The First Solid-State Systems Symposium – VLSIs & Related Technologies (4S-2010) 275 A MOSFET parameter extraction tool using EKV model and Matlab Le Duc Hung, Vo Thanh Tri, Nguyen Thi Thien Trang Faculty of Electronics and Telecommunications University of Science – VNUHCM Abstract—This paper presents a MOSFET parameter extraction tool using Matlab. The purpose of this tool is to extract parameters to characterize CMOS devices. Parameter extraction is implemented in behavior of transistors in conditions which consist of long-wide devices, short-wide devices and long-narrow devices. The program has GUI interface, easy-to-use. It can import measurements data, manage and save MOSFET parameters, display voltage – current characteristics, etc. Keywords: parameter extraction, MOSFET, Matlab, Gui interface 1. INTRODUCTION There are a lot of parameter extraction tools for MOSFET devices, however most of them are too expensive to own. The popular parameter extraction tools can be listed as IC-CAP, UTMOST, etc. The objective of our project is developing an automated parameter extraction tool which is made in Vietnam. Our program will have low cost meanwhile we can also understand a whole parameter extraction process. Initially, we developed a core program and parameter extraction modules for MOS Level 1, 2, 3. All routines of the program have been based on Matlab. With the advantage of MATLAB in mathematics and computing, especially in numerical computation, statistics, we can develop our tool rapidly and effectively. The program can apply the most popular MOSFET models such as MOS level 1, 2, 3 and EKV. We also upgrade the PSP and BSIM models in the future. I ds Weff Cox 2 Leff (Vgs Vt )2 (1 Vds ) 2.2. MOSFET level 2 This model is identical to MOS level 1, except for DC current formulation and addition of sub-threshold region. This model also improves linear-to-saturation current characteristics. 2.3. MOSFET level 3 MOSFET level 3 describe the first- and second-oder effects: - The short, narrow channel and Drain induced barrier lowering effect the threshold voltage. - Carrier mobility dependence (degradation) on both the transversal and longitudinal components of the electric field. - Saturation of carrier’s velocity. - Channel length modulation. - Weak inversion conduction. - The effect of temperature. 2.3.1. Threshold voltage Threshold voltage is defined as, 2. MODELS VTH VFB 2F V . fs 2F VBS fn(2F VBS ) 2.1. MOSFET level 1 MOSFET level 1 or Shichman-Hodges FET model provides square-law characteristic and includes two gate junction capacitances. Equation of drain current in linear region is given as, I ds ,lin And in saturation region: Weff C ox Leff Vds 2 (V gs Vt ).Vds 2 Identify applicable sponsor/s here. (sponsors) VFB 2F VTO. 2F With V ETA. 5.15E 22 .VDS is the increase threshold Cox.L3 voltage by DIBL effect (Drain-Induced Lowering). γ is body factor effect. Fs = correction factor of short channel effect. Barrier 276 The First Solid-State Systems Symposium – VLSIs & Related Technologies (4S-2010) 1 fs 1 Leff If VMAX is not specified, Vdsat is written as follow: 1/ 2 Wp 2 (Wc LD) 1 ( ) LD Xj W p V D SA T V gs V T H 1 FB fn = correction factor of narrow channel effect. fn DE LT A 2.3.6 Channel Length Modulation si 2 C oxW ff LD is the lateral diffusion length, ETA, XJ, DELTA are model parameters. VTO is threshold voltage at Vbs = 0V. L 2.3.2. Drain current equation Model’s author proposed a unique Ids equation for all MOSFET operation regions. It is formulated as: 1 FB I DS VGS VTH VDS VDE 2 W L a VDSAT (V V ) V KAPPA. DS DSAT DSAT 2.a.Leff a 2.a.Leff q.NUSB 2. Si NSUB is substrate doping parameter which is extracted from body-factor effect. KAPPA is also a model parameter. With eff Cox When VDS become greater than VDSAT, channel length will be reduced. The channel length reduction, ΔL, is formulated as follow: If VMAX is not specified, channel length reduction is written as: VDE MINV ( DS,VDSAT ) 1 . fS FB fn 4 2F VBS KAPPA.(Vds Vdsat ) 2 L a Finally, the full Ids equation is rewritten as: 2.3.3 Mobility modulation by the gate voltage In MOSFET level 3 model, model’s author proposed a simple equation to explain the decrease of carrier mobility by vertical electric field. U0 s (*) 1 THETA(Vgs VTH ) UO is carrier mobility at low electric field. THETA is a model parameter. e ff s s .V D E 1 V M A X . L e ff 2.3.7 Weak inversion conduction In the weak inversion region, model level 3 proposed an equation which provides both the continuity of the drain current, the proper bias dependence and sufficient computational efficiency. Von Vt n. VMAX is mode parameter, must be extracted from experimental values. µs is calculated as previous equation, VDE = min (VDS, VDSAT). If VMAX is not specified, µeff = µs. 2.3.5 Saturation voltage The saturation voltage of short-channel MOSFET is defined as the Drain voltage at which the carriers reach the maximum velocity. The LEVEL 3 model determines the saturation voltage (VDSAT) due to the channel pinchoff at the drain side. The VMAX parameter specifies the reduction of the saturation voltage due to the carrier velocity saturation effect. 2 VDSAT W 1 FB VGS VTH VDS VDE L L 2 I ds Ione 2.3.4 Velocity saturation Velocity saturation affects carrier mobility as follow: IDS eff Cox 2 VGS VTH VMAX.L VGS VTH VMAX.L 1 FB S 1 FB S q (Vgs Von )/ nkbT kb .T q 1/2 q.NFS 1 fs . .(2 f Vbs ) fn.(2 f Vbs ) n 1 Cox Cox 2(2 f Vbs ) NFS is also a model parameter. 2.3.8 Temperature effect Model level 3 provides the effect of temperature on carrier mobility. At the higher temperature, mobility decreases. As the result, the drain current is also reduced. The relationship between temperature and mobility is formulated as follow: T (T ) (Tnorm ). Tnorm BEX In this equation, Temperature is measure on Kelvin absolute temperature scale and Tnorm is the room The First Solid-State Systems Symposium – VLSIs & Related Technologies (4S-2010) temperature. µ(Tnorm) is carrier mobility which is measured at Tnorm. BEX is a model parameter that default value is -1.5. 277 simulating and compare with experimental values: IDSVGS, IDS-VDS, gm, gDS. With simulation function, we can check the error between simulated value and experimental values one by one. 3. MODEL IMPLEMENTATION USING MATLAB GUI This senior project focuses on developing software which the main function is to extract model parameters automatically. We base on MOSFET level 1, 2, 3 models. Based on this result, we can upgrade for other models such as EKV, BSIM, etc. You can image the function of the software as following figure: With Matlab, we easily build a simple but effective graphic user interface (GUI). The program is flexibility with the database system and results of each parameter extraction methodology can be compared to the default result for each model. Extracted parameter values are showed in table below as using MOSFET level 3 model: Default value Extracted value 0.848 0.686 V 600 627.3 2 cm /V.s THETA 0 0.032 V-1 DELTA 0 1.161 XJ 0 0 M NSUB 1E+15 6.67E+15 cm-3 VMAX 0 8.596E+4 m/s ETA 0 0.006 0.2 0.341 V-1 NFS 0 6.927E+11 cm-2 BEX -1.5 -1.5 Name VTO UO KAPPA Unit 4. RESULT The main GUI is the following figure: Figure 4.2 shows the transfer characteristics ID vs. V G , ID vs. V D, g m vs. V GS, g ds vs. VDS with longwide-channel device. The transfer characteristics shown on Figure 4.3 demonstrate the influence of short channel effects. Figure 4.1. Main GUI Providing three data input files, wide- long-channel device, narrow- long-channel device and wide- shortchannel device respectively, the program can plot the diagrams which manifest relationship between values, or calculate and show automatically extracted parameters which describe the behavior of devices. To obtain model parameters, the software use a lot of algorithms, such as regression, interpolate, extrapolate, etc. which based on extraction methods. After extracting all model parameters, the software permits us to export them to text file or database. The software can implement simultaneously many tasks corresponding to different samples of devices by database system. We also use these extracted parameters for Figure 4.2. W/L = 50µm/50µm 278 The First Solid-State Systems Symposium – VLSIs & Related Technologies (4S-2010) Figure 12.4.1 W/L = 50µm/0.7µm The simulation results is quite accurate with a small error (see Figure 4.2). When channel length becomes smaller, however, the simulation results do not maintain the accuracy (see Figure 4.2). In that case, the simulation values is smaller the experimental values. This is the constraint of MOSFET Level 3. 5. CONCLUSION The paper presents characteristics and behavior based on the MOSFET models using open source Matlab implementation of the program code. The simulation results of the modeled characteristics show good accuracy in all operational regions. The applicability, flexibility and usefulness of this tool is clearly demonstrated. 6. REFERENCES [1] Daniel Foty, “MOSFET Modeling with SPICE: Principles and Practice”, Prentice Hall, 1997. [2] Y. P. Tsividis, “Operation and Modeling of the MOS Transistor”, McGraw-Hill, 1987. [3] H. G. Lee, S. Y. Oh and g. Fuller, “A simple and accurate Method to Measure the Threshold Voltage of an Enhancement-Mode MOSFET”, Trans. On Elec. Device, Vol. ED-29, No.2, 1982. [4] Y. Tsividis and K. Suyama, “MOSFET Modeling for Analog Circuit CAD: Problems and Prospects”, JSSC, Vol. 29, No. 3, 1994 [5] A.I.A. Cunha, M.C. Schneider and C. Galup-Montoro, “An explicit physical model for the long channel MOS transistor including small-signal parameters”, SolidState Electronics 1945-1952, 1995. [6] “HSPICE User's Manual: Elements and Device Models, Volume II”, Meta-Software Inc., pp. 16103–16-113, 1996

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