Y]
[DEPTH.STR=<n>] [WIDTH.STR=<n>]
Description
This command sets up the mesh from either a rectangular specification or from a previous structure
file. The statement also initializes the background doping concentration in all regions.
Material Related Parameters
MATERIAL specifies the material to be initialized (see Section 6.2.9: “Standard and User-Defined
Materials” for the list of materials).
ORIENTATION specifies the substrate orientation. Only 100, 110 and 111 are recognized. The
default is 100.
ROT.SUB specifies the major flat of the silicon substrate. It is measured in degrees from the external
x-axis of the crystallographic coordinate system. By default, ROT.SUB=-45, i.e., it represents the
[101] plane. This parameter is used only in BCA implantation module.
C.FRACTION.specifies the fractional component of the first element of a ternary compound substrate
(i.e., Al is the first component for AlGaAs). The fractional component of the second component (i.e., Ga
is the second component for AlGaAs) is 1 - C.FRACTION. This parameter is valid for standard ternary
materials AlGaAs and InGaAs or user-defined ternary materials with the following standard names:
AlInAs, InGaP, GaSbP, GaSbAs, InAlAs, InAsP, GaAsP, HgCdTe, InGaN, and AlGaN
Dopant Related Parameters
C.IMPURITIES specify the uniform impurity concentration in substrate material (see Section 6.2.10:
“Standard Impurities” for the list of impurities). Multiple parameters can be used to define
compensated doping in the substrate material.
RESISTIVITY specifies the resistivity of the initial substrate material. If RESISITVITY is specified,
the impurity concentration specified by C.*** parameter will be ignored and calculated from the
resistivity vs. concentration tables, which are available only for boron, phosphorus, arsenic, and
antimony. The units are Ω-cm.
C.INTERST specifies the uniform interstitial concentration in substrate material. Units are cm-3.
C.VACANCY specifies the uniform vacancy concentration in substrate material. Units are cm-3.
BORON, PHOSPHORUS, ARSENIC, ANTIMONY specify the type of impurity when initial doping
is defined by RESISTIVITY parameter.
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INITIALIZE
NO.IMPURITY specifies that the calculation be performed without impurities. No impurities will be
introduced during the simulation. This speeds calculation and allows quick analysis of oxidation,
deposit, and etch results.
Parameters Related to Dimensionality of Simulation
ONE.D, TWO.D, AUTO set whether the run will be in 1D, 2D, or the dimensionality automatically
determined from the process flow. AUTO is the default. If ONE.D is used to select a 1D calculation. The
calculation will be performed at a location indicated by the X.LOCAT parameter. TWO.D selects that
all process steps will be done in a full two dimensional calculation. If the parameters are unspecified or
AUTO is used, ATHENA will then perform 1D calculation until a two-dimensional calculation is
required. This is typically at the first ETCH statement, which doesn’t remove material across the whole
width of the structure.
X.LOCAT specifies the position within the defined 2D mesh for performing 1D simulation.
CYLINDRICAL specifies the boundary conditions for cylindrically symmetrical structure. In this
case, the axis of rotation is X=0.0 and no negative x coordinates are allowed.
Parameters Related to Initialization from a File
INFILE specifies a file name for reading. This file must contain a previously saved structure or
intensity distribution (see Section 6.63: “STRUCTURE”). IN.FILE is a synonym for this parameter.
STRUCTURE and INTENSITY specify which type of file is to be initialized. STRUCTURE is the
default.
Grid and Structure Related Parameters
SPACE.MULT specifies a global spacing multiplier to be applied to the spacings defined on the
previously specified LINE statements.
INTERVAL.R is the maximum ratio between the distances of adjoining mesh lines. The default is 1.5.
RATIO is a synonym for this parameter.
LINE.DATA specifies that locations of mesh lines be printed during execution.
SCALE allows an incoming mesh to be scaled. The default is 1.0.
FLIP.Y is a Boolean parameter that dictates the mesh should be mirrored about the x axis.
DEPTH.STR and WIDTH.STR specify the depth and width of the initial substrate structure
dimension for use with the Process Adaptive Meshing algorithm. Units are microns.
Example Starting from a file
The following statement reads in a previously saved structure from the TEST.STR file.
INITIALIZE INFILE=TEST.STR
Example Using an GaAs Substrate
The following statement creates GaAs substrate doped with Selenium concentration of 1×1015cm-3.
INITIALIZE GAAS C.SELENIUM=1E15
For more examples, see BOUNDARY, LINE, REGION, STRUCTURE, and BASE.MESH.
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INTERSTITIAL and VACANCY
ATHENA User’s Manual
6.31: INTERSTITIAL and VACANCY
INTERSTITIAL specifies coefficients of interstitial diffusion, recombination, and generation.
VACANCY specifies coefficients of vacancy diffusion, recombination, and generation.
Note: These two statements are almost equivalent. Most parameters that exist in the INTERSTITIAL statement are also
on the VACANCY statement.
INTERSTITIAL|VACANCY
[MATERIAL] [D.0=<n>][D.E=<n>] [CSTAR.0=<n>][CSTAR.E=<n>]
[NEU.0=<n>][NEU.E=<n>] [NEG.0=<n>][NEG.E=<n>
[DNEG.0=<n>][DNEG.E=<n>] [POS.0=<n>][POS.E=<n>
[DPOS.0=<n>][DPOS.E=<n>]
[KR.0=<n>][KR.E=<n>] [IVFACTOR=<n>] [IIFACTOR=<n>]
[KTRAP.0=<n>][KTRAP.E=<n>] [DAMALPHA=<n>]
[/MATERIAL=] [TIME.INJ] [GROWTH.INJ] [RECOMB]
[KSURF.0=<n>][KSURF.E=<n>] [KRAT.0=<n>][KRAT.E=<n>]
[KPOW.0=<n>][KPOW.E=<n>]
[VMOLE=<n>] [THETA.O=<n>][THETA.E=<n>] [GPOW.0=<n>[GPOW.E=<n>]
[WET02|DRY02] [REC.STR=<n>][INJ.STR=<n>]
[A.0=<n>][A.E=<n>] [T0.0=<n>][T0.E=<n>] [TPOW.0=<n>][TPOW.E=<n>]
[DCARBON.E=<n>][KCARBON.0=<n>][KCARBON.E=<n>]
Description
These two equivalent commands specify transport and generation/recombination coefficients for
interstitials and vacancies. The statements allow you to specify coefficients for any material, though it
is only practical for semiconductors. ATHENA has measured (or calibrated) default values only for
silicon and some interfaces with silicon.
MATERIAL specify the material for which the interstitial (or vacancy) parameters apply as well as
MATERIAL1 for the segregation and transport parameters on the boundary between two materials
(see Section 6.2.9: “Standard and User-Defined Materials” for the list of materials). Default is
Silicon.
Defect Diffusion Parameters
D.0 and D.E specify the interstitial (or vacancy) diffusion coefficient. D.0 is the pre-exponential
constant (the units are cm2 /sec), and D.E is the activation energy (the units are eV).
CSTAR.0 and CSTAR.E specify of the total equilibrium concentration of interstitials (or vacancies) in
intrinsically-doped conditions. CSTAR.0 is the pre-exponential constant (the units are cm-3), and
CSTAR.E is the activation energy (the units are eV).
NEU.0, NEU.E, NEG.0, NEG.E, DNEG.0, DNEG.E, POS.0, POS.E, DPOS.0 and DPOS.E specify
the relative concentration of interstitials (or vacancies) in the various charge states (neutral, negative,
double negative, positive, double positive) under intrinsic doping conditions. All *.0 parameters are
unitless. All *.E parameters are in eV.
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INTERSTITIAL and VACANCY
Bulk Defect Recombination Parameters
KR.0 and KR.E specify the interstitial (or vacancy) bulk recombination rate. KR.0 is the preexponential constant (the units are cm-3sec-1), and KR.E is the activation energy in eV.
IVFACTOR and IIFACTOR specify I/V Bimolecular recombination ratios in HIGH.CONC model.
These parameters are valid only for the INTERSTITIAL statement.
KTRAP.0 and KTRAP.E specify the interstitial trap reaction rate. KTRAP.0 is the pre-exponential
constant (the units are cm-3sec-1), and KTRAP.E is the activation energy in eV.
Note: At present, it is very difficult to extract exact values for these parameters. The default values assume the trap reaction is
limited by the interstitial concentration.
DAMALPHA specifies the interstitial recombination rate in the dislocation loop region. The units are
sec-1.
Interface Defect Generation and Recombination Parameters
/MATERIAL specify MATERIAL2 for setting generation and recombination parameters on the
boundary between two materials (see Section 6.2.9: “Standard and User-Defined Materials” for the list
of materials).
TIME.INJ, GROWTH.INJ and RECOMB specify the type of reactions occurring at the specified
interface. The TIME.INJ parameter means that a time dependent injection model should be chosen.
The GROWTH.INJ parameter ties the injection to the interface growth velocity. The RECOMB parameter
indicates a finite surface recombination velocity
KSURF.0, KSURF.E, KRAT.0, KRAT.E, KPOW.0 and KPOW.E specify the interstitial (or vacancy)
surface recombination rate. KSURF.0 is the pre-exponential constant for surface recombination rate
under inert conditions (the units are cm/sec). KSURF is corresponding activation energy in eV. KRAT.0
is the pre-exponential constant for the growth rate dependent component of the surface recombination
rate (unitless). KRAT.E is the corresponding activation energy in eV. KPOW.0 is the pre-exponential
constant of the power parameter in the surface recombination rate formula (unitless), and KPOW.E is
the corresponding activation energy in eV.
VMOLE, THETA.0, THETA.E, GPOW.0 and GPOW.E specify interstitial (or vacancy) generation
parameters of the growth dependent generation model. VMOLE is the lattice density of the consumed
material (the units are cm-3). THETA.0 specifies the pre-exponential constant for the fraction of
consumed atoms injected as interstitial (or vacancy). THETA.E specifies the activation energy for the
fraction (the units are eV). GPOW.0 and GPOW.E specify pre-exponential constant and activation
energy of the power parameter of the growth injection formula.
WETO2, DRYO2 specify whether the parameters THETA.0 and THETA.E are for wet oxidation or
dry oxidation. The default is DRYO2.
REC.STR and INJ.STR allow you to specify experimental models for interstitial (or vacancy)
recombination or injection at interfaces. Three macros are defined for use: T is the time in seconds, and
X and Y is the coordinates. If these are specified, they are used in place of any default model.
A.0, A.E, T0.0, T0.E, TPOW.0 and TPOW.E specify parameters for time-dependent injection model
TIME.INJ. A.0 is the pre-exponential constant for the injection rate and A.E is the corresponding
activation energy. T.0 and T.E are the pre-exponential constant and activation energy for the time
constant in the time-dependent injection formula. TPOW.0 and TPOW.E are the pre-exponential
constant and activation energy for the power constant in the time-dependent injection formula.
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Parameters for Carbon Effects in SiGeC
KCARBON.0 and KCARBON.E specify interstitial recombination rate in carbon sink. KCARBON.0
is the pre-exponential constant for the rate in sec-1, and KCARBON.E is the corresponding activation
energy in eV.
DCARBON.E specifies the coefficient of interstitial diffusion retardation in SiGe in presence of
carbon impurity. The units are eV.
Basic Example
The following statement specifies the silicon diffusion and equilibrium values for interstitials.
INTERST SILICON DI.0=5.0E-7 D.E=0.0 CSTAR.0=1.0E13 CSTAR.E=0.0
Defect Injection during Oxidation Example
The following statement specifies the oxide-silicon interface injection for DRYO2 ambient is to be
computed using the oxide growth velocity and with 1% of consumed silicon injected as interstitials.
INTERST SILICON /OXIDE GROWTH VMOLE=5.0E22 \
THETA.0=0.01 THETA.E=0.0
Surface Recombination Example
The following statement specifies the surface recombination velocity at the nitride silicon interface is
3.5 × 10-3 cm/sec.
INTERST SILICON /NITRIDE KSURF.0=3.5E-3 KSURF.E=0.0 KRAT.0=0.0
Experimental Injection Model Example
The following statement describes an injection at the silicon oxide interface that exponentially decays
in time.
INTERST SILICON /OXIDE INJ.STR = (10.0E4*EXP( T / 10.0 ))
General Comments
The equivalence of INTERSTITIAL and VACANCY statement syntax is done regardless of physical
meaning. For example, you can define vacancy injection during oxidation although default parameters
are zero.
The models used here are involved in ongoing research. Many of the parameters have unknown
dependencies, such as stress, temperature, starting silicon material, and stacking fault density.
For more examples, see DIFFUSE and TRAP.
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LAYOUT
6.32: LAYOUT
LAYOUT describes manual input of mask features for OPTOLITH.
Syntax
LAYOUT
[LAY.CLEAR=<n>]
[X.LOW=<n>][Z.LOW=<n>][X.HIGH=<n>][Z.HIGH=<n>][X.TRI=<n>][Z.TRI=<n>]
[HEIGHT=<n>][WIDTH=<n>][ROT.ANGLE=<n>][X.CIRCLE=<n>][Z.CIRCLE=<n>]
[RADIUS=<n>][RINGWIDTH=<n>][MULTIRING][PHASE=<n>][TRANSMIT=<n>]
[INFILE=<c>][MASK=<c>][SHIFT.MASK=<c>]
Description
This command is used to enter mask information for OPTOLITH. Several LAYOUT statements can be
used in sequence to define complete mask patterns. All coordinate and size parameters are in microns.
LAY.CLEAR specifies that the currently defined layout should be deleted prior to the execution of the
new layout definition.
X.LOW specifies the minimum x coordinate of the rectangular feature.
Z.LOW specifies the minimum z coordinate of the rectangular feature.
X.HIGH specifies the maximum x coordinate of the rectangular feature.
Z.HIGH specifies the maximum z coordinate of the rectangular feature.
X.TRI specifies the x coordinate of the right angle corner of the triangular feature.
Z.TRI specifies the z coordinate of the right angle corner of the triangular feature.
HEIGHT specifies the height of the right angle triangle feature.
WIDTH specifies the base width of the right angle triangle feature.
ROT.ANGLE specifies the angle of rotation of the feature (-180°≤ROT.ANGLE≤180°) with respect to
the x-axis. The default value is 0°. The center of rotation is at the center of the rectangle and at the
right angle corner of the triangle, respectively.
Note: You can only use the X.TRI, Z.TRI, HEIGHT, WIDTH, and ROT.ANGLE parameters for projection printing
model.
X.CIRCLE specifies the x coordinate of the center of the circular or ring feature.
Z.CIRCLE specifies the z coordinate of the center of the circular or ring feature.
RADIUS specifies the radius of the circular feature or the outermost radius of the ring or multiring
feature.
RINGWIDTH specifies the width of ring(s) of the mask feature shaped as a single ring or a series of
concentrated rings.
MULTIRING specifies that mask feature consists from series of concentered rings with ring widths
and distances between rings specified by the RINGWIDTH parameter. The number N of the rings in the
feature should satisfy the following relation 2N * RINGWIDTH<RADIUS.
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Note: You can only use the RINGWIDTH and MULTIRING parameters for proximity printing model specified by the
GAP parameter in the IMAGE statement.
PHASE specifies the phase shift produced by the feature (-180°≤PHASE≤180°). The default value is 0°.
TRANSMIT specifies the intensity transmittance of the feature (0≤TRANSMIT≤1). The default value is
unity.
INFILE specifies the name of the MASKVIEWS layout file. This file contains the mask information. The
MASKVIEWS mask information is a set of polygons for each mask layer with attributes (transmittance
and phase shift) for each polygon.
MASK specifies the name of mask to be used for image calculation.
SHIFT.MASK specifies the name of the additional mask layer - usually phase shifting layer.
Examples
The following statement describes a mask feature that is 2 microns in the x dimension and 0.4 microns
in the z direction and rotated by 45° with respect to the x-axis.
LAYOUT X.LO=-1 X.HI=1 Z.LO=-0.2 Z.HI=0.2 ROT.ANGLE=45 \
TRANSMIT=1
For more examples, IMAGE, ILLUMINATION, PROJECTION, ILLUM.FILTER, PUPIL.FILTER,
ABERRATION, and the VWF INTERACTIVE TOOLS USER’S MANUALS.
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LINE
6.33: LINE
LINE specifies a mesh line during grid definition.
Syntax
LINE
X|Y LOCATION=<n> [SPACING=<n>] [TAG=<c>] [TRI.LEFT|TRI.RIGHT]
Description
This statement defines the position and spacing of mesh lines. All LINE statements should come before
the REGION and BOUNDARY statements, which should then be followed by an INITIALIZE statement.
X and Y specify whether a mesh line is horizontal or vertical.
LOCATION specifies the location along the chosen axis (in microns) at which the line should be
positioned. The x coordinate increases from left to right; the y coordinate increases progressing from
top to bottom going into the substrate. This is the opposite of normal Cartesian y-axis progression
which increases going upward.
SPACING specifies the local grid spacing (in microns). ATHENA adds mesh lines to the ones given
according to the following recipe. Each user line has a spacing whether user-specified or inferred from
the nearest neighbor. These spacings are then smoothed out so no adjacent intervals have a ratio
greater than the value given by INTERVAL.R on the INITIALIZE statement (default is 1.5). New grid
lines are then introduced so that the line spacing varies geometrically from one end of the interval to
the other. Refer to the example below.
TAG labels lines for later reference by BOUNDARY and REGION statements. The tag label can be any
word.
TRI.LEFT and TRI.RIGHT can be specified in the LINE X statement to control triangle orientation
in the initial grid. Initial simulation area is divided into non-uniform rectangular elements defined by
the LINE X and LINE Y statements. By default each box element is then divided into two rectangular
triangles by a diagonal going from the bottom-left to upper-right corner of the box. In some
applications it is preferable to have a symmetrical grid triangle orientation locally.
One of the examples is etching of a non-vertical trench. If TRI.RIGHT (default) is specified all boxes
between this line and the line with TRI.LEFT (or the last line) will be divided by a "bottom-left to
upper-right" diagonal. If TRI.LEFT is specified the boxes will be divided by a diagonal going from
upper-left to bottom-right corner of the box.
Example
In the following specifications, there are 3 user-specified x lines and 2 user-specified y lines. Spacing of
the x lines is finer in the center than at the edges. After processing, ATHENA produces a mesh with x
lines at 0.0, 0.42, 0.69, 0.88, 1.0,1.12, 1.31, 1.58, 2.0. Around the center, the spacing is 0.12,
approximately what was requested. At the edge, the spacing is 0.42 because that was as coarse as the
line spacing could get without having an interval ratio greater than 1.5. If the interval ratio is set to 9,
then we would have one interval of 0.9 and one interval of 0.1 on each side. In this example, specifying
a spacing of 1 would produce an x line at 0.0 and 1.0.
LINE X LOC=0 SPA=1 TAG=LEFT
LINE X LOC=1 SPA=0.1
LINE X LOC=2 SPA=1 TAG=RIGHT
LINE Y LOC=0 SPA=0.02 TAG=SURF
LINE Y LOC=3 SPA=0.5 TAG=BACK
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Note: It is difficult to predict how many lines are going to be generated in each interval. The initial mesh specification is quite
important to the success of the simulation. Use the geometric mode by specifying the NO.IMP parameter on the
INITIALIZE statement to perform a fast simulation without impurities to determine if the grid spacings are appropriate.
For more examples, see INITIALIZE, REGION, BASE.MESH, and BASE.PAR.
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MASK
6.34: MASK
MASK deposits and patterns photoresist or artificial masking material barrier via the MASKVIEWS
interface.
Syntax
MASK
NAME=”<c>” [REVERSE] [DELTA=<n>]
Description
MASK is used in DECKBUILD to provide interface to Silvaco’s general purpose layout editor, MASKVIEWS.
When you specify a mask statement, ATHENA will deposit photoresist and pattern it by etching. The
etched pattern is determined by selected cut line in MASKVIEWS. See the VWF INTERACTIVE TOOLS USER’S
MANUAL, VOL. I for a complete description of this feature.
NAME specifies the name of the layer that defines the photoresist patterning. Mask names must
appear inside of double quotes. This name must correspond to a mask name contained in the layout
file invoked using DECKBUILD. The mask names are case sensitive and cannot be abbreviated.
REVERSE specifies that the mask polarity should be reversed or that negative type photoresist
should be modeled.
DELTA specifies an offset in mask size. The offset corresponds to a change in CD (critical dimension)
of the mask. Each edge of the mask is moved by a distance DELTA to enlarge or contract the mask
feature.
Examples
The following statement deposits photoresist on the top of the simulation structure and etches it with
the pattern prescribed by the MASKVIEWS layout. The layout file must be specified using the MASKVIEWS
interface as described in the VWF INTERACTIVE TOOLS USER’S MANUAL, VOL. II or in Chapter 2: “Tutorial”.
MASK NAME="CONT"
For more examples, see STRIP.
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MATERIAL
ATHENA User’s Manual
6.35: MATERIAL
MATERIAL sets the coefficients for materials.
Syntax
MATERIAL
[MATERIAL] [NI.0=<n>] [NI.E=<n>] [NI.POW=<n>] [EPS=<n>][E.FIELD]
[VISC.0=<n>][VISC.E=<n>][VISC.X=<n>] [WETO2|DRY02]
[YOUNG.M=<n>][POISS.R=<n>][LCTE=<c>][INTRIN.SIG=<n>]
[OXIDIZABLE][DENSITY=<n>] [COMPONENTS]
[AT.NUM.1=<n>][AT.NUM.2=<n>][AT.NUM.3=<n>][AT.NUM.4=<n>]
[AT.MASS.1=<n>][AT.MASS.2=<n>][AT.MASS.3=<n>][AT.MASS.4=<n>]
[ABUND.1=<n>][ABUND.2=<n>][ABUND.3=<n>][ABUND.4=<n>]]
[REFLOW][GAMMA.REFLO=<n>] [NO.FLIP]
[NIFACT.SIGE=<n>][EAFACT.SIGE=<n>][NIFACT.SIC][EAFACT.SIC]
Description
MATERIAL specify the material for which all parameters apply (see Section 6.2.9: “Standard and
User-Defined Materials” for the list of materials).
Parameters Related to Impurity Diffusion
NI.0, NI.E, and NI.POW specify parameters of the intrinsic electron concentration as a function of
temperature. NI.0 is the preexponential constant in the intrinsic electron concentration formula.
NI.E is the corresponding activation energy. NI.POW is the unitless power constant. These
parameters are used only in diffusion calculation and not in EXTRACT electrical calculations
EPS specifies the relative dielectric permittivity of the material. This value is used to calculate electric
field in semiconductors during diffusion simulation. This value isn’t used in EXTRACT electrical
calculations.
E.FIELD specifies that electric field term will be included in the impurity diffusion equations for this
material. The default is true.
Parameters Related to Material Stress and Viscosity
VISC.0, VISC.E, and VISC.X specify the material viscosity parameters. VISC.0 is the preexponential coefficient, in g/(cm·s). VISC.E is the activation energy, in eV. VISC.X is the
incompressibility factor.
WETO2 and DRYO2 specify whether the viscosity parameters are for wet or dry oxidation. These
parameters are valid only if the specified material is oxide.
YOUNG.M specifies the Young’s modulus for the material in dyne cm-2. This parameter is used in
stress calculations and also with the compress model for oxidation (Also see METHOD LIFT.POLY).
POISS.R specifies the Poisson’s ratio for the material. This parameter is used in stress calculations.
LCTE specifies the linear coefficient of thermal expansion as a function of temperature (T). It is
expressed as a fraction rather than a percentage.
INTRIN.SIG specifies the initial uniform stress state of a material, such as a thin film of nitride
deposited on the substrate. It can be specified as a function of temperature by using an expression and
the variable T in °K.
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MATERIAL
OXIDIZABLE specifies that the material could be oxidized. If you set OXIDIZABLE to TRUE, then all
oxidation related parameters for this material will be set equal to those specified earlier for Silicon.
You can specify different values in the OXIDE statement.
Parameters Related to Material Characteristics used by Monte Carlo Implant
DENSITY specifies the density of the material in g/cm3.
COMPONENTS specifies number of atomic components in the material.
AT.NUM.1, AT.NUM.2, AT.NUM.3, and AT.NUM.4 specify the atomic numbers of the constituent
atoms of the material. The number of AT.NUM parameters specified must correspond to
COMPONENTS.
AT.MASS.1, AT.MASS.2, AT.MASS.3, and AT.MASS.4 specify the atomic masses of the constituent
atoms of the material in atomic mass units. The number of AT.MASS parameters specified must
correspond to COMPONENTS.
ABUND.1, ABUND.2, ABUND.3, and ABUND.4 specify the relative fraction of the constituent
atoms of the material. The number of ABUND parameters specified must correspond to COMPONENTS.
Note: At least one parameter from each of the four lines above are required to define materials for Monte Carlo implants.
Parameters Related to REFLOW Calculations
REFLOW specifies that the material will flow when a DIFFUSE step including REFLOW is defined.
GAMMA.REFLO specifies the surface tension parameter used in the reflow calculation. Units are
dyne/cm. The material viscosity (VISC.* parameters) will also affect the reflow rate.
Parameters Related to the Grid Control
NO.FLIP specifies that triangle flipping procedure should not be applied to the specified material.
Parameters Related to the Boron Diffusion Model in SiGe/SiGeC
NIFACT.SIGE specifies the linear coefficient for Ge dependency formula of intrinsic carrier
concentration for Boron diffusion model in SiGe/SiGeC.
EAFACT.SIGE specifies the linear coefficient for Ge dependency formula of intrinsic carrier
concentration for Boron diffusion model in SiGe/SiGeC.
NIFACT.SIC specifies linear coefficient for Ge content dependency formula of intrinsic carrier
concentration for Boron diffusion model in SiGe/SiGeC.
EAFACT.SIC specifies linear coefficient for Ge content dependency formula of intrinsic carrier
concentration for Boron diffusion model in SiGe/SiGeC.
Example
The following statement defines some properties of a material called BPSG. The material is composed
of silicon, oxygen, boron, and phosphorus with fraction composition 0.3, 0.6, 0.05, and 0.05 respectively.
Monte Carlo Implants could be performed into this material based on this definition.
MATERIAL MATERIAL=BPSG AT.NUM.1=14 AT.NUM.2=8 AT.NUM.3=5 \
AT.NUM.4=15 AT.MASS.1=28.086 AT.MASS.2=16 AT.MASS.3=10.8 \
AT.MASS.4=31 ABUND.1=.3 ABUND.2=.6 ABUND.3=.05 ABUND.4=.05
For more information, see OXIDE, STRESS, and DIFFUSE.
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METHOD
ATHENA User’s Manual
6.36: METHOD
METHOD selects numerical methods and models for diffusion and oxidation.
Syntax
METHOD
[FERMI|TWO.DIM|STEADY|FULL.CPL]
[PLS] [IC] [VC] [DDC] [SS]
[CLUSTER.DAM] [HIGH.CONC] [I.LOOP.SINK] [POLY.DIFF]
[CLUST.TRANS] [DOSE.LOSS]
[SiGECDF.MOD] [SiGECNI.MOD] [MODEL.SIGEC] [MIN.TEMP=<n>]
[IMPURITY|INTERST|VACANCY|OXIDANT|VELOCITY|TRAPS|PSI|PAC]
[REL.ERROR=<n>][ABS.ERROR=<n>]
[FE.RELERR=<n>][FE.ABSERR=<n>] [TD.RELERR=<n>][TD.ABSERR=<n>]
[ST.RELERR=<n>][ST.ABSERR=<n>] [FU.RELERR=<n>][FU.ABSERR=<n>]
[MIN.FILL] [MIN.FREQ=<n>] [GAUSS|CG] [BACK=<n>] [BLK.ITLIM=<n>]
[TIME.STR|ERROR|NEWTON] [DIAG|KNOT|FULL.FAC] [TRUNC.DEF=<n>]
[INIT.TIME=<n>][PDINIT.TIME] [T.DEFECT=<n>]
[OXIDE.GDT=<n>] [REDO.OXIDE=<n>] [TRBDF|FORMULA]
[ERFC|ERFG|ERF1|ERF2|COMPRESS|VISCOUS]
[LIFT.POLY][LIFT.OXIDE][LIFT.NITRID] [OX.THRESH=<n>] [SKIP.SIL]
[GRID.OXIDE=<n>][GRIDINIT.OX=<n>]
[GRID.SILICI=<n>][GRIDINIT.SI=<n>
[GLOOP.IMAX=<n>][GLOOP.EMIN=<n>][GLOOP.EMAX=<n>]
[OXIDE.EARLY=<n>][OXIDE.LATE=<n>][OXIDE.REL=<n>]
[OX.OBFIX=<n>][FILL] [PERIMETER=<n>]
[ADAPT][DEPO.SMOOTH]ETCH.SMOOTH][DIFF.SMOOTH][STEP.SMOOTH]
[STRESS.HIST]
Description
This statement is used to set flags to select the various mathematical algorithms that will be used to
produce the simulation and to select the desired diffusion and oxidation model complexity. Appropriate
defaults for the numerical parameters are included in the athenamod file so that you only need to
specify the desired diffusion and oxidation model. The numerical methods used in ATHENA for the
solution of the diffusion equations are described in [7].
Parameters Related to DIFFUSION models
FERMI, TWO.DIM, STEADY, and FULL.CPL specify the type of diffusion equations to be solved
with particular regard to the point defect models (see Chapter 3: “SSUPREM4 Models”, Section 3.1:
“Diffusion Models”). The FERMI parameter specifies the defects are assumed to be a function of the
Fermi level only. The TWO.DIM parameter specifies that a full time dependent transient simulation
should be performed. The STEADY parameter specifies that the defects are assumed to be in a steady
state. The FULL.CPL parameter specifies that full coupling between defects and dopants should be
included. The default is FERMI. PD.FERMI is an alias for FERMI. PD.TRANS is an alias for
TWO.DIM. PD.FULL is an alias for FULL.CPL. PD.FERMI is an alias for FERMI. PD.TRANS is an
alias for TWO.DIM. PD.FULL is an alias for FULL.CPL.
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METHOD
Note: Chapter 2: “Tutorial” shows a complete description of the use of these diffusion models for typical applications.
PLS, IC, VC, DDC, and SS specify advanced diffusion models (see Chapter 3:3.2: “Advanced Diffusion
Models”). If only the PLS parameter is specified, the classical dopant diffusion model will be used. The
parameters IC and VC will invoke additional interstitial and vacancy clustering models. The DDC
parameter switches on the dopant-defect clustering model. The SS parameter will include the solid
solubility model.
Note: These advanced diffusion models can be used only for boron, phosphorus and arsenic in silicon technologies Also, these
models cannot be used when oxidation or silicidation or both occur during the simulated diffusion step. There are also some
limitation on complexity of the 2D structures, which can be handled by the solver. In most cases, when the solver cannot handle
the structure, materials, impurities or other conditions, it returns control to standard diffusion models.
CLUSTER.DAM specifies that the Stanford {311} cluster model is enabled, allowing a scaled profile of
{311} clusters during a subsequent implant. Only use this model when FULL.CPL is also specified. It
further causes a transient dissolution of the {311} clusters leading to bulk interstitial injection. The
CLUSTER statement is used to set parameters for this model.
Note: For correct operation, set METHOD CLUSTER.DAM FULL.CPL before the IMPLANT statement that generates
the {311} clusters.
HIGH.CONC specifies that extra dopant concentration dependent point defect recombination model
is enabled. The IIFACTOR and IVFACTOR parameters on the INTERSTITIAL command are used when
METHOD HIGH.CONC is enabled.
I.LOOP.SINK specifies that a dislocation loop band can be specified during a subsequent implant and
that the loops may behave as an interstitial sink during diffusion. The DISLOC.LOOP command is used
to set parameters for this model.
POLY.DIFF specifies that the two-stream polysilicon diffusion model should be used. To operate
accurately, set this model before the deposition of the polysilicon material. See Section 6.29:
“IMPURITY” and Chapter 3: “SSUPREM4 Models”, Section 3.1.7: “Grain-based Polysilicon Diffusion
Model” for more information.
CLUST.TRANS enables the Transient Activation Model.
DOSE.LOSS specifies that Interface Trap Model for dose loss at Silicon/Oxide Interface is enabled.
MODEL.SIGEC enables special B diffusion model in SiGeC/SiGeC.
SIGECDF.MOD specifies the name of the C-Interpreter file for boron diffusivity model in SiGe.
SIGECNI.MOD specifies the name of the C-Interpreter file instrinic carrier concentration model used
in boron diffusion mode in SiGe/SiGeC.
MIN.TEMP specifies the minimum temperature for which impurity diffusion is considered. At
temperatures below MIN.TEMP, the impurities are considered immobile. The default is 700°C. With
caution, you can set this parameter to a lower value for certain diffusion steps.
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Parameters Related to Numerics of Diffusion/Oxidation
IMPURITY specifies impurity for which one or several bound (tolerance) parameters will be applied
during diffusion/oxidation simulation (see Section 6.2.10: “Standard Impurities” for the list of
impurities).
INTERST, VACANCY, OXIDANT, VELOCITY, TRAPS, PSI and PAC specifies type of solution for
which one or several bound (tolerance) parameters will be applied during diffusion/oxidation
simulation.
REL.ERR indicates the precision with which the impurity solution must be solved. In general, the
actual error will be less than half of the indicated error. The defaults are 0.01 for all impurities except
the potential, which is solved to 0.001. If this parameter is used an impurity should also be specified.
ABS.ERR specifies the error tolerance absolute value. For dopants, the absolute error defaults to
1.0×109. For defects, the absolute error defaults to 1.0×105. For the potential, the error defaults to
1.0×10-6. If this parameter is used, an impurity should also be specified.
FE.RELERR and FE.ABSERR specifies the relative error and absolute errors for the FERMI model.
TD.RELERR and TD.ABSERR specifies the relative and absolute errors for the TWO.DIM model.
ST.RELERR and ST.ABSERR specifies the relative and absolute errors for the STEADY model.
FU.RELERR and FU.ABSERR specifies the relative and absolute errors for the FULL.CPL model.
MIN.FILL and MIN.FREQ specify a minimum fill. It defaults to true. This is a highly recommended
option since it can reduce the matrix sizes by a factor of two or more and operation speed is a function
of the size of the matrix. MIN.FREQ is a parameter that controls the frequency of the minimum fill
reorderings. It is only partially implemented and has no effect on the calculation.
GAUSS and CG specify the type of iteration performed on the linear system as a whole. CG specifies
that a conjugate residual should be used.
BACK specifies the number of back vectors that can be used in the CG outer iteration. The default is
three and the maximum possible value is six.
Note: A higher value of BACK will give faster convergence at the cost of more memory usage.
BLK.ITLIM is the maximum number of block iterations that can be taken. The block iteration will
finish at this point independent of convergence.
TIME.STE, ERROR, and NEWTON specify the frequency with which the matrix should be factored.
The default is TIME. The TIME parameter specifies that the matrix should be factored twice per time
step. This option takes advantage of the similarity in the matrix across a time integration. The ERROR
parameter indicates that the matrix should be factored whenever the error in that block is decreasing.
The NEWTON parameter forces factorization at every NEWTON step.
DIAG, KNOT, and FULL.FAC specifies the amount of fill to be included in the factorization of the
matrix. FULL.FAC indicates that the entire amount of fill is to be computed. The DIAG parameter
indicates that only the diagonal blocks should be factored in the matrix. The KNOT parameter is
inactive. DIAG is the default parameter. Although under certain conditions (one-dimensional stripes),
FULL.FAC will perform better.
TRUNC.DEF specifies that defect concentrations that become negative due to numerical difficulties
be forced to a positive value.
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Parameters Related to Timestep Control
INIT.TIME specifies the initial timestep value. The default is 0.1 seconds.
PDINIT.TIME specifies the initial time step for point defect diffusion. Point defects are held fixed for
the first timestep. The default is 10-5 seconds.
T.DEFECT specifies time in seconds for which point defect injection will be neglected during an
oxidation. The default is 5 seconds.
OXIDE.GDT limits the timestep during oxidation to a fraction (OXIDE.GDT) of the time required to
oxidize the thickness of one grid layer (GRID.OXIDE). The timestep may be limited by oxidation and
by diffusion, and the value of OXIDE.GDT will limit the timestep if it is more stringent than the limits
imposed by diffusion. OXIDE.GDT<<1 is recommended to improve resolution of oxidizing diffusions.
The default is 0.25.
REDO.OXIDE saves time by not computing the oxide flow field every time the diffusion equation for
impurities is solved. The REDO.OXIDE parameter specifies the percentage of the time required to
oxidize the thickness of one grid layer, which should elapse before resolving the flow field. Usually
REDO.OXIDE is much less than OXIDE.GDT, which is an upper bound on how long the solution
should wait. It is mainly intended to exclude solving oxidation at each and every one of the first few
millisecond time steps when defects are being tracked.
TRBDF and FORMULA specify the time integration method to be used. The TRBDF parameter
indicates that a combination trapezoidal rule/backward difference should be used. The error is
estimated using Milne’s device. The FORMULA method allows you to specify the time step directly as a
function of time (t), previous time step (dt), and grid time (gdt). This option is primarily for
testing. The TRBDF method is the default.
Parameters related to OXIDATION models
ERFC, ERFG, ERF1, ERF2, COMPRESS, and VISCOUS are oxidation models (see Chapter 3:
“SSUPREM4 Models”, Section 3.3: “Oxidation Models”). The ERFC parameter indicates that a simple
error function approximation to a bird’s beak shape should be used. The ERF1 and ERF2 models are
analytic approximations to the bird’s beak from the literature. The ERFG model chooses whichever of
ERF1 or ERF2 is most appropriate. All erf models are applicable only to the simplest case of oxidation
to the right of the mask edge. All relevant parameters in the OXIDE statement must be explicitly
specified when using any of the ERF* models. The COMPRESS model regards the oxide as a
compressible liquid. The VISCOUS model treats the oxide as an incompressible viscous liquid. Oxide is
actually believed to be incompressible, but the compressible model runs faster. The default is the
COMPRESS model.
Note: For Hints on the use of the different oxidation models, see Chapter 2: “Tutorial”.
Note: Use of the VERTICAL model is not recommended in ATHENA
LIFT.POLY, LIFT.OXIDE, and LIFT.NITRID specifies that the polysilicon, oxide, and nitride
materials can be lifted by oxidation or silicidation processes. These are true by default, but you set
them to false to eliminate the lifting portion of the calculation for geometries where lifting is not
expected to occur.
OX.THRESH specifies that the oxidation threshold model is enabled. This doesn’t allow oxidation
when the concentration of oxidant drops below a critical threshold value set by MIN.OXIDANT on the
OXIDE statement.
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ATHENA User’s Manual
SKIP.SIL is a Boolean parameter which controls the computation of stress in silicon. SKIP.SIL
defaults to true. stress can only be computed when the VISCOUS oxide model is used. The silicon
substrate is treated as an elastic solid subject to the tensions generated by the oxide flow.
Indiscriminate use is not recommended. The silicon grid is usually much larger than the oxide grid
and stress computation is correspondingly more lengthy.
Parameters related to Grid Control during Oxidation
Many grid related problems during oxidation are related to the initial oxide deposition. See Section
6.40: “OXIDE” for more about initial oxides.
GRID.OXIDE specifies the desired thickness, in microns, of grid layers to be added to the growing
oxide. It has an effect on time steps (refer to OXIDE.GDT). The default is 0.1 microns.
GRIDINIT.OX specifies the initial oxide grid spacing (in microns). The default is 0.1 microns.
GRID.SILICI specifies the maximum silicide grid spacing (in microns). The default is 0.1 microns.
GRIDINIT.SI specifies the initial silicide grid spacing (in microns). The default is 0.1 microns.
GLOOP.EMIN, GLOOP.EMAX, and GLOOP.IMAX controls loop detection during grid
manipulation. The default value is GLOOP.IMAX=170æ. Loop detection checks for intrusions and
extrusions in the boundary. The intrusion-fixing algorithm is triggered by angles greater than
GLOOP.IMAX. A larger value means that more extreme intrusions can develop and increases the
possibility of a tangled grid. A smaller value leads to earlier intrusion-fixing; too small a value will
lead to inaccuracy due to premature intervention. Similar concerns apply to the other parameters. The
values are a compromise between safety and accuracy. The extrusion-fixing algorithm is always
triggered by angles greater than GLOOP.EMAX. It may be triggered by lesser extrusions, anything
greater than GLOOP.EMIN, if the extrusion is a single-triangle error in the boundary. The default value
is GLOOP.EMIN=130°. Neither of these parameters should be less than 90° because the rectangular
edges of the simulation space would be smoothed.
OXIDE.EARLY, OXIDE.LATE, and OXIDE.REL should not normally be modified. They relate to
internal numerical mechanisms and are described here only for the sake of completeness. A node
whose spacing decreases proportionally by more than OXIDE.LATE is marked for removal. Also, if any
nodes are removed, then all nodes greater than OXIDE.EARLY are also removed. For earlier node
removal (fewer obtuse triangles), try OXIDE.LATE=0.3 and OXIDE.EARLY=0.1. Though not logical, it
is harmless for OXIDE.EARLY to be greater than OXIDE.LATE. The OXIDE.REL parameter is the
percentage error in velocities for the non-linear viscous model. The default is 1.0×10-2 (that is, a 1.0
percent error). OXIDE.REL can be increased for a faster solution.
OX.OBFIX specifies the cosine squared of the worst angle allowed during oxidation.
FILL and PERIMETER specify which action to apply to voids that may form during oxidation. FILL
specifies that you must fill the voids with oxide materials. Default is false. PERIMETER specifies the
maximum perimeter of the voids to fill. Default is 0.2 microns.
Parameters related to Grid Control during ETCH
ETCH.EPS sets a tolerance on the grid movement during ETCH statements. This parameter is defined
in relative units. The default is 10-6 that corresponds to about 10 Angstroms. Reducing this number
will allow sub-10A etches to be exact. But the possibility of small triangles being created during etches
is high if the parameter is set too low. This parameter should not be set to zero.
Parameters used in the Adaptive Meshing Module
ADAPT specifies that the adaptive meshing should be performed on the IMPLANT, DIFFUSE, or
EPITAXY statements (the default is false).
DEPO.SMOOTH specifies that the mesh smoothing should be performed after each DEPOSIT
statement.
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ETCH.SMOOTH specifies that the mesh smoothing should be performed after each ETCH statement.
DIFF.SMOOTH specifies that the mesh smoothing should be performed after each DIFFUSE
statement.
STEP.SMOOTH specifies that the mesh smoothing should be performed after each time step on each
DIFFUSE statement.
Miscellaneous Parameters
STRESS.HIST specifies that stresses to be calculated during etching, deposition, diffusion, and
epitaxy process steps.
Example setting tolerances
The following statement specifies that the arsenic equation should be solved with a relative error of 1%
and concentrations below 1 x 109 can be ignored.
METHOD ARSEN REL.ERR=0.01 ABS.ERR=1.0E9
Example setting numerical techniques
The following statement specifies that minimum fill reordering should be done and that the entire
system should be solved using a conjugate residual technique with three back vectors. The initial time
step should be 0.1 seconds and time should be integrated using the TRBDF parameter. The FERMI
model should be used for diffusion and the COMPRESS model for the oxide growth.
METHOD MIN.FILL CG BACK=3 INIT.TI=0.1 TRBDF FERMI COMPRESS
Example setting diffusion model for power devices
The following step specifies that a simple diffusion model should be used appropriate for power
electronic devices.
METHOD POWER
DIFFUSION TEMP=1000 TIME=300 NITROGEN
Example setting diffusion models for RTA
The following statement invokes all {311} cluster models for RTA simulation. It must be set before the
IMPLANT statement that generates the cluster damage.
METHOD NEWTON FULL.CPL CLUSTER.DAM I.LOOP.SINK HIGH.CONC BACK=6
IMPLANT ....
DIFFUSE ....
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MOMENTS
ATHENA User’s Manual
6.37: MOMENTS
MOMENTS specifies tables and spacial moments used in analytical implant models.
Syntax
MOMENTS
[SVDP_TABLES | STD_TABLES | USER_STDT] [USER_TABLE=<c>]
[MATERIAL] [I.IMPUTITY] [DOSE=<n>] [ENERGY=<n>]
[RANGE=<n>] [STD.DEV=<n>] [GAMMA=<n>] [KURTOSIS=<n>
[LSTD.DEV][LGAMMA][LKURTOSIS] [SKEWXY]
[SRANGE=<n>][SSTD.DEV=<n>][SGAMMA=<n>][SKURTOSIS=<n>]
[LSSTD.DEV][SSKEWXY][SKURTXY][SKURTT][DRATIO=<n>]
[IGNORE_MOM]
Description
Parameters Used to Select Moment Tables
SVDP_TABLES specifies that the SIMS Verified Dual Pearson (SVDP) moments tables will be used
with dual Pearson implant model. Default is true (See Chapter 3: “SSUPREM4 Models”, Section 3.5.1:
“Analytic Implant Models”).
STD_TABLES specifies that SVDP_TABLES are ignored and standard tables are used with the
subsequent implant statements.
USER_STDT specifies the user-defined moments file (see the USER_TABLE parameter) will be used
with standard format. You can find a template for the user-defined moments file in
<install.area>/lib/athena/<version>/common/userimp.
USER_TABLE=<c> specifies the file that contains user-defined look-up implant parameter tables.
Implant Definition Parameters
MATERIAL specifies the material for which the implant moments are set (see Section 6.2.9:
“Standard and User-Defined Materials” for the list of materials).
I.IMPURITY specifies the implanted impurity for which the moments are set (see Section 6.2.10:
“Standard Impurities” for the list of impurities). I.BF2 can be also specified.
DOSE is an incident ion dose (/cm2).
ENERGY sets the incident ion energy (keV).
Parameters Used for Specification of Spacial Moments
RANGE (RP) specifies the projected range. Units are microns.
STD.DEV (DRP) specifies the standard deviation Units are microns.
GAMMA (SKEWNESS) specifies the third moment. Default is 0.0.
KURTOSIS specifies the fourth moment. Default is 3.01.
LSTD.DEV(LDRP) specifies the lateral standard deviation Units are microns.
SKEWXY specifies the mixed third moment.
KURTXY specifies the lateral mixed fourth moment.
KURTT specifies the lateral fourth moment. Default is 3.0.
SRANGE (SRP) specifies the projected range for second Pearson Units are microns.
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SSTD.DEV(SDRP) specifies the standard deviation for second Pearson Units are microns.
SGAMMA (SSKEW) specifies the third moment for second Pearson function. Default is 0.0.
SKURTOSIS specifies the fourth moment for second Pearson function. Default is 3.01.
LSSTD.DEV(LSDRP) specifies the lateral standard deviation for second Pearson Units are microns.
SSKEWXY specifies the mixed third moment for second Pearson. Default is 0.0.
SKURTXY specifies the mixed fourth moment for second Pearson. Default is 0.0
SKURTT specifies the lateral fourth moment for second Pearson. Default is 3.0.
DRATIO specifies the dose ratio R in the double Pearson function. Default is 0.9
Reset Parameter
IGNORE_MOM specifies that all previous MOMENTS statements will be ignored.
Examples
The MOMENTS statement is used to define user moments through a convenient command language.
The following example sets the moments for boron implantation into the user-defined material
SAPPHIRE.
MOMENTS MATERIAL=SAPPHIRE I.BORON DOSE=1.6e12 ENERGY=25 \
RANGE=0.098 STD.DEV=0.045 GAMMA=-0.04 KURTOSIS=3.5
For more examples, see IMPLANT.
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OPTICAL
ATHENA User’s Manual
6.38: OPTICAL
OPTICAL sets the optical parameters of materials for OPTOLITH.
Syntax
OPTICAL
[MATERIAL][NAME.RESIST=<c>]
[LAMBDA=<n>][I.LINE|G.LINE|H.LINE|DUV.LINE]
[REFRAC.REAL=<n>][REFRAC.IMAG=<n>]
[DELTA.REAL=<n>][DELTA.IMAG=<n>]
Description
This command sets the optical parameters, reflective index, and extinction coefficient or REFRAC.REAL
and REFRAC.IMAG for each material at a particular wavelength. If photoresist is used, NAME.RESIST
must also be specified.
MATERIAL specifies the material for which the optical parameters to be set (see Section 6.2.9:
“Standard and User-Defined Materials” for the list of materials)
NAME.RESISTspecifies the name of the photoresist.
I.LINE, G.LINE, H.LINE, DUV.LINE, and LAMBDA specifies the line or the wavelength. Units for
LAMBDA are microns. WAVELENGTH is an alias for LAMBDA.
REFRAC.REAL specifies the real component of the refractive index.
REFRAC.IMAG specifies the imaginary component of the refractive index.
DELTA.REAL specifies the difference between the real components of the refractive index for
completely exposed and unexposed resist. This value is used when dose effect on the refractive index is
simulated.
DELTA.IMAG specifies the difference between the imaginary components of the refractive index for
completely exposed and unexposed resist. This value is used when dose effect on the refractive index is
simulated.
Examples
The OPTICAL statement is used to load refractive index values into ATHENA for each wavelength. The
following shows a typical statement.
OPTICAL SILICON WAVELENGTH=.365 REFRAC.REAL=4.5 REFRAC.IMAG=5.2
You can enter user-defined materials in the following format.
OPTICAL MATERIAL=XXX WAVELENGTH=.365 REFRAC.REAL=1.4 \
REFRAC.IMAG=.3
For more examples, see EXPOSE and IMAGE.
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OPTION
6.39: OPTION
OPTION specifies the level of run-time output.
Syntax
OPTION
[QUIET|NORMAL|VERBOSE|DEBUG|WARNING]
Description
This statement specifies the level of information sent to the TTY Terminal Window of DECKBUILD.
QUIET, NORMAL, VERBOSE, DEBUG, and WARNING determines the amount of information
that is output about errors, CPU times, and behavior of the algorithms. The default is QUIET. The
VERBOSE and DEBUG modes are intended mainly for debugging by developers.
Examples
The following statement sets the routine output to include more information.
OPTION NORMAL
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OXIDE
ATHENA User’s Manual
6.40: OXIDE
OXIDE specifies coefficients for use during oxidation steps. AMBIENT is a synonym for OXIDE.
Syntax
OXIDE
DRY02|WET02 [ORIENT=<n>]
[LIN.L.0=<n>][LIN.L.E=<n>] [LIN.H.0=<n>][LIN.H.E=<n>
[L.BREAK=<n>][L.PDEP=<n>]
[PAR.L.0=<n>][PAR.L.E=<n>] [PAR.H.0=<n>][PAR.H.E=<n>]
[P.BREAK=<n>][P.PDEP=<n>]
[ORI.DEP][ORI.FAC=<n>]
[HCL.PC=<n>][HCLT=<n>][HCLP=<n>][HCL.PAR=<n>][HCL.LIN=<n>]
[THINOX.0=<n>][THINOX.E=<n>][THINOX.L=<n>][THINOX.P=<n>]
[BAF.DEP][BAF.EBK=<n>][BAF.PE=<n>][BAF.PPE=<n>]
[BAF.NE=<n>][BAF.NNE=<n>][BAF.K0=<n>][BAF.KE=<n>]
[STRESS.DEP][VC=<n>][VR=<n>][VD=<n>][VT=<n>][DLIM=<n>]
[MATERIAL][/MATERIAL]
[DIFF.0=<n>][DIFF.E=<n>] [SEG.0=<n>][SEG.E=<n>] [TRN.0=<n>][TRN.E=<n>]
[HENRY.COEFF=<n>] [THETA=<n>] [ALPHA=<n>] [MIN.OXIDANT=<n>]
[INITIAL=<n>] [SPLIT.ANGLE=<n>]
[SPREAD=<n>][MASK.EDGE=<n>][NIT.THICK=<n>][ERF.Q=<n>]
[ERF.DELTA=<n>][ERF.LBB=<n>][ERF.H=<n>]
Description
All parameters relating to oxidation are specified in this statement. Oxidation models are specified in
the METHOD statement. All oxidation models are described in Chapter 3: “SSUPREM4 Models”, Section
3.3: “Oxidation Models”. To properly set values for most coefficients, you need to know whether to use
wet or dry oxidation and to know the substrate orientation.
Note: If a required parameter is omitted (e.g., orientation when a linear rate coefficient is being specified), then the statement
is ignored without warning.
Oxide Growth Rate Parameters
DRYO2, WETO2 specifies the type of oxidation to which specified coefficients apply. Required for
everything except for one-dimensional coefficients and the volume ratio.
ORIENT is the substrate orientation the coefficients specified apply to the required for orientation
factor (see ORI.FAC) and thin oxide coefficients. Only 100, 110, and 111 are recognized. The default is
100.
LIN.L.0, LIN.L.E, LIN.H.0, LIN.H.E, L.BREAK, and L.PDEP specifies the linear rate coefficients
(B/A). A doubly activated Arrhenius model is assumed. L.BREAK is the temperature breakpoint
between the lower and higher ranges in degrees Celsius. LIN.L.0 is the pre-exponential factor in
microns/min. LIN.L.E is the activation energy in eV for the low temperature range. LIN.H.0 and
LIN.H.E are the corresponding high temperature numbers. L.PDEP is the exponent of the pressure
dependence. The value given is taken to apply to <111> orientation and later adjusted by ORI.FAC
according to the substrate orientation present.
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PAR.L.0, PAR.L.E, PAR.H.0, PAR.H.E, P.BREAK and P.PDEP specifies the parabolic rate
coefficients (B).
ORI.FAC is the ratio of B/A on the specified orientation to the orientation.
ORI.DEP specifies whether the local orientation at each point on the surface should be used to
calculate B/A. The default is true. If it is false, the substrate orientation is used at all points.
THINOX.0, THINOX.E, and THINOX.L specifies coefficients for the thin oxide model proposed by
Massoud [14]. THINOX.0 is the pre-exponential factor in microns/min, THINOX.E is the activation
energy in eV, and THINOX.L is the characteristic length in microns.
THINOX.P is the thin oxide model pressure dependence.
HCL.PC, HCLT, HCLP, HCL.PAR, and HCL.LIN is where the numerical parameter, HCL.PC, is the
percentage of HCl in the gas stream. It defaults to 0. The HCl dependence of the linear and parabolic
coefficients is obtained from a look-up table specified in the model file. The table rows are indexed by
HCl percentage. Specify the row entries with the parameter HCLP, which is an array of numerical
values surrounded by double quotes and separated by spaces or commas. The columns are indexed by
temperature. Specify the column entries with the parameter HCLT, which is an array of numerical
values surrounded by double quotes and separated by spaces or commas. Specify the dependence of
B/A with the parameter HCL.LIN, which is an array of numerical values surrounded by double quotes
and separated by spaces or commas. The number of entries in HCL.LIN must be the product of the
number of entries in HCLP and HCLT. Specify the dependence of B with the parameter HCL.PAR, which
is an array of numerical values surrounded by double quotes and separated by spaces or commas. The
number of entries in HCL.PAR must be the product of the number of entries in HCLP and HCLT.
BAF.DEP, BAF.EBK, BAF.PE, BAF.PPE, BAF.NE, BAF.NNE, BAF.K0, and BAF.KE relates to the
doping dependence of the oxidation rate. The doping dependence is activated when BAF.DEP is true
(default). MATERIAL1 must be specified with these parameters (only SILICON and POLYSILICON
make sense here).
STRESS.DEP, VC, VR, VD, VT, and DLIM controls the stress dependence of oxidation, which is only
calculated under the VISCOUS model. STRESS.DEP turns on the dependence. VC is the activation
volume of viscosity. VR is the activation volume of the reaction rate with respect to normal stress. VT is
the activation volume of the reaction rate with respect to tangential stress. VD is the activation volume
of oxidant diffusion with respect to pressure. DLIM is the maximum increase of diffusion permitted
under tensile stress.
MATERIAL specifies MATERIAL1 for which parameters to be set (see Section 6.2.9: “Standard and
User-Defined Materials” for the list of materials).
/MATERIAL specifies MATERIAL2 for which parameters to be set (see Section 6.2.9: “Standard and
User-Defined Materials” for the list of materials).
DIFF.0, DIFF.E, SEG.0, SEG.E, TRN.0, and TRN.E specifies the diffusion coefficients of oxidant in
MATERIAL1 and the boundary coefficients (“transport” and “segregation”) from MATERIAL1 to
MATERIAL2 as defined above. DIFF.0 is the diffusivity pre-exponential factor in cm2/sec. DIFF.E is
the energy in eV. The transport coefficient represents the gas-phase mass transfer coefficient in terms
of concentrations in the solid at the oxide-gas interface, the chemical surface-reaction rate constant at
the oxide-silicon surface, and a regular diffusive transport coefficient at other interfaces. The
segregation coefficient is 1 at the oxide-gas interface, it is infinity at the oxide-silicon interface, and is
a regular segregation coefficient at other interfaces.
Note: Oxidant in materials other than oxide is allowed to diffuse and segregate but its concentration is then ignored (for
instance, no oxynitridation).
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OXIDE
ATHENA User’s Manual
HENRY.COEFF (Henry’s coefficient) is the solubility of oxidant in MATERIAL1 measured in cubic
centimeters (cm3) at one atmosphere. THETA is the number of oxygen atoms incorporated in a cubic
centimeter of oxide. In the case of dry oxidation, it is equal to THETA and in the case of wet oxidation,
it is equal to 2 THETA. Usually, the Deal-Grove coefficients should be changed instead of
HENRY.COEFF.
THETA specifies the concentration of O2 atoms incorporated in the material. Units are cm-3.
ALPHA specifies the volume expansion ratio between MATERIAL1 and MATERIAL2. Only SILICON,
POLYSILICON and OXIDE make sense here.
MIN.OXIDANT specifies the minimum oxidant concentration for oxidation to occur. Units are cm-3.
This parameter is active only if METHOD OX.THRESH is used.
Parameters Related to Grid Control
INITIAL specifies the thickness of the native (initial) oxide at the start of oxidation step. If any
oxidizable surface of the structure is bare, an oxide layer of this thickness is deposited before oxidation
begins. Units are microns. Default is 0.002.
Note: The oxidation algorithm requires selective deposition of a native oxide onto all exposed silicon or polysilicon areas prior
to oxidation. Grid problems can result in complex structures. To resolve these problems, adjust INITIAL or use the
DEPOSIT statement to create the native oxide.
SPLIT.ANGLE governs the minimum angle at which the oxide will split open one more grid spacing
when oxidizing at a triple point (i.e., where silicon, oxide, and nitride coincide together at a point). The
default for the split angle is 22.5°. The SPLIT.ANGLE parameter for triple point oxidation is material
dependent. Specify the oxidizing MATERIAL1 without a “/” and MATERIAL2 with a “/” using the
following format: OXIDE SPLIT.ANGLE=35 SILICON /NITRIDE. There are only three possible
combinations and they are SILICON /NITRIDE, SILICON /POLYSILICO, and POLYSILION/
NITRIDE. You can use this to control lateral encroachment during oxidation.
Parameters of the Analytical Oxidation Models (ERF*)
SPREAD and MASK.EDGE are used only in the error-function approximation to a bird’s beak shape.
SPREAD is the relative lateral to vertical extension, which defaults to 1. The fitting parameter makes
the “erfc” bird’s beak look realistic. MASK.EDGE is the position of the mask edge in microns and
defaults to negative infinity. Oxide grows to the right of the mask edge.
ERF.Q and ERF.DELTA are the DELTA and Q parameters for the “erfg” model. Normally, you don’t
need to change them but they are available if necessary.
ERF.LBB is the length of the bird’s beak and applies to the “erfg” model only. It can be specified as an
expression in Eox (the field oxide thickness (µm)), eox (the pad oxide thickness (µm)), Tox (the
oxidation temperature (Kelvin)), and en (the nitride thickness, µm). The published expression can be
found in the models file. Specifying ERF.LBB=EOX, for instance, would give a lateral spread equal to
the field thickness, similar to the Hee-Gook Lee model with a spread of one.
ERF.H is the ratio of the nitride lifting to the field oxide thickness. It corresponds to the Guillemot “H”
parameter except that it is normalized to the field oxide thickness. It is specified as an expression of
Eox, eox, Tox, en.
NIT.THICK specifies the nitride thickness to substitute for the parameter EN.
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OXIDE
Note: The ERFG model uses both oxide and nitride thickness. These values are not inferred from the structure. Instead, the
nitride thickness is user-specified in the OXIDE statement and the oxide thickness is computed by adding the total oxide
grown and the initial user-specified oxide thickness. If the structure has more than 20 angstroms (the default) of native oxide on
it when diffusion begins, then thickness must be specified. Beware of this when continuing a diffusion by any means (e.g., after
reading in a previous structure).
Examples
The following modifies the parabolic oxidation rates for {100} silicon in a dry oxygen ambient.
OXIDE DRY ORI=100 PAR.L.0=283.333 PAR.L.E=1.17
Note: If a required parameter is omitted (e.g., orientation when a linear rate coefficient is being specified), then the statement
is ignored without warning.
The following set the native oxide thickness at 10 Angstroms.
OXIDE INITIAL=0.001
The following defines that stress-dependent oxidation rates will be used with the viscous oxidation
model.
METHOD VISCOUS
OXIDE STRESS.DEP=t
For more examples, see DIFFUSE and METHOD.
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POLISH
ATHENA User’s Manual
6.41: POLISH
POLISH runs the chemical mechanical polishing (CMP) module.
Syntax
POLISH
MACHINE=<c>[TIME=<n>][HOURS|MINUTES|SECONDS]
[DX.MULT=<n>][DT.FACT=<n>][DT.MAX=<n>]
Description
This statement executes the chemical mechanical polishing module of ELITE. The POLISH statement
must be preceded by a RATE.POLISH statement to define the polishing machine.
MACHINE specifies the name of the polish machine.
TIME specifies the time the machine is to be run.
HOURS, MINUTES, and SECONDS specifies the units of the TIME parameter.
DX.MULT is the accuracy multiplier for ELITE polishes. The discretization size used for the polish
calculation will be multiplied by DX.MULT. For improved accuracy, decrease the value of DX.MULT. For
improved speed, increase the value of DX.MULT.
DT.FACT controls the timestep size. By default, the movement of a string node is limited to less than
or equal to one quarter of the median segment length. This is a good compromise between simulation
speed and the danger of loop formation. The optimization factor DT.FACT must not exceed 0.5 but can
decrease if necessary for more accuracy.
DT.MAX is used with ELITE type polish calculations. By default, the upper limit for the micro
timestep DT.MAX is one tenth of the total etch time specified. This is a good compromise between
calculation accuracy and calculation time. But, sometimes it is useful to adapt this value to the specific
simulation problem. Allowing the time steps to become greater gives a higher simulation speed but the
accuracy may suffer. For smaller time steps, the simulation speed will decrease but the accuracy may
be greater.
Examples
The following statements illustrate running the chemical mechanical polish module. A RATE.POLISH
statement sets the values for the polish model and must precede the POLISH statement.
RATE.POLISH OXIDE MACHINE=cmp u.s MAX.HARD=0.15 MIN.HARD=0.03 \
ISOTROPIC=0.001
POLISH MACHINE=cmp TIME=5 MIN
For more examples, see RATE.POLISH and ETCH.
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Silvaco
PRINT.1D
6.42: PRINT.1D
PRINT.1D prints values along a one–dimensional cross section or an material interface.
Note: Use of this statement is not recommended. All functions are available using the EXTRACT command within
DECKBUILD.
Syntax
PRINT.1D
[X.VALUE=<n>|Y.VALUE=<n>]
[MATERIAL][/MATERIAL] [ARCLENGTH][LAYERS]
[X.MIN=<n>][X.MAX=<n>][FORMAT=<c>]
Description
This command prints the values along cross sections through the device. You can also use to integrate
along a specified line. The value printed is the value that has been selected (see Section 6.55:
“SELECT”).
X.VALUE specifies the x coordinate of a vertical cross-section along which the selected values are to
be printed. Units are microns.
Y.VALUE specifies the y coordinate of a vertical cross-section along which the selected values are to be
printed. Units are microns.
MATERIAL specifies the selected values in the named material at the interface with another
material named by /MATERIAL are to be printed (see Section 6.2.9: “Standard and User-Defined
Materials” for the list of materials).
ARCLENGTH is only relevant when printing along an interface. If ARCLENGTH is chosen, the printed
ordinate is the arclength, measured in microns, along the boundary from the left most point of the
curve. If ARCLENGTH is not chosen, the x value of the interface location is printed. The coordinate of
the left most point is equal to its x coordinate in the mesh layers.
LAYERS instructs the selected print variable to integrate in each material it crosses. The integrated
value and material width is reported. Zero crossings of the variable are treated the same as material
interfaces.
X.MIN and X.MAX specify the minimum and maximum positions along the cross-section to be
printed.
FORMAT changes the print format for the variable, using standard format expressions of the Clanguage. Default is “%-16e”.
Examples
The following statement prints the selected value at x equal to one micron between the top of the mesh
and the 3.0 micron point.
PRINT.1D X.VAL=1.0 X.MAX=3.0
The following prints the selected variable along the silicon side of the silicon/oxide interface.
PRINT.1D SILICON /OXIDE
For more examples, see SELECT and PRINTF.
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PRINTF
ATHENA User’s Manual
6.43: PRINTF
PRINTF is a string printer and desk calculator.
Note: Functions of this statement have been replaced by the EXTRACT statement
Description
The ECHO statement merely prints the string given to it. This is useful for placing comments in an
output file. The statement attempts to parse the string to a legal real number if possible. It has a
regular expression parser built-in. This allows ECHO to be used as a desk calculator.
Examples
The following command will send the string “Athena Is My Favorite Process Simulator”
to standard output.
ECHO Athena Is My Favorite Process Simulator
The following command will print 4096.
ECHO (2^3^4)
The following command will print 8.373, which is the solution to the arithmetic expression.
ECHO ( 15.0 - 12.0 * EXP( 4.0 - 2.0 / 6.0 ) )
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Silvaco
PROFILE
6.44: PROFILE
PROFILE reads a 1D doping profile into ATHENA.
Syntax
PROFILE
[INFILE=<c>] [MASTER]
[IMPURITY|INTERST|VACANCY|CLUSTER.DAM|DIS.LOOP]
[LAYER1.DIV=<n>] [LAYER2.DIV=<n>]....[LAYER20.DIV=<n>)
Description
This statement can be used to load a 1D stream of doping data into an ATHENA structure. The data
might come from a Secondary Ion Mass Spectroscopy (SIMS) profile or from a 1D simulation in
SSUPREM3. Data is applied in 1D across the width of the mesh for subsequent 2D simulation.
INFILE specifies the name of the profile data file or Standard Structure File to be loaded.
MASTER or SSF indicates that the file to be loaded is an Silvaco Standard Format file. Files
generated by SSUPREM3 are in this format.
IMPURITY specifies the impurity type for profile data file. Corresponding active impurity will be also
added. See Section 6.2.10: “Standard Impurities” for the list of impurities.
INTERST, VACANCY, CLUSTER.DAM and DIS.LOOP specify that profile data file includes a
profile of interstitials, vacancies, {311} clusters or dislocation loops, correspondingly.
LAYER1.DIV, LAYER2.DIV,..., LAYER20.DIV specifies the number of subdivisions for each layer
when loading SSUPREM3 Structure files.
Examples
An example of a PROFILE statement is given below.
PROFILE INF=BORON.SIMS BORON
In this case, the PROFILE statement specifies that only boron information will be added to the current
working silicon structure. The data file BORON.SIMS should be in the following format.
#THIS IS SIMS DATA
0.01
1E15
0.02
1.1E15
0.04
1.3E15
0.06
1.5E15
0.1
1.7E15
0.2
1.9E15
0.4
2.6E15
. . .
In the following example, the PROFILE statement will read in a 1D Silvaco’s standard format (SSF)
file. All doping and layer information will be preserved. This allows you to start a simulation in, for
example, SSUPREM3 and finish it in ATHENA. The ATHENA grid must be set up in the conventional
manner first. The PROFILE statement will then include any overlying layers that may have been
deposited or grown in creating the SSUPREM3 structure. The value LAYER<n>.DIV controls the
number of grid points in the overlying layers. The default grid spacing generated for overlying layers is
0.05 µm.
PROFILE MASTER INF=SSUPREM3.STR LAYER1.DIV=3 LAYER2.DIV=6
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PROFILE
ATHENA User’s Manual
The first layer above the substrate will have 3 vertical grid spacings and the second layer above the
substrate will have 6 vertical grid spacings. The file SSUPREM3.STR must be a SSF file.
The following is a list of special cases and their solutions.
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•
If a SSUPREM3 structure is deeper than the ATHENA structure, the PROFILE statement will
extend the value of the bottom grid point.
•
If a SSUPREM3 structure is shallower than the ATHENA structure, the PROFILE statement will
clip the ATHENA profile.
•
Loading a SSF file works only with a bare silicon wafer as a starting point. If you try to use some
other material for a substrate, the results are unreliable and unpredictable.
•
Any concentrations of dopant initialized in ATHENA will be overwritten if a PROFILE statement
is used to load a SSF file.
Silvaco
PROJECTION
6.45: PROJECTION
PROJECTION specifies the basic optical projection parameters for OPTOLITH.
Syntax
PROJECTION
[NA=<n>][FLARE=<n>]
Description
This statement specifies the numerical aperture NA, the defocus distance, and the possible flare in the
optical or resist systems.
NA is the numerical aperture of the optical projection system.
FLARE is the amount of flare for the particular imaging problem. FLARE must be expressed in
percentages.
Examples
The following statement sets the numerical aperture and flare value for the projection system.
PROJECTION NA=.5
FLARE=2
For more examples, see IMAGE, ILLUMINATION, ILLUM.FILTER, PUPIL.FILTER, LAYOUT, and
ABERRATION.
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PUPIL.FILTER
ATHENA User’s Manual
6.46: PUPIL.FILTER
PUPIL.FILTER specifies the projection pupil type and filtering for OPTOLITH.
Syntax
PUPIL.FILTER
CIRCLE|SQUARE|GAUSSIAN|ANTIGAUSS
[GAMMA=<n>][IN.RADIUS=<n>][OUT.RADIUS=<n>][PHASE=<n>]
[TRANSMIT=<n>][CLEAR.FIL]
Description
This command allows you to specify four different pupil types and allows spatial filtering in the
Fourier transform plane.
CIRCLE, SQUARE, GAUSSIAN, and ANTIGAUSS defines or changes the shape of the exit pupil of
the projection system. The shape of the pupil must be entered as a character string.
GAMMA defines or changes the GAMMA value for GAUSSIAN and ANTIGAUSS pupil transmittance.
GAMMA is a parameter that defines the truncation of the GAUSSIAN by the pupil. In the limit of
GAMMA→0, the pupil transmittance will be uniform.
IN.RADIUS and OUT.RADIUS defines or changes the intensity transmittance and phase
transmittance of an annular zone inside the exit pupil or either the illumination or the projection
system. This qualifier is used to simulate spatial filtering techniques. IN.RADIUS and OUT.RADIUS
are used to define an annular zone in the exit pupil having the pupil transmittance equal to TRANSMIT
and producing the phase angle equal to PHASE. Radius values are specified in fractions of unity and
phase is specified in degrees. Note that the annular zones should not overlap. The outer radius of an
inner zone must be smaller than the inner radius of an outer zone. The shape of the annular zone is
specified by the shape parameter above. The maximum radius is one.
PHASE specifies the phase shift in degrees produced by the pupil filter-180° ≤ PHASE ≤180°).
TRANSMIT specifies the pupil transmittance caused by the pupil filter.
CLEAR.FIL resets the projection filter list.
Examples
This set of commands defines a square aperture in the projection pupil that is opaque over a square
annular region.
PUPIL.FILTER SQUARE
PUPIL.FILTER IN.RADIUS=.1 OUT.RADIUS=.2 PHASE=0 TRANSMIT=0
For more examples, see IMAGE, ILLUMINATION, PROJECTION, ILLUM.FILTER, LAYOUT, and
ABERRATION.
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QUIT
6.47: QUIT
QUIT terminates execution of ATHENA. The EXIT, STOP and BYE statements are synonyms of the
QUIT statement.
Syntax
QUIT
Description
All statements after a QUIT statement will not be checked or executed.
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RATE.DEPO
ATHENA User’s Manual
6.48: RATE.DEPO
RATE.DEPO specifies the deposit rates of a machine, which is used in a subsequent DEPOSIT
statement.
Syntax
RATE.DEPO
MACHINE=<c> MATERIAL | NAME.RESIST=<c>]
CONICAL|CVD|PLANETAR|UNIDIRECT|DUALDIRECT|
HEMISPHERIC|MONTE1|MONTE2|CUSTOM1|CUSTOM2
DEP.RATE=<n> [INFILE=<c>]
[A.H|A.M|A.S|U.S|U.M|U.H|N.M]
[STEP.COV=<n>] [ANGLE1=<n>][ANGLE2=<n>][ANGLE3=<n>]
[C.AXIS=<n>] [P.AXIS=<n>] [DIST.PL=<n>]
[SIGMA.DEP=<n>] [SIGMA.0][SIGMA.E]
[SMOOTH.WIN=<n>][SMOOTH.STEP=<n>][MCSEED=<n>][STICK.COEF=<n>
Description
This statement is used to define deposition parameters and the machine name for one of ten deposition
models available in ELITE.
MACHINE specifies the machine name for the RATE.DEPO statement.
MATERIAL specifies material to be deposited by the deposit machine (see Section 6.2.9: “Standard
and User-Defined Materials” for the list of materials).
NAME.RESIST specifies the name of photoresist to be deposited.
CONICAL, CVD, PLANETARY, UNIDIRECT, DUALDIRECT, HEMISPHERIC, MONTE1,
MONTE2, CUSTOM1 and CUSTOM2 specify a particular model for the machine definition
DEP.RATE specifies the deposition rate used by the models CONICAL, CVD, UNIDIREC, DUALDIREC,
HEMISPHE, PLANETAR, MONTE1, and MONTE2. DEP.RATE is a rate multiplier for the CUSTOM1 and
CUSTOM2 models.
INFILE specifies the name of a file containing angle and deposition rate information for the CUSTOM
model.
A.H, A.M, A.S, U.H, U.M, U.S, and N.M specify that the deposition rate DEP.RATE is in Angstroms
per hour, Angstroms per minute, Angstroms per second, microns per hour, microns per minute,
microns per second, and nanometers per minute, respectively. Default is A.S.
STEP.COV specifies the step coverage used by the model CVD.
ANGLE1 specifies the angle parameter used by the models HEMISPHE, CONICAL, UNIDIREC,
DUALDIREC, and PLANETAR.
ANGLE2 specifies the angle parameter used by the models DUALDIREC, PLANETAR, and HEMISPHE.
ANGLE3 specifies the angle parameter used by the model PLANETAR.
C.AXIS specifies the central axis length used by the models CONICAL and PLANETAR.
P.AXIS specifies the planetary axis length used by the models PLANETAR and CONICAL.
DIST.PL specifies the distance from wafer to planetary axis used by the model PLANETAR.
SIGMA.DEP specifies the surface diffusion parameter used by the models UNIDIRECT, DUALDIRECT,
HEMISPHERIC, PLANETARY, CONICAL, MONTE1, and MONTE2.
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RATE.DEPO
SIGMA.0 and SIGMA.E specify pre-exponential coefficient and activation energy of temperature
dependent surface diffusion. The temperature is specified on the DEPOSIT command.
SMOOTH.WIN and SMOOTH.STEP specifies a window size in microns and a number of smoothing
passes for the simple geometric deposit smoothing algorithm.
MCSEED specifies a seed to be used for random number generation in the Monte Carlo deposit
models: MONTE1 and MONTE2.
STICK.COEF specifies the sticking coefficient for the MONTE1 model. Unitless, which must be
between 0.0 and 1.0.
Examples
The following statement defines a machine named TEST that deposits silicon nitride with a rate of
1500 A/minute using the CVD model with step coverage of 75%.
RATE.DEPO MACHINE=TEST NITRIDE DEP.RATE=1500 A.M CVD STEP.COV=.75
For more examples, see DEPOSIT.
Silvaco
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RATE.DEVELOP
ATHENA User’s Manual
6.49: RATE.DEVELOP
RATE.DEVELOP sets development rate and exposure bleaching parameters for each type of
photoresist in OPTOLITH.
Syntax
RATE.DEVELOP
[NAME.RESIST=<c>][G.LINE|H.LINE|I.LINE|DUV.LINE|LAMBDA=<n>
[A.DILL=<n>][B.DILL=<n>][C.DILL=<n>]
[E1.DILL=<n>][E2.DILL=<n>][E3.DILL=<n>
[RMAX.MACK=<n>][RMIN.MACK=<n>][MTH.MACK=<n>][N.MACK=<n>]
[RO.TREFONAS=<n>][Q.TREFONAS=<n>
[RO.HIRAI=<n>][RC.HIRAI=<n>][ALPHA.HIRAI=<n>
[R1.KIM=<n>][R2.KIM=<n>][R3.KIM=<n>][R4.KIM=<n>][R5.KIM=<n>]
[R6.KIM=<n>][R7.KIM=<n>][R8.KIM=<n>][R9.KIM=<n>][R10.KIM=<n>]
[C0.EIB=<n>][C1.EIB=<n>][C2.EIB=<n>][C3.EIB=<n>]
[DIX.0=<n>][DIX.E=<n>]
Description
This command sets the development rate parameters and exposure parameters for each type of
photoresist. These statements can be entered into the athenamod file, so that the parameters are
loaded each time ATHENA is started.
NAME.RESIST is the photoresist name for this set of parameters.
G.LINE, H.LINE, I.LINE, DUV.LINE, and LAMDBA specify the wavelength for each set of
photoresist parameters.
A.DILL, B.DILL, and C.DILL are the A, B, and C constants for the Dill exposure model.
E1.DILL, E2.DILL, and E3.DILL defines the E1, E2, or E3 parameter for Dill’s development rate
function. These parameters are dimensionless.
RMAX.MACK, RMIN. MACK, MTH.MACK, and N.MACK are the constants for the Mack
development model. RMAX.MACK specifies the development rate of the fully exposed resist. RMAX.MACK
must be specified in microns/sec. RMIN.MACK specifies the development rate of the unexposed resist.
RMIN.MACK must be specified in microns/sec. MTH.MACK is the threshold normalized PAC
concentration. MTH.MACK is dimensionless. N.MACK specifies the developer sensitivity. N.MACK is
dimensionless.
R0.TREFONAS and Q.TREFONAS are constants for the Trefonas development model.
R0.TREFONAS specifies a development rate constant. R0.TREFONAS must be specified in microns/sec.
Q.TREFONAS specifies a development rate constant.
R0.HIRAI, RC.HIRAI, and ALPHA.HIRAI are constants for the Hirai development model.
R0.HIRAI specifies the development rate of the fully exposed resist material. R0.HIRAI must be
specified in microns/sec. RC.HIRA specifies a development rate for unexposed resist. RC.HIRAI must
be specified in microns/sec. ALPHA.HIRAI specifies a dimensionless reaction constant.
R1.KIM, R2.KIM, R3.KIM, R4.KIM, R5.KIM, R6.KIM, R7.KIM, R8.KIM, R9.KIM, and R10.KIM
are constants for the Kim development model. R1.KIM corresponds to the dissolution rate of the resist
material if it has been fully exposed, that is if all the PAC has been decomposed. R1.KIM must be
expressed in microns/sec. R2.KIM corresponds to the dissolution rate of the unexposed resist material.
R2.KIM must be expressed in microns/sec. R3.KIM corresponds to the dissolution sensitivity of the
resist material. R3.KIM is dimensionless. R4.KIM corresponds to a specific depth into the resist film
for surface retardation effects. R4.KIM must be specified in microns. R5.KIM describes extraordinary
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RATE.DEVELOP
retardation effects. R5.KIM is dimensionless, positive, and less than one. R6.KIM describes
extraordinary retardation effects. R6.KIM is dimensionless, positive, and less than one. R7.KIM
describes extraordinary retardation effects. R7.KIM is dimensionless, positive, and less than one.
R8.KIM describes extraordinary retardation effects. R8.KIM is dimensionless, positive, and less than
one. R9.KIM describes extraordinary retardation effects. R9.KIM is dimensionless, positive, and less
than one. R10.KIM describes extraordinary retardation effects. R10.KIM is dimensionless, positive,
and less than one.
CO.EIB, C1.EIB, C2.EIB, and C3.EIB are the parameters for the Eib development model.
DIX.0 and DIX.E specify pre-exponential constant in cm2/sec and activation energy in eV for diffusion
of photoactive compound that are used in the post exposure bake.
Examples
The following statement defines the Dill development parameters for a user-defined resist called
SECRETX.
RATE.DEVELOP NAME.RESIST=TEST E1.DILL=1 E2.DILL=0.5 E3.DILL=.003
For more examples, see EXPOSE, BAKE, and DEVELOP.
Silvaco
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RATE.DOPE
ATHENA User’s Manual
6.50: RATE.DOPE
RATE.DOPE specifies the enhancement parameters for dopant enhanced etching in ELITE.
Syntax
RATE.DOPE
MACHINE = <c>
MATERIAL I.IMPURITY
[ENH.MAX = <n>] [ENH.SCALE = <n>] [ENH.MINC = <n>]
Description
This statement is used to define dopant enhanced etching and can be applied to an etch machine
defined using the RATE.ETCH statement.
Note: Dopant enhanced etching is not applicable to MC.PLASMA etch model.
MACHINE specifies the machine name for which the dopant enhanced model to be applied.
MATERIAL specifies material in which the dopant enhanced model to be used (see Section 6.2.9:
“Standard and User-Defined Materials” for the list of materials).
IMPURITY, INTERST, VACANCY, SXX, SYY, and SXY specify impurity (or other solution) which
concentration is used in the dopant enhanced etching model (see Section 6.2.10: “Standard Impurities”
for the list of impurities).
ENH.MAX specifies the maximum enhancement.
ENH.MINC specifies the solution value below which enhancement decays.
ENH.SCALE specifies the spread of the enhancement over solution values (i.e., how quickly the
enhancement factor reach its maximum).
Note: For exponentially varying solutions, e.g., oxidation stress and dopant concentrations, both C and ENH.MINC are taken to
be log base 10 of their respective value.
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Silvaco
RATE.ETCH
6.51: RATE.ETCH
RATE.ETCH specifies the etch rate parameters for a machine, which is used in a subsequent ETCH
statement in ELITE.
Syntax
RATE.ETCH
MACHINE=<c> MATERIAL | NAME.RESIST=<n>
WET.ETCH | RIE | PLASMA | MC.PLASMA
A.H | A.M | A.S | U.H | U.M | U.S | N.M
[DIRECTIONAL=<n>] [ISOTROPIC=<n>] [CHEMICAL=<n>] [DIVERGENCE=<n>]
[PRESSURE=<n>] [TGAS=<n>] [TION=<n>] [VPDC = <n>] [VPAC=<n>]
[LSHDC=<n>][LSHAC=<n>][FREQ=<n][MGAS=<n>][MION=<n>][QIO=<n>][QCHT= <n>]
[CHILD.LANGM|COLLISION|LINEAR|CONSTANT] [IONS.ONLY]
[NPARTICLES=<n>] [ENERGY.DIV = <n>][OUTF.TABLE = <<n>>][OUTF.ANGLE = <c>]
[ER.LINEAR|ER.INHIB|ER.COVERAGE|ER.THERMAL]
[K.I=<n>][K.F=<n>][K.D=<n>][SPARAM=<n>][THETA=<n>]
[IONFLUX.THR=<n>][MAX.IONFLUX=<n>][MAX.CHEMFL=<n>][MAX.DEPOFL=<n>]
[ION.TYPES = <n>] [MC.POLYMPT = <n>] [MC.RFLCTDIF = <n>]
[MC.ETCH1 = <n>] [MC.ETCH2 = <n>] [MC.ALB1 = <n>] [MC.ALB2 = <n>]
[MC.PLM.ALB = <n>] [MC.NORM.T1 = <n>] [MC.NORM.T2= <n>]
[MC.LAT.T1 = <n>] [MC.LAT.T2= <n>] [MC.ION.CU1= <n>] [MC.ION.CU2= <n>]
[MC.PARTS1 = <n>] [MC.PARTS1 = <n>] [MC.ANGLE1=<n>] [MC.ANGLE2=<n>]
Description
This statement is used to define parameters and the machine name for one of four etch models
available in ELITE.
MACHINE specifies the machine name for the RATE.ETCH statement.
MATERIAL specifies material for which parameters of the etch machine to be applied (see Section
6.2.9: “Standard and User-Defined Materials” for the list of materials).
NAME.RESIST specifies the name of photoresist to be etched.
WET.ETCH,RIE, PLASMA, and MC.PLASMA specify a particular model for the machine definition.
Parameters used for RIE and WET.ETCH models
A.H, A.M, A.S, U.H, U.M, U.S, and N.M specifies that the etch rates are in Angstroms per hour,
Angstroms per minute, Angstroms per second, microns per hour, microns per minute, microns per
second, and nanometers per minute respectively.
DIRECTIONAL specifies the directional component of the etching rate used by the RIE model. The
ionic etch rate is the contribution of the ions to the chemically oriented etching mechanisms. The ions
are assumed to have an anisotropic angular distribution specified by divergence parameter.
ISOTROPIC specifies the isotropic etch rate used by the WET.ETCH and RIE models. The isotropic
etch rate is the contribution of thermal atoms, radicals, and molecules coming out of the plasma. These
are assumed to have an isotropic angular distribution. Therefore, the isotropic etching may lead to an
underetching of the mask.
CHEMICAL, DIVERGENCE: CHEMICAL is the etch rate in the RIE model normal to the ion beam
when the DIVERGENCE is specified as non-zero. DIVERGENCE specifies the beam divergence used by the
RIE model. The angular distribution of the ions coming down to the wafer is Gaussian.
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RATE.ETCH
ATHENA User’s Manual
Parameters used for Plasma Etch Model
PRESSURE specifies the plasma etcher reactor pressure. Units are mTorr. Default 50 mTorr.
TGAS specifies the plasma etcher reactor gas temperatures. Units are oK. Default is 300 oK.
TION specifies the plasma etcher reactor ion temperatures. Units are oK. Default is 300 oK.
VPDC specifies the DC bias in the plasma sheath. Units are V. Default is 32.5 V.
VPAC specifies the AC voltage in the sheath-bulk interface. Units are V. Default is 32.5 V.
FREQ specifies frequency of the AC current Units are Mhz. Default is 13.6 Mhz.
LSHDC specifies the mean sheath thickness. Units are mm. Default is 0.005 mm.
LSHAC specifies the AC component of the sheath thickness. Units are mm. Default is 0.0.
MGAS specifies the atomic mass of the gas atoms. Default is 40.
MION specifies the atomic mass of the plasma ions. Default is 40.
QIO specifies the momentum transfer cross-section. Units are m2. Default is 1.7e-19
QCHT specifies the charge exchange cross-section. Units are m2. Default is 2.1e-19.
CHILD.LANG, COLLISION, LINEAR, and CONSTANT specify a model used in calculation of the
voltage drop in the plasma sheath. Default is LINEAR.
IONS.ONLY specifies that neutrals to be ignored in plasma simulation. Default is false
NPARTICLES specifies number of particles used for Monte Carlo calculation of the ion flux coming
from plasma. Default is 10,000.
ENERGY.DIV specifies number of energy divisions used for calculation of the plasma ion flux. Default
is 50.
OUTF.TABLE specifies the name of an output file in which complete table of simulated plasma ions
and neutral distributions is saved. The table cannot be loaded using TONYPLOT. The meanings of the
columns in the table are:
•
i - index of energy from 0 to Nrow=ENERGY.DIV -1, where ENERGY.DIV is the number of
energy divisions specified in the RATE.ETCH statement (default is 50).
•
k - index of angle from 0 to Ncol=14. The interval [0, 90] degrees is divided into 15 intervals and
each of them are divided into 4 sub-intervals each of 1.5 degrees wide.
•
Cergy<n> - number of ions in each sub-intervals, n=0. .3.
•
Cergyn<n> - number of neutrals in each sub-intervals, n=0. .3.
•
Angadd - the sum of Cergy<n> and Cergyn<n> for each (i,k) pair. It corresponds to the energyangle distribution of the particles.
•
Angtot - the sum of Angadd for each k, it corresponds to the angle distribution of particles.
•
Erel - the result of i/Nrow +1/(2*Nrow) corresponding to the medium energy in eV of the 50
normalized intervals [0.0, 0.02], [0.02, 0.04] . . . [0.98, 1.0].
OUTF.ANGLE specifies the name of an output file in which energy-angular ion flux distribution is
saved. The distribution can be plotted using TONYPLOT.
ER.LINEAR, ER.INHIB, ER.COVERAGE, and ER.THERMAL specify surface kinetics model to be
used: Simple linear, Adsorbed inhibiting layer, threshold coverage, and thermal spike models,
correspondingly. Default is ER.LINEAR.
K.I specifies the plasma etch rate linear coefficient related to the ion flux.
K.F specifies the plasma etch rate linear coefficient related to the chemical flux.
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RATE.ETCH
K.D specifies the plasma etch rate linear coefficient related to the deposition flux.
SPARAM specifies S-parameter of threshold coverage and thermal spike models.
THETA specifies theta parameter of threshold coverage and thermal spike models.
IONFLUX.THR specifies the flux threshold value below which the flux is not considered for etching.
Default is 0.0.
MAX.IONFLUX specifies a multiplier for ion flux generated by the plasma etching machine. Default
is 1.0.
MAX.CHEMFL specifies a multiplier for chemical flux generated by the plasma etching machine.
Default is 1.0.
MAX.DEPOFL specifies a multiplier for deposition flux generated by the plasma etching machine.
Default is 1.0.
Parameters used for Monte Carlo Plasma Etch Model
ION.TYPES specifies the number of different ions in etching plasma.
MC.POLYMPT specifies the number of MC simulated polymer particles normalized to the volume of
the ejected material.
MC.RFLCTDIF specifies the reflection diffusiveness. 1 corresponds to completely diffusive reflection,
0 corresponds to ideal mirror reflection.
MC.ETCH1 specifies the etch rate parameter for the first type of ions, unitless.
MC.ETCH2 specifies the etch rate parameter for the second type of ions, unitless.
MC.ALB1 specifies the reflection parameter for the first type of ions, unitless. This coefficient can
vary from 0 (no reflection) to 1 (100% reflection).
MC.ALB2 specifies the reflection parameter for the second type of ions, which is unitless. This
coefficient can vary from 0 (no reflection) to 1 (100% reflection).
MC.PLM.ALB
specifies the reflection parameter for polymer particles, which is unitless. This
coefficient can vary from 0 (no reflection) to 1 (100% reflection).
MC.NORM.T1 specifies the plasma normal temperature for the first type of ions, which is unitless.
MC.NORM.T2 specifies the plasma normal temperature for the second type of ions, which is unitless.
MC.LAT.T1 specifies the plasma lateral temperature for the first type of ions, which is unitless.
MC.LAT.T2 specifies the plasma lateral temperature for the second type of ions, which is unitless.
MC.ION.CU1 specifies the plasma ion current density for the first type of ions, ions/second/cm2.
MC.ION.CU2 specifies the plasma ion current density for the second type of ions, ions/second/cm2.
MC.PARTS1 specifies the number of MC simulated particles for the first type of ions.
MC.PARTS2 specifies the number of MC simulated particles for the second type of ions.
MC.ANGLE1 specifies the incident angle for the first type of ions. The default is 0 (normal incidence).
MC.ANGLE2 specifies the incident angle for the second type of ions. The default is 0 (normal
incidence).
Wet Etch Example
The following example defines an etch machine that attacks silicon with wet etch characteristics and
an etch rate of 0.1 micron/minute.
RATE.ETCH MACHINE=TEST SILICON WET.ETCH ISOTROPIC=.1 U.M
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RATE.ETCH
ATHENA User’s Manual
Monte Carlo Plasma Etch Example
The following statement defines parameters of Monte Carlo Plasma Etch machine as well as etching
characteristics of Silicon associated with this machine.
RATE.ETCH MACHINE=MCETCH SILICON MC.PLASMA ION.TYPES=1 \
MC.PARTS1=20000 MC.NORM.T1=14.0 MC.LAT.T1=2.0 \
MC.ION.CU1=15 MC.ETCH1=1e-05 MC.ALB1=0.2 MC.PLM.ALB=0.5 \
MC.POLYMPT=5000 MC.RFLCTDIF=0.5
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RATE.POLISH
6.52: RATE.POLISH
RATE.POLISH specifies the polishing parameters for a chemical mechanical polishing (CMP) module.
Syntax
RATE.POLISH
MACHINE = <c> MATERIAL | NAME.RESIST=<n>
[A.H|A.M|A.S|U.S|U.M|U.H|N.M]
[SOFT.RATE][HEIGHT.FAC=<n>][LENGTH.FAC=<n>][KINETIC.FAC=<n>]
[MAX.HARD=<n>] [MIN.HARD=<n>]
[ISOTROPIC=<n>]
Description
This command sets the parameters for the CMP machine used in the POLISH statement. The
parameters must be set for each material to be polished. There are two polish models, hard and soft,
that can be used together or separately. Define these models by specifying their parameters.
MACHINE specifies the machine name.
MATERIAL specifies material for which parameters of the CMP machine to be applied (see Section
6.2.9: “Standard and User-Defined Materials” for the list of materials).
NAME.RESIST is the user-defined photoresist to be polished.
A.H, A.M, A.S, U.H, U.M, U.S, and N.M specifies that the rates are in Angstroms per hour,
Angstroms per minute, Angstroms per second, microns per hour, microns per minute, microns per
second, and nanometers per minute respectively.
SOFT.RATE is the rate for the soft polish model.
HEIGHT.FAC is the vertical deformation scale for the soft polish model. Units are microns.
LENGTH.FAC is the horizontal deformation scale for the soft polish model. Units are microns.
KINETIC.FAC is the Kinetic factor (soft polish model). The vertical polish rate increases as the
surface becomes more vertical.
MAX.HARD is the maximum rate for the hard polish model. Corresponds to a pattern factor of zero.
MIN.HARD is the minimum rate for the hard polish model. Corresponds to a pattern factor of one.
ISOTROPIC specifies the isotropic etch rate used by the POLISH model.
Examples
The following statements describe a polishing machine named CMP for nitride and oxide.
RATE.POLISH MACHINE=cmp NITRIDE SOFT=4 N.M HEIGHT.FAC=0.02 \
LENGTH.FAC=80 KINETIC.FAC=10 \
RATE.POLISH MACHINE=cmp OXIDE SOFT=25 HEIGHT.FAC=0.02 \
LENGTH.FAC=30 KINETIC.FAC=10
For more examples, see POLISH and RATE.ETCH.
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REGION
ATHENA User’s Manual
6.53: REGION
REGION specifies a material to be assigned to a defined mesh region.
Note: Typically, the REGION statement is not required since initial substrate material is specified on the INIT statement.
Syntax
REGION
MATERIAL [XLO=<c>][YLO=<c>][XHI=<c>][YHI=<c>]
Description
This command specifies the material in a rectangular mesh. REGION statements should follow LINE
statements. Material must be specified for every triangle in a mesh. Therefore for each rectangular
mesh, there must be at least one REGION statement specifying, which material is included within the
mesh. If you do not include REGION statement between the LINE statement and the INITIALIZE
statement, you can define the material on the INITIALIZE statement.
MATERIAL specifies the material in a region (see Section 6.2.9: “Standard and User-Defined
Materials” for the list of materials).
XLO, YLO, XHI, and YHI specifies the bounds of the region rectangle. The value <string> should
be one of the tags created in a preceding LINE statement.
Examples
The following REGION statement specifies silicon as the material for the entire mesh.
LINE X LOC=0 SPA=1 TAG=LEFT
LINE X LOC=1 SPA=0.1
LINE X LOC=2 SPA=1 TAG=RIGHT
LINE Y LOC=0 SPA=0.02 TAG=SURF
LINE Y LOC=1 SPA=0.1 TAG=BACK
REGION SILICON XLO=LEFT XHI=RIGHT YLO=SURF YHI=BACK
INIT
Note: If you do not use REGION statement and no material appears on the INIT statement, then ATHENA assumes Silicon
is the starting material. If you do not specify enough regions to describe the material at every part of the grid, it may not be
detected until the execution of a subsequent command.
For more examples, see INITIALIZE.
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RELAX
6.54: RELAX
RELAX loosens the grid in an ATHENA mesh.
Syntax
RELAX
[MATERIAL] [X.MIN=<n>][X.MAX=<n>][Y.MIN=<n>][Y.MAX=<n>]
[DIR.X|DIR.Y] [SURFACE][DX.SURF=<n>
Description
This statement allows you to increase grid spacing. You can place the RELAX statement anywhere
within the input file. RELAX commands, however, are ignored if ATHENA is in 1D mode. The RELAX
statement also includes an algorithm for relaxing grid on the surface of the simulation structure.
MATERIAL specifies that RELAX will only apply to the regions of this MATERIAL (see Section 6.2.9:
“Standard and User-Defined Materials” for the list of materials). If MATERIAL is not specified, RELAX
will be applied to all materials in the box.
X.MIN, X.MAX, Y.MIN, and Y.MAX specifies the corner coordinates of the RELAX box. Units are
microns. Default is bounding box of the current simulation structure.
DIR.X or DIR.Y allow the direction of the grid relax to be controlled. DIR.X and DIR.Y are true by
default (i.e., when the RELAX statement is encountered, the grid is relaxed in both directions by
default). When DIR.X or DIR.Y is selected as false (i.e., DIR.X=F or DIR.Y=F), then the grid is only
relaxed in the direction that is left as true.
SURFACE specifies to relax the surface grid.
DX.SURF specifies a minimum size for surface segments.
Examples
RELAX SILICON X.MAX=1 Y.MIN=0
This statement changes a grid over a rectangular area in silicon from the left side of a structure to 1
and from y=0 to the bottom of the silicon.
Note: RELAX will not make any changes to a grid if obtuse triangles would result from the mesh relaxation. Consequently,
RELAX will typically only work on meshes that were initially defined using LINE statements in ATHENA. For other structures,
you can use DEVEDIT.
For more examples, see VWF INTERACTIVE TOOLS USER’S MANUAL, VOLUMES I AND II.
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SELECT
ATHENA User’s Manual
6.55: SELECT
SELECT selects the variable for printing using the PRINT.1D statement.
Note: This command has been superseded for use with PRINT.1D by the EXTRACT command. See VWF INTERACTIVE
TOOLS USER’S MANUAL VOL. I.
Syntax
SELECT
[Z=<c>][TEMPERATURE=<n>]
Description
SELECT specifies the variable that will be printed by the PRINT.1D statement. You can only use one
variable at a time. Each SELECT statement overrides any previous statements.
Z is set equal to the selected variable. The operators *, /, +, -, ^ all work as standard algebraic
operators would. Z can be set to any of the vector variables shown on the next page.
Table 6-4. Select Operator Variables.
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Vector Variables
Description
ANTIMONY
antimony concentration
ARSENIC
arsenic concentration
BORON
boron concentration
CI.STAR
equilibrium interstitial concentration
CV.STAR
equilibrium vacancies concentration
DOPING
net active concentration
ELECTRONS
electron concentration
INTERSTITIAL
interstitial concentration
NI
intrinsic electron concentration
OXYGEN
oxygen concentration
PHOSPHORUS
phosphorus concentration
Sxx, Sxy, Syy
components of stress in rectangular coordinates
TRAP
unfilled interstitial trap concentration
VACANCY
vacancy concentration
X
x coordinates
Y
y coordinates
X.V
x velocity
Y.V
y velocity
Silvaco
SELECT
Table 6-5. Select Functions.
Function
Description
abs
absolute value
active
active portion of the specified dopant
erf
error function
erfc
complimentary error function
exp
exponential
gradx
numerically differentiates the argument with respect to x location
grady
numerically differentiates the argument with respect to y location
log
logarithm
log10
logarithm base 10
<mat1>@<mat2>
returns the y value of the interface between <mat1> and <mat2>
along a vertical slice at the given location
scale
scales the value given by the maximum value
sqrt
square root
TEMPERATURE specifies the temperature at which expressions are evaluated. It defaults to the last
diffusion temperature. This parameter has to be specified (by default or explicitly) when printing a net
active concentration or preparing a ATLAS structure file.
Examples
The following example will choose the base 10 logarithm of the arsenic concentration as the PRINT.1D
variable.
SELECT Z=LOG10(ARSEN)
The following chooses the difference between the phosphorus and an analytic profile as the PRINT.1D
variable.
SELECT Z=(PHOS - 1.0E18 * EXP (Y * Y / 1.0E-8))
The following chooses the excess vacancy interstitial product as the PRINT.1D variable.
SELECT Z=(INTER * VACAN - CI.STAR * CV.STAR)
Note: When using log or log10 functions, make sure the argument is positive and non-zero. For example, always use
log10(abs(doping)+1).
For more examples, see the PRINT.1D
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SET
ATHENA User’s Manual
6.56: SET
SET specifies strings or numbers for variable substitution.
Note: This commands executed under DECKBUILD and is documented fully in the VWF INTERACTIVE TOOLS MANUAL,
VOLUME I.
Syntax
SET
variable = <value>
Numerical Variable Example
The following statement defines a variable and performs an expression on it for use later within the
ATHENA processing syntax.
SET MYDOSE=1e13
SET HALFMYDOSE=$”MYDOSE”/2
IMPLANT BORON DOSE=$”HALFMYDOSE”
String Variable Example
The following uses SET to define a string variable. The saved file will be called mosfet_fred.str.
SET MYNAME=fred
STRUCTURE OUTFILE=mosfet_$”myname”.str
For more examples, see EXTRACT.
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SETMODE
6.57: SETMODE
SETMODE specifies execution mode parameters.
Syntax
SETMODE
[NOEXECUTE | ECHO]
Description
This command turns on the following execution mode parameters. The UNSET statement allows the
same parameters to be turned off.
NOEXECUTE puts all entered statements into a check only mode. If this flag is on, ATHENA will only
check the legality of the input syntax and not execute any statements.
ECHO instructs ATHENA to echo all input lines to the run-time output. Note that in DECKBUILD, this is
not required as all lines are echoed to the bottom run-time window or run-time output file by default.
Examples
The following statement causes ATHENA to echo each command it receives.
SETMODE
ECHO
For more examples, see UNSETMODE.
Note: The parser does not recognize abbreviated forms of these commands. It requires that you enter NOEXECUTE and
ECHO verbatim.
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SILICIDE
ATHENA User’s Manual
6.58: SILICIDE
SILICIDE specifies the silicidation coefficients.
Syntax
SILICIDE
[SILICON|POLYSILICON|TUNGSTEN|TITANIUM|PLATINUM|COBALT|
WSIX|TISIX|PTSIX|COSIX|MATERIAL=<c>]
[/SILICON|/POLYSILICO|/TUNGSTEN|/TITANIUM|/PLATINUM|/COBALT
/WSIX|/TISIX|PTSIX|/COSIX|/MATERIAL=<c>]
[MTTYPE=<c>] [/MTTYPE=<c>] [ALPHA=<n>]
Description
SILICON, POLYSILICON, TUNGSTEN, GAAS, TITANIUM, PLATINUM, COBALT, WSIX,
TISIX, PTSIX, and MATERIAL specify the first material to which the parameters apply.
/SILICON, /POLYSILICO, /TUNGSTEN, /TITANIUM, /PLATINUM, /COBALT, /WSIX,
/TISIX, /PTSIX, / COSIX and /MATERIAL specify the second material to which parameters apply.
MTTYPE specifies the type (metal or silicide) of the user-defined MATERIAL.
/MTTYPE specifies the type (metal or silicide) of the user-defined /MATERIAL.
ALPHA specifies the volume expansion ratio between MATERIAL and /MATERIAL.
Examples
The following example specifies the volume expansion between user-defined material TiSi2 and
standard material titanium.
SILICIDE MATERIAL=TISI2 MTTYPE=SILICIDE /MATERIAL=TITANIUM ALPHA=0.4
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SOURCE
6.59: SOURCE
SOURCE executes statements from the specified file.
Syntax
SOURCE
<filename>
Description
SOURCE reads statements from an input file. Statements are read from the file until an end-of-file
marker is found. SOURCE is especially useful for executing a large group of statements. SOURCE places
the named file in the current input stream. SOURCE statements can be nested up to the limit of open
file descriptors (system dependent).
Examples
The following statement causes the contents of a file named test.in to be included into the input
stream.
SOURCE TEST.IN
Note: To support the use of this function when running under the VWF AUTOMATION TOOLS, place the file to be sourced into
a directory directly visible to the simulation run, regardless where the simulator is executing.
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STRESS
ATHENA User’s Manual
6.60: STRESS
STRESS calculates elastic stresses.
Syntax
STRESS
[TEMP1=<n>][TEMP2=<n>][NEL=<n>]
Description
This command calculates stresses due to thin film intrinsic stress or thermal mismatch.
TEMP1 and TEMP2 are the initial and final temperatures in oC for calculating thermal mismatch
stresses.
NEL is the number of nodes per triangle to use. Currently, only 6 or 7 are allowed. 6 nodes are faster
than 7 and usually gives adequate results. Default is 6.
Examples
The following calculates the stresses in the substrate and film arising from a nitride layer, which has
an intrinsic stress of 1.4 ×1014 dynes cm-2 when deposited uniformly.
MATERIAL NITRIDE INTRIN.SIG=1.4E10
STRESS
The following calculates thermal mismatch stress in the whole structure as the result of a temperature
change from 1000 to 100 oC.
STRESS TEMP1=1000 TEMP2=100
For more examples, see MATERIAL.
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STRETCH
6.61: STRETCH
STRETCH stretches structures about a specified location.
Syntax
STRETCH
MATERIAL=<c> [LENGTH=<n>] [X.VAL=<n>] [Y.VAL=<n>][STRETCH.VAL=<n>]
[SPACING=<n>][DIVISION=<n>][SNAP]
Description
This statement specifies that the device is to be stretched about a specified location. If device
characterization as a function of length is of interest, the stretch function will save massive amounts of
CPU time in generating multiple gate length structures. The stretch capability is also useful for power
devices.
MATERIAL specifies material that defines the stretch region (see Section 6.2.9: “Standard and UserDefined Materials” for the list of materials). Default is SILICON.
LENGTH specifies the final value in microns to which the specified material region is stretched.
Alternatively, you can specify X.VAL using STRETCH.VAL to specify the position of a vertical cut line
and the distance to be stretched respectively. The grid spacing within the stretched region is defined
either by spacing or by division.
X.VAL and Y.VAL specifies the horizontal or vertical position in microns at which stretch occurs.
LENGTH overrides the STRETCH.VAL, X.VAL and Y.VAL parameters. If LENGTH is specified, the cut
line stretch location defaults to the center of the specified material. The default material is polysilicon.
SPACING specifies the grid spacing within the stretched region. Units are microns.
DIVISION specifies the number of grid divisions within the stretched region.
SNAP indicates that X.VAL should “snap” (change value or locate) to the nearest grid point before
stretching. SNAP is recommended to minimize the potential for obtuse triangle generation. SNAP is set
to true by default.
Stretch Examples
The following statement will stretch a device about the center of its polysilicon region. This device can
have been a MOSFET with a polysilicon gate 1 micron long. The STRETCH command creates a 1.8
micron-long MOSFET in this case.
STRETCH LENGTH=1.8
The following example will stretch an oxide isolation structure from the x position of 2.3 microns by a
value of 1.3 microns. The stretched region contains 14 grid spaces. This case can be useful for
generating large isolation regions that take too long to simulate numerically.
STRETCH OXIDE X.VAL=2.3 DIVISIONS=14 STRETCH.VAL=1.3
Note: The stretch function may not be valid or physically correct in the case of very short initial structures (e.g. with RSCE
effect in MOSFETs). The location selected for stretching should correspond exactly to a grid line for best results. It will provide
best grid quality if the stretch location does not touch areas in which the grid has been relaxed. The STRETCH command often
results in grid failure for complex structures and is not recommended for complex topographies. DEVEDIT provides a superior
stretch feature for these cases.
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STRIP
ATHENA User’s Manual
6.62: STRIP
STRIP removes all photoresist and barrier materials.
Syntax
STRIP
[MATERIAL]
Description
MATERIAL specifies the material to be stripped (see Section 6.2.9: “Standard and User-Defined
Materials” for the list of materials). If no material is specified, the STRIP command removes both
photoresist and barrier materials.
Examples
The following sequence of statements deposits photoresist patterned with the mask level named CONT,
etches oxide through the mask, and removes the photoresist with the STRIP statement.
MASK NAME="CONT"
ETCH OXIDE DRY THICK=.2
STRIP
This example requires the use of MASKVIEWS.
For more examples, see MASK and ETCH.
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STRUCTURE
6.63: STRUCTURE
STRUCTURE writes the mesh and solution information, aerial image information, or flips or mirrors the
structure. SAVEFILE is a synonym for this statement.
Syntax
STRUCTURE
[OUTFILE=<c>][INFILE=<c>][OPC=<n>]
[FLIP.Y][MIRROR][LEFT|RIGHT|TOP|BOTTOM]
[INTENSITY][MASK][REMOVE.GAS] [SIGE.CONV][TWO.DIM]
Description
This statement writes the entire mesh and solution set to a file. The saved data is from the current set
of solution and impurity values.
OUTFILE specifies the name of the file to be written. Existing files with the same name are
overwritten by newly specified files. OUT.FILE is an alias for this parameter.
INFILE specifies the name of the section file generated by MASKVIEWS to be imported. This file is
assumed to contain the unbiased layout structures and will be used as a reference to calculate the
percentage area of deviations in performing optical proximity correction. Thus, it must be used
together with the OPC parameter.
OPC specifies the normalized intensity level for OPC evaluation. An image file (.SEC) will be
generated for this particular intensity level and is to be used by MASKVIEWS.
FLIP.Y indicates that the structure should be flipped around the x axis. This is used to invert
structures for backside processing.
MIRROR, LEFT, RIGHT, TOP, and BOTTOM mirrors the grid about its left or right, top or bottom
boundary respectively. This is useful for turning half of a MOSFET simulationstructure into full
structure for subsequent ATLAS simulation. The default reflection is about the right axis.
INTENSITY specifies the aerial image intensity distribution to be saved in the output file.
MASK specifies layout mask information to be saved in the output file.
REMOVE.GAS specifies that the gas region is to be removed from the output structure. Currently,
the overlaying gas region is automatically added to the structure for Monte Carlo etch and BCA
implant simulations.
SIGE.CONV converts the layer of silicon that is highly doped with Ge into a Si1-x Gex layer so it can
be used in ATLAS.
TWO.DIM specifies that the structure to be transformed into 2D if it’s still 1D.
Examples
The following statement writes the current structure to a file called test.str.
STRUCTURE OUTFILE=TEST.STR
The following statement saves an aerial image and masks calculated by OPTOLITH to a file called
test.str.
STRUCTURE OUTFILE=TEST.STR INTENSITY MASK
The following statement mirrors the structure about its left boundary.
STRUCTURE MIRROR LEFT
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STRUCTURE
ATHENA User’s Manual
Note: The STRUCTURE command will only save all mesh and solution information. It will not save any defined model or
machine methods. If you exit a simulator the middle of an input file, you may need to manually parse the preceding METHOD
and IMPURITY commands to reinitialize specified parameters. This function is handled automatically when running under
the VWF AUTOMATION TOOLS.
For more examples, see INITIALIZE.
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SYSTEM
6.64: SYSTEM
SYSTEM allows execution of any UNIX C-shell command within an input file
Note: The SYSTEM statement is executed by DECKBUILD and is fully documented in the VWF INTERACTIVE TOOLS
USER’S MANUAL, VOL. I.
Note: The SYSTEM command must be enabled using an option on the D ECK B UILD Main Control menu under
Category→Options.
Examples
The following command will remove all files named test*.str before a DIFFUSE statement where
the DUMP parameter is used.
system \rm -rf test*.str
DIFFUSE .... DUMP=1 DUMP.PREF=test
The SYSTEM command and UNIX commands are case sensitive.
UNIX commands can be concatenated on a single line using the semicolon (;) operator. For example, to
run a third party program that reads and writes Silvaco format files with the fixed names input.str
and output.str.
STRUCTURE OUTF=mysave.str
system mv mysave.str input.str; source myprog.exe; mv output.str
myrestart.str
INIT INF=myrestart.str
The UNIX re-direct symbol, >, is not supported by the system command. The UNIX echo and sed
syntax can be used instead to output values or variables to a given filename. For example, to save the
extracted value of the variable, $myvariable, to the file called myfile.
system echo $”myvariable” | sed -n “w myfile”
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TONYPLOT
ATHENA User’s Manual
6.65: TONYPLOT
Tonyplot starts the graphical post-processor TONYPLOT.
Note: The Tonyplot statement is executed by DECKBUILD, which is fully documented in the VWF INTERACTIVE TOOLS
USER’S MANUAL, VOL. I.
Examples
All graphics in ATHENA is performed by saving a file and then loading the file into TONYPLOT. The
command
tonyplot
causes ATHENA to automatically save a file and plot it in TONYPLOT. The TONYPLOT window will appear
displaying the material boundaries. Use the Plot:Display menu to see more graphics options.
The following command will display the myfile.str file.
tonyplot -st myfile.str
The following command will overlay the results of myfile1.str and myfile2.str.
tonyplot -overlay myfile1.str myfile2.str
Note: For documentation of the extensive features of TONYPLOT for graphical display and analysis, consult the TONYPLOT
chapter of the VWF INTERACTIVE TOOLS USER’S MANUAL, VOL. I.
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TRAP
6.66: TRAP
TRAP sets the coefficients of interstitial traps.
Syntax
TRAP
MATERIAL [ENABLE] [TOTAL=<n>] [FRAC.0=<n>][FRAC.E=<n>]
Description
This statement allows you to specify values for coefficients of the interstitial traps. The statement
allows coefficients to be specified for each of the materials. ATHENA has default values only for silicon.
Polysilicon parameters default to those for silicon.
MATERIAL specifies the material for which the parameters apply (see Section 6.2.9: “Standard and
User-Defined Materials” for the list of materials).
ENABLE indicates that traps should be enabled in the material specified.
TOTAL specifies the total number of traps, in cm-3. The default for silicon is 5.0×1017 cm-3. This value
is appropriate for Czochralski silicon material.
FRAC.0 and FRAC.E allows the specification of the equilibrium empty trap ratio.
Examples
The following statement turns on interstitial traps and sets the total to 5.0×1017 and the fraction to a
half.
TRAP SILICON TOTAL=5.0E17 FRAC.0=0.5 FRAC.E=0.0 ENABLE
Note: The trap concentration depend upon the thermal history of the wafer, starting material, stress and temperature. This
history is not considered in the trap model in ATHENA.
For more examples, see INTERSTITIAL and VACANCY.
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UNSETMODE
ATHENA User’s Manual
6.67: UNSETMODE
UNSETMOD unsets execution mode parameters defined in the SETMODE statement.
Note: When SET variable=value is used in DECKBUILD, it is impossible to UNSETMODE the variable
Syntax
UNSETMODE
[NOEXECUTE | ECHO]
Description
This command turns off the following execution mode parameters. The SETMODE statement allows you
to turn on the same parameters.
NOEXECUTE puts all entered statements into a check only mode. If this flag is on, ATHENA will only
check the syntax of the input commands and not actually run them.
ECHO instructs ATHENA to echo all input lines.
Examples
The following turns off statement echoing.
UNSETMODE ECHO
Note: UNSET is a synonym for this command.
Note: The parser does not recognize abbreviated forms of these commands. It requires that you enter NOEXECUTE and
ECHO verbatim.
For more examples, see SETMODE.
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Appendix A:
C-Interpreter
A.1: C-Interpreter Overview
ATHENA has a C language interpreter (C-Interpreter) that allows you to modify the models contained
in ATHENA. In order to use this capability, write a C language analytical function describing the
model. If you’re not familiar with the C language, then we suggest that you read any of the popular C
language books such as [119]. Additional information about the C-Interpreter can be found in the
SILVACO C-INTERPRETER USER’S MANUAL.
The function arguments of the C-Interpreter functions are fixed in ATHENA. Thus, you need to make
sure that the arguments and return values match those expected by ATHENA. To help you, a set of
templates for functions available for the current release of ATHENA can be obtained by typing:
athena -T filename
The filename is the name of the file where you want the template to be copied. You can also obtain
the C-Interpreter templates by selecting Commands→Templates... in DECKBUILD. The following
example shows how to use the C-Interpreter function get_damage_values to modify the default Plus
One Model (See Chapter 3: “SSUPREM4 Models”) for interstitials generated during ion implantation.
A.2: Example
/*
Template for the C-Interpreter function for defect formation
during ion implantation
*/
void get_damage_values
(
/* input parameters */
int imp, /* impurity index: As - 2; P - 3; Sb - 4; B - 5; etc. */
int mater, /* material index: Si - 3 */
double x,
/* x-coordinate in micron*/
double y,
/* y-coordinate in microns */
double implanted_conc,/* implanted concentration in 1/cm**3 */
double implanted_dam, /*accumulated damage in eV/cm**3),
do not use without Monte Carlo BCA */
/* return parameters */
double *I_val,
/* Interstitial concentration */
double *V_val,
/* Vacancy concentration */
double *CL_val,
/* 311-Cluster concentration */
double *DL_val
/* Dislocation loops concentration */
)
{
if ( mater == 3 ) /* only in Silicon */
{
/* The function modifies +1 interstitial generation model.
The interstitials are generated only in unamorphized layer
where damage is less than 0.1 of atomic density of Si */
if ( implanted_dam < 5e21)
*I_val = implanted_conc;
}
return;
}
Silvaco
A-1
ATHENA User’s Manual
The function receives the following input values:
•
material index,
•
x and y coordinates of the point in the structure where damage is calculated,
•
implant concentration at this point,
•
implant damage but only when the Monte Carlo BCA model is used for the current implant
calculations.
This allows you to return the values of interstitial and vacancy concentration, and concentrations of
{311} clusters and dislocation loops. If one or few of return values are not modified in the function the
corresponding concentrations will remain unchanged after the implant.
The function then needs to stored as a file (i.e., damage.lib). The model stored in the function can
then be activated by specifying the DAM.MOD=DAMAGE.LIB parameter in the IMPLANT statement.
Note: Prior to ATHENA version 5.4.0.R, DAMAGEMOD.FN (DAM.MOD) was a parameter in the MOMENTS statement
When you execute the IMPLANT statement using analytical or Monte Carlo models, the specified CInterpreter function will be used in place of the build in function.
A-2
Silvaco
Appendix B:
Default Coefficients
This appendix contains the list of impurity and material default coefficients, default model
parameters, and other parameters used in ATHENA calculations. Most of these coefficients are
initialized in the athenamod file. The file athenamod will appear when you select
Commands→Models in DECKBUILD while ATHENA is the current simulator. Almost all of these
coefficients can be modified to match measured results.
You should check the contents of athenamod for updates to default values that may be more current
than those shown in the following lists.
B.1: Oxidation Rate Coefficients
B.1.1: Dry Ambient For <111> Orientation
These parameters are from the bibliography reference [34].
Table B-1. Parabolic and Linear Rate Constants for Dry Ambient
Parameter
Value
PAR.H.0(µm2/min)
12.8667
PAR.H.E (eV)
1.23
P.BREAK (ºC)
0.
LIN.H.0 (µm/min)
1.038×105
LIN.H.E (eV)
2.0
L.BREAK (ºC)
0.
B.1.2: Wet Ambient for <111> Orientation
These parameters are from the bibliography reference [36].
Table B-2. Parabolic and Linear Rate Constants for Wet Ambient
Silvaco
Parameter
Value
PAR.L.0 (µm2/min)
283.333
PAR.L.E (eV)
1.17
PAR.H.0 (µm2/min)
7.0
PAR.H.E (eV)
0.78
P.BREAK (ºC)
950.
B-1
ATHENA User’s Manual
Table B-2. Parabolic and Linear Rate Constants for Wet Ambient
Parameter
Value
LIN.L.0 (µm/min)
3.45×104
LIN.L.E (eV)
1.6
LIN.H.0 (µm/min)
2.95×106
LIN.H.E (eV)
2.05
L.BREAK (ºC)
900.
B.1.3: Orientation Factors For Linear Coefficients (both Ambients)
Table B-3. Linear Coefficient Orientation Factors
Orientation
Value
For <100> orientation (unitless)
ORI.FAC = 0.595
For <110> orientation (unitless)
ORI.FAC = 0.833
For <111> orientation (unitless)
ORI.FAC = 1.0
B.1.4: Pressure Dependence
For Dry Oxidation, DRY: L.PDEP = 0.75 and P.PDEP = 1.0. For Wet Oxidation, WET: L.PDEP
= 1.0 and P.PDEP = 1.0.
Table B-4. Thin oxide coefficients (only for dry ambient)
B-2
Orientation
THINOX.0
(µ2/min)
THINOX.E (eV)
THINOX.L (µ)
THINOX.P [14]
<111>
5.87 x 106
2.32
0.0078
1.0
<110>
5.37 x 104
1.80
0.0060
1.0
<100>
6.57 x 106
2.37
0.0069
1.0
Silvaco
Default Coefficients
B.1.5: Chlorine Dependence
Table B-5. Chlorine dependence of dry coefficients for three temperatures: 900, 1000, 1100ºC
HCL.PC
HCL.LIN
HCL.PAR
900
1000
1100
900
1000
1100
0.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.75
1.25
1.621
1.083
1.658
1.355
3.0
1.75
1.486
2.207
1.25
1.840
1.490
5.0
1.75
1.486
2.207
1.444
2.075
1.641
7.0
1.75
1.486
2.207
1.639
2.332
1.816
10.0
1.75
1.486
2.207
2.028
2.759
2.102
B.1.6: Doping Dependence Of Oxidation Rate
Table B-6. Doping Dependence of Oxidation Rate
Parameter
Value
BAF.EBK
241.6
BAF.PE
0.46
BAF.PPE
1.0
BAF.NE
0.145
BAF.NNE
0.62
BAF.K0
2.6e3
BAF.KE
1.1
See the bibliography reference [37] for more details.
B.1.7: Coefficients for the Analytical Guillemot Model
l
Table B-7. Coefficents for the Analytical Guillemot Model
Silvaco
Parameter
Value
Spread
1.0
INITIAL
0.002
MASK.EDGE
-200
ERF.Q
0.05
B-3
ATHENA User’s Manual
Table B-7. Coefficents for the Analytical Guillemot Model
Parameter
Value
ERF.DELTA
0.04
ERF.LBB
(8.25e-3*(1580.3 - Tox)*
(Eox ^0.67)*(eox ^0.3)*exp
(-( en -0.08)^2)/0.06))
ERF.H
(402*(0.445 - 1.75*en)*exp
(- Tox /200)
See the bibliography reference [40] for more details.
B.1.8: Numerical Oxidation Coefficients
For Dry Oxidation, HENRY.COEFF=5E16,THETA= 2.2E22, TRN.0= 1E+3.
For Wet Oxidation, HENRY.COEFF= 3e19,THETA= 2.2e22,TRN.0= 1e+6.
B.1.9: Stress-dependent Growth Model Coefficients
Vc = 78,
Vr = 9.7 ,
Vd = 1.9,
Vt = 0.0 ,
Dlim = 1.0
See the bibliography reference [120] for more details.
B.1.10: Mechanical Parameters For Stress Calculations
Table B-8. Parameters that can be accessed by the MATERIAL statement
B-4
Parameter
VISC.0
VISC.E
VISC.X
YOUNG.M
POISS.R
OXIDE
(wet)
1.99×10-7
5,292
0.499
8.3×1011
0.2
OXIDE
(dry)
3.1×10-3
7.405
0.499
8.3×1011
0.2
NITRIDE
1.8×1015
0
0.499
1.0×1014
0.3
SILICON
1×1030
0
0.499
1.7×1012
0.28
POLY
5×1011
0
0.499
1.7×1012
0.28
OXYNI
5×1012
0
0.499
3.89×1012
0.3
Silvaco
Default Coefficients
B.1.11: Linear Coefficients Of Thermal Expansion
These parameters can be accessed by specifying the LCTE parameter in the MATERIAL statement.
Table B-9. Linear Coefficients of Thermal Expansion
Parameter
Value
SILICON
OXIDE
ALUMINUM
NITRIDE
POLY
LCTE
LCTE
LCTE
LCTE
LCTE
=
=
=
=
=
3.052e-6
1.206e-7
2.438e-5
3.0e-6
3.052e-6
+ 2 * 6.206e-10 * ( T - 293)
+ 2 * 2.543e-10 * ( T - 293)
+ 2 * 6.660e- 9 * ( T - 293)
+ 2 * 6.206e-10 * ( T - 293)
B.1.12: Volume Expansion Ratio
The volume expansion ratio, ALPHA, can be set in the OXIDE statement.
Table B-10. Volume Expansion Ratio
Ratio
Value
silicon/oxide (unitless)
poly/oxide (unitless)
Other combinations (unitless)
0.44
0.44
1.00
B.2: Impurity Diffusion Coefficients
Table B-11. Impurity Diffusion Coefficients
Parameter
Antimony
Arsenic
Boron
Phosphorus
Silicon [121]
DIX.0 (cm2/s)
0.214
8.0
0.037
3.85
DIX.E (eV)
3.65
4.05
3.46
3.66
DIP.0 (cm2/s)
0.0
0.0
0.72
0.0
DIP.E (eV)
0.0
0.0
3.46
0.0
15.0
12.8
0.0
4.44
4.08
DIM.0
(cm2/s)
DIM.E (eV)
4.05
0.0
4.00
DIMM.0 (cm /s) 0.0
0.0
0.0
44.2
DIMM.E (eV)
0.0
0.0
4.37
2
0.0
2
CTN.0 (cm /s)
5.19×10
CTN.E (eV)
0.60
FI (unitless)
0.05
-24
0.20
0.94
Polysilicon
DIX.0 (cm2/s)
21.4
6.6
3.66
385.0
DIX.E (eV)
3.65
3.44
3.46
3.66
0.0
0.0
72.0
0.0
2
DIP.0 (cm /s)
Silvaco
B-5
ATHENA User’s Manual
Table B-11. Impurity Diffusion Coefficients
Parameter
Antimony
Arsenic
Boron
Phosphorus
0.0
0.0
3.46
0.0
DIM.0 (cm /s)
1500.0
1200.0
0.0
443.9
DIM.E (eV)
4.08
4.05
0.0
4.05
0.0
0.0
0.0
4420.0
0.0
0.0
0.0
4.37
1.75
3.16×10-4
7.6×10-3
4.89
3.53
3.5
DIP.E (eV)
2
DIMM.0
(cm2/s)
DIMM.E (eV)
2
CTN.0 (cm /s)
5.19 X 10
CTN.3(eV)
0.60
-24
Oxide
2
DIX.0 (cm /s)
1.31×10
DIX.E (eV)
8.75
16
Tungsten Silicide [122]
2
DIX.0 (cm /s)
2.6
2.6
1.0×10-4
4.2
DIX.E (eV)
2.11
2.11
1.17
2.14
Titanium Silicide [122]
2
DIX.0 (cm /s)
4.8
4.8
1.5×10-7
392.0
DIX.0 (eV)
2.13
21.3
2.0
2.64
DIX.0 (cm /s)
2.6
2.6
1.0×10-3
4.2
DIX.0 (eV)
2.11
2.11
1.17
2.14
Platinum Silicide [122]
2
All other coefficients for refractory metals and their silicides are set to 0.0.
B.3: Impurity Segregation Coefficients
Table B-12. Impurity Segregation Coefficients
Parameter
Antimony
Arsenic
Boron
Phosphorus
Silicon/oxide
SEG.0
(unitless)
30.0
30.0
1126.0
30.0
SEG.E (eV)
0.0
0.0
0.91
0..0
30.0
1126.0
30.0
0.0
0.91
0..0
Poly/oxide
SEG.0
(unitless)
30.0
SEG.E (eV)
0.0
Other Impurities and Pairs of Materials
SEG.E (eV)
B-6
0.0
Silvaco
Default Coefficients
B.4: Interface Transport Coefficients
Table B-13. Interface Transport Coefficients
Parameter
Antimony
Arsenic
Boron
Phosphorus
1.5
27.9
1.5
1.99
2.48
1.99
1.5
27.9
1.5
1.99
2.48
1.99
Silicon/gas [123]
TRN.0 (unitless)
2.5×10
TRN.E (eV)
1.04
-3
Poly/gas
TRN.0 (unitless)
2.5×10
TRN.E (eV)
1.04
-3
Other Impurities and Pairs of Materials
TRN.0 (unitless)
1.55 x 10-7
TRN.E (eV)
0.0
B.5: Solid Solubility In Silicon
Solubility can be modified for a particular temperature using the SS.TEMP and SS.CONC parameters
in each of the impurity statements.
Table B-14. Solid Solubility in Silicon[124], [125]
Temperature
(ºC)
Silvaco
Boron
[cm3]
800
3.4499×1019
825.0
4.1291×1019
850.0
4.9027×1019
875.0
5.7777×1019
900.0
6.7615×1019
925.0
7.8610×1019
950.0
9.0832×1019
975.0
1.0435×1020
1000.
101922×1020
1025.
103552×1020
1050
1.5331×1020
1075
1.7263×1020
1100.
1.9356×1020
1125.
201613×1020
1150.
204041×1020
1175.
2.6643×1020
1200.
2.9423×1020
Phosphorus
[cm3]
Antimony
[cm3]
2.3000e19
2.7943×1020
3.1585×1020
3.0000×1019
303981×1020
4.0000×1019
3.7943×1020
4.8000×1019
B-7
ATHENA User’s Manual
Table B-14. Solid Solubility in Silicon[124], [125]
Phosphorus
[cm3]
Boron
[cm3]
Temperature
(ºC)
1225.
3.2387×1020
1250.
3.5536×1020
1275.
3.8876×1020
Antimony
[cm3]
6.6200×1019
B.6: Point Defect Parameters
These parameters are for silicon and polysilicon only.
Table B-15. Point Defect Parameters [126]
Bulk Parameters
Interstitial
Vacancy
D.0
600.0
0.1
D.E (eV)
2.44
-3
2.0
22
2.0×1023
CSTAR.0 (cm )
5.0×10
CSTAR.E (eV)
2.36
2.0
KR.0
3.16×10-6
3.16×10-6
KR.E (eV)
2.44
2.44
Table B-16. Point Defect Parameters
Charge State Information
Interstitial
Vacancy
NEU.0
1.0
1.0
NEU.E (eV)
0.0
0.0
NEG.0
5.68
5.68
NEG.E (eV)
0.50
0.145
DNEG.0
0.0
32.47
DNEG.E (eV)
0.0
0.62
POS.0
5.68
5.68
POS.E (eV)
0.26
0.45
B.7: Defect Interface Recombination Parameters
Table B-17. Defect Interface Recombination Parameters
B-8
Silicon/oxide
Interstitial
Vacancy
KSURF.0
1.76×10-04
7.0×108
KSURF.E (eV)
0.06
4.08
KRAT.0
1000.0
0.0
KRAT.E (eV)
0.0
0.0
KPOW.0
0.5
1.0
KPOW.E (eV)
0.0
0.0
Silvaco
Default Coefficients
Table B-17. Defect Interface Recombination Parameters
Silicon/oxide
Interstitial
Vacancy
Silicon/nitride
1.0×10-05
KSURF.0
1.0×10-09
Silicon/oxynitride
KSURF.0
1.0×10-02
1.0×10-05
KSURF.0
1.0×10
-04
KSURF.E (eV)
0.0
4.08
KPOW.0
1.0
1.0
Silicon/gas
7.0×10-08
All parameters for other combinations are 0.0.
B.8: Defect Growth Injection Interface Parameters
Table B-18. Defect Growth Injection Interface Parameters
Silicon/oxide
Interstitial
Vacancy
THETA.0
3.67×10-05
0.0
THETA.E (eV)
-0.902
0.0
GPOW.0
0.0
1.0
GPOW.E (eV)
0.0
VMOLE
0.0
5.0×10
22
5.0×1022
All parameters for other combinations are 0.0.
B.9: Material Parameters
Table B-19. Material Parameters
Parameter
Silicon
Poly
Oxide
Oxynitride
Nitride
Photo
Alumin
NI.0 [127]
3.9×1016
3.9×1016
1.0
1.0
1.0
1.0
1.0
NI.POW [127]
1.5
1.5
0.0
0.0
0.0
0.0
0.0
NI.E [127]
0.605
0.605
0.0
0.0
0.0
0.0
0.0
EPS
11.9
11.9
3.9
7.5
7.5
1.0
1.0
Silvaco
B-9
ATHENA User’s Manual
This page is intentionally left blank
B-10
Silvaco
Appendix C:
Hints and Tips
This appendix is a collection of answers to commonly asked questions about the operation of ATHENA.
Some of these questions and answers have been previously published in articles in “The Simulation
Standard”TM, Silvaco’s trade publication. The original articles can be viewed at Silvaco’s home page at
http://www.silvaco.com.
Question:
Simulating the whole process in ATHENA may take a long time. How can the process flow be checked or
tuned quickly?
Answer:
Several methods are available in ATHENA that enable you to do quick look-and-see simulations of a
complex process flow. Deciding which method to use in a given situation depends on the particular
items of interest. Three modes that can be useful are outlined below:
1. 1D Mode - This is used to perform 1D analysis at any x-location in the 2D structure. This mode
can be invoked from the ATHENA Mesh Initialize menu (Figure 2-10) by selecting the 1D box
under Dimensionality. The X Position item of the menu will become active, so you should
choose the x location at which the 1D analysis will be performed. These changes in the menu will
add two parameters (ONE.D and X.LOCAT=<real>) to the INITIALIZE statement. ATHENA
automatically takes into account all masking and etching steps at the specified location. This
mode is particularly useful for optimization and process tuning. For example, it can be used to
rapidly check MOS source/drain junction depth or the intrinsic base profile of a BJT
2. Geometrical Mode - In this mode all impurities are turned off by checking the No Impurities
box in the ATHENA Mesh Initialize menu. This will add the NO.IMPURITY parameter to the
INITIALIZE statement, disabling all implantation and dopant diffusion steps. Impurity
diffusion, which usually limits the timesteps during oxidation and uses additional equations, is
not present in the geometrical mode. Therefore, the DIFFUSION statements usually execute much
faster when only the oxidation is being simulated. This mode can be used to check the geometry
generated by etching and deposition processes as well as the validity of mask steps. Since
oxidation still occurs, oxide thicknesses as well as bird’s beak shapes can be estimated. But, you
should be aware that dopant enhanced oxidation effects are not taken into account in this mode.
3. Coarse Grid Mode - In this mode you can alter the number of grid points without changing the
LINE statements. It can be done by changing the Parameter Spacing factor in the ATHENA Mesh
Initialize menu. This will change the parameter SPACE.MULT in the INITIALIZE statement. The
value of SPACE.MULT is the amount by which the grid spacing specified in the ATHENA Mesh
Define menu is multiplied. A value for SPACE.MULT that is greater than 1.0 will reduce the total
number of grid points. (A SPACE.MULT value that is less than 1.0 will create a finer mesh
throughout the initial structure). Reducing the number of grid nodes greatly increases speed. You
can still observe dopant diffusion in 2D, and get valuable information about the accuracy of the
input file before committing to the full simulation.
Each of these three fast modes of operation have the advantage. They only require minor modification
during mesh initialization to convert a complete input file to the appropriate fast mode, and back to
normal operation.
Question:
It is known that Silvaco’s device simulator ATLAS allows the simulation of device structures with cylindrical symmetry. Does ATHENA support the grid with cylindrical symmetry?
Silvaco
C-1
ATHENA User’s Manual
Answer:
Yes, you can specify the cylindrical coordinate system in the INITIALIZE statement (choose Cylindrical in the ATHENA Mesh Initialize Menu). The axis of symmetry is always at x=0.
Question:
In some cases the grid within oxide generated during the oxidation step is very coarse. Does this affect
accurate estimation of dopant segregation? Does the shape of the oxide region depend on the quality of
internal grid? Is it possible to control the grid during oxidation?
Answer:
The thickness of grid layers during oxidation is controllable. Two parameters of the METHOD statement
affect the oxide grid: GRID.OXIDE and GRIDINIT.OXIDE. GRID.OXIDE specifies the maximum grid
layer thickness (in microns). GRIDINIT.OXIDE specifies the maximum thickness of the very first grid
layer generated in the growing oxide. For both parameters, the default is 0.1 microns. These defaults
are reasonable for simulation of thick (0.6 - 1.0µ) field oxide growth. But, for thinner oxides these
parameters should be decreased. For example, if an 0.025µ gate oxide is growing, it is a good idea to set
GRIDINIT.OXIDE to 0.005 and GRID.OXIDE to 0.01. This allows a better simulation of impurity segregation and a more accurate prediction of the important surface doping concentration parameter under
the gate. These parameters should be chosen extremely carefully. If you set a small value of
GRID.OXIDE for thick oxide, it will result in a considerable slowing down because as this parameter is
decreased, time steps are shortened and more grid points are generated.
Question:
In some cases oxidation of a complex structure fails right in the very first time step. How can this situation be fixed?
Answer:
ATHENA uses a special algorithm for depositing a native oxide layer on the oxidizing surface. This
algorithm sometimes fails when using highly nonplanar surfaces. This can be fixed by the selection of
a thinner native oxide using the INITIAL parameter in the OXIDE statement. Default is 0.002
microns. Decreasing this value down to 0.001 microns, or even less, may help overcome the problem.
Direct deposit of native oxide could also be used.
Question:
The relative oxidation rate of polysilicon compared to silicon varies depending on the properties of the
polysilicon and the oxidizing ambient. How is this modeled in ATHENA/SSUPREM4?
Answer:
The oxidation rate coefficients in ATHENA/SSUPREM4 are specified separately for bulk silicon and
polysilicon. This allows you to tune the growth rates on the two materials independently. For example,
to change the high temperature linear steam oxidation rate for silicon, the following syntax can be
used:
OXIDE SILICON WET LIN.H.0=<real> LIN.H.E=<real>
whereas for polysilicon the syntax is:
OXIDE POLY WET LIN.H.0=<real> LIN.H.E=<real>
C-2
Silvaco
Hints and Tips
Question:
When simulating a structure with a heavily doped polysilicon gate, unreasonably high concentration of
the impurity is sometimes observed at silicon/oxide interface under the gate. Is it possible to avoid this
situation?
Answer:
The impurity transport through oxide is controlled by the impurity diffusion coefficients within oxide
and the impurity transport coefficients at the poly/oxide and oxide/silicon boundaries. Not all of these
coefficients are well characterized. If you know that for your process the impurity diffusion through
oxide is negligible, you may prevent the impurity transport from polysilicon through oxide into the
substrate by specifying zero transport coefficient as follows:
<IMPURITY NAME> POLY /OXIDE TRN.0=0.0
If the impurity concentration at the gate oxide/silicon interface is measured, you can use the
measured value for tuning the TRN.0 parameter.
Question:
In which cases should the viscous oxidation model with stress dependence be used? Which parameters
should be tuned to match experimental shape of the grown oxide?
Answer:
The viscous stress-dependent model is described in Chapter 3: “SSUPREM4 Models”, “Viscous Model”.
There are also two examples in the ATHENA/SSUPREM4 section of the Deckbuild Examples
Window (See Figure 2-2) that demonstrate the use of the model for LOCOS and SWAMI isolation
processes. The following considerations should be kept in mind when using this model.
1. The stress-dependent viscous oxidation model is an extremely time consuming simulation
method. Therefore it should be used only when it is absolutely necessary and alternative
approaches fail.
2. Typical cases for use of the model are those where a kinked oxide surface is observed and when
the simulated bird’s beak is longer than the measured one.
3. In some cases, the alternative compress method with increased Young’s modulus for nitride could
give a reasonable shape (see the ATHENA/SSUPREM4 example in the “Online Help” Section).
4. The grid for the stress-dependent viscous oxidation should be as simple as possible, but it cannot
be too coarse in the direction of oxidant diffusion (x-direction in the case of simple LOCOS).
5. The higher than default relative error for oxidation rate should be chosen to allow faster
convergence. For example:
METHOD OXIDE.REL = 0.01
6. The main parameter for tuning the model is nitride viscosity, which is specified in the NITRIDE
statement:
MATERIAL NITRIDE VISC.0=<real>
The higher the nitride viscosity the stronger the stress dependence. It is important to know that
nitride viscosity depends on the oxidation temperature as well. You may use the parameter
VISC.E when the temperature dependence of the oxide shape is considered.
7. Model parameters VC, VR, and VD (see Equations 3-147 - 3-149) can also be used for tuning.
Default parameter values are reasonable for temperatures of 1000° C and higher. For several test
structures the alternative set of these parameter values (VC=300, VD=60, and VR=12.5) are more
appropriate for lower temperatures (~950o C).
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Question:
How can a self-aligned silicide process be modeled in SSUPREM4? Are there any special model
parameters required?
Answer:
The formation of metal silicides can be simulated using the optional silicide module in SSUPREM4. In a
typical self-aligned silicide (salicide) process, the goal is to form a silicide layer on the polysilicon gate
and MOS source/drain regions. The silicide layer in the source and drain regions permits device
designs with shallow junctions that still have low n+ or p+ sheet resistances. On the gate, the silicide
layer forms a low resistance interconnect. The process is self-aligned since the oxide spacer on the gate
sidewall is used to prevent the silicide shorting gate to drain.
The usual sequence for salicide is to deposit a refractory metal layer. Commonly used metals are
titanium, tungsten, and platinum. Then a short, fairly low temperature heat cycle is applied to react
the metal with the silicon and polysilicon. The remaining metal is then etched away.
The SSUPREM4 syntax used to model silicidation seems very natural to an experienced user. For
titanium silicide, for example, the syntax is:
DEPOSIT TITANIUM THICK=0.1 DIV=8
DIFFUSE TIME=5 TEMP=650
ETCH TITANIUM ALL
The results of a salicide simulation are that a titanium layer is formed correctly in the source/drain
and gate areas with no reaction with the oxide spacer.
No special model syntax needs to be used with the silicide module in order to achieve the silicidation.
But, a good parameter to be aware of is GRID.SIL on the METHOD statement. This controls grid
spacing within the silicide layer as it grows. This is similar to the way the GRID.OX parameter
controls the grid within thermally grown oxides.
Question:
How is implant damage enhanced diffusion modeled by ATHENA? Which tuning parameters should be
used for matching experimental results?
Answer:
The effect of implant damage enhanced diffusion is important in many technologies. Typical cases are
the source and drain diffusion in MOSFETs and the emitter diffusion in bipolar devices. Damage
generated by implantation leads to an enhancement to the diffusion of these dopants during
subsequent heat cycles.
Simulation of the enhanced diffusion effects are divided between two processes. First, ATHENA must
simulate the implant damage generated by a given implant and secondly it must model the effect that
these defects have on subsequent impurity diffusion.
ATHENA considers implant damage as point defect generation. Point defects are silicon interstitials
and lattice vacancies that are created as energetic implanted ions collide with silicon lattice atoms.
The most practical model for coupling implant damage to subsequent diffusion calculations is the +1
model. In its simplest form, the +1 model adds exactly one interstitial for each implanted ion. This is a
reasonable approximation if one assumes that the vacancies and interstitials created by the implant
recombine quickly relative to the time scale needed to produce significant diffusion. This leaves one
extra interstitial for each ion (assuming the implanted ion has replaced it on the lattice).
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Hints and Tips
This model is applicable to both Monte Carlo and the default analytic implants, and can be invoked by
including the UNIT.DAM parameter on the IMPLANT statement. A commonly applied variation to this
model is to scale the number of generated interstitials.
In ATHENA, this can be done using the parameter DAM.FACT on the IMPLANT statement. A
corresponding profile of lattice vacancies is introduced in this model with the maximum of zero and (1DAM.FACT) times the implanted ion profile.
The diffusion models that will include the effect of the point defects are either the TWO.DIM or
FULL.CPL models. Both models include the local point defect concentration in the diffusion rate of the
dopants. Both interstitials and vacancies diffuse quickly compared with dopant ions. The point defects
also recombine as the implant damage is annealed out.
When it comes to tuning to match measured doping profiles, two approaches are possible. Either the
damage during implant or the diffusion effect of the point defects could be used. The amount of point
defects generated during an implant is extremely difficult to measure. Similarly the model parameters
for both diffusion and recombination rates for point defects are uncertain. All are areas of current
academic research.
Typically, the most effective tuning parameter in this type of simulation is the DAM.FACT value itself.
Figure C-1 shows how fairly small changes in this parameter affect the doping profile. A value of 0.01
is typical. An Athena implant statement for an MOS source/drain might be:
IMPLANT ARSENIC DOSE=3.0E15 ENERGY=60 UNIT.DAMAGE DAM.FACT=0.01
Figure C-1: Variations in diffusion due to tuning of DAM.FACT parameter.
Figure C-2 illustrates how the damage produced by source drain implants affects the center of a MOS
transistor with varying gate length. For shorter gate length devices, the damage at the source drain
area produces additional diffusion in the center that is not seen for longer channel devices. This
phenomenon explains some of the reverse short channel effects seen in certain processes.
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Figure C-2: Enhanced diffusion of MOS channel profile.
Question:
I use SSUPREM4 for process simulation, but I need more realistic models for deposition and etch. How
can I use the ELITE module of ATHENA to do this? How does the interface from ELITE to SSUPREM4
work?
Answer:
ATHENA is a general purpose two-dimensional process simulator that includes modules for implant,
diffusion and oxidation for silicon and compound semiconductors (SSUPREM4), topography (ELITE)
and lithography (OPTOLITH). This means that it is simple to include physical etch or deposition steps
using ELITE models in an existing SSUPREM4 input file.
As device dimensions shrink the need for more physical simulation of the deposition and etch steps in
a process increases. ELITE provides these physical deposition and etch models. SSUPREM4 users can
only use conformal deposition and geometrical etch features built into ATHENA. These simple models
may not be sufficient to describe certain steps in the process satisfactorily.
For example, in a typical sub-micron CMOS process, ELITE models might be required for:
• Trench isolation.
• Spacer formation.
• Reflow of oxides over non-planar surfaces.
• Metal to active area contact cuts.
• Metal deposition over step.
• Inter-metal dielectric formation.
In general, ELITE should be used for any etch process with a degree of isotropy, since perfectly
anisotropic etches can be handled geometrically in SSUPREM4. For deposition processes, ELITE is
appropriate when the deposition is significantly non-conformal.
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Hints and Tips
Many topography simulators exist, but interfacing them to process simulation programs such as
SSUPREM4 has traditionally been a problem. Without the tight integration of ATHENA, the interface
has traditionally been one way (for example, creating a non-planar topography such as a trench and
then using the surface to create the initial structure for a SSUPREM4 simulation).
In ATHENA the bi-directional interface between topography and process simulation is completely
automatic and transparent to the user.
Figure C-3 shows this interface used to form a self-aligned trench isolation for a sub-micron CMOS
process. The initial part of the simulation uses SSUPREM4 to set up a LOCOS oxidation next to a nitride
spacer. ELITE is then used to remove the nitride and etch a trench into the silicon. SSUPREM4 is used
to oxidize the trench sidewalls. Then, the ELITE deposition models are used to fill the trench with
oxide. Finally a planarization etch is performed.
Figure C-3: Simulation of self aligned trench isolation process using the ELITE and SSUPREM4 modules of
ATHENA. SSUPREM4 is used for the LOCOS and trench oxidation. ELITE is used for the trench etch and refill. The
interface between SSUPREM4 and ELITE is completely automatic and transparent to the user.
The syntax needed to access the ELITE models can be found using the Deckbuild Command Menus.
The main parameters are RATE.ETCH MACHINE=<name> to set up parameters for the etch machine
and ETCH MACHINE=<name> TIME=<value> to run that machine for a given time. Analogous
commands exist for depositions.
One key parameter for users of ELITE is DX.MULT=<value> on the ETCH statement. This parameter
sets the ratio between the grid spacing used by SSUPREM4 and the surface accuracy used by ELITE.
The default is 1.0. Lower DX.MULT values will improve the accuracy and smoothness of etch shapes at
the expense of some additional CPU time.
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Question:
Can dopant diffusion be modeled simultaneously with the material reflow?
Answer:
An extremely important feature of ATHENA is that simulation of topography effects such as reflow in
ELITE can be combined with in-wafer simulation of dopant diffusion or oxidation in SSUPREM4. A
previous “Hints and Tips” column (April 1995) showed how ATHENA can simulate individual process
steps from SSUPREM4 and ELITE with seamless integration. In this case, the ELITE and SSUPREM4
simulation is done on the same process step. The reflow heat cycle will also trigger diffusion of the
dopants in the silicon, including transient enhanced diffusion effects where appropriate.
A single DIFFUSE statement with the REFLOW parameter can both produce reflow and dopant
diffusion. Figure C-4 shows an example of a 0.5mm contact cut to an arsenic diffusion. During the
reflow cycle at 875° C the edges of the contact cut are flowed while the arsenic is diffusing.
Figure C-4: Simulation of simultaneous dopant diffusion and glass reflow in ATHENA
Question:
How can dielectric reflow be modeled? Which calibration parameters are important for tuning the
reflow?
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Hints and Tips
Answer:
ATHENA contains a model for the reflow of materials as part of the ELITE module. The model treats
the dielectric material (i.e., SiO2, BPSG) as an incompressible viscous fluid. The material is then
deformed under the driving force of the surface tension of the topography. The calculation of the
changing topography of the material then proceeds according to the applied time and temperature.
The reflow model for a given material is enabled by setting the REFLOW parameter on a MATERIAL
statement. In addition, the parameter REFLOW should be given on a DIFFUSE statements
corresponding to the flow heat cycle. The following is typical syntax:
MATERIAL OXIDE VISC.0=1.862E-20 GAMMA.REFLO=1E3 REFLOW
DIFF TIME={time} TEMP={temp} REFLOW
This example syntax also includes two of the most useful tuning parameters. VISC.0 sets the viscosity
of the oxide. GAMMA.REFLO sets the surface tension factor for the flow calculation.
Figure C-5 shows the results of an example of reflow calculation with ATHENA. The initial structure
has a set of 1 micron contacts with a 2 micron pitch after the anisotropic contact etch. The final profile
shows the reflow shoulders and the proximity effects seen following a 10 minute reflow heat cycle at
950 C.
Figure C-5: Reflow of a via array
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ATHENA User’s Manual
Question:
How can the reverse short channel effect (RSCE) in MOSFETs be simulated using
How can the physical effect behind RSCE be tuned?
ATHENA
and
ATLAS?
Answer:
RSCE in MOSFETs is where the threshold voltage increases with decreasing channel length. At very
short channel lengths the normal short channel effect takes over and the threshold voltage decreases.
The cause of the increasing threshold voltage is a non-uniform enhancement of diffusion of the channel
implant laterally along the MOS channel. This non-uniformity arises from the extra point defects
generated in the source and drain areas of the MOSFET. The source of these point defects is most
commonly the damage caused by the heavy n+ and LDD implants. Other possible causes that can be
modeled in ATHENA are oxidation or silicidation of the source and drain area.
The amount of implant damage from the source/drain implants is controlled using the DAM.FACTOR
parameter. The effect of the damage on subsequent diffusions are modeled in ATHENA using the fully
coupled diffusion model (METHOD FULL.CPL). A previous Hints and Tips covered a description of this
in the “Simulation Standard”, February 1995.
To model RSCE in ATHENA and ATLAS it is necessary to construct MOSFETs of different channel
lengths. This can be done either using the MASKVIEWS layout interface, or using the STRETCH
command in ATHENA or DEVEDIT. The user should simulate the shortest channel length up until the
polysilicon etch and stretch the device to the desired length. The FULL.CPL model is only required for
diffusion after the source/drain implants.
Figure C-6 shows the result of a threshold voltage simulation versus gate length for various values of
implant damage. VWF was used to automatically generate and run this experiment. VWF handles the
automatic interface to ATLAS and the extraction of the threshold voltages. Looking horizontally along
the y=0 line, it is seen that with zero implant damage the threshold voltage decreases with decreasing
length. No RSCE is seen. However as DAM.FACT is increased, the threshold voltage starts to rise
before falling at very short lengths. It is clear the size of the RSCE increases with implant damage
factor.
It is also interesting to note that even the threshold voltage for the 20mm long device is affected
slightly by the implant damage. This is to be expected from Figure C-7, which shows point defects
diffusing 30mm into the substrate. The lateral diffusion length of point defects should be of a similar
order.
Many parameters can be used to tune the fully coupled diffusion model. The most effective for RSCE is
the surface recombination of the interstitials (KSURF.0). Figure C-7 shows threshold voltage versus
channel length as a function of KSURF.0 for a fixed DAM.FACT.
High values of KSURF.0 show no RSCE effect while lower values show strong increases in threshold at
lengths around 1.0 micron.
Tuning RSCE using DAM.FACT and KSURF.0 is possible using ATHENA, ATLAS, and VWF. Users
should note that both these parameters will affect process simulation results such as source/drain
junction depth.
Figure C-8 shows a graph of junction depth of an arsenic implant after a fixed diffusion as a function of
DAM.FACT and KSURF.0. For a given measured result for junction depth it is clear there are a whole
set of DAM.FACT and KSURF.0 combinations that can produce the correct answer. However, the effect
of each combination that matches a junction depth is not the same on RSCE.
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Hints and Tips
Figure C-6: Threshold voltage vs. gate length for various values of implant damage
Figure C-7: Threshold voltage vs. channel length as a function of KSURF.0 for fixed DAM.FACT
Figure C-8: Junction depth of an arsenic implant after a fixed diffusion as a function of DAM.FACT and KSURF.0
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ATHENA User’s Manual
Question:
Which are the key parameters for tuning RTA simulations when using the new Stanford diffusion
models in ATHENA version 4.0?
Answer:
For RTA applications it is recommended to use the new set of models from Stanford University
included in ATHENA version 4.0. These models include effects of {311} defect clusters, dislocation loops
and high concentration effects. To enable all these models the syntax used is:
METHOD FULL.CPL CLUSTER.DAM I.LOOP.SINK HIGH.CONC
The syntax METHOD NEWTON is also recommended to improve the speed of simulations.
Since these models are an extension of the existing FULL.CPL models many of the same tuning
parameters apply. Previous simulations {311}}have shown how the surface recombination rate of
interstitials KSURF.0 is a key tuning parameter for reverse short channel effect where damage
enhanced diffusion is significant. This is also true in the {311} cluster models.
In RTA simulations with the FULL.CPL model all point defects are created by the implantation. They
are at a maximum at t=0 of the RTA and their concentration decays rapidly with time due to diffusion
and recombination. A very important effect of the {311} cluster model is that the free point defect
concentration is not created at the time of the implant. The implant creates some interstitials but also
creates {311} defect clusters. These clusters decay with time releasing point defects over an extended
period of time. This effect is particularly apparent at low temperatures.
Clearly then a key parameter for tuning RTA effects is the time constant for the dissolution of {311}
clusters to interstitials. This is controlled by the syntax:
CLUSTER SILICON TAU.311.0=<val> TAU.311.E=<val>
Measured data [128] shows that the enhanced diffusivity due to point defects extends over minutes at
800C. Figure C-9 shows ATHENA results matched to the measured data in Figure C-10 of [128]. In this
case the value of TAU.311.0 is adjusted to show lower diffusion in the first 15 seconds than the
FULL.CPL model predicts. For comparison, a lower value of TAU.311.0 is used in Figure C-10. It is
clear that this does not match the data in [128] as a significant part of the complete diffusion is in the
first 15 seconds.
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Figure C-9: RTA of a 5.0e13 phosphorus implant matched to experimental data in [128].
Figure C-10: The effect of lower TAU.311.0 is to speed up the diffusion over the initial time period.
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Question:
How can I determine implant range for non-standard materials such as silicides or photoresist?
Answer:
The analytical implant tables in ATHENA/SSUPREM4 cover implantation of the common silicon
dopants (B, P, As, Sb, In) into the commonly used set of materials in semiconductor processing (Silicon,
SiO2, Si3N4, polysilicon, aluminum). For other materials or implant species, the lack of complete data
means full analytic tables are not available. The only alternative approach was to use Monte Carlo
(MC) Implant simulation.
Implantation using MC with the crystalline model is usually required for silicon implantation. For
realistic 2D cases these implants may take up to 30 minutes to run. In order to overcome this problem
an alternative approach is available in ATHENA. This approach uses MC implant in 1D mode to run
implantation simulations into the material of interest. Then the analytical implant moments are
extracted from the implanted doping profile. These analytical moments can be used in a MOMENTS
statement to set the correct doping profiles for an analytical implant. The syntax for this is shown in
Figure C-11 with a comparison of the two different implants in Figure C-12.
Photoresist is a special case in ATHENA. Although analytical implant tables exist for photoresist, they
are specific only to one type of photoresist (AZ-111). Photoresist materials do vary considerably in
density and material abundances. Syntax exists in ATHENA to set the required parameters for MC
implantation modeling.
MATERIAL
MATERIAL=my_resist DENSITY=3 ABUND.1=0.6 AT.NUM.1=8 \
AT.MASS.1=16 ABUND.2=0.4 AT.NUM.2=6 AT.MASS.2=12
ABUND sets the relative abundance of elements in the photoresist. AT.NUM and AT.MASS set the atomic
number and weight of the elements respectively. DENSITY sets the overall material density. From
these parameters, MC implant can calculate the implanted profile. The syntax from Figure C-11
allows the user to fit, extract and re-use the analytical moments calculated from the MC implant
profile.A similar technique can be used for implants of non-standard species too. It is possible for users
to build up their own user-defined implant moment tables.
Figure C-11: Syntax for extracting implant parameters from a Monte Carlo simulation.
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Figure C-12: Comparison of doping profiles analytical extraction versus Monte Carlo. Analytical implants are run
instantaneously whereas Monte Carlo takes up to 30 minutes
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Appendix D:
ATHENA Version History
This appendix lists the release notes in reverse chronological order for each ATHENA release. The
initial release of ATHENA incorporates the standalone capabilities of previously released versions of
SSUPREM4, ELITE, and other functionalities. Version histories for SSUPREM4 are included here for
reference.
D.1: ATHENA Version 5.16.0.R Release Notes
D.1.1: SSUPREM4 Features
1. The Monte Carlo (BCA) implantation module has been multithreaded.
By default, ATHENA runs on the maximum number of CPUs available online. You can specify the
number of CPUs to be used by the parameter "-P <n>" in the athena command line as follows:
athena -P 2 input.in
When running athena within DECKBUILD, add the "-P 2" option to the "simflags" parameter of
the GO statement
The speedup achieved with the multi-threading of the BCA module is close to linear for simulation
of large number of trajectories (N.ION > 50000). This almost optimal behavior is due to the
inherent parallel structure of the BCA implantation module.
There are following limitations for using multi-threading version of MC Implant Module. If
you specify the TRAJ.FILE parameter (option to save ion trajectories in a special structure file for
subsequent display in TONYPLOT) in the IMPLANT statement, the multi-threading capability will
switch off. The FULLROTATION parameter of the IMPLANT statement couldn't be specified
simultaneously with multi-threading. Multiple rotation statements should be used instead.
2. Implemented BCA implantation models for {110} and {111} silicon.
3. Added capability to MC Implant Module that allows to simulate damage or preamorphization
induced by arbitrary "inert" ion bombardment. You can specify atomic number Z1 and atomic
weight M1 in the IMPLANT statement. Only implant damage will be introduced into the structure
after the completion of the Z1 ion implant. The level of this damage will affect subsequent "normal"
implant profiles.
Note: If M1 is not specified, the atomic weight of the main isotope of element Z1 will be used.
4. Memory management of all modules is substantially improved. As the result, the limits on number
of grid points, nodes, and triangles in simulation structure are removed. This allows to perform
simulation in large multilayer structures without sacrificing accuracy.
5. Fixed the capability to specify diffusion through "impurity-vacancy pairs" defined by parameters,
such as DVX.0, DVX.E.
6. Added positively charged vacancy/impurity pair diffusion parameters to the IMPURITY statement:
DVP.0, DVP.E, DVPP.0, and DVPP.E.
7. Added values for diffusion and activation parameters of B, P, As, and SB in Germanium. The
experimental data from [132] and [133] were used for parameter estimations.
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D.1.2: Optolith Features
1. Added the multi-image capability to the proximity printing lithography module.
2. Improved MULT.EXPOSE capability. ATHENA now takes into account different values of Dill's
C-parameter for each wavelength in case of broadband illumination.
D.2: ATHENA Version 5.14.0.R Release Notes
D.2.1: SSUPREM4 Features
1. Introduced new parameters to control the trajectory visualization capability in Monte Carlo
implant: TRAJ.FILE. Specifies the name of the file in which ion trajectories calculated with the
Monte Carlo (BCA) method are to be saved and N.TRAJ, which specifies the number of ion
trajectories to be saved in the TRAJ.FILE.
2. Improved statistics and consequently the effective accuracy of Monte Carlo (BCA) ion implantation
simulation in 2D structures. This is achieved by more accurate estimation of number of trajectories
near the side edges of the simulation structure.
3. Improved stopping power model for 11-20 channel in SiC. This is a rare event channel for standard
wavers (0001). But it has some influence in case of angled implants into trenches parallel to the 1120 plane.
4. Added capability to control triangle orientation of initial ATHENA grid. New parameters TRI.LEFT
and TRI.RIGHT are added to the LINE X statement.
5. Added C.VACANCY and C.INTERST to the INITIALIZE statement.
6. Added new standard impurity HELIUM. The only practical application available in the moment is
Monte Carlo ion implantation of Helium.
7. Added capability to oxidize materials other than Si and Poly. New parameter OXIDIZABLE is added
to the MATERIAL statement. If OXIDIZABLE is set to TRUE, then all oxidation related parameters
for the specified material will be set equal to those for Silicon. You can specify the different values
for oxidation parameters in the OXIDE MATERIAL ... statement.
8. Improved gridding in oxide that results in smaller number of extremely small triangles are
generated in areas of slow oxidation. For example, under the polysilicon gate during reoxidation
process.
D.2.2: ELITE Features
1. Added new parameter OUTF.TABLE=<filename> in the RATE.ETCH statement. This can be used
for detailed analysis of plasma ions and neutrals distributions. The old parameter OUTFILE in the
RATE.ETCH statement has changed to OUTF.ANGLE because it specifies a file with ions vs. angle
distribution output.
D.2.3: OPTOLITH Features
1. Reimplemented Proximity Printing Model in OPTOLITH, which simulates imaging without any
reduction lens. To use this model, specify the GAP parameter in the IMAGE statement. The model is
implemented for Manhattan, Circular, Ring and Multi-Ring masks.
2. Added capability to load mask information directly from MASKVIEWS layout file for image
calculations in OPTOLITH. This capability has several advantages when comparing with old
interface through a special “section” file. The “section” file approximates an arbitrary shaped mask
features with only rectangulars. The new interface doesn't do any approximations and internally
divides mask polygons into triangles and rectangulars for exact image calculations.
3. Considerable speeded up and improved accuracy of image calculations for big area mask layouts
when complex geometry light sources are used.
4. Added additional standard wavelengths to the ILLUMINATION statement: KRF.LASER (alias is
DUV.LINE), ARF.LASER and F2.LASER.
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ATHENA Version History
5. Added capability to save intensity and mask information separately into the structure file after
OPTOLITH image calculations. Now, the MASK parameter in the STRUCTURE statement will save
only mask layout information. The INTENSITY parameter now saves only intensity distribution.
When you specify both parameters, both mask layout and intensity will be saved.
D.3: ATHENA Version 5.10.7.R Release Notes
1. Additional TSUPREM4 compatibility feature is implemented. If you set the E.FIELD parameter to
FALSE in the MATERIAL statement, the electrical term will be ignored during diffusion simulation
in the specified material.
2. Added the boolean parameter CENTER to the IMAGE statement. If specified, the layout loaded with
.sec file generated in MASKVIEWS will be shifted so its center is in the point (0,0) - the origin of
coordinates for computational window. This parameter should be specified when .sec file is
generated from the GDS2 file where absolute coordinates of mask features could be arbitrary.
3. Removed obsolete parameter NA in the EXPOSE statement. Nonvertical light propagation was not
implemented for non-planar structures.
4. Added new standard impurity HYDROGEN. The only practical application available in the moment is
Monte Carlo ion implantation of hydrogen.
5. If you specify METHOD PLS before the Monte Carlo IMPLANT statement, the initial distribution of
impurity-defect pairs will now calculate the same way as for analytical implants.
6. Fixed a bug for the ETCH START/CONTINUE/DONE sequence when etched window width is zero
while using MASKVIEWS.
7. Fixed the bug for the case of deposion of ternary materials with variable composition fraction. For
example:
deposit material=InGaAs thick=0.50 div=20 c.fract=0.1 f.fract=0.5
8. Fixed a bug in analytical ETCH with the ANGLE parameter. In some cases when the THICKNESS
parameter exceeded the total thickness of the structure, a part of the etched layer was not
removed.
9. Fixed a bug for the case when using EPITAXY C.INTERST=<n> after ATHENA starts and before
any DIFFUSE statement.
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D.4: ATHENA Version 5.10.0.R Release Notes
D.4.1: General Features
1. Added multiple features to provide compatibility with TSUPREM4 and TSUPREM3 (see Appendix E:
“TSUPREM4 and TSUPREM3 Compatibility Features”).
2. LEX_LM and OMNI licensing.
D.4.2: SSUPREM4
1. BCA module has now two different engines for ion trajectory calculations. One of these engines is 2
to 4 times faster than another. In some cases, the faster engine might be slightly less accurate. The
new parameter FAST for IMPLANT BCA statement is introduced. This parameter allows you to
specify, which engine to be used during current Monte Carlo simulation.
If FAST=true (default), the fast engine is used. If FAST=false, the slower (potentially more accurate) engine is used.
2. The default version of parameter DIVERGENCE (the alias is BEAMWIDTH) in the IMPLANT statement
has changed from 0 to 1°. 0° ion beam divergence is very difficult to achieve. A typical ion beam
divergence of industrial implanters is 1 to 1.5°.
3. New parameter IV.SCALE is introduced in the IMPLANT statement to control estimation of after
implant interstitial and vacancy distributions from BCA damage calculations using parameter
DAMAGE.
4. DAM.FACTOR=0.0 can now be specified in the IMPLANT statement. This is used with Advanced
Diffusion Module (DifSim).
5. Wafer miscut feature is implemented for BCA implant in crystalline materials. Two new
parameters are introduced:
•
MISCUT.TH - Target wafer polar angle miscut measured in the XY plane, Y being the inward
direction.
• MISCUT.PH - Target wafer azimuth angle miscut measured in the XZ surface plane, Z pointing
away from the observer.
6. Fixed wrong damage scaling when sampling capability is used.
7. Improved algorithm of SSUPREM4 deposition. Now, it guarantees that non-uniform spacing
specified by DY and YDY parameters is preserved even when number of divisions is changed due to
complex grid.
8. The SSUPREM4 deposition is improved for the case when number of DIVISIONS is not specified.
For thin layers with thickness less than 0.012 microns, an uniform grid with spacing of
approximately 0.001 microns will be generated. A non uniform grid with spacing equal to 0.001
microns at the top and bottom of the deposited layer will be generated for thicker layers. The
number of divisions is automatically selected dependent on the layer thickness. It is 12 for the
layers thinner than 0.02 microns and 18 for layers thicker than 2 microns.
9. Improve specification of POLY.DIFF model. The model flag used to be set to false unless the
statement METHOD POLY.DIFF was immediately before DEPOSIT POLY GR.SIZE=<n> statement.
10. Default value for the MIN.TEMP in the METHOD statement is returned to original 700°C. The
manual had always stated that it is 700°C, though few previous versions get reduced value of
475C. It is more appropriate to set 700°C temperature limit since for most models the default
diffusion parameters are not well known at lower temperatures.
11. Numerical rounding bug is fixed in geometrical calculation for very flat triangles during oxidation.
12. Improved triangulation during oxidation which reduced probability of creating extremely small
triangles.
13. The parameter TWO.DIM in the STRUCTURE statement now always forces 1D to 2D transformation
of the current structure. Before it was applied, this happened only when structure was written into
the outfile.
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14. Increased number of material regions up to 1000, which allows you to create a super lattice
structures consist of hundreds of layers.
D.4.3: ELITE
1. Etch rate retardation can be specified in the RATE.DOPE statement.
D.5: ATHENA Version 5.8.0.R Release Notes
D.5.1: SSUPREM4
Diffusion Simulation Features
1. A complete set of Advanced Diffusion Models is implemented (see Section 3.2).
2. The earlier implemted CNET model and all related parameters are removed.
3. The Boron diffusion model in SiGe is extended to include effect of diffusion suppression by carbon
incorporation.
4. Additional model for suppression of boron transient diffusion in SiGeC is implemented. There are
experimental indications that interstitials tend to "disappear" or "get trapped" more intensively in
SiGe layer with substitutional carbon. This model introduces an additional sink for interstitials
in the layers with high carbon concentration.
5. Additional parameter to control diffusion of interstitial in SiGeC region DCARBON.E is added to the
INTERSTITIAL statement. It allows to decrease interstitial diffusivity in SiGeC and indirectly
supresses transient boron diffusion in this region.
6. C-Interpreter functions are now available for Boron diffusion model in SiGeC.
7. It is now possible to include non-equilibrium interstitials into epitaxially grown or simply
deposited silicon layer.
8. Handling of impurity activation models has been improved. Now, the type of activation model can
be specified for each impurity/material combination in the IMPURITY statement. The SOL.SOLUB
and CLUSTER.ACT parameters haven been added to the IMPURITY statement.
9. The TWO.DIM and FULL.CPL models can be used for all semiconductor materials. There are no
verified default parameters for vacancies, interestitials and traps in materials other than Si, but
user can specify those parameters for any semiconductor material.
10. POLYDIFF model is completely rewritten. The following new names for the model parameters are
specified in the IMPURITY statement: PD.DIX.0, PD.DIX.E, PD.EFACT, PD.SEG.E, PD.TAU,
PD.SEGSITES, PD.SEG.GBSI, PD.CRATIO, PD.GROWTH.0, and PD.GROWTH.E. Use "help
impurity" in the ATHENA command line to find a short description of these parameters.
Implant Simulation Features
1. Three types of silicon carbide materials are added: SIC_6H, SIC_4H, and SIC_3C
2. BCA implantation model for the silicon carbide materials is implemented..
3. BCA implantation model for two superconductor materials Ba2YCu3O7 and Ba2NdCu3O7 is
implemented.
Silicide Simulation Features
1.
Two or more metal/silicide pairs can be simulated simultaneously.
2. The volume reduction effect is now specified by two volume ratio parameters ALPHA for silicide/
metal and silicide/silicon (or polysilicon).
3. Cobalt and CoSix materials are added.
4. User-defined metals and silicides specified by parameters MATTYPE and /MATTYPE in the
SILICIDE statement will be recognized as electrodes in the ELECTRODE statement.
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Etch and Deposition Features
1. It is now possible to simulate deposition or epitaxy of the layers with linearly graded impurity or
point defect content. New parameters F.BORON, F.PHOSPHORUS ... F.INTERST, F.VACANCY are
added to the DEPOSIT and EPITAXY statements.
D.5.2: ELITE Capabilities
1. Fixed dopant enhanced etching in ELITE. It is applicable for all etching machines except Monte
Carlo Plasma Etch. All impurities are now explicitly specified in the RATE.DOPE statement.
D.5.3: OPTOLITH Capabilities
1. Time units parameters SECONDS, MINUTES, and HOURS are added to the BAKE statement.
D.5.4: Miscellaneous Features and Bug Fixes
1. It is now possible to use clust.trans model when impurities other than B. P, As, and Sb present in
the structure. Also, the model can be used in Polysilicon.
2. Solid solubility tables are extended down to T = 600C. Also, solid solubility in polysilicon is set
equal to that in silicon.
3. Added a NEUTRAL type impurity as an alternative to DONOR/ACCEPTOR in the IMPURITY
statement. For example, I.SILICON is considering as DONOR in GaAs but should be NEUTRAL in Si.
As the result, Si atoms implanted in order to preamorphized silicon crystal would not affect
diffusion of other impurities and will not contribute into the net concentration.
4. New impurities Nitrogen and Oxygen are added to all relevant statements. Also, impurity Fluorine
is now available in all statements.
5. Standard material GERMANIUM is added.
6. Fixed a bug in initial gridding. The fix makes sure that the distances betweem vertical grid lines
remain constant if the SPACING parameters are equal at the adjacent LINE statements.
7. Add several aliases to command names to achieve better syntax compatibility with TSUPREM4:
DIFFUSION (for DIFFUSE), LOADFILE (for INITIALIZE from a structure file), SAVEFILE (for
STRUCTURE) and AMBIENT (for OXIDE).
8. Made SILICON to be a default material in the STRETCH statement.
9. Removed obsolete parameters LABEL and TITLE from the PRINT.1D statement.
10. The following changes are made in the METHOD statement. The LOWTHER parameter is removed. It
had been set to TRUE as default all along. Obsolete parameters SU.MOD, GRIFFIN.MOD, and
V.LOOP.SINK are removed. Obsolete diffusion model POWER is removed. It was effectively
equivalent of FERMI model.
11. All parameter names related to vacancies and interstitials are standardized to VACANCY and
INTERST (i.e., C.VACANCY, F.INTERST, and so on).
12. Removed obsolete PAUSE command. DECKBUILD has built-in Pause capability.
13. Fixed long time broken command CPULOG.
14. Removed obsolete command ECHO.PRINTF has the same capabilities.
15. Removed obsolete DEFINE and UNDEF commands. DECKBUILD has extensive SET capability.
16. Removed obsolete command ECHO.PRINTF has the same capabilities.
17. Renamed SET command to SETMODE to distinguish with DECKBUILD’s SET. Similarly UNSET is
renamed to UNSETMODE. Old names are also available as synonyms.
18. The composition fraction (the C.FRACTION parameter) could be now specified (INITIALIZE and
DEPOSIT statements) not just for standard ATHENA ternary material AlGaAs and InGaAs but
also for the user-defined materials corresponding to the following standard SILVACO ternary
materials: AlInAs, InGaP, GaSbP GaSbAs GaSbAs InAlAs, InAsP, GaAsP, HgCdTe, InGaN, and
AlGaN.
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D.6: ATHENA Version 5.6.0.R Release Notes
D.6.1: SSUPREM4
Diffusion Simulation Features
1. Time for diffusion and epitaxy can be specified in seconds, minutes or hours. New parameters:
SECONDS, MINUTES, and HOURS are added to the DIFFUSE and EPITAXY statements. MINUTES is
the default.
2. Diffuse time output is now presented in a new standard. Total time is in hours:minutes:seconds
(hh:mm:ss.t) and time increment is in seconds.
3. The POLY.DIFF diffusion model can be now applied to Poly regions formed during Si deposition
over non-silicon surfaces using the SI_TO_POLY parameter (see below).
Implant Simulation Features
1. Now the damage in BCA model is calculated strictly using the modified Kinchin-Pease damage
model. The Damage Amorphization model (Implant Damage) is based on the concept of criticalenergy-density model, while the damage generation rate (vacancies and interstitials) is based on
the modified Kinchin-Pease model. The energy dependence of lattice disorder is analyzed with
respect to spatial density of deposited energy, substrate temperature and ionization events.
2. The statistical sampling method is introduced for BCA ion implantation simulation. This method
increases statistics for low probable events, which results in better quality of ion implant profile
tails. Using the sampling method allows you to reduce calculation time between 5 and 100 times
without reducing statistical accuracy of resulted profiles. The method is switched on by using the
SAMPLING parameter in the IMPLANT statement.
Silicide Simulation Features
1. Silicide models have been revised. Silicide growth rates are now based on experimental data for
TiSix [41], [42].
2. New data for diffusivities and transport coefficients for B, As, Sb, and P inTiSi2 [129], [130].
3. New data for As [131] and improved implementation of segregation model at TiSi2/Si interface.
4. New ALPHA parameter has been added in the SILICIDE statement. It is similar to the volume
expansion parameter (also called ALPHA) in the OXIDATION statement. It specifies the ratio
between consumed silicon volume and volume of grown silicide.
5. The obsolete parameters: DSV.0, DSV.E, NSILICON, and NMETAL are removed.
6. More realistic silicide shapes near spacer corners are obtained. This has been achieved by
suppressing lateral silicide encroachment and empirical decrease of silicide growth rate near the
spacer corners.
7. Silicidation process stops when the whole thickness of metal is consumed.
Etch and Deposition Features
1. The DRY geometrical etch is extended to include the ANGLE and UNDERCUT parameters. These
parameters allow you to obtain the etch regions with tilted sidewalls and undercuts under the
material mask.
2. Selective deposition and epitaxy for crystalline silicon and polysilicon. When silicon deposition and
epitaxy is performed with the SI_TO_POLY parameter specified in the DEPOSIT or EPITAXY
statement, the crystalline silicon layer will be grown only over silicon, while Poly-Si will be grown
elsewhere.
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Stress Simulation Feature
The Stress History Model has been added. This model is specified by using the STRESS.HIST
parameter in the METHOD statement. The default is FALSE. If this method is specified, ATHENA then
calculates stresses when the structure changes after etching, deposition, epitaxy, and diffusion
processes.
D.6.2: ELITE Capabilities
1. The capability to specify direction of incident ion beams for Monte Carlo plasma etch module is
activated. The MC.ANGLE1 and MC.ANGLE2 parameters have been introduced.
2. The old limit of ~6000 on the number of nodes in the structure allowed during reflow simulation is
removed.
D.6.3: Miscellaneous Features and Bug Fixes
1. Capability to transform 1D structure into 2D structure when writing standard structure file in the
STRUCTURE statement has been added. When the TWO.DIM parameter is specified and the current
simulation structure is 1D, it will be transformed into 2D before saving in the specified *.str file.
2. User-defined materials with the names corresponding to SILVACO standard materials are now
saved in Standard Structure Files as standard materials so that they will be recognized by ATLAS,
DEVEDIT and other SILVACO tools. The ELECTRODE statement now recognizes the regions with
material names specified as metals in the list below.
3. A bug in ELITE deposition of oxide when voids are formed has been fixed.
4. A bug in boundary conditions during impurity diffusion from ambient has been fixed.
5. Specified ambient concentration is now guaranteed at the surface points.
6. A bug in image simulation for the case of contact printing has been fixed.
D.7: ATHENA Version 5.4.0.R Release Notes
D.7.1: SSUPREM4
Diffusion Simulation Features
1. Transient impurity activation model is implemented. Parameters of the models: TRACT.0,
TRACT.E, and TRACT.MIN are specified in the IMPURITY statement. See the Section “Transient
Activation Model” in Chapter 3: “SSUPREM4 Models”..
2. The Interface Trap Model is implemented. The model simulates effect of the dose loss at the
silicon/oxide interface. See the “Interface Trap Model (Dose Loss Model)” Section in Chapter 3:
“SSUPREM4 Models” for more information.
3. A special capability to simulate Boron diffsuion in SiGe is implemented. It includes a feature to
deposit the SiGe layer with graded Ge content and two empirical models which modify Boron
difusivity as a function of Ge content.
Implant Simulation Features
1. Old Monte Carlo simulation capabilities both for amorphous and crystalline materials are phased
out.
2. Binary Collision Approximation Monte Carlo module capabilities now supercede those of old
MONTE models and are to be used for all non-analytical implant simulations.
3. All parameters related to old Monte Carlo models are removed.
4. Improved Kinchin-Pease Model for interstitials and vacancies generated during BCA implant is
implemented.
5. AMORPHOUS parameter is now applicable to the BCA simulation.
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D.7.2: FLASH Capabilities
1. FLASH diffusion model now completely corresponds to FERMI Model for silicon.
2. Generic diffusivity formulae are now used for all available dopants instead of specific terms for
each dopant.
3. The DIPP.0 and DIPP.E parameters for diffusivity with doubly positive defects are added to the
IMPURITY statement.
4. The electric field effect on diffusion in GaAs materials is fixed. Now the type of impurity (donor/
acceptor) specified in the IMPURITY statement is properly taken into account.
5. Germanium is set as n-type dopant in GaAs and all appropriate parameters are added.
6. Equilibrium interstitial and vacancy concentrations in compound semiconductors are now
available in the structure file and TONYPLOT.
D.7.3: OPTOLITH Capabilities
New model for simulation of resist exposure process is implemented instead of old one, which used ray
tracing algorithm. It is based on the Beam Propagation Method (see Chapter 5: “OPTOLITH Models”,
Section 5.4: “The Exposure Module”). The main advantage of the new method is its capability to take
into account dose dependency of the local optical properties (refraction index) of the photoresist.
We’ve added a new model which allows you to simulate the image in the case of contact printing. The
GAP parameter enables the model and specifies the mask-to-wafer gap.
D.7.4: ELITE Capabilities
The ELITE etching algorithm has been improved. Now, if the ETCH.RATE parameter for a material
specified in the MACHINE statement is equal to zero or is not specified all regions for this material, it
will not be changed during all etch process steps, which utilize this machine.
D.7.5: Miscellaneous Features and Bug Fixes
1.
The C-interpreter capability in the DIFFUSE statement has been removed. This capability will be
re-implemented and expanded, using a newer, more flexible and extensive SILVACO
C-INTERPRETER.
2. The standard tables for BF2 implants were extended down to 1 keV.
3. Fixed a bug in Pearson-VI function which occasionally resulted in a non-physical tail in case of
high energy implants in photoresist.
4. The flip triangle procedure after etching, deposit, and epitaxy steps has been removed.
5. The bug in saving and loading standard structure files after using the POLY.DIFF model has been
fixed.
6. The bug in separation of floating and substrate oxidizable regions has been fixed. This bug use to
distort the substrate in some structures obtained from DevEdit.
D.8: ATHENA Version 5.2.0.R Release Notes
D.8.1: Ion Implant BCA Model
1. Considerable speed up for 2D simulations.
2. Profile smoothing capability is available after BCA implant.
3. The PRINT.MOM parameter now works for BCA simulation.
4. Improved damage model and electronic stopping.
5. Now the value of 'Implant Damage' is in atomic density per cm3.
6. Improved BCA model for indium and germanium implants.
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D.8.2: Miscellaneous Features and Bug Fixes
1. The memory problem that use to result in failure during multiple implant steps with
FULLROTATION has been fixed.
2. Several problems related to switching from 1D to 2D simulation have been fixed.
3. Missing donor/acceptor concentrations after BCA implant have been added.
4. 311-cluster distribution after BCA implant has been added.
5. Wrong oxide thickness after several consequent viscous oxidation steps has been fixed.
6. Reading of some DEVEDIT structures into ATHENA have been fixed.
7. The license for SILICIDE material model is now checked only when silicidation process starts.
This allows to have structures with deposited silicide materials without having the license.
D.9: ATHENA Version 4.5.0.R Release Notes
D.9.1: SSUPREM4
Implant Simulation Features
1. New Binary Collision Approximation Module for Monte Carlo type simulation of ion implantation
in amorphous and crystalline materials is implemented.
The parameter BCA is used to turn on this model. BCA and MONTE are mutually exclusive.
This module is much more accurate than previous Monte Carlo implementations. It is able to
accurately calculate implant profiles in difficult cases of well channeled implants. It is applicable
to a wide energy range (from ~1 keV to few MeV). It includes damage accumulation model
which allows accurate simulation of dose-dependency effect.
2. Several improvements are made in analytical implant models:
Improved handling of wrong user-defined or tabulated combinations of skewness and kurtosis for
longitudinal profiles. The values are corrected to provide legitimate bell-shaped profiles. The corrected values could be checked by using the parameter, PRINT.MOM, in the IMPLANT statement.
Calculations of cluster and dislocation bands from implant profiles (parameters: MIN.CLUSTER,
MAX.CLUSTER, MIN.LOOP and MAX.LOOP) are fixed and available for both analytical and Monte
Carlo methods.
A new parameter, FULL.DOSE , has been added. If it is set to TRUE the adjusted full dose for the
angled implant will be applied.
A more accurate integration of non-Gaussian lateral distribution functions
is implemeted.
3. User specified models for implant damage, < 311 > clusters and dislocation loops can be controlled
through a C-Interpreter file. The name of the file is specified in the parameter, DAMAGEMOD.FN in
the MOMENTS statement.
Diffusion Simulation Features
A new numerical scheme for diffusion calculations, the Implicit Linear Finite Element Method
(ILFEM), is implemented. The ILFEM uses a new internal data structure, an advanced spatial
discretization scheme, an extremely fast and robust linear solver, and an object-oriented hierarchical
representation of the impurity and defect transport models. The ILFEM module solves impurity and
defect transport equations much faster than previous SSUPREM4 solvers. It also has better
convergency.
The following diffusion models are currently implemented within the ILFEM module: FERMI,
TWO.DIM, FULL.CPL, 311-CLUSTERS, and HIGH.CONC. It also handles all corresponding boundary
conditions, including impurity segregation, defect generation and recombination models.
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To activate ILFEM use:
METHOD ILFEM
To disable ILFEM use: METHOD ILFEM=f
The ILFEM module is currently applicable to the following:
•
impurities: boron, phosphorus, arsenic, antimony, and indium.
•
materials: silicon, polysilicon, oxide, nitride, and aluminum.
D.9.2: ELITE Capabilities
A new Monte Carlo Etch Module is implemented. The main application of this module is the
simulation of plasma or ion assisted etching. The module can take into acccount the redeposition of the
polymer material generated as a mixture of incoming ions with etched (sputtered) atoms and
molecules of substrate material.
C-Interpreter can be used for introduction of user-defined etch and ejection rate models.
D.9.3: Generic ATHENA Capabilities
Active concentration calculations are improved. Previously, all existing impurities in the structure
were set to completely active after any implant, depo, or profile statement. Now, only newly added
impurities are activated completely.
D.10: ATHENA Version 4.0.0.R Release Notes
D.10.1: SSUPREM4
Diffusion Simulation Features
Physical RTA Model - A new TED model including the dynamic transient release of interstitial point
defects has been added to SSUPREM4. <311>- Clusters release Interstitials over time with a user
defined time constant. This model was derived from Dr. Peter Griffin work at Stanford.
Dislocation Loop based point defect sink model - A dislocation loop based interstitial sink model
is now included for high dose RTA situation and may be used in conjunction with the <311>-Cluster
model. This model was derived from the work of Dr. Peter Griffin at Stanford University.
Point Defect - Dopant Pair Recombination Capture Cross Section Control - To account for
high concentration effects extra terms have been added to the fully coupled diffusion model allowing
for higher order dopant-point defect dopant pair recombination. Recombination may be controlled
independently both in the bulk and as an extended surface recombination velocity. This model was
derived from the work of Dr Peter Griffin at Stanford University.
Extended Defects - Extended defects may now be in introduced during Ion Implantation. Both
<311> - Clusters and Dislocation Loops may be introduced during ion implantation along with an
overlying amorphous region. This damage may be introduced in addition to a distribution of point
defects and is usable in a subsequent RTA diffusion step. Damage is specified as a profile scaled to an
implanted profile. Independent vertical and lateral control of the scaled damage is definable.
CNET Diffusion Models - A new series of models from CNET under the guidance of Dr. Daniel
Mathiot have been implanted and calibrated to better describe high dose effects during diffusion. The
series of five extra models include: Impurity Defect pairing statistics, static clustering, percolation,
correlated interstitial & vacancy mediated impurity diffusivities, bimolecular recombination of defects
through impurity states.
Temperature Dependent Fractional Interstitialcy - The parameters for fractional interstitialcy,
Fi have been extended to include temperature dependence. (Fi.0 and Fi.E). If Fi is stated it will remain
a fixed value.
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Indium Added as New Dopant Species - The Indium dopant species has been included as it has
shown promise as a good shallow junction forming alternative to Boron and BF2 implanted species.
Indium may further be passed though DEVEDIT and into ATLAS as part of the active net dopant
calculation.
Gridding Capabilities
Power Device Diffusion Model - A new model for power device diffusion has been added. This
model will run around 4 times faster than the standard fermi model in SSUPREM4, enabling Athena to
simulate larger power device structures in a given time frame.
Adaptive Meshing During Ion Implantation and Diffusion - A series of important improvements
are now available in SSUPREM4 in the area of automated adaptive meshing. Improvements include,
efficient 1D adaption and a new basemesh generation routine during the auto-transition to a 2D
structure. 2D adaption employs a new smoothing capability. Time stepping control also allows greater
versatility. Templates for a range of technology are supplied to more automatically generate the mesh.
Implant Simulation Features
Advanced 2D Implant Distribution Model - Analytical 2D distribution model which takes into
account depth dependence of lateral standard deviation is implemented. It is invoked using parameter
FULL.LAT in the IMPLANT statement. In order to use this advanced model the following additional
spatial moments should be furnished: LSTD.DEV, LGAMMA, and LKURTOSIS. Corresponding
parameters could be specified for the second. Pearson distribution in the case of double Pearson model.
All above mentioned new parameters can be specified in seriously improved MOMENTS statement or
in user-defined tables (see below). Also, they are added into the standard look-up table for a few ion/
material combinations.
Flexible Control of Lateral Distribution - More accurate and flexible modeling is implemented
also in the case of simple lateral implant distribution with constant lateral standard deviation. The
lateral standard deviation now can be specified independently from the depth standard deviation. The
LSTD.DEV parameters can be specified in seriously improved MOMENTS statement or in user-defined
tables (see below). Also, they are added into the standard look-up table for a few ion/material
combinations. Simplified control of the lateral distribution could be achieved by using LAT.RATIO
parameter in the IMPLANT statement.
Generic Pearson Distribution - To achieve better compatibility to several other implant simulation
programs (e.g., UT at Austin), deviations from standard Pearson-IV distribution formula could be
allowed using new ANY.PEARSON parameter. It means that kurtosis (fourth moment) could be slightly
smaller than the critical kurtosis of the Pearson-IV formula.
Range Parameters are Eliminated from the IMPLANT statement - This capability has become
obsolete after complete implementation of the MOMENTS statement. The capability was very limited
because it could be used only for unimaterial structures.
New PRINT.MOM parameter of the IMPLANT statement - Tells ATHENA to printout range
parameters used for all ion/material combinations for specified energy and dose. It also refers user to a
source where these parameters are taken from (standard tables, user-specified tables, or the
MOMENTS statement). In the case of Monte Carlo simulation PRINT.MOM prints spatial moments
calculated from the Monte Carlo based profile.
Improved Control of Moments Selection - The selection of implant moments used by the
IMPLANT statement is controlled now by the MOMENTS statement. Parameter DEF_TABLE
specifies that only the default look-up implant table athenaimp should be used. Parameter
USER_TABLE=<filename>; specifies that the user-defined table should be used as a first choice for
the moment search. In other cases parameters specified in the MOMENTS statements (if any) will be
checked first of all.
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Template for the User-Defined Implant Tables - Auxiliary file USERIMP provides template for
specifying implant moment sets for all types of analytical implant models from the simplest Gauss to
double Pearson with advanced lateral distribution.
High Energy Implant Tables - 1 to 8 MeV implant tables are now available for all major impant
species for Silicon Oxide.
Si Ion Implant into Silicon - results in the interstitial distribution, which allows estimation of
preamorphization effect.
Trajectories of Primary Ions and Substrate Atoms Knocked-on in the Implant Cascade - can
be now saved in a special TRAJ.FILE and subsequently plotted using TonyPlot. This frees ATHENA
from the last dependency on old graphic library plotlib.
PRE.FACTOR and POW.FACTOR Parameters are Eliminated from the IMPLANT Statement
- Instead PRE.FACTOR parameter is added to the IMPURITY statement, so electronic stopping can
be control for each implant ion -substrate material combination separately. POW.FACTOR does not
make any sense because ATHENA uses Biersack-Brandt-Kitagawa stopping model where sqrt(E)
dependency doesn’t exist explicitly.
Moments are Calculated during Monte Carlo Implant Simulation - All spatial moments are
integrated during Monte Carlo calculations and then can be printed out when PRINT.MOM parameter
is specified.
BEAMWIDTH Capability for Monte Carlo Implant - now works properly for any number of
trajectories. It used to wrongly estimate random angle.
Boundary Conditions PERIODIC and REFLECT - now work properly even in the case of 1D
simulation.
SMOOTH Capability - now works in all cases (used to fail for several combinations of other
parameters).
Oxidation
Oxidation Threshold Model - Oxidation only occurs for oxidant concentration above some critical
value.
Miscellaneous Features
Solid Solubility Tables Extended - Boron Solid Solubility Tables have been extended down to 700,o
minimum temperature.
New PD Time Stepping Control - The initial time step may not be set independently for point
defects to dopant. This allows greater flexibility to study events occurring during the initial time of an
RTA time cycle, specifically when employing a new TED diffusion model.
Equilibrium Point Defects Concentration - The equilibrium point defects concentrations (Ci* and
Cv*) are now output into the SSF file. These may now be visualized in TONYPLOT.
Dump filename extended - the files dumped during a diffusion now include three extra decimal
places in the name of the file, so as to be able to movie diffusion effects during the initial short time
steps. Simulated Structure can be Truncated from a Side or from the Bottom by using NOEXPOSE
parameter in the ETCH LEFT/RIGHT or ETCH BELOW statements.
Alternative Model Files - With ATHENA V4.0.0.R, users may now select alternative model files
using the -modfile command option. The option argument names the alternative model file ATHENA
should use during the simulation. ATHENA V4.0.0.R is shipped with a new updated model named
smod96a. This file contains improved model parameters and its use is recommended.
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D.11: ELITE
Monte Carlo Plasma Etching - A new monte carlo plasma simulation function is available to
calculate the angular energy distribution of ions emitted from a RIE machines dark space sheath.
Shadowing is calculated and etch rates over complex topograhical surfaces result. Sputtering
efficiency as a function of angle is also controllable.
Doping Concentration Dependent Etch Rate - A doping level etch rate enhancement factor allows
user control over the relative etch rates of doped materials. This function is unique to the mesh based
ATHENA product and can not be treated with a simple string based tool.
Stress Dependent Etch Rate - Etch rates may be enhanced as a function of material stress.
Oxidation induced stress creates defectivity in materials that will increase the local etch rates. This
function, is only available in the mesh based ATHENA framework and can not be implemented into a
string based tool.
Void Formation Control - Extra control has been added to allow the control of the formation of a
void in the case of two encroaching CVD fronts.
D.12: OPTOLITH
Image Routines Enhancement - The algorithm in evaluating the aerial image of the mask has now
been streamlined. Approximately, the speed improvement is equivalent to a change from n*n to
n*log(n). For a complex mask, the speed can be as high as 20X. A minor bug in calculating the
diffraction pattern has now been removed.
Exposure Routines Improvement - Optolith Exposure now runs around 4~5 times faster than
version 3.0. This has been achieved by restructuring the ray tracing algorithm used to expose a given
non-planar device structure.
In addition, an error in setting up the boundary conditions for the electromagnetic wave has been
corrected to yield the proper standing wave pattern. The asymmetry in energy deposition for a
symmetric structure has also been fixed.
New Material RSM Calibration System - When used with the VWF system Optolith may be used
to calibrate physical model parameters. Example model parameters include A, B, C bleaching
parameters and Development rate parameters for all Development rate models. The system will fit
simulation model parameters to a range of experimentally measured CD data.
D.13: ATHENA Version 3.0.1.R Release Notes
D.13.1: ATHENA Capabilities
• The default value for nitride viscosity has been changed from VISC.0 = 5e12 to VISC.0 = 1.8e15.
This value is changed in the athenamod file using the following MATERIAL statement.
MATERIAL NITRIDE VISC.0 = 1.8E15 VISC.E=0 VISC.X = 0.499
• The parameters WET and DRY were changed to WETO2 and DRYO2 on the INTERSTITIAL,
OXIDE, and MATERIAL statements.
• The MOMENTS statement has been added to ATHENA to facilitate the entering of user defined
moments for analytic implant. The MOMENTS statement includes the following parameters: material SILICON ..., impurity I.ARSENIC ..., DOSE incident ion flux (/cm2), ENERGY incident ion
energy (KeV), RANGE projected range (microns), STD.DEV standard Deviation (microns), GAMMA
third moment, KURTOSIS fourth moment SRANGE projected range for second Pearson (microns),
SSTD.DEV standard Deviation for second Pearson (microns), SGAMMA third moment for second
Pearson, SKURTOSIS fourth moment for second Pearson, DRATIO dose ratio in the double Pearson
formula.
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• The parameters WETO2 and DRYO2 were added to the INTERSTITIAL statement for THETA.0
and THETA.E.
• A parameter FLIP.FACTOR has been added to the METHOD statement to let the user change criteria for controlling triangle flipping. FLIP.FACTOR is a measure of the obtuseness of the angles of
the opposite nodes of a pair of triangles. The default is 1e-6. It is unitless.
• Four new materials have been included into ATHENA. They are AlGaAs, InGaAs, SiGe, and InP.
These materials are accessible via the INITIALIZE or DEPOSIT statement by specifying ALGAAS,
INGAAS, SIGE, or INP. The fractional components of the elements can be entered via the parameter C.FRAC on either the INITIALIZE or DEPOSIT statements. The DEPOSIT statement also
allows a linearly graded variation in the fractional components by use of C.FRAC as the fractional
component of the first element (ie. for ALGAAS Al is the first component) at the bottom of the
deposit and C.FINAL as the fractional component of the first element at the top of the deposit. The
fractional component of the second component (i.e., for ALGAAS Ga is the second component) is 1 C.FRAC and 1 - C.FINAL. These materials are also available on other statements such as
STRETCH, ETCH etc.
• Ten more user materials were added to make a total of 20 user definable materials.
• The parameters DONOR and ACCEPTOR have been added to the IMPURITY statement. This
allows an impurity to be specified as either donor or acceptor for a given material.
• Active impurities are now part of the output file as well as chemical impurities. Donors and acceptors are calculated from the active impurity concentration. All impurity data can be entered via the
IMPURITY statement. The old statements BORON, ARSENIC, PHOSPHORUS, and ANTIMONY
can still be used as before, as they are aliased to the IMPURITY statement.
• Due to numerous additions to the standard structure file in Version 3 of ATHENA the structure
files created by Version 3 are not compatible with previous versions of ATHENA. Structure files created by old versions of ATHENA can be read by Version 3 of ATHENA.
Adaptive Meshing Capabilities
A 2-D mesh adapting module has been incorporated into ATHENA. The module is invoked by
specifying boolean flag ADAPT on the METHOD statement preceding IMPLANT, DIFFUSE, or
EPITAXY statements, or by specifying boolean flag ADAPT on the ADAPT.MESH statement to do
stand alone mesh refinements. A mesh smoothing algorithm has also been integrated into the module
to improve the mesh quality after mesh adapting or after normal deposit/etch/oxidation/ silicidation/
diffusion process steps. A set of parameters can be specified on ADAPT.PAR statement to adjust the
mesh adapting process.
The parameters available on the METHOD statement are as the following:
• Boolean ADAPT specify that the adaptive meshing should be performed on the following IMPLANT,
DIFFUSE or EPITAXY statements (default false).
• Boolean DEPO.SMOOTH specify that the mesh smoothing should be performed after each
DEPOSIT statement.
• Boolean ETCH.SMOOTH specify that the mesh smoothing should be performed after each ETCH
statement.
• Boolean DIFF.SMOOTH specify that the mesh smoothing should be performed after each DIFFUSE
statement.
• Boolean STEP.SMOOTH specify that the mesh smoothing should be performed after each time step
on each DIFFUSE statement.
• Integer IMPLANT.MES specifies which adapting algorithm to use on IMPLANT statements, currently IMPLANT.MES = 0 corresponds to University of Florida’s algorithm. This is the default.
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The parameters available on the ADAPT.PAR statement are as follows:
• Adaptive meshing control variables are available on the ADAPT.PAR statement. They are
MIN.ADD, IMPL.SUB, DIFF.SMOOTH, and IMPL.SMOOTH.
• MIN.ADD stops point addition in IMPLANT when the number of points added in the current loop is
less than MIN.ADD * (total number of points). The default value for MIN.ADD = 0.05.
• IMPL.SUB is a boolean flag that stops point removal during IMPLANT adaptive meshing. The
default value for IMPL.SUB = false signifies that points are not being removed.
• Integer DIFF.SMOOTH specifies which annealing algorithm to use after each adaption step, currently DIFF.SMOOTH = 0 corresponds to no annealing during DIFFUSE. DIFF.SMOOTH = 1 corresponds to Laplacian smoothing and the dose conservation interpolation algorithm. The default is
DIFF.SMOOTH=0.
• Integer IMPL.SMOOTH specifies which annealing algorithm to use after each adaption step, currently IMPL.SMOOTH = 0 corresponds to no annealing during IMPLANT. IMPL.SMOOTH = 1 corresponds to Laplacian smoothing and the dose conservation interpolation algorithm. The default is
IMPL.SMOOTH=1.
• Boolean SILICON, OXIDE, ... specify material regions to be adapted on. This may be one or several
materials at a time. The default materials include SILICON, OXIDE, POLYSILICON etc.
• Boolean I.BORON, I.ARSENIC, ... specify impurities to be adapted on. This may be one or several
impurities at a time. The available impurities include I.BORON, I.ARSENIC, I.PHOSPHORUS,
I.ANTIMONY, I.INTERST, I.VACANCY etc.
• Boolean DISABLE specifies that materials/impurities combinations given are disabled to be effective on mesh adapting or smoothing.
• Float MAX.ERR specifies the maximum error allowable before adding points to the mesh, (unitless).
Error calculated above this value causes points to be added.
• Float MIN.ERR specifies the minimum error below which points may be deleted from the mesh,
(unitless). Error calculated below this value causes points to be removed. Both MAX.ERR and
MIN.ERR are calculated using the Bank-Weiser error estimator which is defined as:
2
2 ∇ Ci
e = h ------------Ci
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where h is the average of the edge lengths associated with node i, Ci is the impurity concentration at
node i.
• Float CONC.MIN specifies the minimum impurity concentration below which adapting will stop,
(units 1.0/cm3).
• Float AREA.MIN specifies the minimum triangle area below which adding points will stop, (units
cm2).
• Float AREA.MAX specifies the maximum triangle area below which deleting points will stop, (units
cm2).
• Float EDGE.MIN specifies the minimum edge length below which adding points will stop, (units
cm).
• Float EDGE.MAX specifies the maximum edge length below which deleting points will stop, (units
cm).
• Integer MAX.POINT specifies the maximum number of points above which adapting will stop.
• Integer MAX.LOOP specifies the maximum loop count above which adapting will stop, effective
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only with implant.
The parameters available on the ADAPT.MESH statement are as follows:
• Boolean ADAPT specify that a stand alone adaptive meshing step should be performed to refine or
relax the current mesh based on the material/impurity specification given on ADAPT.PAR statement, (default false).
• Integer ADAPT.COUNT specifies the number of adapting loops during the stand alone adaptive
meshing operation, (default 1).
• Boolean SMOOTH specifies to do stand alone annealing (default false).
• Integer SMTH.COUNT specifies the number of smooth loops during the smooth operation, (default
1).
• Float ADD.I.LINE specifies that a mesh line is to be added at the interface between two materials
as defined by the booleans MATERIAL1 and /MATERIAL2. The line is added in MATERIAL1 a distance ADD.I.LINE from /MATERIAL2. Boolean SILICON, OXIDE, ... Specify material1 for
ADD.I.LINE.
• Boolean /SILICON, /OXIDE, ... specify /material2 for ADD.I.LINE.
SSUPREM4 Capabilities
• Oxidation enabled for polysilicon diffusion model.
• Vacancy and interstitial diffusion in polysilicon have been decoupled from impurity diffusion for the
TWO.DIM model.
• A new parameter has been added to the OXIDE statement. It is called SPLIT.ANGLE. It governs
the minimum angle at which the oxide will split open one more grid spacing when oxidizing at a triple point (i.e. where silicon, oxide, and nitride coincide together at a point). The default for the split
angle is 22.5 degrees. The SPLIT.ANGLE parameter for triple point oxidation is material dependent. Specify the oxidizing material without a “/” and the second material with a “/” using the following format:
OXIDE SPLIT.ANGLE=35 SILICON /NITRIDE
There are only three possible combinations: SILICON /NITRIDE, SILICON /POLY, and POLY /
NITRIDE.
• A new parameter for scaling analytic implants has been added to the MATERIAL statement. A multiplicative factor, IMPL.SCALE, is specified on the MATERIAL statement along with the material
name in which the implant is to be scaled. An example format would be:
MATERIAL IMP L.SCALE=0.5 PHOTORESIST
This scales the implant RANGE, STD.DEV, SRANGE, and SSTD.DEV parameters with this factor
when they are take from the implant moments file athenaimp. This is intended to be a convenient
way to modify these tables with a constant multiplicative factor.
Monte Carlo Implant Capabilities
• Secondary recoil in Monte Carlo implantation model has been implemented. The model is invoked
by specifying REC.FRAC=<number> together with the DAMAGE flag on the IMPLANT statement.
The model calculates the trajectory of secondary ions generated by the collision between the primary ion and crystal lattice atom. REC.FRAC controls the fraction of the secondary ions generated
by primary ions to be simulated.
• Work in MC Implant has changed the results so that the peaks for crystalline and amorphous
implants are now at the same position.
• Substrate rotation is now taken into account for Monte Carlo implants. This parameter is set on the
INITIALIZE statement and is called ROT.SUB. The default for ROT.SUB is 45 degrees.
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• Access to implant parameters for electronic stopping have been added to the IMPLANT statement.
These parameters affect the electronic stopping model and the angle for the Monte Carlo implant.
First, the BEAMWIDTH parameter has been added. This parameter allows specification of the
implant beamwidth in degrees. When the BEAMWIDTH angle is specified the TILT angle is varied
between TILT +/- BEAMWIDTH/2.0. Each ion will have an angle somewhere in this range decided
by a random number generator. There are two electronic stopping models. The first, default model,
is a simple model that uses the atomic mass of the ion and the current ion energy after each collision to calculate the electronic stopping.
• A parameter called PRE.FACTOR has been added as a multiplier to the atomic mass factor. The
default value of PRE.FACTOR = 1. A parameter called POW.FACTOR has been added as the power
of the energy ratio (energy ratio = 1000*[current ion energy]/[initial ion energy]) of the ion. The
default value of POW.FACTOR = 0.5 or is the square root of the energy ratio. These parameters
apply to both the CRYSTAL and AMORPH implants.
• The Hobler electronic stopping model and its parameters were originally for Boron in Si crystal
implants. The Hobler model is used by default for Boron in Silicon. It can also be used for Si with
any impurity by specifying HOBLER on the IMPLANT statement. The Hobler parameters and their
default values are PMAX.HOBLER = 2.35, XNL.HOBLER = 0.4, and F.HOBLER = 0.8. PRE.FACTOR can also be used with the HOBLER model.
C Interpreter Capabilities
The C Interpreter has been integrated into ATHENA. The first models accessible by the C Interpreter
are for the phosphorus, arsenic, antimony, boron, interstitial and vacancy diffusion coefficients. The
latter two are only applicable for the advanced diffusion models. The file name for model substitution
is set on the DIFFUSE statement with the string parameter P.DIF.COEF = <filename>. This syntax is
valid for all of the above with the string parameters being P.DIF.COEF, AS.DIF.COEF, SB.DIF.COEF,
B.DIF.COEF, I.DIF.COEF and V.DIF.COEF for phosphorus, arsenic, antimony, boron, interstitial and
vacancy diffusion coefficients respectively. The segregation calculation can also be accessed by the C
Interpreter for phosphorus, arsenic, antimony and boron. For the segregation calculation the file name
for model substitution is set on the DIFFUSE statement with the string parameter P.SEG.CALC =
<filename>. This syntax is valid for all of the above with the string parameters being P.SEG.CALC,
AS.SEG.CALC, SB.SEG.CALC and B.SEG.CALC. The activation calculation can also be accessed by
the C Interpreter for phosphorus, arsenic, antimony and boron. For the activation calculation the file
name for model substitution is set on the DIFFUSE statement with the string parameter P.ACT.CALC
= <filename>. This syntax is valid for all of the above with the string parameters being P.ACT.CALC,
AS.ACT.CALC, SB.ACT.CALC and B.ACT.CALC.
All of these parameters can be used at the same time or separately as desired. Templates for all these
functions are located in a file called athena.lib located in the directory $SILVACO/lib/athena/
common. A sample function is given for each of the diffusion coefficient calculations, segregation
calculations, and activation calculations. All these functions should have different names. The
template file is copied to the current directory by typing “athena -T <filename>” in a C shell.
D.13.2: ELITE Capabilities
CHEMICAL and DIVERGENCE parameters have been added to the RIE model on the RATE.ETCH
statement. These account for ions that hit the structure at other than normal incidence. A Gaussian
distribution of ions as a function of the angle is assumed. DIVERGENCE is the standard deviation of
this distribution in degrees. CHEMICAL is the etch rate for this component of the RIE model.
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Chemical Mechanical Polish
• Two models for chemical mechanical polishing have been added to ELITE. They are the Burke
model (hard polish) and the Warnock model (soft polish). The Burke model polishes the structure at
a rate proportional to the pattern factor of the structure. The Burke parameters MAX.HARD and
MIN.HARD are the maximum and minimum polish rates and are entered via the RATE.POLISH
statement. MAX.HARD corresponds to a pattern factor of zero and MIN.HARD corresponds to a
pattern factor of one. The actual polishing rate is calculated on the line between MAX.HARD and
MIN.HARD depending on the pattern factor of the structure being polished.
• The Warnock model has four parameters on the RATE.POLISH statement. SOFT sets the polish
rate. HEIGHT.FAC is the vertical deformation scale in microns. LENGTH.FAC is the horizontal
deformation scale in microns. The polishing rates for tall features and holes are calculated using
HEIGHT.FAC and LENGTH.FAC. HEIGHT.FAC measures how much the polishing pad will deform
with respect to the height of the feature. LENGTH.FAC measures the distance the effect of a tall
feature will be felt. LENGTH.FAC is a measure of the stiffness of the pad and the distance at which
shadowing will be felt by a tall feature where HEIGHT.FAC is a measure of the spring like nature of
the pad surface. KINETIC.FAC is the multiplier which increases the vertical component of the horizontal polish rate on sloped surfaces. KINETIC.FAC increases the vertical polish rate as the surface
becomes more vertical.
• An isotropical rate component is also available on the RATE.POLISH statement via the ISOTROPIC parameter.
• The two polish models, HARD and SOFT, can be used together or separately. The isotropic component can be added to either polish model. The polish is initiated by the POLISH statement. The syntax of the POLISH statement is very similar to the ETCH statement for machine etches.
• Temperature dependence has been added to the surface diffusion model for ELITE deposits. The
RATE.DEPO statement now includes SIGMA.0 and SIGMA.E for this model. The dependence is
SIGMA.DEP = SIGMA.0*EXP(-SIGMA.E/KT). Temperature is entered on the DEPOSIT statement.
• The string advance algorithm and the diffusion algorithm have been modified to give a more realistic movement.
• The WET, RIE, etch capabilities of ELITE have been converted from a string based algorithm to a
mesh based algorithm. This gives greater accuracy when etching near boundaries.
• The CUSTOM deposit has been renamed to USER.DATA.1. CUSTOM remains as an alias for this
deposit model. A new user deposit model was created that allows the same form of input file as
USER.DATA.1 but also contains all of the functionality of the UNIDIREC model including shadowing and surface diffusion effects (SIGMA.DEP parameter). This new model is called USER.DATA.2.
The necessary parameters are in an ASCII input file of the same form as the USER.DATA.1 model.
Angle and deposition rate are the input values in the file where the deposition rate is taken as a relative deposition rate and the overall deposition rate is determined by the DEP.RATE parameter.
• SUBSTEPS has been added to the DEPOSIT statement. This parameter controls the number of
steps made for each division of the deposit. This parameter is very important in terms of shadowing
effects as these effects are calculated every time there is a change in SUBSTEPS or DIVISIONS. In
general, the larger the number of SUBSTEPS the more accurate the calculation. However, a large
number of SUBSTEPS also increases calculation time. SUBSTEPS = 1 is useful for the
USER.DATA.2 model if there are a large number of points in the ASCII input file. This will speed
up depositions made with this model and will not affect the accuracy of the shadowing as shadowing
effects are calculated for each point in the ASCII input file. The default value for SUBSTEPS is 8.
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D.13.3: FLASH Capabilities
For the new materials, AlGaAs, InGaAs, SiGe, and InP, implantation and diffusion models were
enabled. Currently diffusion in AlGaAs, InGaAs, and InP have the same parameters as GaAs as
specified in the model file. SiGe uses the parameters for Si, again as specified in the model file. The
analytic implant capabilities for these materials are as follows: SiGe uses Si moments tables where
they are available. AlGaAs, InGaAs, and InP use moments tables for GaAs where they are available.
The Monte Carlo implant capabilities are as follows: SiGe uses the Si crystal lattice. AlGaAs and
InGaAs use the GaAs crystal lattice. InP uses its own crystal lattice.
Carbon has been added as a dopant for GaAs with diffusion coefficients and implant tables borrowed
from Beryllium until better data is found.
D.13.4: OPTOLITH Capabilities
Problem with annular sources for exposure has been fixed.
D.13.5: Known Bugs
GPLOT visualization plots do not work when remotely displaying on Solaris 2.4.
D.14: ATHENA Version 2.0
Version 2.0 of ATHENA incorporates a number of new models as well as convenience features. The
FLASH module is now available as a component of ATHENA. ATHENA now includes a Monte Carlo
based deposit algorithm and a reflow calculation.
D.14.1: ATHENA Capabilities
ATHENA Framework capabilities have been enhanced by the inclusion of some helpful geometric
manipulations. Namely:
• The STRETCH statement has been extended to allow vertical stretches to easily extend structures
for device analysis or point defect based diffusion calculations. The parameter, Y.VAL on the
STRETCH statement specifies the vertical position in the structure at which the stretch will occur.
• The ETCH statement has been extended to include syntax ABOVE and BELOW to facilitate the
truncation or planarization of structures for interfacing to device analysis or following point defect
based diffusion. ETCH ABOVE and ETCH BELOW both sustain one-dimensional calculation and
can be used in the inverse of the STRETCH operations described above.
• The STRIP statement has been enhanced to include material specification. This allows strip of any
material. If no material is specified, STRIP removes all photoresists and BARRIER materials.
• The IMPURITY statement has been added. The IMPURITY statement allows the specification of
parameters for the new impurities for FLASH and SSUPREM4 that have been introduced in this
release. The IMPURITY statement is intended to stop proliferation of multitudinous statements of
the form PHOSPHORUS, BORON, ARSENIC, etc. as new impurities are added. Parameters for
boron, for example, can be specified with IMPURITY I.BORON instead of the BORON statement.
The IMPURITY statement allows setting of atomic mass and atomic number using the AT.MASS
and AT.NUMBER parameters respectively. These parameters effect the Monte Carlo ion implant
and allow user defined impurities for ion implant by redefining an existing impurity with the
desired characteristics.
• The number of user definable materials has been increased to 10.
• Shell statements such as QUIT and HELP have been made case insensitive.
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• A new algorithm for surface grid removal has been included in the functionality of the RELAX
statement. This algorithm allows elimination of surface segments that are smaller than a value
specified by parameter, DX.SURF in microns. This is useful for removing excess grid created during
high resolution machine etches.
• A new set of examples is included that illustrate calibration of coefficients for several typical calibration problems.
D.14.2: SSUPREM4 Capabilities
• Gallium, Aluminum, and Gold impurities have been added. The statement language for DEPOSIT,
DIFFUSION, INITIALIZE, and a number of other statements has been modified to include these
impurities. The IMPURITY statement described above has been added to allow coefficient setting
for these impurities.
• A two stream polysilicon diffusion model has been added. This model takes into account the diffusion of impurities via grain and grain boundary components. The relative magnitude of the two
components is controlled by the GB.VOL.RATIO parameter on the MATERIAL statement. The
grain size of the columnar grains can be set by the parameter GRAIN.SIZE on the MATERIAL
statement. Grain boundary directionality is included in the DEPOSIT calculation. Grain size evolution is calculated during diffusion and is controlled by the GRAIN.SIZE and GB.ENERGY parameters on the MATERIAL statement. Impurity segregation into and out of grains is calculated during
diffusion. The impurities in the grains are treated similar to diffusion in silicon. Impurities in the
grain boundary diffuse more quickly as set by the GB.DIX.0 and GB.DIX.E parameters on the
IMPURITY statement. The advanced polysilicon diffusion model is invoked by specifying the
POLY.DIFF parameter on the METHOD statement. The METHOD POLY.DIFF statement should
precede the deposition of the polysilicon.
• The CRYSTAL parameter on the IMPLANT statement is now true by default. This parameter
determines whether silicon materials will be treated with a full crystal representation during
Monte Carlo ion implant calculations. The previous default can be obtained by including CRYSTAL=f on the IMPLANT statement. Monte Carlo implant calculations will now take longer to perform due to the use of the more complete crystalline model. The AMORPH parameter can now be
used instead of CRYSTAL=f to determine which model for Monte Carlo ion implant will be used.
Either AMORPH or CRYSTAL=f can now be used to specify that statistics for amorphous silicon be
used for analytic ion implant calculations. The UNIT.DAMAGE model now has a default value for a
DAM.FACTOR of 0.01
• Dynamic amorphization is now included in the Monte Carlo ion implant capability. This models the
amorphization that takes place during implantation.
• The MATERIAL statement includes the boolean parameter, DAM.THRESH=, that specifies the
implant damage threshold in eV. This can be used to control the extent of amorphization that occurs
during implant. The parameter MAX.DAMAGE on the IMPLANT or MATERIAL statements also
controls the rate at which the implanted material will amorphize.
• The silicide model has been enhanced to improve volume conservation during silicide calculations.
Parameters DSV.0 and DSV.E have been added to the SILICIDE statement to control the dissolution of a contributing material during the silicide calculation.
• Improvements to the TWO.DIM model and cylindrical coordinates to address bug fixes and model
extensions have been included.
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D.14.3: ELITE Capabilities
• Reflow capabilities that allow spin on glass modeling with a physically based calculation that simultaneously calculates impurity diffusion are now included. Reflow capability is now available with
ELITE for individual materials by specifying the REFLOW parameter on the MATERIAL statement. Specifying the REFLOW parameter on the DIFFUSION statement invokes the reflow model.
The VISCOUS model should be selected on the METHOD statement prior to performing reflow. The
parameter GAMMA.REFLOW=<n> has been added to the MATERIAL statement to specify surface
tension sigma for the reflow calculation. When used in conjunction with either SSUPREM4 or
FLASH, the reflow capability allows simultaneous calculation of material flow and impurity diffusion.
• Monte Carlo deposit capabilities are now available as an optional functionality. These allow physically based calculations that include deposited species reflection/sticking coefficient, surface diffusion, and density variations.
• A tuning parameter, DX.MULT=<n> has been added to the ETCH statement to allow enhanced discretization during individual ELITE etch steps. Increasing the value of DX.MULT from its default of
1.0 will result in larger surface segments and a reduced discretization. Decreasing DX.MULT will
result in better discretization in both space and time during the etch calculation. Reducing the
value of this parameter allows realistic modeling of wet etches that previously were poorly resolved.
• A new machine type specified by the parameter CUSTOM is now available for ELITE deposits. This
machine type reads deposit rate vs. angle information from a user specified ASCII file. This can be
used as an interface to deposit rates produced by non-Silvaco simulators. If a full range of deposit
angles is not specified the simulator will interpolate rates between the closest angle and a rate of
zero at an angle of +/- 180 degrees. The rates at +/- 180 degrees are assumed to be the same.
• The limits on number of regions and number of surface segments for machine etch calculations have
been increased. The new limits should be adequate for most applications of ELITE.
D.14.4: OPTOLITH Capabilities
• A new defocus model that directly couples the imaging module to the exposure module has been
introduced. The DEFOCUS parameter on the EXPOSE statement is now obsolete and the NA
parameter on the EXPOSE statement is used only to specify that the vertical propagation model be
used (NA=0.0). The default is the large numerical aperture model.
• Multiple exposure capability has been added to the EXPOSE statement. Using the boolean parameter MULT.EXPOSE allows an arbitrary number of exposures to be simulated in the same resist.
Applications are multiple focal planes (FLEX method) and multiple wavelengths.
• Multiple image capability has been added to the IMAGE statement. Using the boolean parameter
MULT.IMAGE allows an arbitrary number of images to be superimposed in the same aerial image.
The application is for superposition of multiple images with different focal planes (FLEX method).
• A new parameter, POWER.MIN=<n>, in the EXPOSE statement has been introduced to control the
extent of the exposure calculation. This parameter controls the amount of loss to be considered in
the calculation. After reflection, transmission and absorption the intensity may be so low as to be
negligible. POWER.MIN sets the level below which the intensity will be ignored.
• The imaging module now includes a one-dimensional mode that allows the calculation of one dimensional as opposed to two dimensional images. The one-dimensional image capability is invoked by
specifying the ONE.DIM parameter on the IMAGE statement. The advantage of the ONE.DIM
mode is realized when using the calculated image in the exposure module. The two-dimensional calculation allows the user to see effects due to lines perpendicular and parallel to the current cross
section being studied but uses a two dimensional array of plane waves in the calculation. The twodimensional mode requires much longer calculation time. The one-dimensional calculation uses
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only lines which are perpendicular to the cross section. This calculation uses only a one dimensional
array of plane waves and is much faster. When a two dimensional mask is defined, only mask features that are on the same level as the desired cross section are included in the calculation.
• The POSTBAKE statement has been replaced by the BAKE statement that performs either postexposure bake or post-development bake. TIME and TEMPERATURE parameters have been added
to be used instead of diffusion length. Associated photoactive component diffusivity parameters are
also included in the RATE.DEVELOP statement. A new post-development bake capability includes
photoresist flow. The REFLOW parameter on the BAKE statement invokes the material flow model.
• The BAKE statement includes the DUMP and DUMP.PREFIX parameters that allow movies of
bake processes to be created. Setting DUMP=1 and DUMP.PRE=test will create a sequence of Silvaco standard structure files that show the time evolution of the structure during the bake. The
files will be named test**.**.str where the **.** indicates the time within the bake.
• The library of default photoresists has been extended with the inclusion of more resists and parameters describing the new models.
D.14.5: FLASH Module
• The FLASH module has been introduced with this release of ATHENA. The FLASH module provides
the ability to model gallium arsenide materials. This involves a number of changes. A partial list of
the FLASH capabilities is provided here for reference.
• GaAs material is now included on the INITIALIZE and DEPOSIT statements as well as a number
of model coefficient statements.
• Impurities appropriate for GaAs processing, namely, beryllium, chrome, germanium, magnesium,
selenium, silicon, and zinc, have been added to a number of statements.
• Ion implantation moments tables have been added that describe implant of these species into materials typical of GaAs processing.
• Monte Carlo ion implant capabilities have been extended to accommodate the new impurities and
GaAs material including crystal effects.
• A diffusion model for impurities in GaAs has been included. This model can be accessed by specifying the DIFFUSE statement.
D.15: ATHENA Version 1.0
• Version 1.0 incorporates a number of new models as well as convenience features. The maximum
number of grid points has been increased to 20000. Dynamic allocation of critical arrays makes this
limit practical. A slight slowdown while dynamic allocation is being performed may be observed
during execution of INITIAL statements. If the grid definitions exceed the limits of 20000 points or
1000 horizontal or vertical points, the program gives an error message and exits.
• Non-integer specification of the DIVISIONS parameter on the DEPOSIT statement is now allowed.
This allows parameterized gridding.
• The INITIALIZE statement now accepts material specifications. This allows the specification of an
initial grid for any material using only LINE and INITIALIZE statements. TAG parameters for
boundary definition do not need to be specified. REGION and BOUNDARY statements are not
needed and for most commonly used boundary conditions are set up by default.
• Improved grid refinements following oxidation, deposition, silicidation, etching, or other grid moving steps.
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• This update includes a new parser function MAT1|MAT2(Y) that will return the x intersection
point between materials mat1 and mat2 for the y value given to the function. The other parser function, MAT1@MAT2(X), returns a y intersection point given x. However, the two functions are very
different. The former allows the intersection point with gas to be found specifically for the application of extracting critical dimensions (CDs) for photolithography applications. The latter will not
handle gas material. In the case of extraction of cds a special format is used.
PRINTF (GAS|PHOTO(Y)-PHOTO|GAS(Y))
This is the right intersection - the left intersection. If there are more than two intersections the
right-most and left-most will be taken. These conditions are only true if gas is specified. If gas is not
specified it returns the x intersection for y in the same manner as MAT1@MAT2(X).
• A bug in the RELAX capability has been repaired. This makes RELAX function more completely
and makes it remove triangles for cases where they were left in the past.
D.16: SSUPREM4 Version 6.0
• Version 6.0 of SSUPREM4 incorporates a number of new models as well as convenience features.
SSUPREM4 now includes the first available two-dimensional silicide model. The DEPOSIT, ETCH
and model statements now include materials TUNGSTEN, TITANIUM, PLATINUM, WSIX, TISIX,
and PTSIX. Silicidation can also be performed using user defined materials for other metal systems.
• The silicide model parameters can be specified in a number of model statements and in the
METHOD statement.
• DEPOSIT, EPITAXY, and DIFFUSION now allow specification of multiple impurities. The multiple
impurity deposition capability is exhibited in an example of BPSG type material.
• The DIFFUSION statement now allows simultaneous oxide growth and impurity predeposition.
This allows physically based modeling of processes such POCL deposition.
• One remaining area of concern for modeling such processes is that impurity diffusion in highly
doped oxide type materials such as BPSG or PSG will tend to be faster. The impurity diffusion coefficient must typically be adjusted in order to model such processes accurately.
• Diffusion calculation has been modified to allow the previous discretization or Rex Lowther’s discretization method. The improved Lowther discretization can be accessed using the parameter
LOWTHER on the METHOD statement.
• The oxidation gridding algorithm has been modified to allow a thin grid at the initial oxidation and
a coarser grid throughout subsequent oxidation. This technique is designed to create a fine grid during gate oxide and similar growth steps but coarse grid for thicker oxidations. The parameter GRIDINIT.OX on the METHOD statement sets the value of the initial grid thickness. A similar
capability for silicidation is available via the GRIDINIT.SIL on the METHOD statement.
• Substrate orientation can now be specified on the INIT statement to set the orientation of trench
sidewalls. This effects oxidation and Monte Carlo implantation.
• The SSUPREM4-MaskViews interface has been replaced by the MaskViews cutfile capability. All
references to the SSUPREM4-MaskViews interface in the INITIAL statement will be ignored during calculation and will produce a warning message.
• The regrid capability has been replaced by the functionality of DEVEDIT. REGRID statements in
SSUPREM4 input will be ignored during calculation and will produce a warning message.
• Regional attribute information can now be set in SSUPREM4. Currently the attributes that are set
by SSUPREM4 are only electrode names.
• Poly Oxidation - Etching in complicated structures (latch-up etc.), memory allocation, and freeing
bugs eliminated
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ATHENA Version History
• Syntax Changes - REGRID and layout interface related syntax for INITIAL statement has been
removed.
D.17: SSUPREM4 Version 5.1.4
• Version 5.1 of SSUPREM4 incorporates a number of new models as well as convenience features, and
numerous bug fixes.
• Eliminated a bug in the PRINT.1D statement for structures including BARRIER material.
• The memory requirements for SSUPREM4 were reduced dramatically through a change to the maximum number of materials and regions allowed in a simulation.
• Boundary conditions bug fixes eliminated some difficulties during TWO.DIM diffusions.
D.18: SSUPREM4 Version 5.1
• Version 5.1 of SSUPREM4 incorporates a number of new models as well as convenience features, and
numerous bug fixes.
• PREDICT2 Feature Incorporation - As part of an ongoing collaboration with the Microelectronics Center of North Carolina, Version 5.1 of SSUPREM4 is coupled with initial model implementation of PREDICT2. The models in PREDICT2 are the most accurate available for high concentration
diffusion, Rapid Thermal Processing (RTP), and Transient Enhanced Diffusion (TED). The use of
these models is described in the DIFFUSION and METHOD statement descriptions and in the Reference Manual.
• DeckBuild example facility added - A set of standard examples for SSUPREM4 and other SILVACO simulators can now be accessed via the DECKBUILD working environment. To run these examples, run DeckBuild, pull down the Main Control-Examples menu, and select SSUPREM4 from the
Section menu. Then select an example name from the scrolling list and select the Load button at the
bottom of the screen. This will copy the example and any associated files to your current working
directory and load the example into DECKBUILD. You can then run the example. The example facility
includes a short description of the example that describes how to run it and some description of the
results that is similar to the manual description. Examples describing interfaces between different
simulators are also accessible.
• SSUPREM3 Interface - The SSUPREM4 PROFILE statement can read a one dimensional (1D)
structure file generated by SSUPREM4. The PROFILE statement reads a MASTER file that contains layer and impurity information from SSUPREM3. The interface between this simulators is best
accomplished by using DECKBUILD. Within DECKBUILD, you simply build the SSUPREM3 portion of
the input deck. Next, specify the command: GO SSUPREM4. Specify the mesh within silicon as you
normally would in SSUPREM4. DECKBUILD will automatically insert the appropriate profile statement following SSUPREM4 initialization.
• User accessible polysilicon oxidation rates - In previous releases of SSUPREM4, polysilicon and
silicon were assumed to oxidize with similar rates. The parameters for polysilicon oxidation were
not independently accessible from those for silicon oxidation. Experiments have shown that polysilicon oxidation can be significantly different from silicon oxidation. All coefficients for oxidation are
now accessible independently for silicon and polysilicon oxidation. By default, the rates for polysilicon and silicon oxidation are the same.
• Geometric Mode Added - The capability to specify at initialization that a simulation is to be performed without impurities has been added as a parameter on the INITIALIZE statement. This
specifies the so-called geometric mode that describes all material layers but produces no impurity
information, speeding up SSUPREM4 execution time immensely.
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• Coarse Grid Mode Added - The parameter SPACE.MULT has been added to the INITIALIZE
statement to globally manipulate the initial grid specification for SSUPREM4. Setting the value of
SPACE.MULT to a value greater than one will increase the effective value of each of the spacing
parameters on preceding LINE statements. This gives a quick way to globally reduce the grid density in a SSUPREM4 simulation for reduced simulation time for preliminary analyses.
• Full Rotation Capability Added To IMPLANT Statement - Full rotation for implant can now
be specified on the IMPLANT statement. Specifying the FULLROTAT parameter will perform
implantation at the specified tilt angle from all rotation angles as would occur with a rotating wafer
mount.
• User definable materials added - The capability to define new materials in SSUPREM4 has
been included in this release. This allows separate treatment of materials deposited using different
processes.
• Ramped DIFFUSION syntax change - The RAMP parameter has been removed from the diffusion statement. If the parameter is present it will be ignored. Temperature ramps for thermal diffusions can now be specified by adding either the T.FINAL or T.RATE parameter to any DIFFUSION
statement. The initial temperature must be specified using the TEMPERATURE parameter.
• Line continuation syntax change - Line continuation is now supported in a manner consistent
with use within DeckBuild. The line continuation character for SSUPREM4 as well as other simulators running under DeckBuild is \ (backslash). The \ character should be the last character on a
line that is to be continued on the following line.
• ETCH statement default change - The TOP.LAYER parameter on the ETCH statement defaults
to true. This parameter can be set to false to etch underlying material layers simultaneously with
exposed layers of a particular material. SSUPREM4 will now give information warning messages for
etches that create voids within a structure. In addition, unexposed materials will not be etched
unless TOP.LAYER is set to false.
• TonyPlot and go syntax supported - The command TonyPlot can be included in a SSUPREM4
input deck and will initiate a TONYPLOT of the structure if run under DeckBuild. For SSUPREM4
standalone operation, the TonyPlot statement is ignored. Also, under DeckBuild, the command GO
SSUPREM4 will initiate SSUPREM4 execution. This statement is ignored in standalone operation.
• Manual improvements and additional examples - The manual for SSUPREM4 has been reformatted and thoroughly revised to be more readable and provide the user with more important
guidelines for effective use of SSUPREM4. The Tutorial section and Getting Started sections have
been added to provide an introduction to the use of SSUPREM4. Additional examples detail the use
of the user defined material capability, bipolar device fabrication and EEPROM device fabrication.
D.19: SSUPREM4 Version 5.0
• Version 5.0 of SSUPREM4 represents a new standard for 2D process simulation. SSUPREM4 Version
5.0 incorporates a number of new models and convenience features briefly described in this chapter.
• One-dimensional mode - Version 5.0 offers a significant enhancement for speed and ease of use
by incorporating a one-dimensional (1D) mode. This may be specified within a conventional twodimensional (2D) input deck. This allows fast analyses of particular points in a 2D structure prior to
complete 2D analysis with the same input deck. The use of this feature is described in the INITIALIZE statement description.
• Analytic angled implant - The implant capabilities of SSUPREM4 have been enhanced by the
inclusion of analytic angled implant models. This implementation removes the use of the rectangular grid that is utilized in other versions of SSUPREM4 and that is frequently responsible for large
memory requirements during implant calculations. This model can be invoked by specifying the
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ATHENA Version History
TILT parameter in the IMPLANT statement.
• Speed enhancements for diffusion and oxidation calculations - Speed enhancements have
been incorporated that provide an overall speed improvement by a factor of two for typical diffusion
calculations.
• Monte Carlo ion implant model - Version 5.0 of SSUPREM4 introduces a fast Monte Carlo ion
implant calculation. This calculation is very general and because of significant developments in
modeling and computational techniques, is from 10 to 100 times as fast as similar calculations from
other sources. The model includes the following effects:
- Implant angle (tilt and rotation)
- Substrate damage and damage temperature dependence
• Reflected Ions - Physical modeling of penetration through multi-layer structures. This model can
be invoked by specifying the MONTECAR parameter on the IMPLANT statement.
• Non-uniform grid capability - A non-uniform grid can now be specified in the vertical direction
for either deposit or epitaxy process steps. This is especially useful for modeling epitaxial processes.
This capability can be invoked by specifying the DY and YDY parameters as described in the EPITAXY and DEPOSIT statement descriptions.
• Gas flow specification - Gas flow can now be explicitly specified during diffusion calculations.
This functionality supports the use of mixed ambients and is described in the DIFFUSION statement description.
• RELAX statement added for improved gridding - A new statement, RELAX, has been added to
allow the removal of excess grid points at any time during the simulation. This greatly enhances
efficiency by allowing free manipulation of the grid.
• Improved MaskViews interface - The interface to MASKVIEWS now can be invoked interactively
during SSUPREM4 simulation. This interface has also been improved to provide for automatic grid
generation that is tied to layout information. This interface and capability are demonstrated in the
first standard example.
• ELECTRODE statement - The name and position of electrodes in a SSUPREM4 structure can now
be defined using the ELECTRODE statement. This information is incorporated in the MASTER
structure file format and can be read transparently by SPISCES 2B.
D.20: Additional SSUPREM4 Changes
D.20.1: Oxidation method defaults to compress
• The HCL.PC parameter has been added to the diffusion statement to allow the inclusion of HCl.
• The readability of the online help facility has been improved, and additional comments have been
added.
• These can be accessed by specifying HELP or HELP <statement name> in interactive mode.
• The initial HELP statement list has been alphabetized.
• The amount of runtime output has been set such that the default level provides appropriate information for day to day use. The level of output may be specified by the OPTION statement and either
QUIET, NORMAL, VERBOSE, or DEBUG parameters. The default is NORMAL.
• The ECHO feature has been set to on by default. This can be altered by specifying UNSET ECHO or
SET ECHO to turn the echo off or on respectively.
• Command line continuation was supported. The + (plus) symbol at the beginning of a line indicates
that it is a continuation of the previous line. The + at the end of a line indicates that the line following it is a continuation. The continuation symbol is now a space followed by a backslash character “
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\” at the end of the line to be continued.
• A smoothing algorithm has been incorporated into the mesh initialization calculation. This guarantees numerically desirable mesh characteristics for meshes with rapidly changing spacing.
• The deposition and epitaxy algorithm has been improved to be more robust and to provide more consistent gridding. The parameter MIN.SPACE has been added to control the resulting grid.
• The parameter TOP.LAYER has been added to the ETCH statement to indicate that only top layers
of the etched material should be removed.
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Appendix E:
TSUPREM4 and TSUPREM3 Compatibility Features
The following changes in ATHENA syntax and functionalities are implemented in order to achieve
better compatibility with TSUPREM4 and TSUPREM3 simulators.
E.1: General Syntax Capabilities
• Added capability to specify that default values of some parameters correspond to those of
TSUPREM4. The modified keyfile athenakey.tma with some modified default values is introduced.
To run ATHENA with default parameters specified in athenakey.tma file the syntax is:
go athena simflags="-tma"
For example, TSUPREM4 defaults for TILT and ROTATION parameters in the IMPLANT statement
are 0°, while ATHENA uses 7 and 30° respectively.
• A plus character '+' can be used as a line continuation sign instead of standard backslash '\'.
• Boolean parameters can be set to false by preceding the parameter name with '^' or '!' character.
• The '$' character can be used to specify the comment line. This should only be used at the beginning of the line, because the '$' character can be used for substitution of parameters defined by SET
or DEFINE statements of DECKBUILD.
• The maximum length of parameter names has extended from 12 to 16 characters. (some TSUPREM3
names are longer than 12 characters).
• The first character of a parameter name can be a numeral now.
E.2: Execution Control Capabilities Provided by Deckbuild
The detailed description on these new functionalities will be published in the DECKBUILD manual.
Here, we highlight only key features related to the compatibility issues.
E.2.1: DEFINE Statement and Substitutions Capability
DEFINE statement specifies strings for substitution in the following input statements until the
UNDEFINE statement is encountered. The following DEFINE statements and corresponding substitutions are allowed.
DEFINE dconditions temp=1000 time=10 dry
DIFFUSE dconditions
DEFINE t1 5.0
DEFINE t2 10
DIFFUSE temp=900 time = ( t1 + t2 )
or
DIFFUSE temp=900 time = $t1 + $t2
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or
DIFFUSE temp=900 time = @t1 + @t2
In case when you have to redefine a string, you should use the %DEFINE statement.
E.2.2: IF/ELSEIF/ELSE/IF.END Capability.
This allows you to perform segments of input deck depending on conditions set in the IF COND=(
condition) or IFELSE COND=(condition). For example, the following sequence extracts the
gate oxide thickness. If it is greater than required 100 A, then the extra oxide thickness is etched.
Otherwise, the lacking oxide thickness is deposited.
extract name="gateox" thickness material="SiO~2" mat.occno=1
x.val=0.5
extract name="gateoxdiff" 1.e-5*($gateox - 100.0)
IF cond=($gateoxdiff > 0.0)
etch oxide thick=$gateoxdiff
ELSE
deposit oxide thick=-($gateoxdiff)
IF.END
E.2.3: LOOP/L.END/ASSIGN/L.MODIFY Capability
LOOP and L.END statements defines the beginning and end of an input deck segment, which will
be processed several times. The number of passes is specified by the STEPS parameter of the LOOP
statement.
The ASSIGN statement allows you to assign a numerical or character value to a name. It is similar
to the DEFINE statement. The main difference is the capability to vary the assigned value within
the LOOP cycle using RATIO and DELTA parameters. Also, only '$' and '@' characters can be used
for substitution.
The L.MODIFY statement allows you to alter the processing of the current LOOP cycle. For
example, if you use BREAK parameter, the current LOOP cycle gets interrupted and control comes to
the first line after the L.END statement.
The following example shows LOOP/L.END/ASSIGN/L.MODIFY capability. It demonstrates a
simple way to estimate a diffusion time needed to grow the gate oxide with the thickness of 100 A.
First, the initial value 0.0 is assigned to the name 'tt'. Within the loop, variable value is
assigned to the name 't'. Its inital value is 1.0 and increases by a factor of 1.2 in each subsequent
loop iteration. The current value of 't' is used as diffusion time.
The next ASSIGN statement calculates the total diffusion time.
The EXTRACT statement finds current oxide thickness 'gateox'. If the required condition is that
extracted 'gateox' exceeds 100 A, the LOOP cycle is interrupted and the total diffusion time is
printed.
ASSIGN name=tt n.val=0.0
LOOP steps=20
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ASSIGN name=t n.val=1.0 ratio=1.2
diffuse time=$t temperature=950 dry
ASSIGN name=tt n.val=$tt+$t
extract name="gateox" thickness material="SiO~2" mat.occno=1 x.val=0.1
IF cond = ( $gateox > 100.0 )
L.MODIFY
break
IF.END
L.END
echo $tt
E.3: MESH Statement
The new MESH statement provides an alternative to standard mesh generation using the LINE
statements. It also specifies some parameters used in automatic grid generation when layout
information is provided by the Mask Data File generated by Taurus Layout and loaded in the MASK
statement.
DX.MAX specifies the maximum grid spacing in the horizontal direction. It is used when the grid
in the x-direction is specified using the Mask Data File.
DX.MIN specifies the minimum grid spacing in the horizontal direction. It is used when the grid
in the x-direction is specified using the Mask Data File.
DX.RATIO specifies the maximum interval ratio between adjacent grid points in the
horizontal direction. You can also specify this parameter in the INITIALIZE statement. The
default is 1.5.
DY.ACTIV specifies the grid spacing in y-direction at the bottom of the active region.
DY.BOT specifies the grid spacing in y-direction at the bottom of the structure.
DY.RATIO specifies maximum interval ratio between adjacent grid points in vertical direction.
This parameter could be also specified in the INITIALIZE statement. The default is 1.5.
DY.SURF specifies the grid spacing in the surface region (i.e., between y=0 and y=LY.SURF).
FAST is equivalent to the AUTO (default) parameter in the INITIALIZE statement.
Note: The MESH statement with LY.SURF and other related parameters cannot be used together with LINE Y
statements.
GRID.FAC specifies a global spacing multiplier, which will be applied to all spacing parameters
when you generate a grid with the INITIALIZE statement. This parameter is equivalent to the
SPACE.MULT parameter of the INITIALIZE statement.
LY.SURF specifies the depth of of the surface region in the default vertical grid (y-direction).
LY.ACTIV specifies the bottom of the active region in the default vertical grid (y-direction).
LY.BOT specifies the depth of the bottom of the structure in the default vertical grid.
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E.4: Using MASK statement with the parameter IN.FILE and XLINES for
Automatic grid generation in the horizontal direction
This capability can be used only if ATHENA runs within DECKBUILD. If DECKBUILD encounters
the MASK statement with the parameters IN.FILE=<maskfile.tl1> and XLINES, it recognizes
that the file should be in Taurus Layout Mask Data format.
The following information from the maskfile.tl1 are used to build the grid:
• The scale factor (units per micron).
• The minimum and maximum coordinates of mask specification, which define the left and right of
simulation space.
• The number of mask in the file.
• The first line of each mask description includes the mask name (e.g., Poly) and number of opaque
segments. Each subsequent line gives the minimum and maximum coordinates of each of these
segments.
DECKBUILD will generate the LINE X statements, which are used by ATHENA according the
following rules.
1. The lines will be generated at each mask edge.
2. The grid spacing at these lines will be equal to DX.MIN specified in the MESH statement.
3. If none of the mask edges coincides with left or right boundary of the simulation space, the LINE
statement corresponding to such boundaries will be without spacing.
4. Additional one or two LINE statements will be generated between the lines corresponding to
mask edges. The SPAC parameters at these additional lines will be minimum of DX.MAX and
DX.MIN*(DX.RATIO)**n, where DX.MIN, DX.MAX and DX.RATIO are parameters specified in
the MESH statements. This will guarantee that grid spacings in the horizontal grid will be
increased far from mask edges.
These rules are illustrated by the following example of a structure with two POLY gates. If the
Mask Data File has the following fragment
1.000000E+03
0
3000
1
POLY
2
800
1200
1800
2200
and the MESH statement
MESH dx.min=0.01 dx.max=0.1 dx.ratio=2 follows, then DECKBUILD will generate the next
sequence of the LINE X statements.
line x loc=0.000000 tag=left
line x loc=0.800000 spac=0.010000
line x loc=0.950000 spac=0.080000
line x loc=1.050000 spac=0.080000
line x loc=1.200000 spac=0.010000
line x loc=1.350000 spac=0.080000
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line x loc=1.650000 spac=0.080000
line x loc=1.800000 spac=0.010000
line x loc=1.950000 spac=0.080000
line x loc=2.050000 spac=0.080000
line x loc=2.200000 spac=0.010000
line x loc=3.000000 tag=right
Note: MASK IN.FILE=<maskfile.tl1> cannot be used together with LINE X statements.
Note: .sec files generated by SILVACO's MaskViews tools provide superior capabilities in generating grid and mask
processing.
E.5: Using mask information with the EXPOSE MASK=<maskname>
statement.
This capability can be used only if ATHENA runs within DECKBUILD. If DECKBUILD encounters
the statement EXPOSE with the parameter MASK=<maskname>, it provides ATHENA with a
sequence of ETCH statements, which will remove photoresist below all transparent regions of the
specified mask. The EXPOSE MASK=<maskname> statement should be preceded by a DEPOSIT
PHOTO statement and followed by a DEVELOP (without parameters) statement. For example, if you
load the same Mask Data File as used above in the MASK statement, the following input deck
fragment appears in the input deck.
DEPO PHOTO THICK=1
EXPOSE MASK=POLY
DEVELOP
DECKBUILD will then generate the next sequence of the ETCH statements.
etch photo start x=-0.100000 y=-1000
etch cont x=-0.100000 y=1000
etch cont x=0.800000 y=1000
etch done x=0.800000 y=-1000
etch photo start x=1.200000 y=-1000
etch cont x=1.200000 y=1000
etch cont x=1.800000 y=1000
etch done x=1.800000 y=-1000
etch photo start x=2.200000 y=-1000
etch cont x=2.200000 y=1000
etch cont x=3.100000 y=1000
etch done x=3.100000 y=-1000
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If you use negative photoresist, the photoresist will be removed underneath all opaque regions.
DEPO PHOTO NEGATIVE THICK=1
EXPOSE MASK=POLY
DEVELOP
In this case, DECKBUILD will generate an alternative sequence of the ETCH statements.
etch photo start x=0.800000 y=-1000
etch cont x=0.800000 y=1000
etch cont x=1.200000 y=1000
etch done x=1.200000 y=-1000
etch photo start x=1.800000 y=-1000
etch cont x=1.800000 y=1000
etch cont x=2.200000 y=1000
etch done x=2.200000 y=-1000
Note: .sec files generated by SILVACO's MaskViews tool provide superior capabilities in the simulation grid generation
and mask processing control.
E.6: Aliases and substitutions for some statements
AMBIENT is alias for OXIDE.
DIFFUSION is alias for DIFFUSE.
Note: PRINT.1D issues a warning message if there is no SELECT statement prior to it.
ELIMINATE is not used in ATHENA and therefore is ignored. A warning is then issued. The
RELAX statement should be used instead. The RELAX capability is similar but more flexible since it
can be used in anywhere in the input deck.
ELECTRICAL and MOBILITY are not used in ATHENA and therefore are ignored. A warning is
issued. The EXTRACT capabilities of DECKBUILD should be used instead.
EXTRACT is not used within ATHENA and therefore is ignored. DECKBUILD has superior extract
capabilities. The EQUATION, REACTION, and INTERMEDIATE statements are not part of ATHENA.
Therefore, they are ignored.
LOADFILE is alias for INITIALIZE.
PLOT (in TSUPREM3 decks) is ignored and TONYPLOT should be used instead.
PLOT.1D, PLOT.2D, PLOT.3D, CONTOUR, LABEL, and COLOR statements are depreciated
in ATHENA. Warnings are issued. TONYPLOT should be used instead.
PRINT (in TSUPREM3 decks) is alias for PRINT.1D.
SAVEFILE is alias for STRUCTURE.
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E.7: Changes in the INITIALIZE statement
Boolean parameters <100>, <110>, and <111> that specify crystalline orientation of the silicon
substrate are aliases for ORIENTATION=100, ORIENTATION=110, and ORIENTATION=111.
DX.RATIO (new parameter) specifies maximum ration between adjacent mesh lines in
x-direction. It is equivalent to the same parameter in the MESH statement.
DY.RATIO (new parameter) specifies maximum ration between adjacent mesh lines in
y-direction. It is equivalent to the same parameter in the MESH statement.
IN.FILE is alias for INFILE.
RATIO is an alias for INTERVAL.R.
There are several additional ways to specify initial substrate doping. You can specify the impurity
name by using IMPURITY=<impname> parameter, where <impname> could be boron, phosphor,
arsenic, and antimony. You can specify the corresponding doping either by I.CONC=<conc> or
I.RESIST=<resistivity>. Alternatively, you specify the concentration of an individual impurity by using BORON=<conc>, PHOSPHOR=<conc>, and so on. Boolean parameters RESISTIVITY
and CONCENTRATION specify which method of initial doping specification to be used.
A one-dimensional grid structure can now be specified without using LINE statements (or their
equivalents MESH, MASK or loading of a .sec file from MASKVIEWS). The syntax of the INITIALIZE
statement of SSUPREM3 and its derivatives can be used:
• DX specifies the nominal grid spacing in the initial grid.
• MIN.DX specifies the minimal grid spacing.
• SPACES specifies the number of the grid spaces in the initial structure.
• THICKNESS specifies total thickness of the initial structure.
• TIF is ignored. ATHENA uses SILVACO Structure File (SSF) format.
• XDX specifies the distance from the top of the initial structure at which nominal grid spacing
is placed.
E.8: Changes in the DEPOSIT statement
There are several additional ways to specify doping in the deposited layer. You can specify the
impurity name by the IMPURITY=<impname> parameter, where <impname> could be boron, phosphor, arsenic, and antimony. You can specify the corresponding doping either by I.CONC=<conc>
or I.RESIST=<resistivity>. Alternatively, you specify the concentration of an individual
impurity by using BORON=<conc>, PHOSPHOR=<conc>, and so on. Boolean parameters
RESISTIVITY and CONCENTRATION specify which method of the doping specification to be used.
ARC.SPACE is an alias for MIN.SPACE.
To provide compatibility with SSUPREM3, the following aliases have been introduced:
• DX for DY
• XDX for YDY
• MIN.DX for MIN.DY
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E.9: Changes in the DIFFUSE statement
There are several additional ways to specify impurity concentration in the ambient gas. You can
specify the impurity name using the IMPURITY=<impname> parameter, where <impname> could
be boron, phosphor, arsenic, and antimony. You can specify the corresponding concentration by
I.CONC=<conc>. Alternatively, you can specify concentration of an individual impurity by using
BORON=<conc>, PHOSPHOR=<conc>, and so on.
The new parameter SS.IMPURITY (where the generic name IMPURITY could be substituted by
any standard impurity name) specifies that concentration of the named impurity in the ambient
gas is set to its solid solubility in silicon at the current temperature.
E.10: Changes in the ETCH statement
TRAPEZOI is an alias for the DRY.
If THICKNESS is not specified, it assumed to be infinite.
E.11: Changes in the STRUCUTURE (SAVEFILE) statement
OUT.FILE is an alias for OUTFILE.
TIF, DEVICE, and MEDICI are ignored because ATHENA and other SILVACO TCAD tools use
the universal SSF data format.
E.12: Changes in the IMPLANT statement.
D.PLUS is an alias for PLUS.ONE and UNIT.DAMAGE.
D.SCALE is an alias for DAM.FACTOR.
IMPL.TAB is ignored. ATHENA usually uses the default set of implant tables. You can define
tables in the MOMENTS statement.
E.13: Changes in the ELECTRODE statement
BOTTOM is an alias for SUBSTRATE.
E.14: Changes in the METHOD statement
OX.ADAPT, IMP.ADAPT, and DIF.ADAPT are aliases for ADAPT.
PD.FERMI is an alias for FERMI.
PD.TRANS is an alias for TWO.DIM.
PD.FULL is an alias for FULL.CPL.
E.15: Changes in the MATERIAL statement
E.FIELD specifies that the electric field terms are to be accounted for in the diffusion calculations.
This parameter is always set to TRUE in semiconductors.
POLYCRYS is an alias for the POLY.DIFF parameter in the METHOD statement.
Silvaco
E-8
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Silvaco
Index
A
Adaptive Meshing
Adaptive Meshing Control ............................................... 2-89
Base Mesh Formation .................................................... 2-89
Heat Cycle.............................................................. 2-87-88
Interface Mesh Control .............................................. 2-89-94
Ion Implantation ............................................................ 2-86
Advanced Diffusion Model Examples
Cowern’s Experiment ..................................................... 3-39
Implantation Diffusion Experiment ................................ 3-41-43
Pelaz Experiment ..........................................................3-40
Predeposition .......................................................... 3-36-37
Advanced Diffusion Models ............................................ 3-23-43
Classical Model of Dopant Diffusion (CNET)................... 3-24-31
Electrical Deactivation and Clustering (DDC) .................. 3-34-36
Interstitials Clusters (IC)............................................. 3-31-33
Solid Solubility .............................................................. 3-31
Vacancy Cluster (VC)......................................................3-33
See also PLS Diffusion Models
Advanced Features
Deposition and Wet/Dry Etching .................................. 2-59-64
MaskViews ............................................................. 2-65-73
Structure Manipulation Tools....................................... 2-56-59
Analytic Implant Models
Dual Pearson ............................................................... 3-68
Gaussian..................................................................... 3-66
Pearson ................................................................. 3-66-68
Screen Oxide Thickness Parameter (S.OXIDE).................... 3-70
SIMS-Verified Dual Pearson (SVDP) Model......................... 3-69
Arrhenius expression ...........................................................3-3
ATHENA Features and Capabilities ..................................... 1-2-3
ATHENA Input/Output ..........................................................2-7
Input .............................................................................2-7
Output ..........................................................................2-8
Standard Structure File Format(SSF) ...................................2-8
ATHENA/OPTOLITH
CD Extraction, Smile Plots, And Looping Procedures ....... 2-84-85
Illumination System................................................... 2-77-79
Imaging Control ....................................................... 2-80-82
Mask ..................................................................... 2-74-77
Material Properties ........................................................ 2-82
Projection System .................................................... 2-79-80
Structure Exposure................................................... 2-82-84
athenaimp .........................................................................2-7
athenamod ......................................................... 2-4, 2-7, 6-5
athenamod.97 ....................................................................2-6
athenares ..........................................................................2-7
B
Bank-Weiser Error Estimator ............................................... 2-88
Basic Diffusion and Oxidation Models.................................... 2-40
Silvaco
Beam Propagation Method (BPM) ..........................5-9, 5-17, D-9
Bimolecular Recombination ................................................. 3-30
Binary Collision Approximation (BCA) .................................... 6-45
Bipolar Process Flow ................................................... 2-48-53
Conclusions ................................................................. 2-53
The Base Current Profile – Low Injection ...................... 2-52-53
The Base Current Profile – Medium Injection ................. 2-51-52
Tuning Base and Collector Currents – All Regions ................ 2-49
Tuning the Base Current – All Regions ............................... 2-49
Tuning the Collector Current – All Regions .......................... 2-50
Buzz Saw Model............................................................... 4-21
See also Hard Polish Model
C
Changing the Method Statement During the Process Flow
Switching Guidelines................................................ 2-31-32
Charge States
CNET ................................................................... 3-24-25
Chemical and Active Concentration Values ............................... 3-1
Chemical Mechnical Polish (CMP)
Hard Polish Model ................................................... 4-21-22
Soft Polish Model .................................................... 4-23-24
C-Interpreter ................................................ 3-89, 4-19, A-1-2
CNET Charge States
Dopant-Defect pairs ................................................. 3-25-26
Point Defects.......................................................... 3-24-25
CNET Flux Equations
Dopant--Defects Pairs .............................................. 3-27-28
Point Defects.......................................................... 3-26-27
CNET Generation-Recombination Terms
Formation of Pairs ......................................................... 3-29
Frenckel Pair Recombination ..................................... 3-29-30
Compound Semiconductor Simulation
Diffusion Models ........................................................... 3-93
Ion Implantation Models .................................................. 3-94
Concentration Jump Condition ............................................... 3-4
Continuity Equation ............................................................. 3-2
See also Diffusion Equation
Correct Substrate Depth Modelling
Diffusion................................................................ 2-37-38
Ion Implantation ...................................................... 2-34-36
D
Damage Amorphization Model .............................................. D-7
See also Implant Damage
DDC
Arsenic ................................................................. 3-35-36
Boron ................................................................... 3-33-34
Phosphorus ................................................................. 3-35
Deactivation Threshold................................................. 3-18-19
Deal-Grove Model ............................................................. 3-59
Index-1
ATHENA User’s Manual
DeckBuild ................................................ 2-1-2, 6-100, 6-109
Batch Mode.................................................................... 2-5
Interactive Mode ............................................................. 2-5
No Windows Batch Mode .............................................. 2-5-6
Running ATHENA inside ................................................... 2-6
defect............................................................................... 3-1
Defect Diffusion
Time Step Control.......................................................... 3-16
DEPOSIT .................................................................. 6-21-23
Deposition Models................................................ 3-91, 4-4-11
CVD ............................................................................. 4-4
Conformal...................................................................... 4-4
Conical ................................................................... 4-9-10
Custom .........................................................................................4-11
Doped Layers ...............................................................3-91
Dual Directional .......................................................... 4-5-6
Epitaxy Simulation .........................................................3-91
Grid Control .................................................................3-91
Hemispheric ............................................................... 4-6-7
Monte Carlo ........................................................... 4-10-11
Planetary................................................................... 4-7-9
Unidirectional ............................................................. 4-4-5
Deposition Wet/Dry Etching
Defining ELITE Deposition Machines ........................... 2-61-62
Defining ELITE Etch Machines .................................... 2-63-64
Modifying ATHENA/ELITE Default Machines ....................... 2-60
Using A Specified Etch Machine ....................................... 2-64
Development Models
Dill ............................................................................. 5-13
Hirai ........................................................................... 5-14
Kim ...................................................................... 5-13-14
Mack .......................................................................... 5-14
Trefonas...................................................................... 5-14
Development Modules.................................................. 5-13-14
Device Structure ........................................................... 2-7-29
Diffusion Equation ........................................................... 3-3-4
Diffusion Models .................................................. 3-1-22, 3-92
Electrical Deactivation and Clustering Models ................ 3-18-20
Fermi........................................................................ 3-5-6
Fully Coupled Model ................................................ 3-16-18
Impurity Segregation .................................................... 3-6-7
Steady State ................................................................ 3-15
Two Dimensional....................................................... 3-7-16
Dislocation Loop Based Enhanced Bulk Recombination............. 3-15
Dislocation Loops.............................................................. 3-15
DLTS ............................................................................... 3-2
dopant ...............................................................................3-1
Dose Loss Model ................................................................ 3-7
See also Interface Trap
E
Electrical Deactivation and Clustering Models
Electrical Activation Model......................................... 3-19-20
Transient Activation Model............................................... 3-20
Epitaxy Simulation............................................................. 3-91
ERFG model.................................................................... 3-58
Silvaco
Etch Models...................................................... 3-92, 4-12-19
Isotropic ..................................................................... 4-12
Linear ........................................................................ 4-18
Monte Carlo ........................................................... 4-14-19
Plasma....................................................................... 4-14
RIE....................................................................... 4-12-13
Exposure Module .......................................................... 5-9-11
Resist exposure with accounting dose effect ....................... 5-11
Resist exposure without accounting dose effect................... 5-11
F
Flux Equations
CNET ................................................................... 3-26-28
Flux Expression ................................................................. 3-4
Flux Jump Condition ........................................................... 3-4
Free Point Defect Damage ................................................. 3-87
Fresnel diffraction .................................................... 5-15, 5-16
Fully Coupled Equations
CNET ........................................................................ 3-26
Fully-Coupled Model
High Concentration Extension ......................................... 3-17
RTA Diffusion Modelling................................................. 3-18
G
Generation-Recombination Terms
CNET ................................................................... 3-29-30
Grain-based Polysilicon Diffusion Models ......................... 3-21-22
Two stream ................................................................. 3-21
Grid Control ........................................................... 2-19, 6-68
Gummel Plot ................................................................... 2-48
H
Helmholtz equation ............................................................. 5-9
Huygens diffraction approximation ....................................... 5-15
I
Imaging Module .............................................................. 5-2-6
impurity............................................................................ 3-1
Impurity Segregation Model ............................................... 3-6-7
Interface Trap ................................................................ 3-7
Initial Structure
Electrodes ............................................................. 2-26-28
Initial Substrate ....................................................... 2-14-16
Rectangular Grid ....................................................... 2-8-14
Reducing Grid Points in Non-Essential Areas
using the Relax Parameter ..................................... 2-22-25
Reflecting a Structure in the “Y” Plane
using the Mirror Parameter..................................... 2-25-26
Simple Film Depositions............................................ 2-16-19
Simple Geometrical Etches........................................ 2-20-22
Structure File for Plotting or Initializing an ATHENA
Input file for Further Processing............................... 2-28-29
Ion Implantation Models....................................... 3-66-89, 3-93
Analytic ................................................................. 3-66-70
Monte Carlo ................................................................ 3-77
Index-2
Index
Multi-Layer ............................................................. 3-70-72
Stopping Powers in Amorphous Materials and
Range Validation .................................................. 3-89-90
Two-Dimensional Implant Profiles ................................ 3-72-75
Ion Implantation Damage
C-Interpreter ................................................................ 3-89
Cluster Model ............................................................... 3-88
Dislocation Loops Model ................................................. 3-88
Plus 1 Model ................................................................ 3-87
Kinchin-Pease model .................................................. D-7, D-8
Klaassen bandgap narrowing model ......................................2-52
MOSFET Process Flow
Conclusion................................................................... 2-47
Input..................................................................... 2-42-43
PMOS Tuning............................................................... 2-46
Predictive Powers of Tuned Process Parameters Checking .... 2-47
Tuning Diffusion Parameters............................................ 2-46
Tuning Implantation Parameters ....................................... 2-45
Tuning Oxidation Parameters..................................... 2-43-44
Using ATLAS for MOS Process Tuning ........................ 2-46-47
Multi-Layer Implants
DOSE.MATCH.............................................................. 3-70
MAX.SCALE ................................................................ 3-71
MOM.SCALE.......................................................... 3-71-72
RP.SCALE................................................................... 3-71
L
N
Linear Rate Constant
Chlorine Dependence..................................................... 3-54
Doping Dependence ................................................. 3-55-56
Orientation Dependence ................................................. 3-52
Pressure Dependence.................................................... 3-53
LPCVD........................................................................... 4-10
Lithography .....................................................................5-15
Nuclear Scattering............................................................. 3-77
K
M
MaskViews
Generating Masks in ATHENA .................................... 2-71-73
Initial Rectangular Grid ................................................... 2-65
Medium Injection
Bandgap Narrowing Effects ............................................. 2-52
Poly-emitter work function ............................................... 2-51
Modelling the Correct Substrate Depth. See Correct Substrate Depth
Modelling
Modified Gaussian Function (MGF)....................................... 3-75
Monte Carlo Etching Model
Incoming Ions and Neutrals ............................................. 4-15
Ion and Neutral Fluxes .............................................. 4-15-17
Polymer Fluxes............................................................. 4-17
Rates ......................................................................... 4-18
Monte Carlo Implant Models
Amorphous Material.................................................. 3-84-85
C-Interpreter ................................................................ 3-89
Cluster Model ............................................................... 3-88
Crystalline Material ........................................................ 3-85
Damage Accumulation Model...................................... 3-81-82
Dislocation Loops Model ............................................ 3-88-89
Electronic Stopping................................................... 3-80-81
Implantation Geometry .............................................. 3-82-84
Interatomic Potential ...................................................... 3-79
Ion Implantation Damage ................................................ 3-87
Nuclear Stopping ..................................................... 3-77-79
Physical Problems......................................................... 3-77
Plus 1 Model ........................................................... 3-87-88
Statistical Sampling .................................................. 3-85-87
Solution ...................................................................... 3-77
Monte Carlo Implant Module................................................ 6-45
Index-3
O
Operation Modes ............................................................ 2-5-6
Optical System ............................................................... 5-7-8
Ostwald ripening ............................................................... 3-11
Oxidation Models .......................................... 3-44-63, 6-67-68
Analytical............................................................... 3-58-59
Compress.............................................................. 3-47-48
Linear Rate Constant ............................................... 3-50-51
Mixed Ambient.............................................................. 3-58
Numerical .................................................................... 3-46
Parabolic Rate Constant ................................................. 3-57
Viscous ................................................................. 3-48-50
Oxidation Simulation Recommendations
Growing Thin Oxides................................................ 3-59-60
Implantation Through Thermally-Grown Oxides
and Dopant Loss During Subsequent Annealing ............. 3-60-61
Oxidation Enhanced Diffusion (OED) .................... 3-5, 3-61-63
Oxidation Retarded Diffusion (ORD) ............................ 3-61-63
P
Pair Diffusion ..................................................................... 3-1
Parabolic Rate Constant
Chlorine Dependence .....................................................3-57
Pressure Dependence .................................................... 3-57
Pearson Differential Equation .............................................. 3-67
Photoresist Bake............................................................... 5-12
Physically-Based Simulation.................................................. 1-4
Plasma Etching Model
Dopant Enhanced Etching ............................................... 4-14
PLS Diffusion Models................................................... 3-23-43
PLS Diffusion Models Examples..................................... 3-37-43
See also Advanced Diffusion Models Examples
point defect........................................................................ 3-1
Proximity Printing
Lithography ..................................................................5-15
Simulation Method .........................................................5-17
Theory of ........................................................... 5-15–5-16
Silvaco
ATHENA User’s Manual
R
T
Rapid Thermal Anneals (RTA)
Epitaxy.................................................................. 2-40-41
Notes.......................................................................... 2-38
Oxidation..................................................................... 2-39
Recombination at the Surface
CNET ................................................................... 3-30-31
Reflow Model ................................................................... 4-20
reverse short channel effect
RSCE ........................................................................ C-10
RTA Diffusion Modeling ......................................................3-18
Technical Support .............................................................. 1-1
TonyPlot ...................................................................... 6-108
Trap Equation ................................................................. 3-10
Two Dimensional Model
Defect Diffusion............................................................ 3-16
Dislocation Loop Based Bulk Recombination ...................... 3-15
Dopants ....................................................................... 3-7
Interstitial Generation .................................................... 3-12
Interstitials ............................................................... 3-9-11
Recombination at Interfaces....................................... 3-12-14
Vacancies.............................................................. 3-14-15
Two-Dimensional Implant Profiles
Convolution Method ................................................. 3-72-73
Depth-Independent Lateral Distribution.............................. 3-73
Gaussian Lateral Distribution Function .............................. 3-73
Implant Parameters in the Moments Statement .................... 3-76
Lateral Standard Deviation.............................................. 3-74
Non-Gaussian Lateral Distribution Functions....................... 3-75
Parabolic Approximation of Depth-Dependent Lateral
Distribution............................................................. 3-74-75
Using PRINT.MOM for Extraction of Spatial Moments ........... 3-76
S
Second Order Fick’s Equation................................................ 3-3
SiGe Process Simulation
DIFFUSE...................................................... 2-55, 6-25-27
MATERIAL ................................................... 2-54, 6-62-63
METHOD..................................................... 2-54, 6-64-69
SiGe/SiGeC Simulation ................................................ 3-95-96
Silicidation Model ........................................................ 3-64-65
Solid Solubility................................................................ B-7-8
See also Deactivation Threshold
SSUPREM4................................................... 2-30-41, 3-1-96
Calibrating ATHENA for a Typical Bipolar
Process Flow .......................................................... 2-48-53
Changing the Method Statement During
the Process Flow..................................................... 2-31-32
Choosing an Appropriate Model.................................. 2-30-31
Modelling the Correct Substrate Depth ......................... 2-32-38
Multiple Models............................................................. 2-30
Process Steps .............................................................. 2-30
Rapid Thermal Anneals (RTA).......................................... 2-38
SiGe Process Simulation........................................... 2-54-55
Standard Examples ......................................................... 2-2-4
Statistical Sampling
rare event trajectory splitting technique............................... 3-85
rare events................................................................... 3-85
restart ......................................................................... 3-85
trajectory splitting .......................................................... 3-85
std-tables ........................................................................ 3-76
Stress Models
Stress History .............................................. 6-69, 3-97, D-8
String Algorithm .............................................................. 4-2-3
Structure Exposure
Development .......................................................... 2-83-84
Post Development Bake.................................................. 2-84
Post Exposure Bake....................................................... 2-83
Structure Manipulation Tools
ATHENA In 1D Mode ..................................................... 2-58
Stretch ........................................................................ 2-56
Structure FLIP .............................................................. 2-56
Surface Recombination
CNET ................................................................... 3-30-31
SVDP implant models .................................................. 3-69-70
See Analytic Implant Models
Silvaco
U
userimp .......................................................................... 3-76
Using ATHENA With Other Silvaco Software ......................... 1-3-4
V
vacancy flux expression ..................................................... 3-14
Index-4
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