Design and Control of a Self-Sensing Piezoelectric

Design and Control of a Self-Sensing Piezoelectric
Design and Control of a Self-Sensing Piezoelectric
Reticle Assist Device
by
Darya Amin-Shahidi
Submitted to the Department of Mechanical Engineering
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
June 2013
c Massachusetts Institute of Technology 2013. All rights reserved.
Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Department of Mechanical Engineering
May 20, 2013
Certified by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
David L. Trumper
Professor of Mechanical Engineering
Thesis Supervisor
Accepted by . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
David E. Hardt
Chairman, Department Committee on Graduate Theses
2
Design and Control of a Self-Sensing Piezoelectric Reticle
Assist Device
by
Darya Amin-Shahidi
Submitted to the Department of Mechanical Engineering
on May 20, 2013, in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
Abstract
This thesis presents the design and control techniques of a device for managing the
inertial loads on photoreticle of lithography scanners. Reticle slip, resulting from large
inertial loads, is a factor limiting the throughput and accuracy of the lithography
scanners. Our reticle-assist device completely eliminates reticle slip by carrying 96%
of the inertial loads. The primary contributions of this thesis include the design and
implementation of a practical high-force density reticle assist device, the development
of a novel charge-controlled power amplifier with DC hysteresis compensation, and
the development of a sensorless control method.
A lithography scanner exposes a wafer by sweeping a slit of light passing through
a reticle. The scanner controls the motion of the reticle and the wafer. The reticlestage moves the photoreticle. To avoid deforming the reticle, it is held using a vacuum
clamp. Each line scan consists of acceleration at the ends of the line and a constantspeed motion in the middle of the line, where exposure occurs. If the reticle’s inertial
force approaches or exceeds the clamp’s limit, nanometer-level pre-sliding slip or
sliding slip will occur. The assist device carries the inertial load by exerting a feedforward force on the reticle’s edge. The device retracts back during the sensitive
exposure interval to avoid disturbing the reticle. The reticle is at the heart of the
scanner, where disturbances directly affect the printing accuracy.
Our reticle assist device consists of an approach mechanism and a piezoelectric
stack actuator. The approach mechanism positions the actuator 1-µm from the reticle edge. The actuator, with 15-µm range, extends to push on the reticle. We have
developed control techniques to enable high-precision high-bandwidth force compensation without using any sensors. We have also developed a novel charge-controlled
amplifier with a more robust feedback circuit and a method for hysteresis compensation at DC. These technologies were key to achieving high-bandwidth high-precision
sensorless force control. When tested with a trapezoidal force profile with 6400 N/s
rate and 60 N peak force, the device canceled 96% of the inertial force.
3
Thesis Supervisor: David L. Trumper
Title: Professor of Mechanical Engineering
4
Acknowledgments
I would like to thank my thesis advisor Professor David L. Trumper for his unconditional support and invaluable feedback throughout the years of my studies. His
teachings and tips provided me with the opportunity to successfully complete each
and every one of my projects. He gave me the freedom to explore and consequently
learn a great amount. He has trusted me with numerous opportunities which were important to my professional development. Throughout the years, he created a friendly
and productive environment for us in the laboratory. It has been an honor and
privilege to work with him.
I would also like to thank my thesis committee for giving me their time and support
and providing me with invaluable feedback. Professor Alex H. Slocum’s energy and
knowledge was an inspiration to me. Not only has he assisted me with my thesis,
but he has also been a wonderful mentor both academically and professionally. I
would like to thank Professor Markus Zahn who taught me important concepts in
electromagnetism. He has been very kind in putting aside his time for my thesis
and closely monitoring my progress. I would also like to thank Professor Martin L.
Culpepper who helped me early on in identifying important research problems and
directing my efforts.
I would like to thank ASML for their collaboration and financial support. I would
like to thank Stephen Roux who was my manager during my internship at ASML. His
support and input was instrumental to the realization of this project. I would also
like to thank Mark Schuster and Christopher Ward for their constant involvement
and feedback. I would like to thank Santiago Del Puerto and Enrico Zordan whose
initial work on the reticle slip problem was a great resource to this project.
I would like to thank National Instruments for the hardware donation and their
technical support. I especially thank Lesley Yu, NI field engineer for her time and
technical support.
My dear labmates created a very friendly atmosphere in our labratory and offered
me their help. I had many stimulating discussions with Mohammad Imani Nejad. He
5
shared his knowledge in manufacturing with me and patiently answered many of my
questions. I enjoyed working with Ian MacKenzie on the control of the reluctance
actuators. Lei Zhou, Zehn Sun, Minkyun Noh, and Jun young Yoon helped me with
using the macro-scale AFM for teaching mechatronics. Roberto Melendez introduced
me to the nice people at MIT Sailing Pavilion and taught me sailing.
I would also like to thank Laura Zaganjori for her efficient and helpful administrative support. I would also like to thank the mechanical department office staff,
especially Leslie Regan. I would like to thank my friends with whom I have spent
many hours either socializing or playing sports. They have made my life a lot more
interesting and enjoyable.
I am indebted to my parents for their boundless support throughout my life and
up until today, without them I would not have been where I am at this moment.
Sophiya Shahla, my wife, has made tremendous sacrifice for my study. She has been
a great friend and has helped me in every step of the way. I thank her for being
extremely supportive and understanding.
This work was sponsored by ASML and performed at the Massachusetts Institute
of Technology.
6
To My Grandparents
7
8
Contents
1 Introduction
27
1.1
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
28
1.2
Prior Art
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
1.2.1
Modified Clamping Mechanisms . . . . . . . . . . . . . . . . .
29
1.2.2
Reticle Assist Devices
. . . . . . . . . . . . . . . . . . . . . .
31
Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37
1.3.1
Solid-State Reticle Assist Device
. . . . . . . . . . . . . . . .
38
1.3.2
Hybrid Charge Amplifier . . . . . . . . . . . . . . . . . . . . .
38
1.3.3
Self-Sensing Contact Detection . . . . . . . . . . . . . . . . .
42
1.3.4
Reticle Assist Device Control and Experimental Results . . . .
42
1.3
2 Reticle Slip Problem and Conceptual Solutions
51
2.1
Reticle Slip Problem . . . . . . . . . . . . . . . . . . . . . . . . . . .
51
2.2
Application Requirements . . . . . . . . . . . . . . . . . . . . . . . .
52
2.3
Conceptual Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . .
54
2.3.1
Piezoelectric Concept . . . . . . . . . . . . . . . . . . . . . . .
54
2.3.2
Magnetostrictive Concept . . . . . . . . . . . . . . . . . . . .
55
2.3.3
Electromagnetic Concept . . . . . . . . . . . . . . . . . . . . .
56
2.3.4
Piezo Stepping Motor Concept . . . . . . . . . . . . . . . . . .
57
2.3.5
Pneumatic/Hydraulic Bellow Concept . . . . . . . . . . . . . .
57
Concept Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
58
2.4
9
3 High-Force-Density Reticle Assist Device
3.1
3.2
61
Fine Stage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
3.1.1
Piezoelectric Actuator . . . . . . . . . . . . . . . . . . . . . .
63
3.1.2
Pushing Tip Design . . . . . . . . . . . . . . . . . . . . . . . .
63
Coarse Stage
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
65
3.2.1
Guide Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
3.2.2
Preload Actuator . . . . . . . . . . . . . . . . . . . . . . . . .
70
3.2.3
Clamp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
72
3.3
Designs for Integration . . . . . . . . . . . . . . . . . . . . . . . . . .
73
3.4
Magnetostrictive Actuator . . . . . . . . . . . . . . . . . . . . . . . .
73
3.4.1
Thermally-Balanced Configuration . . . . . . . . . . . . . . .
75
3.4.2
Magnetic Design . . . . . . . . . . . . . . . . . . . . . . . . .
76
3.4.3
Mechanical Design . . . . . . . . . . . . . . . . . . . . . . . .
77
4 Hybrid Charge Controller
81
4.1
Prior Art Charge Amplifiers . . . . . . . . . . . . . . . . . . . . . . .
82
4.2
Analysis of Conventional V-Q Charge Amplifier . . . . . . . . . . . .
86
4.3
Novel V-Q-V Charge Amplifier . . . . . . . . . . . . . . . . . . . . .
92
4.4
Charge Amplifier Hardware . . . . . . . . . . . . . . . . . . . . . . .
95
4.4.1
Mechanical Design . . . . . . . . . . . . . . . . . . . . . . . .
95
4.4.2
Circuit Design . . . . . . . . . . . . . . . . . . . . . . . . . . .
96
4.5
Hybrid Hysteresis Compensation . . . . . . . . . . . . . . . . . . . . 100
4.6
Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.7
Magnetic Analogue . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.8
4.7.1
Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . 110
4.7.2
Magnetic-Flux Sensing and Control . . . . . . . . . . . . . . . 113
4.7.3
Force Control . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
4.7.4
Position Control . . . . . . . . . . . . . . . . . . . . . . . . . . 128
4.7.5
Finite Element Analysis . . . . . . . . . . . . . . . . . . . . . 132
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
10
5 Self-Sensing Contact Detection
141
5.1
Prior Art Self-Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.2
Self-Sensing Contact-Detection Principle . . . . . . . . . . . . . . . . 144
5.3
5.4
5.5
5.6
5.2.1
Piezoelectric Devices . . . . . . . . . . . . . . . . . . . . . . . 144
5.2.2
Electromagnetic Devices . . . . . . . . . . . . . . . . . . . . . 148
Application to Piezoelectric Actuator . . . . . . . . . . . . . . . . . . 150
5.3.1
Self-Sensing Method . . . . . . . . . . . . . . . . . . . . . . . 151
5.3.2
Implementation on an FPGA . . . . . . . . . . . . . . . . . . 153
5.3.3
Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 155
Application to Atomic Force Microscope . . . . . . . . . . . . . . . . 158
5.4.1
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
5.4.2
High-Accuracy Atomic Force Microscope . . . . . . . . . . . . 159
5.4.3
Self-Sensing Probe . . . . . . . . . . . . . . . . . . . . . . . . 162
5.4.4
Frequency Measuring AFM . . . . . . . . . . . . . . . . . . . 163
5.4.5
Probe Electronics . . . . . . . . . . . . . . . . . . . . . . . . . 167
5.4.6
Tracking Controller . . . . . . . . . . . . . . . . . . . . . . . . 171
5.4.7
Tapping-Synchronous Controller Sampling . . . . . . . . . . . 175
5.4.8
Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 179
Application to Magnetic Self-Sensing Imager . . . . . . . . . . . . . . 182
5.5.1
Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5.5.2
Macro-Scale Magnetic AFM Probe . . . . . . . . . . . . . . . 183
5.5.3
Self-Actuation . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
5.5.4
Self-Sensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
5.5.5
Control System . . . . . . . . . . . . . . . . . . . . . . . . . . 186
5.5.6
Scanner Hardware
5.5.7
Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 193
. . . . . . . . . . . . . . . . . . . . . . . . 191
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
6 Reticle-Assist Device Control and Experimental Results
6.1
197
Control System Design . . . . . . . . . . . . . . . . . . . . . . . . . . 197
11
6.2
6.3
6.1.1
State-Machine Design . . . . . . . . . . . . . . . . . . . . . . . 197
6.1.2
System Architecture Designs . . . . . . . . . . . . . . . . . . . 201
6.1.3
Force Calibration and Control . . . . . . . . . . . . . . . . . . 203
6.1.4
Motion Control . . . . . . . . . . . . . . . . . . . . . . . . . . 206
6.1.5
Self-Sensing Contact Detection . . . . . . . . . . . . . . . . . 209
Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
6.2.1
Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . 209
6.2.2
Experimental Methods . . . . . . . . . . . . . . . . . . . . . . 212
6.2.3
Strain-Controlled Reticle Assist Experiment . . . . . . . . . . 215
6.2.4
Charge-Controlled Reticle Assist Experiment . . . . . . . . . . 218
6.2.5
Additional Experimental Results . . . . . . . . . . . . . . . . 222
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
7 Conclusions and Suggestions for Future Work
227
7.1
Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227
7.2
Suggestions for Future Work . . . . . . . . . . . . . . . . . . . . . . . 229
7.2.1
Design for Integration and Scan Testing . . . . . . . . . . . . 229
7.2.2
Charge Amplifier Automation . . . . . . . . . . . . . . . . . . 230
7.2.3
Macro-Scale AFM . . . . . . . . . . . . . . . . . . . . . . . . . 230
7.2.4
Thermally-Balanced Magnetostrictive Actuator . . . . . . . . 231
12
List of Figures
1-1 Schematic diagram of Nikon’s mechanical clamping mechanism invented by Shibazaki shown in open (left) and closed (right) positions.
Figure is taken from US Patent 8,253,929 [74]. . . . . . . . . . . . . .
30
1-2 Schematic diagram of ASML’s active clamping mechanism invented by
Baggen et al. Figure is taken from US Patent 7,459,701 [12]. . . . . .
31
1-3 ASML’s compliant clamp design invented by Enrico Zordan. Figure is
taken from US Patent Application 13/168,109 [87]. . . . . . . . . . .
32
1-4 Schematic drawing of Canon’s reticle assist device idea by Iwamoto.
Figure is taken from US Patent 6,469,773 [35]. . . . . . . . . . . . . .
33
1-5 Schematic drawing of ASML’s active pivoted reticle assist device idea
by Jacobs et al. Figure is taken from US Patent 7,667,822 [36]. . . . .
34
1-6 Schematic drawing of ASML’s reticle assist device idea by Baggen et
al. Figure is taken from US Patent 7,459,701 [12]. . . . . . . . . . . .
35
1-7 ASML’s reticle assist device design by Del Puerto and Zordan. Figure
is taken from US Patent Application 12/627,771 [69] . . . . . . . . .
35
1-8 ASML’s force-limiting pushing tip mechanism by Zordan. Figure is
taken from US Patent Application 13/022,247 [86]. . . . . . . . . . .
36
1-9 ASML’s solid-state reticle assist device idea by Amin-Shahidi. Figure
is taken from US Patent Application 13/281,718 [4]. . . . . . . . . . .
37
1-10 Photo (top) and CAD drawing (bottom) of the piezoelectric reticle
assist device. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
39
1-11 Photos of the charge amplifier box (left) and circuit board (right). . .
40
13
1-12 Piezoelectric actuator’s displacement versus reference command using
different control methods: voltage control (V-Ctrl), charge control (QCtrl), and inverse-hysteresis feedback compensation (Q-Ctrl & HHC).
41
1-13 Piezoelectric actuator’s voltage to current signals phase difference when
excited at its natural frequency shown versus the tip-reticle contact
force. The sharp change in the phase difference is used to detect tipreticle contact. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
43
1-14 The high-accuracy atomic force microscope (HAFM) is installed on the
sub-atomic measuring machine (SAMM). HAFM and the SAMM are
used to capture the inset image of the triangular grating. . . . . . . .
44
1-15 Macro-scale atomic force microscope profiler (MAP) is shown capturing
an image of an MIT key chain. . . . . . . . . . . . . . . . . . . . . . .
45
1-16 Time trace of the inertial load profile and the piezo charge reference
required for canceling the load generated by the control system. . . .
46
1-17 Assist device’s resulting compensation force versus the inertial load
plotted for 10 consecutive cycles. . . . . . . . . . . . . . . . . . . . .
47
1-18 Picture of the experimental setup used for testing and development of
the reticle assist device (RAD). . . . . . . . . . . . . . . . . . . . . .
48
1-19 The reticle motion relative to the stage as a result of a 60-N simulated
inertial load profile with and without using our reticle assist device
(RAD).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
49
2-1 Simplified diagram of a lithography scanner. . . . . . . . . . . . . . .
52
2-2 Conceptual design of a piezoelectric reticle assist device. . . . . . . .
55
2-3 Conceptual design of a magnetostrictive reticle assist device. . . . . .
56
2-4 Conceptual design of an electromagnetic reticle assist device, inspired
by actuator design of Lu [50]. . . . . . . . . . . . . . . . . . . . . . .
57
2-5 Piezo stepping motor concept. . . . . . . . . . . . . . . . . . . . . . .
58
14
3-1 CAD design of the reticle assist device. The device consists of two
sub-assemblies: a coarse approach mechanism and a fine actuation
mechanism. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
3-2 CAD model of the actuator used for exerting the pushing force on the
reticle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
62
3-3 CAD design of the coarse approach mechanism (top) and a crosssectional view (bottom); the top membrane is made transparent to
better show the coarse stage’s design. . . . . . . . . . . . . . . . . . .
66
3-4 CAD model and partial drawing of the coarse stage’s guide flexure
showing its design. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
68
3-5 Top-view of the coarse flexural stage (top) showing the flexure design.
The steps for the EDM manufacturing process are shown for one flexure
leg. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69
3-6 First two vibration modes of the reticle-assist device computed with
the vacuum clamp activated. . . . . . . . . . . . . . . . . . . . . . . .
70
3-7 CAD cross-sectional view of the coarse approach mechanism showing
the bellow and the vacuum clamp design. . . . . . . . . . . . . . . . .
71
3-8 Ideas for more efficient packaging of the reticle assist device into a ‘1L’
design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
74
3-9 Thermally-balanced actuation method: the actuator is shown in its
neutral position (a), positive extension (b), and negative extension (c).
75
3-10 An example embodiment of the thermally balanced solid-state actuator’s magnetic design using magnetostrictive elements. . . . . . . . .
76
3-11 CAD Model of the thermally-balanced magnetostrictive actuator design (top) and its cross-sectioned view (bottom). . . . . . . . . . . . .
79
4-1 Comstock’s charge amplifier design. This figure is copied from US
Patent 4,263,527 [15]. . . . . . . . . . . . . . . . . . . . . . . . . . . .
83
4-2 Charge amplifier design by Tonoli et al. The diagram has been reproduced from [82]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
84
4-3 Yi and Veillette’s charge amplifier design. The diagram has been reproduced from [84]. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
85
4-4 Fleming and Moheimani’s charge amplifier design. The diagram has
been reproduced from [24]. . . . . . . . . . . . . . . . . . . . . . . . .
85
4-5 PiezoDrive’s charge amplifier design. The diagram has been reproduced from [1]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
4-6 Block diagram of the charge amplifier design shown in Figure 4-5. . .
87
4-7 Charge amplifier design with the resistor Rc modeling the resistance of
the cable connecting the piezo actuator the amplifier . . . . . . . . .
89
4-8 Frequency responses of the amplifier open-loop GP A (s), feedback F(s),
loop transmission LT(s), and the closed loop CL(s) transfer functions
showing the amplifier loop-shaping design
. . . . . . . . . . . . . . .
90
4-9 Feedback phase lag at the cross over for different cable resistance (Rc )
values displayed for the V-Q and V-Q-V charge amplifiers. . . . . . .
92
4-10 Schematic design of the new V-Q-V charge amplifier design. . . . . .
93
4-11 The assembled custom charge amplifier (left) and CAD design (right).
96
4-12 Side cross-sectional view of the charge amplifier. . . . . . . . . . . . .
97
4-13 Circuit design of the charge amplifier showing the power device and its
feedback circuit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
98
4-14 Schematic design of the charge amplifier showing the buffers measuring
the piezo current (left), the feedback voltage (middle), and the piezo
voltage (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
99
4-15 Circuit design of the charge amplifier showing its 110-V AC-DC power
supply. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4-16 The amplifier’s printed circuit board design (left) and manufactured
circuit board (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4-17 Block diagram showing the charge amplifier, piezoelectric device, and
the hybrid hysteresis compensation algorithm. . . . . . . . . . . . . . 102
16
4-18 Schematic diagram of the Maxwell slip model with n elements with
stiffness ki and force limit Fi , where i is an integer from 1 to n. The
model simulates the presiding friction hysteresis between force (F) and
the displacement (x). . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4-19 Experimental voltage-charge hysteresis of our piezo actuator and the
fitted Maxwell’s slip model. . . . . . . . . . . . . . . . . . . . . . . . 106
4-20 Time plot of piezo’s strain in response to 10-Hz 0 to 80 V sinusoidal
reference signal using the power amplifier in voltage control mode (V
Ctrl), voltage-charge-voltage control mode (VQV Ctrl), and VQV control mode with hybrid hysteresis compensation (HHC). . . . . . . . . 108
4-21 XY plot of the piezo’s strain versus a 10-Hz 0 to 80 V sinusoidal reference signal using the power amplifier in voltage (V Ctrl) control mode,
voltage-charge-voltage (VQV Ctrl) control mode, and VQV control
mode with hybrid hysteresis compensation (HHC). . . . . . . . . . . 109
4-22 Assembled experimental setup used for researching soft-linearization
of normal flux actuators through magnetic-flux control. . . . . . . . . 112
4-23 CAD model of the experimental setup used for researching soft-linearization
of normal-flux reluctance actuators. . . . . . . . . . . . . . . . . . . . 112
4-24 CAD Model showing a closer view of the encoder assembly . . . . . . 113
4-25 Experimental setup’s system diagram.
. . . . . . . . . . . . . . . . . 114
4-26 CAD model of the normal-force electromagnetic actuator (left) and the
core structure of the actuator before assembly (right). . . . . . . . . . 114
4-27 Electromagnetic normal-flux actuator with a flux sensing coil wrapped
around the center pole piece using miniature coaxial shielded cable. . 115
4-28 Block diagram of the flux estimation algorithm . . . . . . . . . . . . . 116
4-29 Experimentally measured mutual inductance of the actuator and sense
coils (Lm ) measured as a function of air gap for the actuators on the
right and the left sides. . . . . . . . . . . . . . . . . . . . . . . . . . . 117
4-30 Block diagram of the flux control system . . . . . . . . . . . . . . . . 119
17
4-31 Experimental frequency responses of the flux-control plant from the
applied voltage V to the sensed magnetic flux linkage λS is plotted
at different air gaps for the actuators on the right (right) and the left
(left) sides. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4-32 Experimental frequency responses of the compensated loop transmission for the flux linkage control system is plotted at different air gaps
for the actuators on the right (right) and the left (left) sides. . . . . . 122
4-33 Experimentally calibrated force map of the right (right) and left (left)
side actuators viewed in 3D. We use the map to find the the linkage
required for generating a certain force at a given gap. . . . . . . . . . 124
4-34 Experimentally captured plots of the force versus flux linkage at different gap sizes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4-35 Plot of the correction constant c(g) versus the gap size (g) for the right
and left actuators.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
4-36 Block diagram of the force distribution subsystem. The subsystem generates a commanded bidirectional force by assigning force commands
to the unidirectional actuators. . . . . . . . . . . . . . . . . . . . . . 127
4-37 Measured output force plotted versus the reference force for the actuators on the left (top left) and right (top right) sides. The force
nonlinearity plotted versus the reference force for the actuators on the
left (bottom left) and right (bottom right). . . . . . . . . . . . . . . . 129
4-38 Block diagram of the position control system consisting of the position
controller, force distribution, and flux linkage controller blocks. . . . . 130
4-39 Bode plot showing the frequency responses of the position control system’s plant, controller, and compensated loop transmission. . . . . . . 131
4-40 Experimentally captured step response of the position control system
tested at different air gap sizes. Position 0.05 mm corresponds to 50µm
away from the left actuator and position 0.95 mm corresponds to 50
µm away from the right actuator. . . . . . . . . . . . . . . . . . . . . 133
18
4-41 A zoomed in view of the position control system’s step response close
to the center and within the calibration range (left), and outside of the
calibration range and close to the actuator face (right). . . . . . . . . 134
4-42 Meshed planar finite element model of the electromagnetic actuator. . 134
4-43 Non-Linear BH characteristic of the SuperPerm49 modeled in the FEA
software. The cores are manufactured by Magnetic Metals. The data
is obtained from the manufacturer’s website . . . . . . . . . . . . . . 135
4-44 Simulation results using a coil current of 2A is shown as a magnetic flux
density plot (top) and a line plot of the normal magnetic flux density
over the face of the actuator’s mover from point A to point B (bottom).136
4-45 The mutual inductance (Lm ) versus the air gap size is plotted based on
the finite element model results and is compared to the experimental
results for the right and left actuators. . . . . . . . . . . . . . . . . . 137
4-46 The force correction constant (c(g)) versus the air gap size is plotted based on the finite element model results and is compared to the
experimental results for the right and left actuators. . . . . . . . . . . 138
5-1 Lumped parameter model of a piezoelectric resonator modeling only
the first resonance mode. The sample surface is modeled with a stiffness ks .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5-2 The shape of the magnitude response shape of the total, capacitive, and
piezoelectric admittances are shown using arbitrary system parameter
values. Note that the capacitive component hides the resonance. . . . 147
5-3 Lumped parameter electromechanical model of an electromagnetic resonator. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
5-4 Piezoelectric actuator’s frequency response from the applied voltage
to the mechanical strain is plotted free in air at different excitation
amplitudes, and in contact with the sample using an increasing range
of preloading pressure values. . . . . . . . . . . . . . . . . . . . . . . 152
19
5-5 Comparing the piezoelectric actuator’s electrical admittance and mechanical frequency response near resonance. . . . . . . . . . . . . . . 153
5-6 Block diagram of the contact detection algorithm implemented on an
FPGA device. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
5-7 Self-sensing contact detection phase (left) and amplitude (right) response plotted versus the contact force. The probe is excited at the
mechanical resonance ωp '25 kHz with approximately 25-nm oscillation amplitude. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
5-8 Self-sensing contact detection is used to detect the reticle’s edge. The
time plots of actuator’s strain (top), contact force (middle), and phase
response (bottom) are shown. In the top plot, the signals Sr , S, and
Edge indicate the reference, the measured strain, and the registered
edge location, respectively. . . . . . . . . . . . . . . . . . . . . . . . . 157
5-9 CAD drawing of the subatomic measuring machine (SAMM) with the
high-accuracy atomic force microscope (HAFM) installed as its metrology probe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
5-10 Photo of the assembled HAFM (right) and cross-sectioned CAD model
of the HAFM (left). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
5-11 Simplified block diagram of the HAFM system. . . . . . . . . . . . . 161
5-12 An Akiyama probe’s admittance frequency response shown based on
our experimental data (blue), the analytical fit(green), and the compensated analytical function (red).
. . . . . . . . . . . . . . . . . . . 162
5-13 Simplified block diagram of the AFM self-resonance loop . . . . . . . 164
5-14 Root locus plot of the self-resonance loop . . . . . . . . . . . . . . . . 165
5-15 Experimentally obtained sense curves for an Akiyama probe under test
at different oscillation amplitudes. . . . . . . . . . . . . . . . . . . . . 166
5-16 Schematic design of the preamplifier board. The picture of the Akiyama
probe is courtesy of NANOSENSORST M . Shield connections are shown
at input terminals of operational amplifier OP 1. . . . . . . . . . . . . 169
20
5-17 Schematic design of the self-resonance control board showing the fullydifferential input buffer and precision comparator module used to digitize the self-resonance signal. . . . . . . . . . . . . . . . . . . . . . . 170
5-18 Schematic design of the self-resonance control board showing the control blocks consisting of amplitude measurement, loop gain control,
and phase shifting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
5-19 Bode plot of the tracking control system’s open-loop and compensatedloop frequency responses. . . . . . . . . . . . . . . . . . . . . . . . . . 172
5-20 The tracking controller’s discrete time control law. The controller will
be sampled at two times the probe’s resonance frequency; i.e. sampling
is synchronous with the edges of the square wave CLKSR , and thus
sampling is at about 2 × 46.8 kHz = 93.6 kHz where the exact value
varies with the tip-sample engagement. . . . . . . . . . . . . . . . . . 173
5-21 The implementation of period estimation and tracking controller on
the FPGA device. The controller within the while-loop is updated at
every rising or falling edge of CLKSR , when a new value is written to
the FIFO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
5-22 The step response of the HAFM’s closed loop tracking system viewed
at 100-Hz and 1-kHz measurement bandwidth. . . . . . . . . . . . . . 174
5-23 The HAFM’s noise when tracking a stationary sample surface, viewed
at 100-Hz and 1000-Hz measurement bandwidths. . . . . . . . . . . . 175
5-24 Block diagram of the HAFM’s tracking control loop including the
discrete-time measurement and control sampling. The dashed line indicates the frequency at which the blocks are updated. . . . . . . . . 176
5-25 Diagram of the model used for simulating the tracking control loop in
MATLAB Simulink.
. . . . . . . . . . . . . . . . . . . . . . . . . . . 177
5-26 Simulated step responses for synchronous or fixed rate sampling with
(noisy) or without (clean) measurement noise. . . . . . . . . . . . . . 178
5-27 The HAFM’s simulated RMS tracking noise for synchronous and fixed
rate control with and without measurement noise. . . . . . . . . . . . 179
21
5-28 Images of the TGX01 (left) and the TGZ01 (right) standard gratings captured using the HAFM integrated with the Veeco Scanner at
10µm/s and 5µm/s scan speeds respectively. . . . . . . . . . . . . . . 180
5-29 Histogram of height over the HAFM’s image of TGZ01 grating. . . . 181
5-30 Trace and retrace line scans of the TGZ01 grating at different scan
speeds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
5-31 Image of the HAFM installed on the SAMM’s metrology frame at UNCCharlotte. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5-32 The HAFM’s image of a saw tooth grating captured by Jerald Overcash
using the HAFM and the SAMM at UNC-Charlotte. . . . . . . . . . 183
5-33 Assembled macro-scale self-sensing and self-actuating magnetic probe
(top left), its CAD model (top right), and detailed side view showing
the clamp design (bottom right). . . . . . . . . . . . . . . . . . . . . 184
5-34 Experimental impedance frequency response of the magnetic probe
shown before (Zt EXP) and after (Zm EXP) compensation for coil
resistance as well as their corresponding analytical fits (Zt AN & Zm
AN). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
5-35 Block diagram of the probe’s control system showing the compensation,
self-resonance control, and tracking control subsystems. For the low
resonance frequency, we let L̂ = 0 . . . . . . . . . . . . . . . . . . . . 188
5-36 Experimental and analytically fitted frequency responses of the amplitude control system’s plant and compensated-loop. . . . . . . . . . . 190
5-37 Experimentally obtained frequency responses of the plant and the compensated loop of the tracking control system. . . . . . . . . . . . . . . 191
5-38 The imager’s scanner hardware (left) and CAD design (right). . . . . 192
5-39 Macro AFM measuring a penny (right) and the captured image (left). 193
5-40 Macro AFM measuring an MIT key chain and the scanned image (top
right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
5-41 Images of a quarter captured using macro AFM visualized in 3D (left)
and 2D (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 194
22
6-1 Reticle assist device’s state-machine design used for automating the
fine-actuation process. . . . . . . . . . . . . . . . . . . . . . . . . . . 199
6-2 Simplified block diagram of the control system design using strain sensor’s feedback for controlling the piezo’s extension. Variable s is the
strain gauge output; signal P M is the phase measurement from the
Contact Detection block. . . . . . . . . . . . . . . . . . . . . . . . . . 202
6-3 Simplified block diagram of the control system design using charge
control for open-loop control of the piezo’s extension. . . . . . . . . . 203
6-4 Experimental plot of the pushing force versus piezo strain with an
overlaid least-squared fit based on the analytical model. . . . . . . . . 204
6-5 A simplified lumped stiffness model of the reticle assist device and the
reticle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
6-6 Frequency responses of the strain control system’s plant (OL), controller (C), and compensated loop transmission (LT). . . . . . . . . . 207
6-7 Experimental setup used for calibrating and testing the reticle-assist
device. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210
6-8 Picture of the strain gauge measurement circuit board. . . . . . . . . 211
6-9 Time plot of the reticle-assist experiment for a strain-controlled reticle
assist device showing 10 acceleration cycles with a corresponding peak
inertial load of 60 N. . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
6-10 Time plot of the reticle-assist experiment for a strain-controlled reticle
assist device showing a single acceleration cycles with a corresponding
peak inertial load of 60 N. . . . . . . . . . . . . . . . . . . . . . . . . 217
6-11 Time plot of the reticle assist device’s piezo motion shown for one
acceleration cycle with the state-machine’s state marked on the plot.
218
6-12 Time plot of the reticle edge displacement for the assist experiment
shown over a longer period of 10 seconds. . . . . . . . . . . . . . . . . 219
6-13 Time plot of the reticle-assist experiment for a charge-controlled reticle
assist device showing 10 acceleration cycles with a corresponding peak
inertial load of 60 N. . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
23
6-14 Time plot of the reticle-assist experiment for a charge-controlled reticle
assist device showing a single acceleration cycles with a corresponding
peak inertial load of 60 N. . . . . . . . . . . . . . . . . . . . . . . . . 221
6-15 Assist device’s output force plotted versus the piezo’s charge (left) and
extension (right). The piezo’s force versus charge is shown for the
charge amplifier with and without the hybrid hysteresis compensation
(HHC) method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
6-16 The self-sensing method’s phase response versus the piezo extension.
The phase response is calculated from piezo voltage to piezo current
at the piezo’s resonance frequency.
. . . . . . . . . . . . . . . . . . . 224
6-17 Assist device vacuum clamp’s force versus displacement behavior within
the pre-sliding regime. The plot shows the experimental data (blue), a
fitted Maxwell slip model (circles), and the model’s simulated output
(black). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
24
List of Tables
3.1
Table of contact parameters . . . . . . . . . . . . . . . . . . . . . . .
65
3.2
Magnetostrictive actuator design parameters . . . . . . . . . . . . . .
78
4.1
Stiffness and force limit values for modeling the hysteresis between the
voltage and charge of our piezoelectric actuator. . . . . . . . . . . . . 106
5.1
Table of the probe sensitivity at different oscillation amplitudes . . . 167
25
26
Chapter 1
Introduction
The semiconductor industry manufactures the chips which are the basic building
blocks of electronic devices, and is among the fastest advancing industries. The
industry’s main technological drivers have been manufacturing denser circuits at faster
rates. In this way, more powerful devices can be built for cheaper prices. Gordon
Moore predicted in 1965 that the number of transistors in a device will double every
two years. His prediction has remained accurate until this day. This has been partly
due to the fact that the Moore’s law has been used as a roadmap for the industry’s
advancement [59]. While shrinking the devices at an exponential rate, the industry
has worked to increase the manufacturing throughput. The two conflicting goals
of improved manufacturing precision and throughput have led to many challenges.
The higher inertial loads of the faster moving next-generation scanners can cause
the reticles to slip. Reticle slip can be a major error source of the next generation
scanners. The main focus of this thesis is addressing the reticle slip problem. In
collaboration with ASML, we have developed a solid-state reticle assist device, which
uses a piezoelectric stack actuator to exert a normal force on the reticle’s edge to cancel
the inertial loads and prevent reticle slip. Using this design, we have successfully
demonstrated the potential to eliminate reticle slip even under high acceleration. By
preventing reticle slip, this technology can help enable higher throughput without
sacrificing precision. In the following sections, we present the background of the
reticle-slip problem. Next, we review the relevant prior art work. Finally, we outline
27
a summary of this thesis and list its main contributions.
1.1
Background
Optical lithography is the semiconductor industry’s most common manufacturing
process, where a master pattern printed on a transparent substrate, called the reticle,
is transferred onto a silicon wafer. The scanners are currently the most common
lithography manufacturing equipment. A scanner moves both the reticle and the
wafer relative to each other and exposes the wafer using a slit of light passing through
the reticle[14]. To achieve faster scan speeds and higher throughput, scanners must
operate at higher accelerations. The reticle can slip as a result of the large inertial
loads of the next generation scanners. To avoid deforming the reticle, it is held in
place using a vacuum chuck. The vacuum chuck’s maximum clamping force is set
by the vacuum surface area, which is limited by the standard size of the reticles.
The inertial loads of the next-generation scanners can exceed the clamping force
limit. Reticle slip can be a major error source and addressing it is key to enabling
higher throughput. At the same time, scanners are complex and highly optimized
machines. Reticle, which holds the master pattern being printed, is at the heart of
these equipments. Modifications close to this sensitive part of the scanner must be
made with care as they can directly affect the scanner’s performance. Interactions
with the reticle must be well regulated to avoid disturbing the its pattern by more than
1nm. The main focus of this thesis has been creating a solution to fully eliminate the
reticle slip problem without hindering the performance of the rest of the system. The
manufacturers of the scanners have considered different solutions to this problem,
which are discussed in Section 1.2. The main focus of this thesis is to create a
technology, which can eliminate the bottleneck on throughput set by the reticle slip
problem without worsening, if not improving, the performance of the scanner in the
other areas. This works has been carried in collaboration with ASML, the world’s
leading provider of the lithography scanners.
28
1.2
Prior Art
ASML, Nikon, and Canon are the main current manufacturers of lithography scanners. They have all searched for methods to solve the reticle slip problem. In the
following subsections, we review the solutions generated by the industry which are
available in the patent literature. The prior art references can be categorized into two
groups according to their general approach toward solving the problem: modifying
the clamp mechanism and externally compensating the inertial forces.
1.2.1
Modified Clamping Mechanisms
The reticle slip problem can occur when the reticle’s inertial load exceeds the reticle’s
clamping force limit. As a result, improving the clamping mechanism is one potential
way to solve the problem.
Shibazaki, of Nikon, has designed a mechanical clamping mechanism, which can
increase the normal force available for clamping the reticle [74][73][74]. A sketch of
the clamping mechanism in the open and closed position is shown in Figure 1-1. The
reticle (R) is clamped between the rigid support (203/211) and the clamp end (322).
A flexible clamp end (322) is used to uniformly distribute the clamping force across
the reticle and avoid generating parasitic forces in the other directions. To operate
the clamp, the actuation end (363) is moved by a cam and follower mechanism. The
locking element (364a) is used to lock the mechanism once it is clamped. This design
relies on a rigid support (203/211) underneath the reticle. However a rigid support
under the reticle will over-constrain it and can deform the reticle. Also, exerting
a clamping force through the reticle can distort the reticle, which will distort the
printed layers.
Baggen et al., of ASML, propose using actuators to exert opposing clamping forces
on the reticle only during the acceleration intervals and not through the constant
speed scan intervals [12]. In this way, the reticle deformation resulting from the
additional clamping forces is not present during the scan interval and thus will not
distort the printed layers. As shown in Figure 1-2, a reticle (20) is clamped to a
29
Figure 1-1: Schematic diagram of Nikon’s mechanical clamping mechanism invented
by Shibazaki shown in open (left) and closed (right) positions. Figure is taken from
US Patent 8,253,929 [74].
stage (10) using the vacuum surfaces (15). Clamping forces (30) are exerted onto
the reticle. Baggen et al. state that the clamping forces can be generated using a
variety of actuators: voice coil motor, piezoelectric, electromagnetic, and pneumatic
bellows. For the clamping forces to be effective their stiffness in the scan direction
(Y) must be higher than the original vacuum clamp stiffness. Although the diagram
shows the clamping forces oriented in the XY plane, Baggen et al. also describe an
arrangement where the clamping forces are oriented in the out-of-plane direction.
The actively applied clamping forces must be synchronized to avoid creating reticle
slip due to a one-sided clamping load. The clamping forces are overconstraining the
reticle and can result in small reticle displacements. As well, the impact forces of the
repeating clamping action can displace or even damage the reticle unless the reticle
is approached under control.
Zordan, of ASML, suggests that a clamping structure which is more compliant
to the shape of the reticle can have a higher slip force limit, even without increasing
the clamping forces [87]. According to Zordan, with higher compliance, high-stress
corners are not formed and the shearing friction stress is distributed more uniformly.
As a result, the slip condition occurs at higher loads. Perspective and cross-sectional
views of one embodiment of this invention are shown in Figure 1-3. A reticle (30)
is held by the vacuum cups (22). The vacuum cups are attached to the stage using
membranes (20). As shown in the perspective view, the vacuum clamp on each side of
the reticle (30) is formed by a series of smaller vacuum clamps. Breaking the vacuum
30
Figure 1-2: Schematic diagram of ASML’s active clamping mechanism invented by
Baggen et al. Figure is taken from US Patent 7,459,701 [12].
clamps into a series of smaller clamps increases the clamp compliance, where each
clamp can easily deform to the shape of the reticle. Also, due to the smaller width
of the membranes (20), the corner stresses resulting from elastic deformation of the
membranes in the Y direction are minimized.
1.2.2
Reticle Assist Devices
The reticle slips if the inertial load carried by the clamp exceeds its force limit. One
way to avoid slip is to use a device to exert an external force on the reticle which
can fully or partially cancel the inertial load. In this way, less force is carried by the
clamp, and slip can be avoided. In this thesis, we call such a device a reticle assist
device.
Iwamoto, of Canon, invented a reticle assist device which generates the compensating forces using the inertia of two masses and a lever [35]. As shown in Figure 1-4,
the reticle (101) is clamped to the stage (113). The mass (104) is attached to the
end of the lever (103) and moves around the pivot (105). As the stage accelerates,
the inertial load of the mass (104) is carried by the reticle (101). Because a pivot is
used, the resulting external load on the reticle is opposite to the reticle’s inertial load.
31
Figure 1-3: ASML’s compliant clamp design invented by Enrico Zordan. Figure is
taken from US Patent Application 13/168,109 [87].
32
Figure 1-4: Schematic drawing of Canon’s reticle assist device idea by Iwamoto.
Figure is taken from US Patent 6,469,773 [35].
The length ratio of L1 to L2 and the mass m can be selected such that the resulting
external load fully cancels the reticle’s inertial load. Two of the pivot devices, one on
each side, are used to cancel the inertial loads in both directions. The design has two
major shortcomings. First, the added inertia and lever can add unwanted dynamics
to the stage. Second, the masses are able to move freely by the inertial loads, and
contact between the reticle and the device is not controlled. Unwanted contact during
the exposure interval can distort the patterns being printed. Additionally, large impact forces between the reticle and the assist device can move or damage the reticle.
Jacobs et al., of ASML, propose using actuators with a lever mechanism to exert a
force on the reticle [36]. As shown in Figure 1-5, linear motors (LM) push on a reticle
(MA) through a lever pivoting around a pivot (PAX). One device is used on each side
to enable cancelation of the inertial loads in both directions. Using the actuators to
33
Figure 1-5: Schematic drawing of ASML’s active pivoted reticle assist device idea by
Jacobs et al. Figure is taken from US Patent 7,667,822 [36].
control the levers’ positions, this device can make controlled contact with the reticle.
Jacobs et al. state that the linear motor can be replaced with a piezoelectric actuator.
As another alternative, the patent lists using a deformable pressurized chamber for
creating a pushing force.
Baggen et al., in the patent, which was discussed in Section 1.2.1, suggests that
the clamping actuators, which are oriented in the scan direction, can be used to exert
a next force on the reticle to cancel the inertial load [12]. As shown in Figure 1-2,
the actuators (60-63) can create a net force on the reticle (52), which is clamped to
the stage (50).
Del Puerto and Zordan have designed a linear reticle assist device, which uses
linear motors to exert pushing forces on the reticle [69]. As shown in Figure 1-7, the
reticle (470) is clamped to the stage (420) through the vacuum surfaces (480A-B).
Linear motors (430A-D) can push on reticle (470) through the rods (492A-B). The
stage (420) is driven using linear motors. The same current driving the stage can be
used to drive the assist device’s linear motors. The force constant of the linear motors
(430A-D) can be set such that the pushing force fully cancels the inertial force.
A key difficulty for devices making repeating contact with the reticle is controlling
them to avoid large impact forces. Zordan, of ASML, has invented a mechanism to
limit the contact forces. As shown in Fig 1-8, the pushing tip (48) is fixed to the
34
Figure 1-6: Schematic drawing of ASML’s reticle assist device idea by Baggen et al.
Figure is taken from US Patent 7,459,701 [12].
Figure 1-7: ASML’s reticle assist device design by Del Puerto and Zordan. Figure is
taken from US Patent Application 12/627,771 [69]
35
Figure 1-8: ASML’s force-limiting pushing tip mechanism by Zordan. Figure is taken
from US Patent Application 13/022,247 [86].
preloaded part (46), which is preloaded by the spring (44) to the actuator’s moving
body (40). If the pushing force exceeds the preload force of the spring, the preloaded
part (46) will detach from the actuator body and the excess force is carried by the
spring (44). If a flexible spring is used, the static force cannot rise significantly
above the spring preload force. To limit the dynamic force, the inertia of the moving
elements (48, 46, and 44) must be limited. The effectiveness of this design in limiting
the impact forces depends on the contact speed and the inertia of the moving elements.
By automatically limiting the contact forces, this design can potentially simplify the
control and operation of reticle assist devices.
In the summer of 2010, following a summer internship at ASML, I filed a patent
application on a solid-state reticle assist device and its operation [4]. As shown in
Figure 1-9, the reticle (470) is clamped to the stage (450). The magnetostrictive
solid-state element (466) can be energized by the coil (462) to extend and exert a
pushing force on the reticle (470). The magnetostrictive element has a short-range
of motion, so it is positioned close to the reticle using the position element (464) and
is fixed using the clamp (465). To set the gap 467, the element is extend by the
desired gap. Next, the element is preloaded against the reticle. Finally the element is
clamped. In this way the gap is set to the desired value when the element’s extension
is reversed. From this position, the magnetostrictive element can extend to make
contact and push on the reticle. The current driving the stage motors can be used
36
Figure 1-9: ASML’s solid-state reticle assist device idea by Amin-Shahidi. Figure is
taken from US Patent Application 13/281,718 [4].
to energize the assist device’s coil (462) as well. The patent application states that
other solid-state actuator elements, such as a piezoelectric element, can replace the
magnetostrictive element.
1.3
Thesis Overview
The main focus of this thesis is to design and test a reticle assist device which advances the state of the art and enables higher manufacturing throughput without
sacrificing accuracy. After considering the different possible reticle-assist technologies, we found solid-state devices to be the most suitable for this application. A
piezoelectric element can have a very high force density. With very low mass and no
moving parts, such a device can have excellent dynamics and good reliability. We
have developed techniques which enable a bare piezoelectric element, without any
force or strain sensors, to cancel the inertial forces by better than 95%. In this way
we can create a practical and effective solution for addressing the reticle slip problem.
In the following subsections, we provide a brief overview of this thesis. We cover the
37
reticle assist device, its enabling technologies, control, and experimental results.
1.3.1
Solid-State Reticle Assist Device
A photo of the completed assist device and its CAD drawing are shown in Fig 1-10.
This design uses a piezoelectric stack actuator to generate the pushing forces. In
the current prototype, the piezo stack has a range of 15 µm and a natural resonance
frequency of approximately 25 kHz with the pusher-tip payload. The piezo actuator is
fixed to a coarse positioning stage, which is used to position the piezo actuator when a
new reticle is loaded. The coarse positioning stage uses a monolithic flexure to guide
its motion. The stage is driven by a pneumatic bellow. The stage has a vacuum
clamp, which is used to clamp and hold the position of the coarse stage. When
positioned near the reticle, the piezo actuator can extend to exert a pushing force
on the reticle. The pushing force is limited by the capacity of the coarse positioning
stage’s vacuum clamp and can be as high as 100 N with the present design. We use
a spherical pushing tip to ensure that the piezo’s load is centered on its axis and
does not create a bending moment on the piezo stack. When scanning the wafer, the
coarse stage is clamped and the reticle assist device has no moving parts except for
the piezo ceramic actuator extending by less than 5 µm. While the piezo actuator
weighs less than 15 g, it can produce forces as large as 100 cN on the reticle. The
detailed design of the reticle assist device is described in Chapter 3.
1.3.2
Hybrid Charge Amplifier
We have designed and built a high performance charge amplifier which improves on
the state of the art in terms of its control robustness and linearity. Piezoelectric
elements exhibit strong hysteresis when used under voltage control. Charge control
can be used to improve their linearity. We have designed and built a high performance charge amplifier using an APEX MP38 [9] linear power device. Pictures of
the amplifier box and the printed circuit board are shown in Figure 1-11. The power
amplifier has better than 100kHz small-signal bandwidth. A switch enables the user
38
Coarse
Stage
Fine
Stage
Z
Y
X
Figure 1-10: Photo (top) and CAD drawing (bottom) of the piezoelectric reticle assist
device.
39
Figure 1-11: Photos of the charge amplifier box (left) and circuit board (right).
to select between voltage or charge-control mode. The amplifier uses a novel feedback
controller which is less sensitive to added series load impedance. Conventional charge
amplifiers control charge in the high-frequency range and voltage in the low-frequency
range. The piezo’s hysteresis appears as a positioning error when a low frequency reference signal is present. We have invented a compensation scheme which enables
controlling charge at all frequencies. The compensation scheme is executed in software and acts at the charge amplifier’s reference terminal. The algorithm can sample
at a relatively low frequency and therefore can be added to the system by using a lowcost micro-controller. Because the algorithm acts at the charge amplifier’s reference
terminal, it can be integrated with existing charge amplifiers as well. The piezoelectric actuator’s motion versus reference curves using different control methods are
shown in Figure 1-12. Charge control is more linear compared to voltage control, and
compensated charge control is significantly more linear than standard charge control.
Using compensated charge control, we can eliminate the need for a strain sensor and
associated closed-loop control of the piezoelectric actuator. We present the charge
amplifier design in detail in Chapter 4.
40
12
HHC
VQV Ctrl
V Ctrl
10
Strain [μm]
8
6
4
2
0
0
10
20
30
40
50
Reference [V]
60
70
80
Figure 1-12: Piezoelectric actuator’s displacement versus reference command using
different control methods: voltage control (V-Ctrl), charge control (Q-Ctrl), and
inverse-hysteresis feedback compensation (Q-Ctrl & HHC).
41
1.3.3
Self-Sensing Contact Detection
A key challenge when using the reticle assist device is registering the device’s position
relative to the reticle’s edge. Relative position to the reticle’s edge is required for
avoiding tip-reticle impacts, and in many cases, for precise force control. We have
applied an innovative self-sensing method for detecting reticle-tip contact with highsensitivity and without the need for any sensors. In a fashion similar to self-sensing
atomic force microscopy, the self-sensing module excites the piezo actuator at its
natural frequency and monitors the piezo’s voltage and current signals and their
phase difference. As shown in Figure 1-13, the phase difference changes sharply
when the tip contacts the reticle. This is used to detect reticle-tip contact. We
have previously used a similar self-sensing method with a high-accuracy atomic force
microscope (HAFM), which has been designed to be used as a metrology probe for
the sub-atomic measuring machine (SAMM). The SAMM stage is a magneticallysuspended positioning stage, which has been designed in the doctorate dissertation
of Holmes [33]. Figure 1-14 shows the HAFM integrated with the SAMM. The image
of the triangular grating, which is shown in Figure 1-14, has been captured using the
HAFM as the probe and SAMM as the XY scanner. We have also used the self-sensing
technique with a macro-scale magnetic AFM profiler (MAP). We have designed the
MAP to be used for teaching Mechatronics (2.737), a graduate-level course offered by
the Mechanical Engineering Department at at MIT. Figure 1-15 shows MAP imaging
an MIT key chain. The self-sensing method and its application to the reticle-assist
device, HAFM, and MAP are presented in Chapter 5.
1.3.4
Reticle Assist Device Control and Experimental Results
We describe our control method, which has demonstrated better than 95% inertial
force cancellation without using any position or force sensors. The algorithm includes a force versus contact-compression calibration map, which is used to control
the force in open-loop. The algorithm uses charge control with nonlinear feedback
42
60
50
Phase [deg]
40
30
20
10
0
-10
-10
0
10
20
30
40
Contact Force [N]
50
60
70
Figure 1-13: Piezoelectric actuator’s voltage to current signals phase difference when
excited at its natural frequency shown versus the tip-reticle contact force. The sharp
change in the phase difference is used to detect tip-reticle contact.
43
30 nm
HAFM
Figure 1-14: The high-accuracy atomic force microscope (HAFM) is installed on the
sub-atomic measuring machine (SAMM). HAFM and the SAMM are used to capture
the inset image of the triangular grating.
44
Figure 1-15: Macro-scale atomic force microscope profiler (MAP) is shown capturing
an image of an MIT key chain.
compensation to linearly control the piezo’s extension without the need for strain
feedback. This is augmented with self-sensing contact detection in every cycle to
register the assist device’s position relative to the reticle. The algorithm includes a
state machine which automatically commands the subsystems to create an arbitrary
inertial load profile. Figure 1-16 shows a time trace of the inertial load profile and
the piezoelectric actuator’s charge reference commanded for canceling that load. The
plot also shows an estimate of the reticle edge location obtained using the self-sensing
contact detection method. When loading a new reticle, the edge location is set by
the coarse approach mechanism. The expected edge location is updated using the
self-sensing method before every pushing cycle. The edge location is determined as
the required amplifier reference voltage for the piezoelectric actuator to arrive at the
reticle edge. The change in this measurement is due to the charge amplifier’s slow
transient resulting from the uncompensated piezo hysteresis and the the noise in the
edge detection algorithm. It is not an actual displacement of the reticle edge. As it
can be seen, the device approaches the reticle to find its edge, pushes on the reticle
45
cancel inertial loads
repeat
… Reference
Edge
Inertial Force
Inertial Force [N]
wait
near
edge
0
0.1
50
approach
wait @
edge
0.15
0.2
Piezo Cha
arge Ref. [V]
50
retract
to stay
clear
0.25
Time [sec]
0.3
0.35
0
0.4
Figure 1-16: Time trace of the inertial load profile and the piezo charge reference
required for canceling the load generated by the control system.
to cancel the inertial load during the acceleration interval, and retracts back to avoid
disturbing the reticle during the exposure interval. The assist device’s resulting force
compensation (F ) is plotted versus the inertial force (FR ) in Figure 1-17. The reticle
assist device’s control system is presented in Chapter 6, Section 6.1.
We have tested the effectiveness of the reticle assist device in compensating the
reticle inertial loads. The experimental setup is shown in Figure 1-18. The setup
consists of a reticle mounted on a stationary vacuum clamp. Coils are attached to
the top and bottom surfaces of the reticle. These coils are used with magnet arrays to
generate forces acting on the reticle’s center of gravity. This allows us to simulate the
reticle inertial loads using a stationary setup. The experimental setup has capacitive
displacement sensors which monitor the location of the reticle and the assist device’s
clamp relative to the base plate. The setup also has the vacuum and pressurized air
46
60
50
Experimental
Ideal
F [N]
40
30
20
10
0
0
20
40
60
FR [N]
Figure 1-17: Assist device’s resulting compensation force versus the inertial load
plotted for 10 consecutive cycles.
lines used with the clamps and the pneumatic bellow. We used the coils to generate
a 60-N simulated inertial load profile and monitored the reticle’s displacement with
and without using the reticle assist device. As can be seen in Fig. 1-19, the reticle
assist device is very effective at preventing reticle-slip. Without an assist device,
the reticle moves as the clamps deform elastically by about 1 µm. However, some
amount of this deformation is not reversed, and the reticle slips by more than 100
nm after 10 acceleration cycles. However, with this reticle assist device, the clamps
elastically deform by only 20 nm and the reticle does not slip even after 10 cycles.
The experimental procedures and results are presented in Chapter 6, Section 6.2.
47
Figure 1-18: Picture of the experimental setup used for testing and development of
the reticle assist device (RAD).
48
0.02
0
-0.02
02
0.2
0.3
0.35
0.4
no RAD
with RAD
Reticle Motion [ μm
m]
0
-0.2
-0.4
-0.6
-0.8
-1T
0
0.5
1
Time [s]
1.5
2
Figure 1-19: The reticle motion relative to the stage as a result of a 60-N simulated
inertial load profile with and without using our reticle assist device (RAD).
49
50
Chapter 2
Reticle Slip Problem and
Conceptual Solutions
In this chapter, we describe the reticle slip problem, present promising conceptual
designs, and conclude by selecting the most suitable concept for designing the reticle
assist device.
2.1
Reticle Slip Problem
A simplified diagram of a lithography scanner is shown in Figure 2-1. The scanner exposes the wafer by sweeping an exposure slit across the reticle. To map the reticle to
a whole die on the wafer, the scanner moves the wafer and the reticle relative to each
other with nanometer-level coordination of motion. The reticle stage holds the reticle
using a vacuum clamp and moves it in the X-direction. The reticle stage’s linear motion path consists of acceleration at the ends of each scan and constant-speed motion
in the middle of the scan. Figure 2-1 shows the reticle stage accelerating (aR ) in the
X-direction, which results in an inertial force (FI ) being in the negative x-direction.
A large inertial force can cause reticle slip and displace the reticle to the location
shown using the dotted box. As the inertial force approaches the clamp’s force limit,
significant pre-sliding slip starts to occur. Sliding slip can occur if the inertial force
exceeds the clamp’s limit. For more perspective on lithography machines, Butler [14]
51
reticle
Z
FI
clamp
X
g
reticle stage
aR
wafer
optical
column
wafer
aW
wafer stage
stator
Figure 2-1: Simplified diagram of a lithography scanner.
provides a detailed description of the operation and position control of lithography
scanners.
To avoid deforming the reticle, a vacuum clamp is used for holding it. The reticle
size and shape is set by the industry standard. Therefore, the available vacuum
clamp area is limited. Given the restriction on the allowable materials, the coefficient
of friction at the clamp’s interface cannot be increased. As a result, a limit is set on
the clamp’s maximum force carrying capacity. The reticle inertial force for the next
generation scanners can approach or even exceed this limit. Consequently, reticle slip
can be a major error source for the next generation scanners.
2.2
Application Requirements
One method to address the slip problem is to use a reticle assist device, which fully
or partially carries the reticle’s inertial force by exerting a force on the reticle’s edge.
The reticle assist device will be placed on the reticle stage and will be interacting
with the reticle. Being so close to the heart of the lithography process, the assist
device must satisfy several application requirements in order to avoid disturbing the
52
lithography process and degrading the scanner’s performance. The main requirements
and guidelines for designing the reticle assist device are as the following:
1. Low added mass from the assist device is required to ensure good reticle stage
dynamics. A total mass budget of 0.3 kg, 0.15 kg per side, is provided to us as
an approximate guideline.
2. Lifetime of at least 7 years with continuous operation is expected. During the
assist device’s life time, 1 million reticle exchanges and 500 million pushing
cycles can occur.
3. High reliability is required. The scanners are designed with high reliability for
operation with minimum down time.
4. Output force must counteract the reticle’s inertial force during the acceleration
interval, such that the remaining net force on the reticle is less than 30% of the
inertial force. The device must be cable of exerting forces up to 50 N.
5. No disturbance on the reticle should cause more than 1-nm reticle motion or
pattern deformation during the exposure interval. A compressive force of approximately 2 N can cause as much as 1 nm deformation within the reticle’s
patterned area.
6. Fast transient time of 1 ms between when the acceleration cycle is complete and
when the assist device creates no disturbance on the reticle is required.
7. Pusher vibration modes must be above 1 kHz to avoid negatively impacting the
stage dynamics and motion control.
8. Reticle size variation of ±0.4 mm and any additional reticle positioning tolerance should be tolerated by the assist device. As a result, the assist device is
required to have a coarse adjustment range of 1 mm.
9. No damage to reticle is allowed. The contact stresses induced within the reticle
must be limited to avoid damage.
53
10. No large impact forces can be tolerated. Large impact forces can damage the
reticle or cause slip. The reticle-tip contact must be controlled to avoid impact.
11. Cables or lines connecting to the assist device can disturb the stage and must
be minimized.
12. Illumination light cone cannot be blocked by the assist device.
13. Contaminating the scanner’s enclosure by particle generation or leakage is not
allowed.
2.3
Conceptual Designs
We considered several different actuation technologies for designing a reticle assist device (RAD). In the following subsections, we describe the most promising conceptual
designs.
2.3.1
Piezoelectric Concept
A simplified diagram of the piezoelectric RAD concept is shown in Figure 2-2. The
device uses a piezoelectric actuator to push on the reticle. The piezoelectric actuator
has a limited range (order of 10 µm), and thus requires a coarse actuation mechanism
to adjust the piezo’s position according to the variations in the reticle size and position. The coarse approach mechanism consists of a pneumatic bellow and a vacuum
clamp. The coarse adjustment is performed by preloading the piezo against the reticle, extending the piezo by the desired gap size, and activating the vacuum clamp.
The bellow and the vacuum clamp can be operated using on-off pneumatic-valves. It
is possible to design a pneumatic circuit logic such that the bellow and the device’s
clamp are actuated from the reticle clamp’s vacuum supply, but with fixed delays. In
this way, no additional vacuum lines need to be brought onto the reticle stage. The
piezoelectric device is solid-state, meaning that it has no moving parts. It has very
fast dynamics and its motion can be controlled with high precision. The piezoelectric assist device also has the advantage of being light. For example, a commercially
54
vacuum clamp
Clamp valve
pneumatic
bellow
coarse stage
piezoelectric
element
bellow valve
vacuum clamp
p
clamp valve
Figure 2-2: Conceptual
design of a piezoelectric reticle assist device.
stator
normal piezo
available piezo stack actuator weighing less than 20 g has a range of 15 µm and can
exert a pushing shear
force aspiezo
high as 100 N [66].
mover
2.3.2
Magnetostrictive Concept
The magnetostrictive assist device concept is similar to the piezoelectric concept,
which was described in Section 2.3.1, except that the piezoelectric element is replaced by a magnetostrictive element and its associated driving coils. A simplified
diagram of the magnetostrictive RAD concept is shown in Figure 2-3. The device
uses a magnetostrictive actuator to push on the reticle. The actuator consists of a
magnetostrictive element with a coil wrapped around it. Energizing the coil creates
a magnetic field through the element, which extends its length. Given the actuator’s limited range, it is used with a coarse adjustment mechanism. Compared to
the piezoelectric assist device, the magnetostrictive assist device has two main disadvantages: it is heavier and less efficient. First the copper coils and magnetic circuit
add to the actuator’s mass. Also, the coil resistive power loss dissipates energy even
when holding a constant extension. The heat from the coils can result in thermal
expansion of the magnetostrictive actuator and other stage components. However,
the magnetostrictive actuator has two advantages. It requires a current source, and
thus can potentially be directly driven in series with the reticle stage’s motor coil
currents. Also, the magnetostrictive element does not have a stack construction and
55
coil
pneumatic
bellow
stator core &
coarse stage
magnetostrictive
element
bellow valve
vacuum clamp
Clamp valve
Figure 2-3: Conceptual design of a magnetostrictive reticle assist device.
pneumatic
bellow
coarse stage
is mechanically stronger, whereas piezoelectric elements can suffer brittle fracture.
For a pushing force of 75 N, an actuation range of 10 µm, and 1.6 W maximum
piezoelectric
dissipation, the expected mass of the assist device’s magnetostrictive
element, coils,
element
and magnetic cores is estimated to be 270 g. This mass estimate does not include the
bellow valve
coarse adjustment mechanism.
vacuum clamp
p
2.3.3
clamp valve
Electromagnetic Concept
stator
Another option is a moving iron actuator similar to the flux-steering actuator designed
normal piezo
by [50]. A simplified diagram of this assist device concept is shown in Figure 2-4.
shear piezo
The electromagnetic
actuator uses a permanent magnet to create a bias magnetic
field in the air gaps onmover
the two sides of the armature. The coils are used to steer the
flux towards one side of the armature and create a net force in that direction. The
permanent magnet makes the actuator more efficient because with a bias a larger net
force can be generated for a given change in the coil current. The main disadvantage
of the electromagnetic actuator is that it is open-loop unstable and requires closedloop control with displacement sensor feedback. The key advantage of the concept
is that it can be designed to have a range of 1 mm, and thus can be used without
a coarse approach mechanism. For a pushing force of 75 N, an actuation range of 1
mm, and 1.2 W maximum power dissipation, the expected mass of the assist device’s
56
stator core
magnet
coil
pushing element
armature
t
core
Figure 2-4: Conceptual design of an electromagnetic
coil reticle assist device, inspired by
actuator
design
of
Lu
[50].
pneumatic
stator core &
coarse stage
bellow
coils and magnetic core is estimated to be 220 g. The mass estimate does not include
the supporting structure.
magnetostrictive
element
2.3.4
Piezo Stepping Motor Concept
bellow valve
A simplified diagram of a piezo stepper assist device conceptvacuum
is shown
in Figure 2clamp
R
Clamp valve
5. Piezo steppers, such as the Physik Instrumente’s
PiezoWalk
linear motors, are
commercially available. The mover is moved forward by the shear piezos and is
pneumatic
clampedbellow
using the normal piezos. A set of two legs can work together to step the mover
coarse stage
forward or backward. We can use the stepping actuation for coarse adjustment and
use the shear piezos, with the normal piezos in the clamped state, for fine actuation
and exerting the pushing forces on the reticle. Disadvantagesmagnetostrictive
of the piezo steppers
element
are their high cost and the possibility of wear as a result of the repeated clamping
bellow valve
action and the shear loading of the normal piezos. The Physik Instrumente N-111.20
R
PiezoWalk
has a range of 10 mm, a maximum force of 50 N,
and weight
vacuum
clamp
p of 245 g.
clamp
The piezoelectric motor is expected to dissipate
littlevalve
energy.
stator
2.3.5
Pneumatic/Hydraulic Bellow Concept
normal piezo
We have also considered
using pneumatic or hydraulic bellows for creating the pushing
shear piezo
forces. The bellows are mover
very light. However, it is very difficult to control their motion
57
bellow valve
vacuum clamp
p
clamp valve
stator
normal piezo
shear piezo
mover
Figure 2-5: Piezo stepping motor concept.
and output force with sufficient speed and precision. To make the bellows compact
enough, they would also require a relatively high actuating pressure. For example,
with a surface area of A = 1 cm2 , a pressure difference of P = 50 × 104 P a ' 5 Atm is
required to create a pushing force of F = P × A = 50 N This introduces a significant
chance of leakage and failure over the life time of the scanner.
2.4
Concept Selection
We have selected the piezoelectric concept for designing the reticle assist device.
The piezoelectric assist device uses solid-state actuation and has no moving parts,
except for micrometer-level elastic extension of the piezo. The main advantages of
the piezoelectric assist device are as the following:
• Low Mass: the piezo actuator mass can be less than 20 g. The total mass
including the coarse approach stage can be less than 100 g.
• Long Life Time: the piezo device has no moving parts and no fundamental wear
mechanism.
• High Reliability: The piezo device is simple and does not have many failure
modes. In its failed state, the device is a solid piece which does not affect the
scanner’s operation.
• Excellent Dynamics: the assist device can be designed to have no low-frequency
vibration modes; first mode can be in excess of 1 kHz.
58
• Open-Loop Stable: the piezo is open-loop stable and can be operated without
a sensor and a closed-loop controller.
• High Control Bandwidth: the piezo’s motion and force can be controlled at a
high bandwidth.
• High Control Resolution: the piezo’s motion can be controlled with high resolution.
Given these advantages, a piezoelectric assist device can provide a practical solution to the reticle slip problem. In the following chapter, we present the detailed
design of an assist device based on the piezoelectric conceptual design.
59
60
Chapter 3
High-Force-Density Reticle Assist
Device
In this chapter, we first present the mechanical design of a piezoelectric reticle assist
device (RAD), which has been designed based on the piezoelectric RAD concept
introduced in Chapter 2. This configuration has been experimentally implemented
and tested. In Section 3.3, we present ideas for more efficient packaging of the assist
device. In Section 3.4, we present a concept for a magnetostrictive fine actuator
design, which can be used as an alternative to the piezoelectric fine actuator.
Figure 3-1 shows a CAD model of the device. It consists of a coarse stage, for
reaching the reticle’s edge, and a fine stage, for exerting pushing forces on the reticle.
The mechanical design of the fine and coarse stages are described in Sections 3.1
and 3.2, respectively.
3.1
Fine Stage
A CAD model of the fine stage is shown in Figure 3-2. The fine stage consists of a
piezoelectric actuator, a spherical push-tip, and an adapter piece for mounting the
actuator to the coarse stage.
61
Z
Y
X
Figure 3-1: CAD design of the reticle assist device. The device consists of two subassemblies: a coarse approach mechanism and a fine actuation mechanism.
Input
Voltage
Strain Gauge
Signals
Adapter
Tip
Tip
Adapter
Piezo
Actuator
Figure 3-2: CAD model of the actuator used for exerting the pushing force on the
reticle.
62
3.1.1
Piezoelectric Actuator
The fine stage uses a Physik Instrumente P-841.10 piezoelectric stack actuator [66].
The actuator has a specified 0-100 V input voltage range and a position range of 15
µm. It has a stiffness of 57 N/µm and can carry up to 1000 N in compression and
50 N in tension. The actuator parts are enclosed by a stainless steel can. The piezo
stack actuator is fixed to the bottom of the can. A part attached to the other end of
the piezo stack extends out of the enclosure and has a threaded hole on the outside.
Inside its enclosure, the piezo stack actuator is preloaded in compression to avoid
damage, which can be caused by tensile loads. Typically, Belleville washers are used
to preload the moving end of the actuator against the inside of the enclosure.
3.1.2
Pushing Tip Design
We use a spherical pushing tip to ensure that the tip-reticle contact and the resulting
pushing force are centered on the piezo actuator’s axis. Eccentric forces can create
a bending moment on the piezo actuator. With a large eccentricity, the bending
moments can create tensile loads, which can damage the brittle piezo stack. Angular
misalignment between the piezo and the reticle edge can result in eccentric loading.
Using a small tip diameter reduces the eccentricity for a given angular misalignment.
We use a plano-convex spherical lens, model 63-479 from Edmund Optics [19], as
our spherical tip. The lens has a spherical radius of curvature of 50 mm. It is made
of N-BK7 uncoated glass. Using a lens provided us with a cost effective off-the-shelf
component of controlled radius. We could not find a lens with an approximately the
same size but a larger radius of curvature. We center the lens and the piezo stack
by centering them to the lens adapter part. The lens is fitted to the adapter using a
interference fit. The adapter is centered to the piezo stack using the threaded bolt.
The adapter is manufactured such that the fit surface and the threaded extrusion
R
are concentric. The lens is preloaded and is fixed to the adapter using Araldite
LY 5052 epoxy [34]. For the final product, the spherical tip and its adapter can be
custom machined as one part. In that case, the tip can also have a larger radius of
63
curvature.
Another concern is the stress induced in the reticle via contact. According to
Slocum [76], the maximum allowable contact pressure (qmax ) for brittle material can
be calculated as
q max =
2σmaxf lex
,
1 − 2ν
(3.1)
where σmaxf lex and ν are the maximum allowable flexural stress and the Poisson’s
ratio for the reticle material, respectively. The contact pressure can be estimated
based on the Hertz contact model using the following equation:
q=
a Ee
π Re
(3.2)
where parameters Re , Ee are the equivalent radius of curvature and equivalent
elastic modulus of contact given as
Ee =
1
1−ν12
E1
Re =
+
(3.3)
1−ν22
E2
1
R1−major
+
1
R1−minor
1
+
1
R2−major
+
1
R2−minor
(3.4)
(3.5)
where E and R are the modulus of elasticity and the radius of curvature of the contact
surfaces 1 and 2, and a is the radius of the resulting contact area and can be calculated
as
a=(
3F Re 1/3
)
2Ee
(3.6)
where F is the contact force.
For our system, using the parameters in table 3.1, the contact pressure is calculated
as 195 MPa. According to equation 3.1, a flexural strength of 67 MPa is required for
allowing a contact pressure of 200 MPa.
64
Table 3.1: Table of contact parameters
Parameter
Description
Value
E1
Elastic Modulus of reticle 74 GPa
ν1
Poisson’s ratio of reticle
0.17
E2
Elastic Modulus of tip
81 GPa
ν2
Poisson’s ratio of tip
0.21
F
contact force
60N
Reticles are typically made from fused silica. Searching in the literature, we have
found a wide range of flexural strength values for fused silica, which depend on the
size of the loading area and the surface defects of the material. Determining the
flexural strength of the reticle material was considered to be beyond the scope of
this thesis. Here, we have presented methods for estimating the stress levels. The
tip radius can be increased to reduce the stress to levels below the allowable flexural
strength of the reticle. For example, using a spherical tip radius of 200 mm, we can
reduce the maximum contact stress to 77.4 MPa and the required flexural strength
to 25.4 MPa. We have loaded the contact for several thousands of cycles, and so far,
our test reticle has not experienced any visible failures.
3.2
Coarse Stage
Due to reticel and handler tolerances, the reticle edge position can vary by as much
as ±500 µm. The pusher fine stage has a limited range of 15 µm. The coarse stage
is thus used to position the fine stage close to the reticle, so the the piezoelectric
actuator can reach and push on the reticle. A CAD model of the coarse stage is
shown in Figure 3-3. The coarse stage consists of a flexural bearing for guiding the
motion, a pneumatic bellow for actuating the stage, and a vacuum clamp for clamping
and holding the stage’s position. The design of the coarse stage parts is described in
the following subsections.
65
Clamp
Bar
Bellow
Guide
Flexure
Membrane
Bellow
Mount
Stage
Mount
Z
Y
X
A A
A-A
Section A-A
Figure 3-3: CAD design of the coarse approach mechanism (top) and a cross-sectional
view (bottom); the top membrane is made transparent to better show the coarse
stage’s design.
66
3.2.1
Guide Flexure
The coarse stage uses a flexural bearing for guiding its motion. The flexure constrains
the motion of the stage to the X-direction. The guide flexure design is shown in
Figure 3-4. The flexural consists of four flexural legs. We use back-to-back flexural
legs to allow a larger range of motion for a given size. With the back-to-back design,
the flexures are not stressed along their length as their deformations in the Y-direction
cancel out. The flexure blades are designed to have a thickness of 0.2 mm. The blades
are joined at their ends using a 1-mm thick link. This thicker link is used to reduce
the torsional compliance of the flexure legs and avoid low-frequency vibration modes.
The flexure guide is made out of Aluminum Alloy 2024-T4 to achieve low mass and
high strength. The flexure blades are machined using an electric discharge machining
(EDM) process. The EDM manufacturing steps are shown in Figure 3-4. The order
of the cuts is selected to ensure that the surfaces are fixed at the time they are being
cut. In this way, the required manufacturing tolerances can be achieved.
The guide flexure’s stiffness can be calculated as the following:
kf = 4 × 2 ×
6EI
= 5 N/mm
L3
(3.7)
where E = 73 MPa, t = 0.2 mm, L = 15 mm, w = 0.74 mm, and I =
1
wt3
12
are the
modulus of elasticity, thickness, length, width, and the bending moment of inertia of
the flexure blades respectively. The maximum bending normal stress in the blades
can be calculated as the following:
σmax =
3tE
× δmax = 48 MPa
2L2
(3.8)
where δmax =0.5 mm is the maximum deformation about the guide flexure’s center
position. We use round corners to limit the stress-concentraion in the corners. Using
COSMOS FEA software we predict a maximum von Mises stress of 80MPa at the
end of the flexure blades. The flexure stage operates once each time a new reticle is
loaded, and thus, as a conservative estimate, we expect the flexure to go through less
67
C
moving
stage
Figure 3-4: CAD model and partial drawing of the coarse stage’s guide flexure showing
its design.
68
Z
Y
X
X
Y
1.
2.
3.
4.
5.
6.
7.
8.
Figure 3-5: Top-view of the coarse flexural stage (top) showing the flexure design.
The steps for the EDM manufacturing process are shown for one flexure leg.
69
Mode 1
1060Hz
Mode 2
1455 Hz
Figure 3-6: First two vibration modes of the reticle-assist device computed with the
vacuum clamp activated.
than a million cycles. The fatigue analysis data provided in [72] shows that notched
2024-T4 Aluminum alloy with 100MPa load did not fail in over 1 million cycles.
It is desired to design the flexures to be soft in the X-direction so that the coarse
stage can be actuated by ±0.5 mm using the bellow at a reasonably low pressure.
Using thin flexure blades provides lower stiffness in the X-direction. It also provides
a larger range of motion for a given stress level. However, reducing the flexure’s
thickness reduces the system’s stiffness in other degrees of freedom as well and can
result in low-frequency vibration modes. Using COSMOS, we calculated the device’s
vibration modes, when in the clamped state. The first two vibration modes are
shown in Figure 3-6. The first mode is mainly translational in the Z-direction, and
the second mode is mainly torsional around the Y-direction. The first two modes
cause a displacement in the Z-direction at the tip, and thus do not affect the reticle
assist device’s control. However, these vibration modes can affect the control of the
scanner stage and must be above 1 kHz, which is satisfied.
3.2.2
Preload Actuator
We use the coarse stage to prelaod the piezoelectric actuator against the reticle’s edge.
Therefore, we need a preloading force with only on-off control to actuate the coarse
70
Bellow
Pressure
Adapter
Inlet
Vacuum
Inlet
Vacuum
Pocket
Clamp
Bar
Membrane
Bellow
Mount
Z
Y
X
Figure 3-7: CAD cross-sectional view of the coarse approach mechanism showing the
bellow and the vacuum clamp design.
stage. We use a Servometer1 FC-6 pneumatic bellow. As shown in Figure 3-7, the
bellow adapter part connects the bellow to the guide flexure. The bellow is connected
to its mount on its other side. We pressurize the bellow through a port on its mount.
The bellow has an effective area of Ab = 47 mm2 and a stiffness of kb = 1.9
N/mm. The bellow’s actuation range (∆xb ) for a given change in pressure (∆P) can
be calculated as the following:
∆xb =
∆P × Ab
kf + kb
(3.9)
where kb and kf are the stiffness of the bellow and the guide flexure in the X-direction
respectively. Using an actuation pressure of 1 Atm a range of 6.8 mm can be reached,
which would be the coarse actuation range if the bellow is used with a vacuum line.
For our experimental setup, we use a 100 psi pressure line with a pressure regulator
to control the bellow’s pressure and expansion. We require 1.5 Atm of differential
pressure for an actuation range of 1-mm. The bellow can create forces in only one
direction. We can use a positioning offset to preload the bellow’s stiffness and shift
the actuator’s output force range to achieve a bi-directional actuation force.
1
www.servometer.com
71
The bellow is connected to its mating parts by soldering according to the procedure
provided by [67]. Brazing is not recommended as the raised temperatures from the
flame can damage the bellow. Stainless steel 304L or 316L is recommenced as the hub
material. The hubs are tinned using a flux for stainless steel, such as Kester #815.
A Superior #30 flux is recommended for the bellows. To connect the bellow to the
hubs, first the bellow and the hubs are fluxed and tinned separately. Next, the two
are joined together. At each stage, the parts are cleaned by placing them in Kester
#5760 neutralizer for 5 minutes and in boiling water for another 5 minutes.
3.2.3
Clamp
Once the piezo actuator is preloaded against the reticle, we use a clamping mechanism
to hold its position. Once activated, the clamping mechanism must be rigid in the
direction of actuation. A high-stiffness mechanical loop is required for achieving large
enough pushing forces within the limited fine actuation range. The clamp must also
be precise, such that the clamp’s activation does not displace the piezo. We use a
vacuum clamp, whose design is shown in Figure 3-7.
Vacuum pockets are machined into the two sides of the coarse stage’s guide flexure.
Two membranes cover the vacuum pockets and are used to clamp the guide flexure’s
moving part to its stator. The membranes are fixed to the guide flexure’s stator
using clamping bars. The vacuum line is connected through the bellow adapter. The
connection between the bellow adapter and the guide flexure is sealed using an Oring. Once vacuum is applied, the membranes are loaded against the guide flexure,
which rigidly constrains the guide flexure in the X-direction.
The vacuum clamp uses the surface area on both sides of the guide flexure and can
thus generate larger clamping force. A symmetric design also improves the clamping
mechanism’s precision by creating a uniform constraint. A symmetric clamp is also
more rigid because the forces are balanced on the top and bottom planes, and thus
the structure is not loaded by bending moments. The total vacuum pocket area,
including both sides, is 1875 mm2 . Based on experimental results, the clamp can
carry more than 80 N of pushing force without sliding.
72
The guide flexure is made from Aluminum Alloy 2024-T4. To increase the hardness
of the vacuum clamp surface and avoid wear, the outer surface of the guide flexure
is hard anodized with a thickness of 5 µm. Blue tempered 1095 Spring Steel with a
hardness of more than 50 RHC is used for the membranes. To achieve a uniform and
close contact, the guide flexure is designed to have its stator and moving parts on the
same plane. To achieve the required flatness on the guide flexure and the membrane
surfaces, the parts are precision machined using milling and are then lapped by hand.
3.3
Designs for Integration
The reticle assist device prototype has been designed for experimental verification of
the design and development of the control algorithms. We have designed the setup
for easy assembly and operation. Currently, we have a series design where the bellow,
the clamp, and the piezo actuator are connected in series. We call this a ‘3L’ design,
since the three lengths add into the overall length. This simplifies the assembly and
the operation of the device. However, for integration with the scanners, the design
can be packaged more efficiently into a ‘1L’ design. Figure 3-8 shows two ways of
nesting the components within the guide flexure. The nested design is expected to
have a lower volume and better vibrational dynamics.
In both designs, the piezo actuator and the bellow are nested inside the guide
flexure. To save volume and cost, the piezo actuator can be custom manufactured
using a piezo-stack. The design on the left uses a pneumatic bellow as the coarse
approach actuator. The design on the right uses a a pressure pocket formed by the
guide flexure, the membranes, and the stator to actuate the coarse approach stage.
3.4
Magnetostrictive Actuator
Magnetostrictive elements are another type of commonly used solid-state actuator.
Application of a magnetic field results in extension of the magnetostrictive element.
The elements are energized using current carrying coils. A magnetostrictive actuator
73
Figure 3-8: Ideas for more efficient packaging of the reticle assist device into a ‘1L’
design.
is suitable for use as a reticle assist device because it uses a current source, and thus
can be driven using the scanner motor currents. However, thermal length changes
can be a significant source of error for magnetostrictive actuators. The heat from
the resistive energy loss in the coils can raise the temperature of the elements and
cause thermal expansion. The motion range of magnetostrictive elements is limited
to less than 0.2% of their active length. Over such a small range of motion, thermal
length variations can become significant. We have designed a thermally balanced
magnetostrictive actuator, which eliminates the thermal variations. It also increases
the actuation range by stacking two elements in series. The design of the actuator is
described in the following subsections.
The thermally-balanced magnetostrictive design is provided as an alternative to
the piezoelectric stack actuator. Compared to the piezoelectric actuator, the magnetostrictive actuator will have a larger mass and higher power dissipation, and hence,
is not selected for detailed prototyping.
74
4
2
4
2
2
x
4
1b
1a
1b
1a
1a
1b
3
3
3
(b)
(a)
(c)
Figure 3-9: Thermally-balanced actuation method: the actuator is shown in its neutral position (a), positive extension (b), and negative extension (c).
3.4.1
Thermally-Balanced Configuration
To eliminate thermal length variation, two actuators are used back to back and are
driven differentially, as shown in Figure 3-9. Element (1a) moves the middle frame
(3) relative to the fixed reference frame (2). Element (1b) rides on the middle frame
(3) and moves the actuation end (4) relative to the middle frame (3). The actuator
is in it neutral position when both elements (1a) and (1b) are driven to their midrange of motion. Driving the elements (1a) and (1b) differentially around this neutral
position results in the motion of the actuation end (4). Contracting element (1a) and
extending element (1b) moves the actuation end (4) in the positive x-direction relative
to the fixed reference frame (2). Extending element (1a) and contracting element (1b)
moves the actuation end (4) in the negative x-direction relative to the fixed frame
(2). However, any thermally induced length change of elements (1a) and (1b) will be
equal and will cancel out. As a result, the actuation end (4) will not move due to
thermal length variations.
75
40
20
x
60
50
N
70
X
X X
10a
10b
S
30
Figure 3-10: An example embodiment of the thermally balanced solid-state actuator’s
magnetic design using magnetostrictive elements.
3.4.2
Magnetic Design
The magnetostrictive elements can only increase in length, a bias magnetic field is
required to enable bi-directional changes in length. To create a thermally balanced
design, two elements should be used as in Figure 3-9. A differential magnetic field
added to one element and subtracted from the other element around a magnetically
biased operating point results in the motion of the actuation end (4) relative to the
reference frame (2). Figure 3-10 shows one possible embodiment of the magnetic
circuit design.
In the design shown in Figure 3-11, the magnetostrictive elements (10a) and (10b)
are used on the outside and the inside respectively. The magnetic cores (20), (30), and
(40) are magnetically permeable and close the magnetic path. Core (20) is fixed to a
reference frame. Core (30) is moved by element (10a) and connects the two elements
(10a) and (10b). Core (40) is moved relative to core (30) by the element (10b). A
permanent magnet (70) is used to create a bias magnetic field through the elements
76
(10a) and (10b) in the same direction. The flux lines generated by the permanent
magnet are shown as dashed lines. The coil (50) wraps around the element (10a).
Coil (60) wraps in the opposite direction around element (10b). A current through
the coils (50) and (60) creates a differential magnetic field within the elements of the
same magnitude but opposite directions and thus one element 10a lengthens while
the other element 10b shortens, and vice versa. The flux lines generated by the coils
are shown as dotted lines. The use of two coils (50) and (60) creates a magnetic
quadrupole, whose stray field will decay much faster. It also balances the differential
field, such that the two elements (10a) and (10b) are driven by the same differential
field amplitude. In this design, the bias magnetic field is provided by a permanent
magnet. In this way, the actuator is at its desired magnetic bias using zero current
and without any loss.
3.4.3
Mechanical Design
Detailed mechanical design is shown in Figure 3-11. The main frame (21) is the
reference frame. The back core (20) is fixed to the main frame (21). The magnetostrictive element (10a) is located between the back core (20) and the middle core
(30). The magnetostrictive element (10b) is positioned between the middle core (30)
and the actuation-end core (40). The permanent magnet (70) is placed at the center and provides the magnetic bias. The outside coil (50) wraps around the outer
magnetostrictive element (10a). The inside coil (60) wraps around the inner magnetostrictive element (10b). The two flexure plates (81) and (82) are used on the
two ends to constrain the actuator’s motion, but more importantly, put the magnetostrictive elements under a bias mechanical compressive stress. The bias mechanical
compressive stress improves the element’s magnetostriction coefficient (strain/field)
and prevents compressive to tensile stress reversals. The coupling (41) is used to
connect the actuating end to the load. To allow misalignments between the coupling
(41) and the load, the coupling (41) is stiff only in the axial direction and flexible
in all other degrees of freedom. For pushing applications, the coupling must have a
high (or infinite) radius of curvature, to avoid large stress concentration at the point
77
Table 3.2: Magnetostrictive actuator design parameters
Parameter
Description
Value
A
Area of a single magnetostrictive element
25 mm2
L
Length of a single magnetostrictive element
25 mm
d
Average magnetostrictive constant
2 × 10− 8 m/A
E
Elastic Modulus of magnetostrictive elements
30 GPa
4
n
Coil turns per unit length
10 turns/m
of contact.
Using the design parameter values provided in table 3.2, the actuator can close a
gap of 2 µm and exert a pushing force of 70N when a excitation current of 1.2 A is
applied. The peak power dissipation is estimated to be 1.9W.
78
21
82
41
30 mm
81
20
40
70
10b
30
10a
x
50
60
Figure 3-11: CAD Model of the thermally-balanced magnetostrictive actuator design
(top) and its cross-sectioned view (bottom).
79
80
Chapter 4
Hybrid Charge Controller
Piezoelectric actuators have excellent motion resolution and high bandwidth. As a
result they are widely used in precision motion applications, such as scanning probe
microscopy and laser mirror alignment. The most common way of driving piezoelectric actuators is using a voltage amplifier to apply a voltage to the actuator in an
open-loop fashion. This relies on the actuator voltage-displacement behavior; however, piezoelectric elements exhibit strong hysteresis. One way to eliminate the error
caused by hysteresis is controlling the actuator in closed-loop using displacementor strain-sensor feedback. Using a closed-loop controller has several disadvantages
for high-frequency applications. It can reduce the system’s control bandwidth, when
compared to the open-loop operation, which is limited by only the actuator’s mechanical dynamics. Using a displacement sensor also can add noise to the system,
and can thus worsen the resolution. Finally, using closed-loop control requires the
addition of a sensor as well as implementing a controller. An effective alternative for
reducing the hysteresis is charge control [15] [62]. Commercial piezo ceramics have
a high relative permittivity (εr > 1000), and thus the displacement charge is almost
equal to the polarization charge (D ' P) [62]. Therefore, controlling charge is almost
equivalent to controlling polarization, which results from alignment of the dipoles
within the piezoelectric ceramic. Polarization and mechanical strain result from the
same ionic movement and are directly related [62][52]. Therefore, charge control can
significantly improve an actuator’s linearity.
81
In this chapter, we first review prior art piezo charge amplifiers. We also present
the design of our novel charge amplifier which advances the state of the art. We
provide experimental results obtained using the amplifier. Finally, we describe a
magnetic analogue of piezo charge control, where controlling magnetic flux can improve a magnetic actuator’s linearity. We present methods for magnetic flux control
supported by experimental results.
4.1
Prior Art Charge Amplifiers
In 1981, Comstock patented a charge amplifier design for improving the linearity
of piezoelectric driven deformable mirror [15]. As shown in Figure 4-1, Comstock’s
design uses a sense capacitor (32) in series with the piezoelectric actuator (10) to sense
accumulated charge via voltage. The sensed voltage is fed back to the power amplifier
(30) for closed-loop charge control. This configuration is however sensitive to the finite
resistance of the capacitors at low frequencies causing the charge to drift after a period
of time. To eliminate the drift problem, Comstock’s design included switches (34, 35,
and 41) controlled by a timer (37) to reset and initialize the piezoelectric actuator
(10) and the charge amplifier. Main et al. use an amplifier with a similar design [52]:
In 1982, Newcomb and Flinn used a current controller to control the charge on a
piezoelectric actuator by controlling the time integral of the current [62]. However,
due to offset errors, the integral of the current can drift with time resulting in a charge
control error. As a result, this control method is only effective for a limited period
of time unless an initialization method is introduced or another feedback is used for
quasi-static tracking.
In 1988, Kaizuka and Siu suggested inserting a capacitor in series with the piezoelectric actuator not for sensing charge but for reducing the sensitivity of the induced
charge to the hysteresis of the piezoelectric actuator when driven using a voltage
source [40]. This can most easily explained at the limit where the inserted capacitor
is significantly smaller than the piezoelectric actuator’s capacitance. At this limit,
the total series capacitance is approximately equal to the small capacitance of the
82
Figure 4-1: Comstock’s charge amplifier design. This figure is copied from US Patent
4,263,527 [15].
inserted capacitor and is thus relatively insensitive to the piezoelectric element’s capacitance. As a result, the induced charge is approximately given by the applied
voltage multiplied by the inserted capacitance (Q = Cv) and is less sensitive to the
changing capacitance of the piezoelectric actuator. A short mathematical proof of
this is also provided in [56]. This method is effective when the inserted capacitor has
a low capacitance when compared to the piezoelectric element’s. Smaller capacitance
results in a larger impedance meaning that most of the voltage is dropped across the
inserted capacitance. Although this is a very simple method to improve the linearity
of the piezoelectric actuators, it requires significantly higher total drive voltage, as
only a portion of the voltage output goes to driving the piezoelectric element.
In 2001, Tonoli et al. added a resistor in parallel to the sensing capacitor to prevent
drift [82]. A simplified schematic of their charge amplifier design is shown in Figure 42. The added resistor (R1) is used to compensate the drift, which can be caused by
the leakage resistance of the piezo actuator (Rp). The resistive feedback formed by R1
and Rp is dominant at low frequencies while the capacitive feedback formed by C1 and
83
Figure 4-2: Charge amplifier design by Tonoli et al. The diagram has been reproduced
from [82].
Cp is active at high frequencies. As a result, charge is sensed and controlled at high
frequencies, and voltage is controlled at low frequencies. The values of R1, Rp, and
C1 are selected such that the resistive and capacitive feedbacks have matching gains
and break-frequencies. In this configuration, the load currents are sourced by the
operational amplifier (OA). This can be a problem in higher frequency applications
where the piezoelectric actuator’s capacitive currents can be too large.
In 2003, Fleming and Moheimani designed a charge controller similar to the design
in [15] but added an auxiliary control loop to eliminate drift by using voltage feedback
in DC [23]. In this way, charge could be controlled at higher frequency and voltage at
lower frequencies. This solution required designing two separate controllers for charge
and voltage.
Another simpler implementation was provided by Yi and Veillette in 2005, where
the architecture of the passive feedback circuit resulted in voltage control in DC and
charge control at higher frequencies [84]. As shown in Figure 4-3, Yi and Veillette
used an inverting amplifier configuration. The feedback voltage is dominated by the
resistors R1 and R2 at low frequencies and by the capacitor C1 and the piezoelectric
element at higher frequencies. In their design, the piezo is referenced to the pseudoground at the op-amp’s inverting input and is not floating. However, the load current
84
Figure 4-3: Yi and Veillette’s charge amplifier design. The diagram has been reproduced from [84].
Figure 4-4: Fleming and Moheimani’s charge amplifier design. The diagram has been
reproduced from [24].
must be supplied at the reference signal terminal (VREF ). The reference signal driver
may have a finite impedance which thus affects the feedback gain. Additionally,
the piezoelectric current at higher frequencies can be too large for the driver of the
reference signal.
In 2006, Fleming and Moheimani [24] suggested an improved configuration where
the passive feedback circuit results in voltage control at low frequency and charge
control at higher frequencies. A simple schematic of this design is shown in Figure 4-4.
In this configuration, the load currents are sunk through ground. In the configuration
presented by [24], the piezoelectric load is referenced to ground and not floating.
However, this configuration requires a high-voltage and high common-mode-rejection
instrumentation amplifier to measure the voltage on C1 [22].
A modified version of this configuration, where no additional active components
85
VREF
VO
CP
VS
+
VP
−
Figure 4-5: PiezoDrive’s charge amplifier design. The diagram has been reproduced
from [1].
are required is provided in a technical report on PiezoDrive’s website1 [1], and reproduced in Figure 4-5. The modified configuration is identical to the design in [15]
but with an added resistive (R1 and R2) feedback path for preventing low-frequency
drift.
4.2
Analysis of Conventional V-Q Charge Amplifier
A common commercial charge amplifier design is shown in Figure 4-5. In this section
we analyze such a charge amplifier configuration. A block diagram of the charge
amplifier is shown in Figure 4-6. The power amplifier is represented by the transfer
function GP A (s). The signals VRef , VO , VS represent the amplifier reference voltage,
output voltage and sensed feedback voltage, respectively. A simple way to understand
this design is to look at the low and high frequency limits. At low frequencies (quasistatic), the feedback is dominated by the resistors because they have a much lower
impendence than the capacitors in this frequency range. At high frequencies, the
capacitors have a lower impedance than the resistors and dominate the feedback. The
voltage on the capacitive feedback circuit is proportional to charge, and therefore, can
be viewed as sensing charge. The resistive network voltage feedback is included to
avoid low frequency drift which can result from static charge measurement. For this
1
PiezoDrive has been founded in 2009 by Dr. Andrew Fleming (http://www.piezodrive.com)
86
VRef
+
GPA(s)
VO
1-F(s)
VP
−
VS
F(s)
Figure 4-6: Block diagram of the charge amplifier design shown in Figure 4-5.
mixed voltage-charge (V-Q) feedback circuit to work uniformly over all frequencies,
the resistors and capacitors must be sized appropriately, as presented below.
The feedback voltage VS is related to the output voltage VO through the transfer
function F(s). For the design shown in Figure 4-5, the transfer function F(s) can be
calculated as
F (s) =
VS
R1 (R2 Cp s + 1)
=
.
VO
R2 (R1 C1 s + 1) + R1 (R2 Cp s + 1)
(4.1)
The feedback transfer function F(s) can be approximated at the high and low
frequency limits as
F (s) '



R1
R1 +R2
Cp
C1 +Cp
s ωV Q Voltage Control
,
(4.2)
s ωV Q Charge Control
where ωV Q is the frequency around which the transition from voltage to charge
control occurs. For a smooth transition from voltage to charge control, a constant
feedback gain across all frequencies is desired. This can be achieved by selecting the
components such that the following condition is satisfied:
R1 C1 = R2 Cp = τV Q =
1
(4.3)
ωV Q
Using the above expression, the transfer functions F(s) can be simplified as
F (s) =
VS
R1 (τV Q s + 1)
R1
=
=
.
VO
R2 (τV Q s + 1) + R1 (τV Q s + 1)
R1 + R2
87
(4.4)
The charge across the piezoelectric actuator is equal to the charge across the sense
capacitor (C1 ) and is given as QP = C1 × VS . Assuming stable operation of the loop,
VS is controlled to be equal to VRef . Thus, the closed-loop charge control gain is given
as
QP
= C1 .
VRef
(4.5)
However, the equivalent closed-loop voltage gain is a more relevant parameter,
when designing the amplifier. Any piezo stack actuator is specified for a certain
operating voltage range. It is important that the closed-loop voltage gain is designed
such that the voltage range of the reference signal (VRef ) is mapped to the full voltage
range of the actuator. The voltage across the piezo actuator (VP ) can be calculated
as below:
VP = VO − VS = VS (
1
R2 + R1
R2
− 1) = VS (
− 1) = VS
F (s)
R1
R1
(4.6)
Assuming large loop gain and stable operation of the amplifier, the signal VR must
be approximately equal to VS . Therefore, the amplifier’s closed-loop voltage gain can
be given as
VP
R2
=
.
VRef
R1
(4.7)
For this research, we use a piezo actuator with a voltage range of 100 V. To map
our controller’s 0-10V output range to the piezo’s 0-100V range, we select a closed
loop gain of 10 as
VP
R2
=
= 10 ⇒ R2 = 10R1 .
VRef
R1
(4.8)
We select the value of C1 according to (4.3) to match the resistive and capacitive
88
VREF
VO
ZC
VS
+
VP
−
Figure 4-7: Charge amplifier design with the resistor Rc modeling the resistance of
the cable connecting the piezo actuator the amplifier
feedbacks:
R1 C1 = R2 Cp ⇒ C1 =
R2
× Cp = 10Cp
R1
(4.9)
Our actuator has a capacitance of Cp = 1.5 µF . We choose R2 = 100 kΩ to achieve
a voltage- to charge-control frequency of 10 kHz. For a closed-loop voltage gain of
10, the component values for our charge amplifier, designed around the configuration
shown in Figure 4-5, can thus be calculated using (4.3) and (4.7) as
R1 = 10 kΩ
R2 = 100 kΩ
.
(4.10)
C1 = 15 µF
Cp = 1.5 µF
Typically, piezo actuators have a voltage range of 100 V or more. On the other
hand, the reference signal drivers have a voltage range of 10 V or less. As a result, a
closed loop gain of larger than 1 is typically required. This means that the feedback
transfer function F(s) has a gain of less than unity. This helps with the stability of the
circuit, as most linear power amplifiers are stable when used with a scalar feedback
gain of less than unity.
The control system’s stability can be analyzed using loop-shaping and the Nyquist
criterion based on the resulting feedback transfer function F(s) and the power de89
Gain [dB]
120
100
80
60
40
20
0
‐20
‐40
GPA
F
LT
CL
1 100 10K 1M Frequency [Hz]
100M 1 100 10K 1M Frequency [Hz]
100M Phase [deeg]
0
‐20
‐40
‐60
‐80
‐100
‐120
‐140
Figure 4-8: Frequency responses of the amplifier open-loop GP A (s), feedback F(s),
loop transmission LT(s), and the closed loop CL(s) transfer functions showing the
amplifier loop-shaping design
90
vice’s frequency response GP A (s). The frequency responses in Figure 4-8 show the
loop shaping design of the charge control loop. We use an APEX MP38A power
device [9] with an external compensation capacitor of 470 pF. The power device’s
frequency response is reproduced from its datasheet [9]. Using (4.2), the feedback
1
gain can be calculated as F(s)= 11
. The loop transmission ratio can be calculated as
LT(s)=GP A (s) × F(s). The loop transmission has a unity gain cross-over frequency
of 100 kHz with 90◦ of phase margin. Given the positive phase margin of 90◦ , the
closed loop response is expected to be stable and damped. The closed loop transfer
function can be calculated as
CL(s) =
VP (s)
GP A (s)
=
[1 − F (s)].
VRef (s)
GP A (s)F (s) + 1
The expected feedback transfer function F(s), as given by 4.1, is based on an
ideal circuit, shown in Figure 4-5, with no series impedances. In practice, the cables
and connections have impedance, which can affect the feedback circuit. Figure 4-7
shows the charge amplifier circuit with the impedance ZC modeling the impedance
of the connection to the piezo actuator. The series impedance can include a resistance and an inductance and can be modeled as ZC =RC +LC s. Using MATLAB, we
recalculate the feedback transfer function to reflect the effect of the series impedance.
MATLAB’s margin function is used to numerically calculate the charge control loop’s
phase margin and unity gain cross-over frequency for different series impedance values. Figure 4-9 shows the phase margin and the unity gain cross-over frequency versus
the load impedance for the conventional V-Q amplifier design presented in this section. As can be seen, the series load impedance can reduce the controller’s phase
margin and even destabilize the amplifier.
The sensitivity of the charge controller to the cabling impedance makes the design
and implementation of charge amplifiers difficult. It also prevents purposeful addition
of a series resistance for passive damping and passive current limiting. In the next
section, we present a new charge amplifier design, which significantly reduces the
charge amplifier’s sensitivity to presence of a series load resistance. We refer to the
91
VQ
Phase Margin
1
Unity Cross-Over
VQ
90
0.8
5
1
x 10
3
0.8
2.5
0.6
0.4
30
VQ
0.2
0.4
0.6
Lc [H]
2
0.4
02
0.2
1
0
0
0.6
1.5
unstable
02
0.2
0
Rc [Ω ]
Rc [Ω ]
60
0.8
1
-6
x 10
0
PM
[deg]
0
0.2
0.4
0.6
Lc [H]
1
-6
x 10
90
0.8
FC
[Hz]
5
VQV
1
1
x 10
3
0.8
25
2.5
60
0.6
0.4
30
Rc [Ω ]
Rc [Ω ]
VQV
VQV
0.8
2
0.4
1.5
0.2
0
0.6
0.2
1
0
0
0.2
0.4
0.6
Lc [H]
0.8
1
-6
x 10
0
PM
[deg]
0
0.2
0.4
0.6
Lc [H]
0.8
1
-6
x 10
FC
[Hz]
Figure 4-9: Feedback phase lag at the cross over for different cable resistance (Rc )
values displayed for the V-Q and V-Q-V charge amplifiers.
this new design as the V-Q-V Charge amplifier.
4.3
Novel V-Q-V Charge Amplifier
In the previous section, we discussed the sensitivity of the conventional charge amplifier designs to the presence of a series load resistance. In this section, we present
a new charge amplifier design which mitigates this problem.
With the conventional V-Q charge amplifier design, the capacitive leg of the feedback circuit is active at the cross over. The phase lag is a result of the series resistance
(Rc ) creating a pole with the capacitors (C1 and Cp ). This effect can be significantly
attenuated if the feedback circuit is designed to be resistive at the cross-over, as in the
proposed design shown in Figure 4-10. This charge amplifier controls charge in the
mid-band and voltage in the low- and high-frequency bands. Because the amplifier
is controlling voltage at the cross-over frequency, and has an active resistive feedback
circuit at that frequency, it is not as sensitive to the addition of any series resistance.
92
VREF
VO
ZC
+
VP
−
VS
Figure 4-10: Schematic design of the new V-Q-V charge amplifier design.
The charge to voltage control transition frequency can be selected to be above the
desired mechanical control frequency and below the amplifier’s cross-over frequency.
In this way, charge is controlled within the desired control bandwidth and voltage
control is active at the cross-over frequency. This improves the charge amplifier’s
robustness without sacrificing its performance within the desired control bandwidth.
To better understand the circuit, first consider the low frequency (ω 1
),
R1 C1
where the capacitors have a higher impedance than their corresponding parallel resistors. In this case, the capacitive leg of the feedback circuit can be ignored and the
feedback voltage Vs is driven by R2 and R1 . This is the low-frequency voltage-control
range. Next, consider the middle frequency range ( R11C1 ω 1
),
R3 C1
where the ca-
pacitors C1 and Cp have a lower impedance than their corresponding parallel resistors
R1 and R2 but higher impedance than their series resistors R3 and R4 . In this range,
the feedback is mainly influenced by the capacitors. This is the charge-control range.
Finally, consider the high frequency range ( R31C1 ω) where the series resistors R3
and R4 have a higher impedance than their corresponding capacitors C1 and Cp . In
this range, the capacitors can be neglected and the feedback voltage is dominated by
resistors R3 and R4 .
93
F (s) '









R1
R1 +R2
Cp
C1 +Cp
ω
1
R 1 C1
1
R1 C1
ω
R3
R3 +R4
ω
1
R 3 C1
Voltage Control
1
R 3 C1
Charge Control
(4.11)
Voltage Control
For the charge amplifier to work without unwanted time transients, the feedback
gain given by (4.11) must be constant over the whole frequency range. Equation 4.3
derived for matching the V-Q amplifier’s feedback also matches the feedback gain for
low- and mid-frequency bands. To match the gain over the high-frequency band to
the low- and mid-frequency bands, the following condition must be satisfied:
R3 C1 = R4 Cp .
(4.12)
The frequency where the charge-control to voltage-control transition occurs can
be calculated as
ωQV =
1
1
=
.
R3 C1
R4 Cp
(4.13)
Given a desired charge-control bandwidth, the values of the resistors R3 and R4
can be calculated using (4.12) and (4.13). The process for selection of the rest of the
circuit component values for the V-Q-V charge amplifier is the same as for the V-Q
charge amplifier.
For our design, we have selected ωQV = 10 kHz, which is 10 times below the designed amplifier’s cross-over frequency and only slightly lower than our piezo actuator’s mechnical resonance frequency of approximately 20kHz. In any case, driving the
piezo above 10 kHz is not practical since near the resonance frequency, the mechanical
dynamics degrade the open-loop accuracy. Overexciting the piezo near resonance can
also damage the actuator. The required R3 and R4 resistor values can be calculated
94
as
R3 =
1
ωQ−V C1
= 1Ω
R4 = R3 CCp1 = 10Ω
.
(4.14)
Given the above component selection, the resulting feedback phase lag at the 100
kHz desired cross-over frequency is plotted versus the series resistance in Figure 4-9.
As can be seen, the new design is significantly less sensitive to the the added series
resistance. This increases the amplifier’s phase margin and improves its robustness
to the addition of series cable resistance.
4.4
4.4.1
Charge Amplifier Hardware
Mechanical Design
To test our charge control method we have built a custom charge amplifier, which is
shown in Figure 4-11. The amplifier’s front panel has connectors for connecting the
piezoelectric actuator, giving a reference voltage, and sensing current, voltage, and
charge. A switch on the front panel allows the user to switch between charge- and
voltage-control modes. A potentiometer is also provided for fine tuning the resistive
leg of the feedback circuit. The amplifier is powered from the wall outlet. The bottom
part of the enclosure is used for the AC-DC power supply components. The printed
circuit board (PCB) and the heat sink are connected to the top side of the enclosure.
A side cross-sectional view of the enclosure box is shown in Figure 4-12. We use an
APEX1 MP38A power device [9]. As shown in Figure 4-12, the power device comes
on its own printed circuit board (PCB). The power device has its components on one
side of that PCB and a plated heat sink on the opposing side. The power device’s
plated side is fixed to the main heat sink using two screws. The main heat sink is
fixed to the top surface of the power amplifier. The enclosure has an opening cutout
for the device pins to pass through and connect to the charge amplifier’s PCB. The
1
Apex Microtechnology: www.apexanalog.com
95
Heat Sink
Transformer
PCB
±15V Supply
Supply
Capacitor
Figure 4-11: The assembled custom charge amplifier (left) and CAD design (right).
amplifier’s PCB has a socket matching the pin pattern of the power device. The PCB
is mounted onto the bottom side of the enclosure’s top. Spacers are used to position
the PCB at the right distance from the power device.[8]
4.4.2
Circuit Design
In this section, we describe the detailed circuit design of the charge amplifier. The
circuit diagram of the power device and its feedback circuit is shown in Figure 4-13.
The design of the measurement buffers is shown in Figure 4-14. The schematic of the
110-V DC supply is shown in Figure 4-15. Net labels, which mark the signals in the
schematic diagrams, are used to identify the signals and show the connection between
the schematic diagrams. The net labels are consistent with the signal convention used
within the rest of this chapter. for example, the amplifier reference, output, feedback,
and piezo voltages are labeled as Vref , Vo , Vs , and Vp , respectively.
As shown in Figure 4-13, the feedback circuit is formed by the resistors R1 , R2 ,
R3 , R4 and capacitor C1 according to the V-Q-V design, which was described in
Section 4.3. The Radj potentiometer in the resistive leg of the feedback circuit can be
used to fine tune the resistive feedback circuit and match it to the capacitive feedback
circuit. The circuit is designed to be flexible. To use as a V-Q amplifier, the resistors
96
MP38A
Device Heat Sink
Standoff
PCB
Supply
Capacitor
Transformer
±15V Supply
H.F.
Choke
Res.
Heat
Sink
Capacitor
Figure 4-12: Side cross-sectional view of the charge amplifier.
R4 and R3 can be short-circuited by placing 0 Ω resistors. The jumpers QF and
VF represent a two-position toggle switch, which enables the user to select between
voltage-control and charge control. Note that the position of the switch must not be
changed when the device is powered on. Switching the feedback configuration, while
the amplifier is powered on, can damage the power device.
Mechanical shocks on the piezo motion system can raise the piezo’s voltage beyond
the power supplies’ range and potentially damage the amplifier’s output circuitry. To
protect the power device’s output, we have added two external fly-back diodes D3
and D4 . Although the amplifier has internal fly back diodes, they should not be
counted on for repeated high-energy pulses. The two back to back diodes D1 and
D2 protect the power device’s differential inputs from large differential voltages as an
input differential voltage beyond ±20 V can damage the power device. The resistor
R7 is placed in series with the output and is used by the power device’s internal
circuitry for current sensing and limiting. The value of R7 = 0.1 Ω limits the output
current to 7 A. [9][7]
The amplifier box has BNC output connectors for sensing the piezo’s current
and voltage. In charge control mode, the feedback voltage can also be used as an
estimate of the piezo charge. The circuit diagram of the buffers measuring piezo
97
N120
TVS_UNI
TVS4
BRIDGE
2
T2_SL
C
DC110
C17 C19
0.1uF
DC-50
C3
1uF0.1uF
C4
1uF
C7
0.1uF
C8
DC-15
C18 C20
1uF
0.1uF
1uF
DC+15
C15 C9 C10 C11
C12 C13 C14 C16
10uF 0.1uF0.1uF 0.1uF
0.1uF0.1uF0.1uF10uF
R5
0
DC+15
7
OP2
DC+110
2
D3
PA_OUT
1
12
6
IN+
IN-
DC-15
Vo
15
OUT
R7=0.7
+
R6=10
C5=470pF
Rp
26
18
2
R9
Vp
R2
100k
47k
Cp
Piezo
DC+15
OP3
VpN
7
D4
DC-20
C22
10pF
VpP
MP38A
6
4
30
-Vb
-Vs
D2
GND
MP38
D1
4
23
24
Iq
29
B
OPAMP
C1 -IL
C2 +IL
Vref
+Vb
+Vs
25
Vfdbk 3
ViP
VpN
R4
10
SGND
2
470k
ViN
VpP
FS
R12
6
3
OPAMP
470k
4
Vs
R14
QF
VF
R13
47k
C1
15u
Radj
DC-15
A
R1
10k
R3
1
PGND
1
2
3
Figure 4-13: Circuit design of the charge amplifier showing the power device and its
feedback circuit.
voltage (Vp /10), current (Vi ), and charge (VsB ) are shown in Figure 4-14. Differential
analog adder-subtractor buffers are implemented using single op-amps and are used
for sensing the piezo’s voltage and current. Current is sensed by measuring the voltage
across the resistor R4 as Vi ' 21 (ViP − ViN ). Piezo voltage is measured by finding the
difference between the voltages on the two sides of the piezo as Vp =
1
(Vp P
10
− Vp N ).
Charge is estimated as the feedback voltage (Vs ) under the charge-control mode and
is buffered using a voltage follower (VsB ). The differential buffers for current and
voltage sensing are designed to work with the ±15V supplies. However, they have
a finite input impedance. This can be a problem when measuring high-impedance
voltage sources, such as the piezo’s negative voltage (VpN ). We have mitigated this
problem by choosing large resistor values for the differential buffer to increase its
input impedance relative to the measurement source impedance.To fully solve the
problem, we can use a voltage follower to buffer VpN before measuring it using the
differential buffer.
The amplifier’s common ground plane is divided into a power ground (PGND) and
a signal ground (SGND). The piezo current returns through power ground (PGND).
The signal ground (SGND) is used by the buffers as a common reference and serves
98
N120
2
CON2
J_15
DC+15
SGND
DC-15
1
2
3
CON3
B
B
15pF
C21
C22
10pF
18
R5
R9
220k
0
47k
DC+15
DC+15
2
ViP
R20
6
3
Vs
4
C31
15pF
VpN
6
Vi
3
OPAMP
R21
220k
DC-15
A
DC-15
SGND
1
R14
MOUNT
MOUNT
2
470k
VsB
VpP
OPAMP
430k
MOUNT
Mount6
0
MOUNT
Mount3
0
7
7
2
430k
MOUNT
Mount5
0
MOUNT
Mount2
0
R12
6
Vp/10
3
OPAMP
470k
4
R19
4
ViN
OP3
Mount1
0
DC+15
OP2
7
OP1
Mount4
0
C32
10pF
R13
47k
DC-15
A
SGND
Figure 4-14: Schematic design
of the charge amplifier showing
the buffers measuring
2
3
the piezo current (left), the feedback voltage (middle), and the piezo voltage (right).
as a return path for the low-current measurement signals. The two grounds are joined
at only a single point. In this way, the relatively large piezo currents cannot return
through the signal ground and thus do not disturb the measurements.
We have built linear AC-DC power supplies into the amplifier box, so that the
amplifier can be directly powered from the wall. The amplifier uses +120V, -20V,
and ±15V DC supplies. We built our own linear AC-DC supply to generate the
+110V and -20V DC supplies from the wall outlet 120V RMS AC voltage. We
use an off the shelf Acopian DB15-20 linear AC-DC supply for generating ±15V
DC supplies. A schematic of the +120-V DC power supply is shown in Figure 415 as an example. The 120-V RMS wall outlet voltage (L120) is connected to the
circuit through a current-limiting fuse (F1). We use a bi-directional TransZorbs to
prevent line voltage transients from reaching the output side [7]. We also use a
unidirectional Tranzorb on the DC output to prevent supply output over voltage. We
use a toroidal transformers to scale the 120V RMS line voltage to 80V RMS, which
corresponds to 113V peak-to-peak voltage. We use a full bridge rectifier to change
the sinusoidal signal into a single-sided positive signal, which charges the supply
capacitors up to 113V minus the diodes’ voltage drop. We have placed a negative
temperature coefficient (NTC) resistor in the current path to limit the inrush currents
at the power up of the amplifier. The NTC resistor has a high initial resistance, which
prevents inrush currents. As current flows, the resistor heats up, and the resistance
drops. An inductive high-frequency choke is added in the current path to filter high99
4
1
2
3
AC120
F1
T1_SH
2
L120
DC+110
FUSE
D
RB1
AC
4
NTC1
NTC
RES
NTC
1
+
TVS2
TVS_BI
_
TVS1
TVS_BI
PGND
AC
L1
CHOKE
R16
RES
C33
680uF
BRIDGE
N120
TVS_UNI
PGND
3
T1_SL
TVS3
3
T2_SH
AC120
DC-50
RB2
INDUCTOR
IRON
Figure 4-15: Circuit design of the charge amplifier
showing
its 110-V AC-DC power
L2
NTC2
1
4
NTC
R17
supply.
+
RES
RES
_
AC
C2
680uF
NTC
AC
Capacitor
BRIDGE
N120
Heat Sink
TVS4
2
T2_SL
H.F. Choke
TVS_UNI
C
DC110
C17 C19
0.1uF
DC-50
C3
1uF0.1uF
C4
1uF
C7
C8
0.1uF
DC-15
C18 C20
1uF
0.1uF
1uF
DC+15
C15 C9 C10 C11
C12 C13 C14 C16
10uF 0.1uF0.1uF 0.1uF
0.1uF0.1uF0.1uF10uF
B
15pF
C21
C22
10pF
R2
R5
0
DC+15
R1
ViP
7
OP3
7
2
2
430k
R3
6
3
VpN
6
Vi
Vfdbk 3
R14
VpP
R12
6
3
OPAMP
4
4
A
frequency supply noise. In this way, we generate a linear DC supply of 110V with
very low high-frequency
noise. The 120-Hz ripple 2 and other low frequency supply
1
3
variations can be rejected by the power device.
The charge amplifier’s assembled printed circuit board is shown in Figure 4-16.
Hybrid Hysteresis Compensation
Practical charge amplifiers control charge in AC and voltage in DC. Assuming a linear
capacitive model for the piezo actuator, voltage-control in DC is an approximation
of charge control . This is an inaccurate approximation because of the very fact that
motivates the design of charge amplifiers: the piezo’s voltage-charge hysteresis. Due
to the existence of voltage-charge hysteresis, the DC and AC feedback will never be
100
2
470k
VfdbkB
OPAMPboard design (left)
OPAMP
430k
470k
Figure 4-16: The amplifier’s printed
circuit
and manufactured
R4
220k
circuit board (right).
DC-15
DC-15
4.5
DC+15
OP2
7
ViN
47k
DC+15
OP1
4
220k
R9
R13
47k
DC-15
Vp
perfectly matched. This mismatch results in slow transients in time, from a correctly
controlled charge value in AC to an incorrectly controlled charge in DC. The transients
occurs with the same time constant as the charge amplifier’s voltage-to-charge-control
transition time constant τV Q given by (4.3). This limitation is not a big problem for
AC motion control applications, such as AFM scanners, which follow a periodic scan
at a certain frequency. However, even in those cases the user must wait for the
transients to die out if the scan signal has a DC component. This is one practical
limitation on using a very long time constant τV Q . The problem is much worse for
applications where DC position control is also of interest. Conventional V-Q charge
amplifiers do not compensate hysteresis in DC and thus open-loop position control
shows inaccuracies.
One common way, which can be found in the literature, for achieving a higher
accuracy in DC is using an inverse hysteresis compensator, where an inverse hysteresis model of the piezo is implemented and is used to soft-linearize the piezo
[39][27][16][58][48]. A path-deterministic hysteresis model is used in [39] which does
not model the non-local memory of hysteresis. Ge and Jouaneh [27] use an inverse
Preisach hysteresis model to compensate for hysteresis. Croft et al. use an inverted
Preisach hysteresis model to compensate for hysteresis. They use separate inverse
models to compensate for the vibration modes and creep. Mokaberi and Requicha
[58] use an inverse Prandtl-Ishlinskii model to compensate for hysteresis and creep.
The Prantl-Ishlinskii model can include both creep and hysteresis and has a unique
analytical inverse. Lee et al. [48] use an inverse Maxwell resistive capacitor hysteresis
(MRC) model, which is a special case of the Prisach model [48]. The effectiveness
of the inverse hysteresis models depends on the accuracy of the hysteresis model.
Obtaining an accurate hysteresis model over a wide frequency band and accurately
calculating the inverse in real-time is difficult. Any inaccuracy in the inverse hysteresis
model can appear as motion control error.
We have developed an alternative hysteresis compensation method, which combines the advantages of both charge-control and inverse hysteresis compensation.
Charge control is a simple and effective way of eliminating hysteresis at all frequen101
fh
V-Q
Q Charge
g Amplifier
p
HHC Algorithm
Hyst. Model
Qp/C1
Vc
ωVQ
+
s + ωVQ
Vp
−
R1
R2
−
Vref
+
Vs
Vsl
+
Vo
GPA(s)
−
s
s + ωVQ
Vp
PZT
Qp
1
C1
+
ωVQ
Vsh
s + ωVQ
R1
R2
V-Q Charge Amplifier
Figure 4-17: Block diagram showing the charge amplifier, piezoelectric device, and
the hybrid hysteresis compensation algorithm.
cies except for quasi-static frequencies. We propose using an inverse hysteresis model
of the piezo to compensate for the amplifier’s hysteresis over quasi-static frequencies
only. In this way, the charge amplifier’s effectiveness at high frequencies is not affected
by any inaccuracy of the hysteresis model. At the same time, an accurate hysteresis
model can be developed over the limited quasi-static frequency range. Since the compensation is active at low frequencies, it does not require a fast sampling rate and is
easier to calculate in real-time. We have developed a configuration where this partial inverse hysteresis compensation technique can be applied to any existing charge
amplifier.
The block diagram in Figure 4-17 shows a V-Q amplifier driving the piezoelectric
device while utilizing the hysteresis compensation algorithm. The naming convention
for this diagram are consistent with the schematic diagram oft he V-Q amplifier
shown in Figure 4-7. The charge amplifier actively changes the voltage (Vp ) applied
102
to the piezo such that the feedback voltage (Vs ) follows the reference voltage (Vref ).
The feedback voltage (Vs ) is an estimate of the piezo charge (Qp ) calculated by a
complementary filter pair based on the piezo charge (Qp ) at high frequencies and
the piezo voltage (Vp ) at quasi-static frequencies. Assuming stable operation of the
amplifier, the feedback voltage (Vs ) can be related to the piezo voltage (Vp ) as
Vs (s)
R1 R2 Cp s + 1
=
.
Vp (s)
R2 R1 C1 s + 1
The resulting transfer function can be divided into low-pass and high-pass transfer
functions as
Vs (s)
R1 1/R1 C1
s
Cp
=
+
.
Vp (s)
R2 s + 1/R1 C1 C1 s + 1/R1 C1
The equation above can be rewritten to relate the feedback voltage (Vs ) to the piezo
voltage (Vp ) and charge (Qp ) as
R1 ωvq
Cp
s
Vp (s) +
Vp (s)
R2 s + ωvq
C1 s + ωvq
1
R1
ωvq
s
=
Cp Vp (s) +
Qp (s),
Cp R2 s + ωvq
C1 s + ωvq
{z
} |
{z
}
|
Vs (s) =
Vsl
(4.15)
Vsh
where ωV −Q is the voltage-to-charge control transition frequency and is given as
ωV −Q = 1/R1 C1 . As can be seen, the feedback voltage (Vs ) is calculated using
a actual charge measurement (Qp ) at high frequencies and an estimate of charge,
which is given by piezo voltage multiplied by an estimate of the piezo the capacitance
(Cp Vp ). As a result, conventional charge amplifiers cannot eliminate hysteresis over
low frequencies. This results in errors and slow time transients which are problematic, specially when quasi-static motion control is required. We solve this problem
by modifying the feedback voltage to include a closer estimate of the charge over
quasi-static frequencies. The compensation algorithm achieves this without requiring
any modification to the charge amplifier hardware. As shown in Figure 4-17, we use
an inverse hysteresis model to estimate charge based on the piezo voltage (Vp ). We
103
use the charge estimate (Q̂p ) to replace the low-frequency portion of the feedback
voltage (Vf l ). We implement this by injecting the difference of the two (Vf l − Q̂p ))
at the charge reference (Vref ) terminal. To match the frequency content, we filter
this difference using a low-pass-filter equivalent to the low-pass-filter of the amplifier’s complimentary filter pair. In this way, the amplifier controls charge based on
an almost hysteresis-free estimate of charge at low frequencies as well and thus can
eliminate hysteresis at low frequencies.
The application of the low-pass filter to the hysteresis model’s output makes it
much easier to calculate the compensator’s output in real-time. The low-pass filter’s bandwidth is typically between 0.1-1 Hz; therefore, the compensator’s sampling
rate does not need to be any faster than 100 Hz, which is very easy to obtain in
practice. Any high-frequency numerical computation noise will be filtered by the
low-pass filter. Finally, any inaccuracy of the inverse hysteresis model does not affect the charge amplifier’s satisfactory performance at eliminating hysteresis at higher
frequencies. The general idea is to compensate the charge amplifier’s feedback over
only the frequencies where inaccuracies exist. The implementation, which is shown
in Figure 4-17, is an effective and simple way of integrating this algorithm with any
existing charge amplifier without requiring any modification to the hardware. With
a small modification in software, hysteresis can be eliminated at both high and quasistatic frequencies. The experimental results in Section 4.6 show the effectiveness of
this method at eliminating hysteresis over quasi-static frequencies.
We use a Maxwell slip model for predicting the hysteresis between the piezo’s
voltage and charge. Such a hysteresis model was first developed by James C. Maxwell
in 1800’s [30]. As shown in Figure 4-18, Maxwell’s slip model consists of n blocks
carrying a load (F) in parallel with different force limits (Fi ) and through connections
with different stiffness (ki ). The model captures how the friction load is carried by
surface asperities whose stiffness and load limits are different. The Maxwell’s slip
hysteresis model can be fitted to the experimental data more closely if more elements
are used. Lazan [47] formulates the model with the number of elements approaching
infinity [30]. The Maxwell slip model can be used to model hysteresis in other domains
104
k1
x
Ff1
k2
Ff2
k3
F
Ff3
.
.
.
kn
Ffn
Figure 4-18: Schematic diagram of the Maxwell slip model with n elements with
stiffness ki and force limit Fi , where i is an integer from 1 to n. The model simulates
the presiding friction hysteresis between force (F) and the displacement (x).
besides mechanical friction. References [30], [48], and [28] have applied the Maxwell’s
slip model to piezoelectric actuators.
We use a Maxwell slip model with four elements to model the hysteresis between
the voltage and charge of our piezo actuator. Figure 4-19 shows the model fitted to
the experimental data. The hysteresis model’s parameters are provided in table 4.1.
To experimentally fit the hysteresis model, charge must be measured versus voltage.
Although no direct measurement of charge is available, the feedback voltage is dominated by charge at frequencies above the amplifier’s V-Q transition frequency (ωV Q ).
To obtain the experimental hysteresis data, we excite the piezoelectric actuator using
a sinusoidal excitation between 0V to 100V at 50Hz, which is 50 times higher than the
charge amplifier’s ωV Q frequency of 1 Hz. Using a significantly higher frequency can
introduce errors resulting from the Q-V transition frequency, limited measurement
bandwidth, and dynamic vibration modes.
We implement the hybrid hysteresis compensation (HHC) algorithm in real-time
on a dSpace controller at a 20-kHz sampling rate. The experimental results in Section 4.6 show the effectiveness of this method at eliminating hysteresis at low frequencies.
105
Index (i)
1
2
3
4
Stiffness (ki ) [V/C]
0.114
0.054
0.092
0.675
Force Limit (Fi ) [V]
2
2
2.4
∞
Table 4.1: Stiffness and force limit values for modeling the hysteresis between the
voltage and charge of our piezoelectric actuator.
80
Experimental Data
Maxwell Slip Model
70
60
V [V]
50
40
30
20
10
0
0
20
40
60
Q/Cp [V]
80
100
Figure 4-19: Experimental voltage-charge hysteresis of our piezo actuator and the
fitted Maxwell’s slip model.
106
4.6
Experimental Results
In this section, we present experimental data demonstrating the performance of the
V-Q-V charge amplifier and the hybrid hysteresis compensation algorithm. We test
the charge amplifier with a 10-Hz sinusoidal reference signal changing from 0 V to
80 V for 10 cycles. The reference signal contains a 40-V quasi-static offset and a
±40V 10-Hz sinusoidal signal. In this way the charge amplifier is tested over both
quasi-static and high frequencies. We use the same reference signal to drive the
amplifier in voltage (V) control mode, voltage-charge-voltage (V-Q-V) control mode,
and V-Q-V control mode with hybrid hysteresis compensation (HHC). The time plot
of the experimental data for this test is shown in Figure 4-20. The experimental
data is viewed as an XY plot of the strain versus reference voltage in Figure 421. As can be seen in Figure 4-21, the resulting hysteresis with voltage control is
approximately 20%. Voltage-Charge-Voltage (VQV) control reduces the per cycle
hysteresis to approximately 5%, but a slow transient exists which results in an offset
drift of more than 15% of the full-scale strain range. Applying the HHC algorithm,
the per-cycle hysteresis is reduced to 2% and the time-transient drift is reduced to
2%. The improvement is a result of eliminating hysteresis in quasi-static frequencies,
and matching the feedback gains for high-frequencies and quasi-static frequencies.
The results could be improved further by using a more accurate hysteresis model.
4.7
Magnetic Analogue
Magnetic actuators have non-linearities resulting from the hysteresis between magnetic field and magnetic flux density within their magnetically permeable core. In
analogy to charge control of piezoelectric devices, magnetic flux control of magnetic
actuators can improve their linearities and eliminate the effect of hysteresis. In this
section, we present a method for controlling magnetic-flux and demonstrate that magnetic flux control can significantly improve an electromagnetic actuator’s linearity.
One common way of linearizing the quadratic current-to-force relation of magnetic
107
Reference [V]
80
60
40
20
0
0
0.5
1
1.5
time [s]
12
HHC
VQV Ctrl
V Ctrl
10
Strain [μm]
8
6
4
2
0
0
0.5
1
1.5
time [s]
Figure 4-20: Time plot of piezo’s strain in response to 10-Hz 0 to 80 V sinusoidal
reference signal using the power amplifier in voltage control mode (V Ctrl), voltagecharge-voltage control mode (VQV Ctrl), and VQV control mode with hybrid hysteresis compensation (HHC).
108
12
HHC
VQV Ctrl
V Ctrl
10
Strain [μm]
8
6
4
2
0
0
10
20
30
40
50
Reference [V]
60
70
80
Figure 4-21: XY plot of the piezo’s strain versus a 10-Hz 0 to 80 V sinusoidal reference
signal using the power amplifier in voltage (V Ctrl) control mode, voltage-chargevoltage (VQV Ctrl) control mode, and VQV control mode with hybrid hysteresis
compensation (HHC).
109
bearings is bias current linearization [54]. This method requires symmetric operation
around a bias current. Bias current linearization also does not compensate for the
hysteresis in the actuator core. Direct control of flux addresses this problem. Groom
has patented a magnetic actuator, which uses permanent magnet bias linearization
and flux feedback [31]. The invention uses Hall effect sensors to measure flux. In this
work, we implement magnetic flux control without the use of Hall-effect sensors. We
estimate the magnetic flux using a sense coil. By eliminating the sensor, the minimum
air gap is no longer limited by the thickness of the Hall effect sensor. Also unlike a
Hall sensor, a sense coil is not sensitive to the changes in temperature.
Normal-flux electromagnetic actuators (such as reluctance actuators) can achieve
a high force-density. However, they have non-linear input-output constitutive equations and have additional non-linearities resulting from hysteresis. As a result, such
actuators are difficult to use for precision applications. The motivation behind the
work presented in this section is to develop control techniques for precisely controlling
the output force of such actuators over a range of changing gaps. We achieve this
by using an internal magnetic-flux control loop. We use lookup tables, based on experimental calibration data, to determine the magnetic flux reference resulting in the
desired output force. We have designed and implemented a setup for experimental
testing of our control methods, as shown in Figure 4-22. We have experimentally
demonstrated successful magnetic flux control, force control, and position control.
The work presented in this section is in collaboration with Ross I. MacKenzie, who
is a PhD candidate in our lab, and has also been supported by ASML.
4.7.1
Experimental Setup
The assembled experimental setup for this work is shown in Figure 4-22. A solid model
of the experimental setup is shown in Figure 4-23. In this solid model a Lorentz actuator replaces one of the reluctance actuators. We use the setup for researching
the linearization of the normal-flux reluctance actuators through magnetic-flux control, and utilizing them for precision motion control. The setup consists of a linear
airbearing driven by two actuators. The reluctance actuators can only generate a
110
pulling force; therefore, we use one on each side to enable generating forces in both
directions. For testing and comparison purposes, it is possible to replace one of the
actuators with a linear voice coil actuator, as shown in the CAD model of Figure 4-23.
We use a linear BH20 Sony encoder head [79] with a 7-mm BE10 linear scale [78] and
a BD96-B1100HC interpolator [77] to measure the linear motion of the airbearing
with 0.25nm resolution. A more detailed view of the encoder assembly is shown in
the CAD model of Figure 4-24. Each actuator is connected to its mounting bracket
through three load cells. In this way, the actuator forces are transferred to the stationary frame through the load cells and can be measured by them. We use Kistler
9212 load cells[42], which primarily measure compressive forces. The load cells have
two threaded holes at their ends. We use a bolt, which passes through the centroid of
the triangle made by the load cells, to preload the load cells in compression. We use
Belleville washers to increase the compliance of the preload mechanism, which facilitates precise adjustment of the preload force. We set the preload by tightening the
bolt and monitoring the load cell signals. We use a Kistler 5010 charge amplifier[43]
to measure the load cells’ charge output. We connect the output of the load cells on
each side in parallel and thus can use a single charge amplifier for each side to measure
their added output charge. In this way the resulting equivalent load cell constant is
the average of the three load cells’ force to charge constants. We use linear voltage
power amplifiers to drive the actuators. The amplifiers use Apex PA12 power devices
[10].
The experimental setup’s system diagram is shown in Figure 4-25. We use a
dSpace DS1103 controller board. The Sony BH20 encoder’s output signals are buffered
and interpolated by a Sony BH1100HC box to provide a resolution of 0.25nm per interpolated count. For every sample time, the encoder’s dSapce driver requests a
position measurement update right after the controller is sampled. In this way, the
measurement is sampled at the exact same frequency as the control frequency, and
aliasing due to non-integer multiple sampling rate mismatch is avoided. We measure
the rate of change of the magnetic flux in the air gap linked by the sense coil (dλ/dt),
the current passing through the actuator winding (Is ), and the force measured by the
111
Charge
Amplifier
Load
Cell
Encoder
+ Mount
Sense
Resistor
Normal
Flux
Actuator
Figure 4-22: Assembled experimental setup used for researching soft-linearization of
normal flux actuators through magnetic-flux control.
Encoder
+ Mount
Normal Flux
Actuator Stator
Load
Cell
Normal Flux
Actuator
Target
Airbearing
Shaft
Airbearing
Stator
Linear Lorentz
Actuator
Load cell
Figure 4-23: CAD model of the experimental setup used for researching softlinearization of normal-flux reluctance actuators.
112
Charge
Amplifier
Load
Cell
Sense
Resistor
Encoder
+ Mount
Normal
Flux
Head
Mount
Airbearing
Stator
Encoder
Head
Airbearing
Shaft
Encoder
Scale
Scale
Mount
Figure 4-24: CAD Model showing a closer view of the encoder assembly
load cells (F). These signals are amplified and low-pass filtered by Tektronix AM502
differential amplifiers[81].
The magnetic actuator’s design is shown in Figure 4-26. The actuator’s stator
consists of two adjacent U-cores with a 280-turn coil wrapped around their contacting
legs. The actuator’s mover consists of an I-core. The cores are SuperPerm49 with
0.1-mm thick lamination and 90% fill-factor [51].
4.7.2
Magnetic-Flux Sensing and Control
Normal-flux actuators’ force output can be linearized by controlling magnetic flux.
In this section, we describe how we sense and control the magnetic flux.
Sensing and Estimating Magnetic Flux
We use a sense coil wrapped on top of the actuator coil to sense the rate of change
of the magnetic flux passing through the center legs. The actuator with the added
sense coil is shown in Figure 4-27. The sense coil has 12 turns and is wound using a
miniature coaxial cable. The voltage across the center conductor is measured as the
rate of change of the magnetic flux linkage. The outer conductor is used for shielding.
It is very important that the shield is connected to the ground only on the side where
113
dSpace
RTC
Enc Count
AM502
Buffer
+
−
Interpolator
B1100HC
dλS dt
Buffer
Sony
BH20
Encoder
(Sensed Linkage)
Kistler
9212
Charge
F Amplifier
Kistler
5010
Airbearing
+
−
Normal Flux
Actuators
IS (Sensed Current)
Power
Amplifier
R
Figure 4-25: Experimental setup’s system diagram.
I-Core Target
0.1mm lamination
90% fill factor
U-Core Stator
0.1mm lamination
90% fill factor
Load
Cell
C il
Coil
N=280
Figure 4-26: CAD model of the normal-force electromagnetic actuator (left) and the
core structure of the actuator before assembly (right).
114
Sense Coil
12 turns
Figure 4-27: Electromagnetic normal-flux actuator with a flux sensing coil wrapped
around the center pole piece using miniature coaxial shielded cable.
the center conductor is referenced to the ground. In this way, both the shield and the
center conductor will have the same voltage distribution along their length; therefore,
no parasitic capacitive coupling will exist between the two of them. If the shield is
connected to the ground on both sides, the shield and the center conductor will have
a voltage difference. Also, changing flux would induce current through the shield
which will oppose the magnetic field. That is, we do not want to create a shorted
transformer turn by grounding both ends.
For simplifying our analysis, we measure and control the magnetic flux linked by
the sense coil, which is proportional to an average of the magnetic flux in the air
gap (g). The block diagram of the flux estimation algorithm is shown in Figure 4-28.
We estimate the flux by integrating the rate of change of flux (dλS /dt). To avoid
integrator drift, we high-pass filter (HPF) the flux estimate from the sense coil. This
will give us an estimate of flux at high frequencies (λHF ). We estimate the flux at
low frequencies (λLF ) using the current passing through the actuator coil. The flux
linkage can be estimated as the mutual inductance between the actuator coil and
the sense coil (LM ) times the actuator coil current (I). We filter the low-frequency
estimate (λLF ) using a low-pass filter (LPF) complementary to the high-pass filter
(HPF).
115
Flux Estimator
LM(g)
LPF
Sense
Resistor
I
λ̂LF
+
Sense
Coil
HPF
dλS dt
∫
λ̂S
λ̂HF
Figure 4-28: Block diagram of the flux estimation algorithm
The actuator’s inductance changes with the air gap (g). We measure the inductance at different gap sizes and build a look-up-table (LUT) for estimating the
inductance (Lm ). At each gap size, we excite the coil using a sinusoidal current at a
frequency high enough so that it can be detected by the sense coil. We estimate the
mutual inductance as the slope of the line fitted to the plot of the magnetic flux linkage versus the current coil current. Figure 4-29 shows the experimentally measured
mutual inductance of the actuator and the sense coil (Lm ) measured at different air
gap sizes for the actuators on the right and the left sides.
We combine the estimates of flux for high and low frequencies using a complementary filter pair (HPF and LPF). The complimentary filter pair is given as
1
(s/ωf p + 1)2
HP F (s) = 1 − LP F (s),
LP F (s) =
(4.16)
(4.17)
where ωf p is the filter pair break frequency and is given as ωf p = 2π rad/s. In
this way, while the filters are used to assign each estimate to a certain frequency
range, the two estimates complement each other to have an overall gain of one over
all frequencies. In this work we use a second order complementary filter pair. In
this way, the integrated flux-rate measurement offset does not propagate to the flux
116
-3
5
x 10
5
1.102 ×10 −3
(g − 0.048)0.66
4.5
4
4
3.5
3.5
3
2.5
2
2
1.5
1.5
0
0.5
gap [mm]
1
Right
1.174 ×10 −3
(g + .007 )0.69
3
2.5
1
x 10
4.5
Lm [H]
Lm [H]
-3
Left
1
0
0.5
gap [mm]
1
Figure 4-29: Experimentally measured mutual inductance of the actuator and sense
coils (Lm ) measured as a function of air gap for the actuators on the right and the
left sides.
117
estimate (λ̂s ).
Controlling Magnetic Flux
We use the magnetic flux estimator’s feedback to control flux in closed-loop. The
plant being controlled can be modeled as a resistor and an inductor, whose inductance
changes with the size of the air gap (g). The magnetic linkage can be related to the
electric voltage and current as
V = RI + dλ/dt,
where V, I, λ, and R are the stator coil’s voltage, current, flux linkage, and resistance,
respectively[55]. To include the effect of the actuator air gap, we define the magnetic
flux linkage as
λ = L(g)I,
where L(g) is the inductance of the actuator as a function of the air gap. The
inductance L(g) can be calculated as
L(g) = NA2
Aµ
.
g
µ is the permeability of the magnetic core, g is the air gap, and A is the area of a
single leg of the U-core. The variations in the gap and their effect on the magnetic
flux are considered as a disturbance and are rejected by the flux controller. The sense
coil acts as a transformer with a turn ratio of NS : NA ; therefore, the sensed flux
λS is scaled as λS = λ × Ns /NA , where NA and NS are the actuator and sense coil
windings’ number of turns respectively. A block diagram of the flux control system
is shown in Figure 4-30. The flux estimator was described in Subsection 4.7.2 and is
assumed to be a constant gain of one for control design purposes. The plant’s transfer
118
Flux Control
g
Plant
λref +
Kp
∫
ωi
-
+
V
+
λ
+
VEMF
PI Flux Controller
1
R
L
I
λ
I
s
λ̂s
λs
Flux
Estimator
NS
NA
|Controller|
|Plant|
|Loop Trans.|
Figure 4-30: Block diagram
of the flux control system
x
=
p
function can be derivedKfrom
the block diagram as
ω
ω
L(g) NS
λS (s)ωi = c 10
=
.
V (s)
L(g)s + R NA
ωb ∝ g
ω
ωb ωi
ωc
ω
(4.18)
The plant transfer function λS (s)/V (s) given by (4.18) is changing with gap. The
transfer function has a break frequency ωb = R/L(g). Well above this frequency, the
actuator’s inductive impedance is much larger than its resistive impedance, and thus
the resistance R in the denominator of the transfer function can be neglected. Well
below the break frequency ωb , the resistance is significantly larger than the inductive
impedance, and thus the inductive impedance in the denominator can neglected. The
transfer function can be approximated over each range as the following:


λS (s)
'

V (s)
L(g) NS
R NA
ω ωb
resistance dominant
1 NS
s NA
ω ωb
inductance dominant
(4.19)
As can be seen, the plant transfer function is independent of the changes in the
inductance for frequencies larger than ωb . The experimental frequency responses of
the plant (λS (s)V (s)) at different air gaps is shown in Figure 4-31 for the actuators
on the right and the left sides. Our targeted crossover frequency is significantly larger
than the possible values of ωb . As a result, the frequency response at the crossover is
119
not affected by the changes in the inductance. Therefore, we can design the controller
for a specific bandwidth and ensure stability independent of the variations of the
inductance resulting from the changes in the air gap. We use a proportional-integral
control law. The integral term is active up to the frequency (ωi ), which is chosen to
be a tenth of the crossover frequency (ωc ). In this way, the integrator phase lag at
the cross-over is negligible. The flux controller transfer function is given as
Cλ (s) = Kp
ωi + s
,
s
where 1/Kp = |λS (s = jωc )/V (s = jωc )| and ωi = ωc /10.
The experimental frequency response of the compensated loop transmission ratio
is shown in Figure 4-32 using the same controller at different air gaps for the actuators
on the right and the left sides. As can be seen, a fixed control law can achieve a unity
cross-over frequency of 1 kHz and 85 degrees of phase margin at the different air
gaps. We used a low cross-over frequency of 1 kHz, so that the controller can be
implemented on the dSpace controller. It is possible to achieve a much higher crossover frequency if the controller is implemented using analog electronics or an FPGA
device. If a faster controller is used, the achievable cross-over frequency would be
limited by the Eddy-current losses of the magnetic core.
4.7.3
Force Control
The output force of the electromagnetic actuators can be calculated using the Maxwell
stress tensor [85] as
I
F =
Aa
1
HBdA,
2
(4.20)
where H and B are the magnetic field and flux density, respectively, and Aa is the
surface enclosing the volume of the actuator components on which force is evaluated.
The magnetic field is zero everywhere on the actuator mover surface, except on the
120
10
|λs/V|
10
10
10
10
LEFT SIDE
-2
10
-3
10
-4
10
|λs/V|
10
-5
10
-6
10
-7
10
0
10
1
10
2
10
3
10
10
4
-5
-6
-7
0
10
1
10
2
10
3
10
4
-40
534 μm
733 μm
305 μm
418 μm
626 μm
-20
∠ λs/V[deg]
∠λs/V[deg]
-4
0
511 μm
719 μm
309 μm
407 μm
603 μm
-20
-60
-80
-100
0
10
-3
10
0
RIGHT SIDE
-2
-40
-60
-80
10
1
2
10
Frequency [Hz]
10
3
10
4
-100
0
10
10
1
2
10
Frequency [Hz]
10
3
10
4
Figure 4-31: Experimental frequency responses of the flux-control plant from the
applied voltage V to the sensed magnetic flux linkage λS is plotted at different air
gaps for the actuators on the right (right) and the left (left) sides.
121
10
10
10
4
10
2
0
10
10
-2
10
∠ NLT[deg]
10
0
10
1
10
2
10
3
10
10
4
4
2
0
-2
-90
-90
-100
-100
-110
-110
-120
511 μm
-130
719 μm
-140
-150
-160
0
10
10
2
10
Frequency [Hz]
10
3
0
10
1
10
2
10
3
10
4
-120
534 μm
-130
733 μm
309 μm
-140
305 μm
407 μm
-150
418 μm
626 μm
603 μm
1
RIGHT SIDE
6
10
∠ NLT[deg]
|NLT|
10
LEFT SIDE
6
|NLT|
10
10
4
-160
0
10
10
1
2
10
Frequency [Hz]
10
3
10
4
Figure 4-32: Experimental frequency responses of the compensated loop transmission
for the flux linkage control system is plotted at different air gaps for the actuators on
the right (right) and the left (left) sides.
122
face opposing the stator. Therefore, (4.20) can be simplified as
Z
F =
Af
1
HBdA,
2
(4.21)
where Af is the area on the face of the mover opposing the stator. Air has a linear
magnetic permeability very close to the magnetic permeability of vacuum (µo ). The
relationship between the magnetic field and flux in air is thus given by B = µ0 H.
Equation 4.21 can be simplified by substituting for H using B:
Z
F =
Af
1 2
B dA
2µ0
(4.22)
The actuator’s force output is proportional to the average of the magnetic flux density
squared over its face. The magnetic flux linked by the sense coil on other hand is
given as
Z
λS = NS
BdA,
(4.23)
As
where As is the sense coil area and is given as As = Af /2. The flux linkage is thus
proportional to the average of the magnetic flux density over the poles faces. If we
assume that the magnetic flux distribution over the actuator’s face is constant, the
electromagnetic force would be proportional to the magnetic flux linkage squared.
However, the magnetic flux is not uniformly distributed in the air gap. Fringing
fields are one main reason why the magnetic flux may have a non-constant spatial
distribution. To make sure that our force control algorithm is not adversely affected by
the constant-flux-distribution assumption, we construct and use a 2D look-up-table
that relates the magnetic flux, force, and air gap. We calibrate the look-up-table
experimentally. The calibrated force maps for the right and left actuators are shown
in Figure 4-33. The same data is viewed in 2D with the use of colors in Figure 4-34.
As can be seen, the force is proportional to the linkage squared for a fixed air gap.
However, the proportionality constant changes slightly with the air gap. This could
be due to the fringing fields growing with the air gap, which results in a wider spread
123
FL = −1.276(g − 2.767 )λ2
FR = −1.508( g − 2.359)λ2
-3
-3
x 10
4
4
3
3
λ [Vs]
λ [Vs]
x 10
2
2
1
1
0
20
0
20
15
1
10
0
0
1
10
0.5
5
Force [N]
15
0.5
5
Force [N]
gap [mm]
0
0
gap [mm]
Figure 4-33: Experimentally calibrated force map of the right (right) and left (left)
side actuators viewed in 3D. We use the map to find the the linkage required for
generating a certain force at a given gap.
flux distribution and a lower linkage-squared to force constant relationship.
To take into account the changes resulting from the variation in the air gap, we
can define the output force as F = c(g)λ2 , where c(g) is a constant gain describing
the variations in the flux-squared to force gain resulting from the changes in the air
gap. A plot of the constant c(g) versus the gap size (g) is shown in Figure 4-35. A
good approximation of the correction constant c(g) can be obtained using a linear fit
to the data. For our force control experiments, we calculate the required linkage as
below:
λref =
p
F/c(g)
(4.24)
where c(g) is given for each actuator by the following expressions:
124
3
λ [Vs]
λ [Vs]
3
2
2
1
1
0
20
0
20
15
1
10
15
0.5
5
Force [N]
0
0
Force [N]
gap [mm]
0
0
gap [mm]
20
F = cλ2
18
18
16
14
14
12
12
Force [N]
16
10
8
6
6
4
4
2
2
0.5
1
1.5
λ [Vs]
2
2.5
3
750µm
10
8
0
F = cλ2
Gap
Force [N]
0.5
5
20
0
1
10
0
250µm
0
0.5
1
1.5
λ [Vs]
-3
x 10
2
2.5
3
-3
x 10
Figure 4-34: Experimentally captured plots of the force versus flux linkage at different
gap sizes.
125
3.3
left
right
3.2
3.1
C(x)=F/ λ2 [N//(mVs)2]
3
cL = 1.276(2.767 − g L )
2.9
2.8
2.7
cR = 1.508(2.359 − g R )
2.6
2.5
2.4
2.3
0.2
0.3
0.4
0.5
average gap [mm]
0.6
0.7
0.8
Figure 4-35: Plot of the correction constant c(g) versus the gap size (g) for the right
and left actuators.

 c (g) = 1.276(2.767 − g )
L
L
 c (g) = 1.508(2.359 − g )
R
R
for left actuator
(4.25)
for right actuator
The force output accuracy can be improved by using a look-up table for c(g) rather
than a linear fit.
The normal-flux reluctance actuators, which we are using for this work can only
exert a pulling force. We can generate bidirectional forces by using the two actuators
together. The normal-flux actuators have a quadratic relationship from linkage to
force. At zero force, they have a local sensitivity of zero to the changes in flux:
F ∝ λ2 ⇒
∂F
|F =0⇒λ=0 = 0
∂λ
(4.26)
To prevent this from adversely affecting the performance of the control system,
126
Force Distribution
+
+
+
Fmax
1/2
FDIF
Fmax
0
+
0
To Right
Actuator
+
−
−
FCOM
Fmax
1/2
+
+
0
+
+
−
Fmax
0
To Left
Actuator
Figure 4-36: Block diagram of the force distribution subsystem. The subsystem
generates a commanded bidirectional force by assigning force commands to the unidirectional actuators.
we operate the actuators around a common mode force setpoint. To create a net
force around this common mode force, we add a differential force to one actuator and
subtract the same differential force from the other actuator. The actuators have a
maximum force output. The force distribution algorithm is shown in Figure 4-36.
The algorithm generates a bidirectional force (FDIF ) by assigning a force commands
to the unidirectional actuators. The algorithm also allows exertion of a commonmode force, with zero net force FCOM , on both sides of the moving assembly. The
force distribution algorithm is designed, such that the assigned force of a saturated
end can be carried by the other actuator. Such a situation could occur if a common
mode force value other than the midpoint of the actuators force range is used.
We calibrate the actuator force maps by measuring their pulling force versus their
flux linkage at different air gaps. To facilitate the experimental data collection, we use
the actuators to actively control the position of the moving mass at a specific air gap.
At each actively controlled air gap, we change the actuators’ common mode force. At
127
the same time, the position controller uses the differential force to control the gap.
In this way, the actuators go through a range of output forces while maintaining the
air gap. We measure the output force of each actuator using its load cells and save
the data along with the measured magnetic flux. For this method to work, we first
need a stable position controller and a estimate of the force-map. Starting with an
analytically derived approximation of the force map, we can iteratively improve its
precision using this experimental method.
We use the open-loop force control algorithm to control the actuators output
force. To experimentally test the effectiveness of our force control method, we use the
actuators to follow a 0.2-Hz sinusoidal force profile at a gap of 0.5 mm on each side.
The actuators output force is measured and is plotted against the reference force in
Figure 4-37. The plotted result has a linearity of better than 0.5%. However, the
accuracy is 1% for the right actuator and 5% for the left actuator. Accuracy can
be improved by using an accurately calibrated look-up-table for the force correction
constant c(g).
4.7.4
Position Control
We design a position controller to actively control the position of the moving mass
using the encoder’s position feedback. The controller commands a differential force
based on the position error. A block diagram of the position control system is shown
in Figure 4-38. The differential force is distributed by the force distribution algorithm
between the left and the right actuators. The calibration data for the actuators is
used to calculate the required flux value for generating the commanded forces. The
flux controller algorithm for each actuator controls the flux to the reference flux.
The frequency responses of the position control system’s plant, controller, and
compensated loop transmission are shown on the Bode plot in Figure 4-39. The expected magnitude response when modeling just the airbearing mass is also plotted.
The expected and experimental frequency responses of the plant match at high frequency. However, the experimental frequency response at low frequency resembles a
stiffness element. We are using an airbearing which ideally should be free of static
128
Left Actuator
Right Actuator
20
20
18
Exp
16
FitL=1.08FRef
Meas. Force [N]
10
8
Ref
12
10
8
6
6
4
4
2
2
0
5
10
15
Ref. Force [N]
0
20
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
Error (ExpL-FitL) [N]
Meas. Force [N]
Error (ExpL-FitL) [N]
R
14
12
0.1
0
-0.1
-0.2
20
20
0
5
10
15
Ref. Force [N]
20
-0.2
-0.4
10
15
Ref. Force [N]
10
15
Ref. Force [N]
-0.1
-0.4
5
5
0
-0.3
0
0
0.1
-0.3
-0.5
R
Fit =0.96F
16
14
0
Exp
18
L
-0.5
Figure 4-37: Measured output force plotted versus the reference force for the actuators
on the left (top left) and right (top right) sides. The force nonlinearity plotted versus
the reference force for the actuators on the left (bottom left) and right (bottom right).
129
Right Actuator
gR
gR
FR
(F,g)→ λ
LUT
FL
(F,g)→ λ
LUT
xRef
x
Encoder
Position
Controller
FC
λR
Linkage
Control
Force
Distribution
gL
λL
Linkage
Control
gL
Left Actuator
Figure 4-38: Block diagram of the position control system consisting of the position
controller, force distribution, and flux linkage controller blocks.
friction and any stiffness. This may be due to small deformation in the airbearing
shaft, which can create a preferred stable positions along the shaft. Particles in the
airbearing pockets could also create static friction, which can act like a stiffness element within the presiding regime. Because this effect is at frequencies far below the
cross-over frequency, it does not affect the controller design. The second roll-off at
about 1-kHz is resulted from the limited bandwidth of the flux linkage controller.
The position control law consists of an integrator, a lead filter, and a roll-off
filter. We use a first order lead filter to add phase at the cross-over and stabilize
the system. We use an integrator to increase the loop gain and improve position
tracking performance at low frequencies. We use the roll-off filter to attenuate the
loop gain past the cross-over frequency and improve the noise performance. As shown
in Figure 4-39, the position control system has a cross-over frequency of 200-Hz and
phase margin of 40 degrees.
We have tested the control algorithm by stepping the reference position command
from 50 µm away from the left actuator to 50 µm away from the right actuator. In
this way, we can get the step response of the actuator at different air gaps. The
test result is plotted in Figure 4-40. Positions of 0 mm and 1 mm correspond to
the left and right actuator gaps being fully closed respectively. As can be seen, the
130
5
Magnitude
10
0
10
-5
10
-10
10
-1
10
0
10
1
2
1
2
10
10
Frequency [Hz]
3
10
4
10
Phase [deg]
0
-100
-200
Plant
-300
1/Ms2
Controller
Loop Trans.
-400
-1
10
0
10
10
10
Frequency [Hz]
3
10
4
10
Figure 4-39: Bode plot showing the frequency responses of the position control system’s plant, controller, and compensated loop transmission.
131
system stays stable within the whole range. The force calibration algorithm enables
the two actuators to stay linear and work together to control the position even when
one actuator has a 50-µm air gap and the other one has a 950-µm air gap. Due
to time constraints, our force and inductance calibration data are from the 0.3mm
to 0.7mm position range only. The calibration outside of this range is estimated by
extrapolation. The position control performance degrades as we get farther outside of
this range. A zoomed-in view of the step response is shown in Figure 4-41 for positions
close to the center and within the calibration range and for positions outside of the
calibration range and close to the right actuator. The controller does not perfectly
track the reference at positions close to one actuator. This is due to the error in
the calibration map. The integrator anti-windup limit is too low for the integrator
to fully cancel this error. This problem can be directly addressed by calibrating the
actuator over the whole motion range.
4.7.5
Finite Element Analysis
In this subsection, we present the finite element model of the electromagnetic actuator,
which is developed using FEMM 2 . We use a 2D planar model of the actuator. The
meshed model is shown in Figure 4-42. We model the core’s lamination. We have
defined MagX, MagY, and MagZ material types, which are SuperPerm49 with their
lamination oriented in the direction normal to the X, Y, and Z axes respectively. It
was not possible to model curved lamination in the corners of the U-cores, so we
modeled the corners using a lamination normal to the Z axis. CoilIn and CoilOut
model the coil currents flowing into and out of the page respectively. We use a
Kelvin transformation for modeling the infinite boundary condition [53]. We model
the saturation of the magnetic core. Figure 4-43 shows the B-H relation, which is
modeled in FEMM. The BH characteristic for SuperPerm49 is taken from the data
available on the manufacturer’s website3 .
As an example, we have solved the model with a gap of 0.3 mm and a coil current
2
3
Finite Element Method Magetics http://www.femm.info/wiki/HomePage
Magnetic Metals: www.magmet.com
132
1
Right
Actuator
09
0.9
0.8
Calibration
n Range
position [mm]
0.7
06
0.6
0.5
0.4
03
0.3
0.2
Left
Actuator
0.1
0
0
1
2
3
4
5
time [s]
6
7
8
9
10
Figure 4-40: Experimentally captured step response of the position control system
tested at different air gap sizes. Position 0.05 mm corresponds to 50µm away from
the left actuator and position 0.95 mm corresponds to 50 µm away from the right
actuator.
133
0.96
0.66
0.94
0.64
0.92
position [mm]
position [mm]
0.68
0.62
0.6
0.9
0.88
0.58
0.86
0.56
0.84
0.54
0.1
0.2
0.3
0.4
time [s]
0.5
0.6
0.82
1.6
1.8
2
2.2 2.4
time [s]
2.6
Figure 4-41: A zoomed in view of the position control system’s step response close
to the center and within the calibration range (left), and outside of the calibration
range and close to the actuator face (right).
X
Y
Z
Figure 4-42: Meshed planar finite element model of the electromagnetic actuator.
134
2.8
2
B [T
T]
1.5
1
0.5
0
0
50
100
H [A/m]
H, Amp/Meter
Figure 4-43: Non-Linear BH characteristic of the SuperPerm49 modeled in the FEA
software. The cores are manufactured by Magnetic Metals. The data is obtained
from the manufacturer’s website
of 2 A. The magnetic flux density plot is shown in Figure 4-44. The line plot of
the normal magnetic flux density over the face of the I-core is shown in Figure 4-44.
Ignoring the reluctance of the magnetic core and the fringing fields, the expected
magnetic flux density in the air gap can be estimated using the Ampere’s law as the
following:
I
H · dl ' 2gH
(4.27)
⇒ H = N I/2gB = µ0 H = µ0 N I/2g = 1.17T
(4.28)
NI =
C
The result from the finite element analysis is very close and shows 1.13 T on the
outer pole faces and 1.21 T on the inner pole faces. As can be seen, the normal
magnetic flux is not perfectly uniformly distributed over the pole faces.
We use the finite element model to simulate the actuator at different air gap values.
At each air gap (g), we measure the actuator’s mutual inductance (Lm ) as well as
135
A
B
X
Z
Y
1
A
B
B . n [T]
0.5
0
-0.5
-1
-40
-30
-20
-10
0
10
x position (mm)
20
30
40
Figure 4-44: Simulation results using a coil current of 2A is shown as a magnetic flux
density plot (top) and a line plot of the normal magnetic flux density over the face
of the actuator’s mover from point A to point B (bottom).
136
-3
3
x 10
FEA
Left
Right
2.8
2.6
Lm [H]
2.4
2.2
2
1.8
16
1.6
1.4
1.2
0.3
0.35
0.4
0.45
0.5
gap [mm]
0.55
0.6
0.65
Figure 4-45: The mutual inductance (Lm ) versus the air gap size is plotted based on
the finite element model results and is compared to the experimental results for the
right and left actuators.
its force correction constant (c). To automate this process, we have written a LUA
script. The script opens the model, sets the air gap, sets the current, simulates the
model, and takes the integrals required for calculating the sensed flux linkage (λS ) and
the output force (F). We use two nested loops for simulating the model at different
coil current values and at different air gap sizes. In Figure 4-45 and Figure 4-46,
the mutual inductance and the force correction constant, which have been calculated
using the FEA model, are plotted versus the air gap size, and are compared to the
experimental results from the right and left actuators.
The experimental and finite element results show the same trend. The mutual
inductances match very closely; however, the force correction constants are slightly
mismatched. The differences may be due to the following reasons:
• A planar model is used instead of an actual 2D model.
137
20
FEA
Left
Right
18
16
C [N/(mVs)2]
14
12
10
8
6
4
2
0
0.3
0.35
0.4
0.45
0.5
gap [mm]
0.55
0.6
0.65
Figure 4-46: The force correction constant (c(g)) versus the air gap size is plotted
based on the finite element model results and is compared to the experimental results
for the right and left actuators.
138
• The manufactured actuator has deformed pole faces which differ from the assumed cuboid pole geometry. The pole faces are deformed by the large grinding
forces exerted on the raised laminated pole faces. This could have been avoided
by burring and supporting the pole faces using resin prior to grinding.
• The material properties and the sizes are not exactly matched between the
model and the actuator.
4.8
Summary
We reviewed the prior art charge amplifiers. We analyzed a conventional charge
amplifier and used it as a benchmark. We presented a VQV charge amplifier with
a new feedback circuit design which is more robust to the addition of series load
impedance. We also described a hybrid hysteresis method (HHC) which can be added
to charge amplifiers to enable piezo hysteresis compensation at low frequencies. We
use the improved VQV charge amplifier with HHC for controlling the extension of the
piezoelectric actuator approximately linearly without the need for closed-loop control
using the strain gauge feedback. In this chapter, we also present a magnetic flux
control method which, in analogy to piezo linearization through charge control, can
linearize normal flux electromagnetic actuators.
In the next chapter, we present a sensorless method for precisely detecting contact
between the piezoelectric actuator and the reticle. The method is used by the control
system to reference the piezo’s extension relative to the reticle edge.
139
140
Chapter 5
Self-Sensing Contact Detection
Jones and Garcia [37] define self-sensing as measuring a signal from a smart-material
actuator, such as piezoelectric or magnetostrictive actuators, without the need for any
sensors or additional components. Self-sensing can improve a system’s performance
without incurring additional cost and space associated with using a separate sensor.
Self-sensing is key to improving the precision of our reticle assist device by detecting
contact between our actuator and the reticle. This method has been adapted from
self-sensing of atomic force microscopy probes as in our high-accuracy atomic force
microscope (HAFM) [83]. In this chapter, first, we present the prior art of selfsensing. Next, we provide an analytical derivation of our self-sensing method applied
to piezoelectric and electromagnetic resonators. Then, we describe the application
of our self-sensing contact-detection method to our reticle-assist device. Finally, we
show the self-sensing contact detection method used with a piezoelectric atomic force
microscope (AFM) and a macro-scale electromagnetic AFM.
5.1
Prior Art Self-Sensing
Self-sensing is referred to extracting a measurement signal without using any separate
sensors or additional components. Typically, self-sensing uses a system’s model to
extract information about its states. An actuator’s electro-mechanical model is used
to relate the actuator’s electric signals to for example its motion or force. This is
141
very similar to using an observer in a control system. For simple implementation
of self-sensing, bridge circuits were initially used to extract such measurements from
actuators. Later, observer-based self-sensing methods running on analog electronics
or digital processors were utilized. Non-linearities of actuators, such as hysteresis and
creep, are not included in the linear model of the actuators and can adversely affect
the performance of the self-sensing algorithm. Observer based self-sensing methods
have been proposed where a hysteresis model of the system is used to compensate for
the actuator’s nonlinearities. These approaches are described in more detail below.
According to reference Jones and Garcia [37], the first instance of self-sensing was
implemented by De Boer in 1961. He used a bridge circuit to extract a measurement
corresponding to the motion of a voice coil actuator and used it as feedback [13].
Dosch et al. applied self-sensing to piezoelectric actuators [18], where they used a
bridge circuit to estimate the piezoelectric actuator’s strain or strain-rate. They
used the measurement for actively damping the vibration of a cantilever. Anderson
and Hagood employed piezoelectric actuators for simultaneous sensing and actuation
[6] and applied them in vibration damping of a strut. Jones and Garcia used selfsensing with a micro positioner [37]. The self-sensing methods, which are based on
a linear model of the piezoelectric actuator, have errors in their measurement and
control resulting from hysteresis non-linearities. Spangler integrated charge control
and self-sensing to eliminate the phase delay resulting from the piezoelectric voltagestrain hysteresis [80]. Simmers et al. suggested that self-sensing can be improved by
capacitor insertion [75]. Jones and Garcia applied hysteresis compensation to selfsensing [38]. They formulated an observer-based self-sensing algorithm which can
estimate the actuator’s force and strain from its voltage and charge. Their self-sensing
algorithm models the piezoelectric actuator’s capacitance using a generalized Maxwell
slip (GMS) model. Self-sensing has also been applied to other smart materials. Pratt
and Flatau applied self-sensing to a magnetostrictive actuator based on its linear
model [68]. Kuhnen et al. [46] applied self-sensing with hysteresis compensation to a
magnetostrictive actuator.
The self-sensing methods described above are for estimating motion or force. Their
142
estimation can be inaccurate due to the actuator hysteresis. If a hysteresis compensator is used, the accuracy limit is set by the compensator’s accuracy. It is difficult
to build a non-linear model of the actuator which is accurate over a broad range of
frequencies. Furthermore, it is difficult to process such a model with good accuracy
in real-time and achieve a fast estimation bandwidth. For our reticle assist device we
are interested in repeatable force control at high bandwidth. In order to achieve this
goal, we use a self-sensing method inspired by self-sensing AFM probes. We measure
the shifts in the actuator’s electrical admittance frequency response to detect contact
between the actuator and the reticle with high sensitivity. Knowing the exact contact
point, we can estimate and control the force by controlling the deformation of the
mechanical force-loop stiffness relative to this contact point.
Gunther et al. used a quartz tuning fork resonator with a sharp vibrating tip for
scanning near-field acoustic microscopy (SNAM), where they monitored the variations in the tuning fork electrical admittance near its resonance resulting from coupling between the resonator and the sample [32]. Karrai and Grober used a quartz
tuning fork with an optical fiber for near-field optical microscopy (NSOM), where
the variations in the tuning fork’s electrical admittance near resonance were used as
feedback for regulating the tip-sample distance [41]. Rychen et al. used a self-sensing
quartz tuning fork with a sharp tip for low-temperature atomic force microscopy [71].
Self-sensing AFM probes eliminate the need for an optical lever mechanism, which
typically consists of optics, a laser shining on the probe, and a multi-cell photodiode
detector. Self-sensing AFM probes are suitable for NSOM because there is no interference from the optical-lever’s laser light with the optical near-field scanning system.
The tuning forks are also attractive for ultra-low-temperature applications because
there is no heat added by a laser close to the measurement point. Tuning forks have
a symmetric vibration mode, where inertial loads from the two prongs cancel. As a
result, they are sensitive resonators with a high quality factor (Q-factor). [29]
Self-sensing AFM probes can be made by attaching a sharp tip to a tuning fork
143
from a watch quartz crystal. Bruker1 and Nanosnesors2 supply commercial selfsensing AFM probes. NanosensorsT M carries the Akiyama probe, which consists
of a cantilever symmetrically attached to the end of the tuning fork’s prongs. Burker
carries the DMASP self-sensing self-actuating probe, which consist of a piezoelectric
cantilever with a sharp tip. We have used a self-sensing Akiyama probe in our HAFM
[83]. We have also designed our own macro-scale self-sensing magnetic AFM. In the
reticle assist device, we have applied self-sensing to a commercial piezoelectric stack
actuator.
5.2
Self-Sensing Contact-Detection Principle
By monitoring the variations in an actuator’s frequency response near resonance, we
can detect contact between the actuator and an object with high sensitivity. To
avoid sensors, we use the actuator’s electrical impedance or admittance frequency
response. The mechanical and electrical actuator models are coupled. Interactions in
the mechanical domain, such as mechanical contact, reflect on the electrical domain
dynamics. As a result contact can be detected by monitoring the electrical frequency
response with highest sensitivity near resonance. In the following subsections, we
model piezoelectric and electromagnetic resonators and show how their mechanical
dynamics can be extracted from sensing of the electrical dynamics.
5.2.1
Piezoelectric Devices
A lumped parameter model of a piezoelectric resonator is shown in Figure 5-1. In
the mechanical domain, the actuator is modeled as mass, stiffness, and damping
with values corresponding to the actuator’s first resonance mode. The surface, with
intermitent contact, is modeled as a stiffness ks . The piezoelectric effect is modeled as
a force Fp exerted on the mass m. In the electrical domain, the resonator is modeled as
a voltage source ve driving a piezoelectric element and a parallel parasitic capacitance
1
2
Burker AFM Probes: www.burkerafmprobes.com
NanoSensorsT M : www.nanosensors.com
144
ie
b
k
ip
ic
+
z
ve
Fp
m
p
C
ks
Sample
Figure 5-1: Lumped parameter model of a piezoelectric resonator modeling only the
first resonance mode. The sample surface is modeled with a stiffness ks .
C. The two domains are coupled by the piezoelectric element. The coupling equations
are defined as
Fp = pve
(5.1)
ip = pż
where the coefficient p is the piezoelectric constant with units of N/V.
We can write the equation of motion in the mechanical domain, use the coupling
relation in (5.1) to substitute ve for Fp , and thus derive a transfer function:
mz̈ + bż + kz = Fp
⇒ mz̈ + bż + kz = pve
ps
Ż(s)
=
.
⇒
2
Ve (s)
ms + bs + k
(5.2)
We can also write Kirchhoff’s current law in the electrical domain, express ip
using the coupling relation in (5.1), and derive a transfer function by substituting for
145
ż using the mechanical transfer function from (5.2):
ie = C v̇e + ip
⇒ ie = C v̇e + pż
⇒ Ie (s) = CVe (s)s + pŻ(s)
Ż(s)
Ve (s)
⇒ Ie (s) = CVe (s)s + p
Ve (s)
Ie (s)
p2 s
⇒
= Yt (s) = Cs +
.
Ve (s)
ms2 + bs + k
(5.3)
According to (5.3), the electrical admittance transfer function seen by the excitation voltage source (ve ) consists of a passive capacitive admittance (Yc ) in parallel
added to a piezoelectric admittance (Yp ):
Yt (s) = Yc (s) + Yp (s)
(5.4)
Yc (s) = Cs
Yp (s) =
p2 s
ms2 + bs + k
The mechanical transfer function given by (5.2) is proportional to the piezoelectric
admittance (Yp ):
Yp (s) = p2
Ż(s)
F (s)
(5.5)
As a result, the mechanical resonance can be sensed by measuring the load admittance and extracting the piezoelectric admittance from it. The piezoelectric current
can be extracted from the source current by injecting a current opposite to the capacitive current at the measurement point. In this analysis we assumed that the
actuator is not in contact with the sample surface. A simple model of contact is a
spring-damper at the point of contact whose magnitude is proportional to the portion of the time that the actuator is in contact with the sample during one oscillation
period. The added rigidity and constraint from the contact increases the natural resonance frequency of the resonator. We can detect contact as the shift in the frequency
146
magnit
tude
Ye
Yc
Yp
ωe ωm
frequency
Figure 5-2: The shape of the magnitude response shape of the total, capacitive, and
piezoelectric admittances are shown using arbitrary system parameter values. Note
that the capacitive component hides the resonance.
response of the piezoelectric admittance near the resonance.
The shape of the magnitude frequency responses for the total, capacitive, and
piezoelectric admittances are shown in Figure 5-2. The total admittance (Yt ) is the
load admittance as seen by the excitation voltage source (ve ). The total admittance
response does not have a sharp resonance. It has an asymmetric magnitude response
consisting of a resonance followed by a notch. We refer to the resonance at frequency
ωe as the electrical resonance. This resonance peak does not however correspond to
the mechanical resonance frequency. By compensating for the capacitive admittance
(Yc ) via subtraction, we can extract the piezoelectric admittance (Yp ) which is proportional to the mechanical transfer function Ż(s)/F (s). The resonance frequency of
the piezoelectric admittance does correspond to the mechanical resonance frequency
(ωm ), and is sharp and symmetric. We use the piezoelectric admittance for contact
detection for two reasons. First, the system’s dynamic stiffness is minimum at the
mechanical resonance frequency (ωm ), and thus the probe is more sensitive to the
addition of a stiffness disturbance from contact. Secondly, a sharp and symmetric
resonance curve improves the robustness of the contact detection by reducing its
sensitivity to other system dynamics.
The changes in the frequency response can be detected in several ways. For in147
stance, the resonator can be excited at its resonance frequency and the changes in the
phase or amplitude response from the excitation voltage (ve ) to the current (ip ) can
be calculated as a measure of the shift in the resonance of the piezoelectric admittance (Yp ). We used this method with the reticle-assist device. The methods, which
use the open-loop amplitude or phase response are referred to as the amplitude- or
phase-measuring methods. Alternatively, a feedback system can be designed to put
the piezoelectric resonator in controlled-amplitude self-resonance at its natural resonance frequency. In this way, the shifts in the natural resonance frequency can be
detected as the changes in the self-resonance frequency. Garcia and Perez provide
a comprehensive review of the different detection methods used for atomic force microscopy, including the amplitude-, phase-, and frequency-measuring methods [26]. In
Section 5.3, we describe how we apply self-sensing to the reticle-assist device’s piezoelectric actuator. We present a high-accuracy atomic force microscope in Section 5.4,
which uses a self-sensing Akiyama probe.
5.2.2
Electromagnetic Devices
The self-sensing contact detection method described previously is not specific to piezoelectric actuators and can be applied to other actuator types near their resonance
frequency. In this section, we describe how an electromagnetically driven resonator
can be used for self-sensing contact detection. A lumped parameter model of an electromagnetic resonator is shown in Figure 5-3. The resonator is modeled as a mass
m supported by a spring k and a damper b, with the electromagnetic actuator force
Fm acting on the mass m. In the electrical domain, a voltage source ve is driving
the coil, which is modeled as a resistance R, inductance L, and electromotive force
(emf) voltage vm in series. The contact with the sample is modeled as an intermittent
stiffness ks . The coupling between the electrical and mechanical domains is described
by
Fm = pie
(5.6)
vm = pż.
148
b
R
k
L
+
vm
z
Fm
m
+
ve
-
ie
ks
Sample
Figure 5-3: Lumped parameter electromechanical model of an electromagnetic resonator.
We can write the equation of motion in the mechanical domain, use the coupling
relation in (5.6) to substitute ie for Fm , and derive a transfer function:
mz̈ + bż + kz = Fm
⇒ mz̈ + bż + kz = pie
ps
Ż(s)
=
.
⇒
2
Ie (s)
ms + bs + k
(5.7)
We can also write Kirchhoff’s voltage law for the electrical model, express vm
using the coupling relation in (5.6), and derive a transfer function by substituting for
ż using the mechanical transfer function from (5.7):
ve = Rie + Li̇e + vm
⇒ ve = Rie + Li̇e + pż
⇒ Ve (s) = Ie (s)(R + Ls) + pŻ(s)
Ż(s)
⇒ Ve (s) = Ie (s)(R + Ls) + p
Ie (s)
Ie (s)
Ve (s)
p2 s
⇒
= Zt (s) = R + Ls +
.
Ie (s)
ms2 + bs + k
(5.8)
The resulting impedance transfer function Zt (s) given by (5.8) can be divided into
a passive electrical impedance (Zrl ) and an electromagnetic impedance (Zm ):
149
Zt (s) = Zrl (s) + Zm (s)
(5.9)
Zrl (s) = R + Ls
p2 s
.
Zm (s) =
ms2 + bs + k
The electromagnetic impedance (Zm ) is proportional to the mechanical transfer
function given by (5.7):
Zm (s) = p2
Ż(s)
F (s)
(5.10)
As a result, the electromagnetic impedance (Zm ) can be used for self-sensing
contact-detection. We can extract the electromagnetic voltage (vm ) by subtracting
an estimate of the resistive and inductive voltage (vrl ) from the voltage measured
across the coil (ve ) as
vm = ve − vrl = ve − Rie + L
di
.
dt
(5.11)
The extracted electromagnetic voltage (vm ) and the excitation current (ie ) can be
used for self-sensing contact detection. Contact creates a shift in the electromagnetic
actuator’s natural mechanical resonance frequency. This shift is visible in the electrical impedance frequency response and can be measured using amplitude-, phase-,
and frequency-measuring methods, which were briefly described in the previous subsection. In Section 5.5, we will describe a macro-scale self-sensing electromagnetic
profiler, which uses self-sensing contact detection.
5.3
Application to Piezoelectric Actuator
We apply self-sensing contact detection to the reticle assist device’s piezoelectric actuator to detect contact between the actautor’s pushing tip and the reticle. Precisely
detecting contact is key to accurate force generation because we control the force by
150
controlling deformation of the mechanical force loop past the contact point. In the
following sections, we describe the self-sensing method, show its implementation on
an FPGA device, and present experimental results demonstrating successful contactdetection.
5.3.1
Self-Sensing Method
The piezoelectric actuator’s frequency response shifts as a result of the constraint
added by contact with the reticle. The shift can be detected with high sensitivity
at the actuator’s resonance, where its dynamic stiffness is minimum. The actuator’s
resonance frequency response from the applied voltage to the mechanical strain is
shown in Figure 5-4. This was taken using the strain gauge built into the acutator;
this gauge is not used in the self-sensing algorithm. The response is shown for the
actuator free in air using different excitation amplitudes and in contact with different
preload force values. The frequency response free in air is repeatable for the same
excitation amplitude. As can be seen, the actuator’s frequency response shifts to
higher frequency with increasing the contact preload force. We have used pressure
regulated air with a bellow to gradually increase the preload. The term ∆P used in
the Figure’s legend refers to an arbitrary positive change in pressure by turning the
regulator knob.
As described in Section 5.2, the shift in the mechanical resonance is visible in the
electrical admittance frequency response as well. The electrical admittance frequency
is compared to the mechanical frequency response in Figure 5-5 for the actuator
free in air. Near the mechanical natural resonance frequency, the two responses
match very well. The added mass of the actuator’s pushing tip has resulted in the
piezoelectric current being significantly larger than the parasitic capacitive current
at the resonance. As a result, the notch resulting from the capacitive current leakage
path has little effect on the resonance peak and does not need to be compensated.
We can detect contact by measuring the change in the total electrical admittance
(Yt ) phase or amplitude response at the resonance frequency. We can apply phaseor amplitude-measuring contact detection to the reticle assist device because they are
151
0
|S/Ve| [μm/V]
10
-1
10
10
20
30
40
50
30
40
50
f [kHz]
Free v =20mV
0
∠ S/Ve [deg]
-50
e
Free ve=20mV
Free ve=10mV
Free v =40mV
e
-100
-150
-200
-250
10
0ΔP
1ΔP
2ΔP
3ΔP
5ΔP
7ΔP
20
f [kHz]
Figure 5-4: Piezoelectric actuator’s frequency response from the applied voltage to
the mechanical strain is plotted free in air at different excitation amplitudes, and in
contact with the sample using an increasing range of preloading pressure values.
152
I/V [Mho]
0
Magnitude
10
S/V [μm/V]
-1
10
-2
10
5
10
15
f [Hz]
20
25
30
35
40 45 50
5
10
15
f [kHz]
20
25
30
35
40 45 50
100
Phase [deg]
50
0
-50
-100
-150
-200
-250
Figure 5-5: Comparing the piezoelectric actuator’s electrical admittance and mechanical frequency response near resonance.
simpler to implement compared to the frequency-measuring AFM, and they provide
a sufficient sensing bandwidth.
5.3.2
Implementation on an FPGA
To detect contact, we add a small sinusoidal excitation to the applied voltage and
measure the amplitude ratio and phase difference between the current and the voltage
signals. We implement the contact detection algorithm on a LabVIEW PXI-7854R
FPGA card. The algorithm is sampled at 325 kHz. A block diagram of the contact
detection system is shown in Figure 5-6. The power amplifier’s reference voltage
(vr ) is passed through the algorithm on the FPGA, where a sinusoidal excitation
(ve × sin(ωp t)) is added to it. The sinusoidal excitation and contact detection can be
153
FPGA
Meas. Resp.
PR
iP
vP
AR
en
~
cos
sin
ve
+
PZT
vr
Power Amp.
Figure 5-6: Block diagram of the contact detection algorithm implemented on an
FPGA device.
enabled or disabled using the enable signal (en). The FPGA reads the piezo current
and voltage measurements from the power amplifier. It uses these signals to calculate
the phase and magnitude response from the actuator voltage to its current at the
excitation frequency.
The response measurement algorithm is described below [25]. It first finds each
signal’s magnitude and phase relative to the excitation signal. The amplitude and
phase responses are calculated as the phase difference and magnitude ratio of the
two signals. To calculate the magnitude and phase at the excitation frequency we
modulate signals using the sine excitation and its matched cosine signal:
iSM = ip × sin(wp t)
sine modulated ip
(5.12)
iCM = ip × cos(wp t) cosine modulated ip
(5.13)
vSM = vp × sin(wp t) sine modulated vp
(5.14)
vCM = vp × cos(wp t) cosine modulated vp
(5.15)
The excitation frequency ωp ' 25 kHz is the actuator’s resonance frequency.
We low-pass filter the modulated signals to obtain its correlation sum with the sine
excitation signal and its matched cosine signal. lpf (t) is the impulse response of a
154
fourth order low-pass Butterworth filter with a cutoff frequency of 1 kHz:
iSC = iSM ∗ lpf (t)
sine-ip correlation
(5.16)
iCC = iCM ∗ lpf (t) cosine-ip correlation
(5.17)
vSC = vSM ∗ lpf (t) sine-vp correlation
(5.18)
vCC = vCM ∗ lpf (t) cosine-vp correlation
(5.19)
The correlation sums can be considered as the Cartesian coordinates of each signal’s complex frequency response at the modulation frequency. We convert the responses into the polar coordinates:
6
6
ip = arctan(iSC /iCC )
p
|ip | = 12 iSC 2 + iCC 2
phase of ip relative to ve
(5.20)
amplitude of ip
(5.21)
vp = arctan(vSC /vCC ) phase of vp relative to ve
√
|vp | = 21 vSC 2 + vCC 2 amplitude of vp
(5.22)
(5.23)
The phase and magnitude response from the applied voltage to the current can
be calculated as the following:
6
Ip (s)
Vp (s) s=wp j
= 6 ip − 6 vp admittance phase @ wp
|
= |ip | ÷ |vp | admittance magnitude @ wp
| VIpp(s)
(s) s=wp j
5.3.3
(5.24)
(5.25)
Experimental Results
We have tested the self-sensing contact detection method. We extend the piezo actuator to make contact with reticle and increase the contact force from 0 N to approximately 70 N. The contact force is calculated as the deformation of the reticle
membranes measured by the capacitive displacement gauges times the membranes
stiffness in the force direction. The resulting phase and magnitude measurements are
plotted versus the contact force in Figure 5-7. As it can be seen, the detection method
155
60
1.1
[Mho]
0.9
|Y (s)| |
ω=ω
e
30
e
20
10
0.8
0.7
0.6
0
-10
-20
10 cycles
1 cycle
1
40
e
∠Ye(s) | ω=ω [deg]
50
0.5
0
20
40
60
Contact Force [N]
80
0.4
-20
0
20
40
60
Contact Force [N]
80
Figure 5-7: Self-sensing contact detection phase (left) and amplitude (right) response
plotted versus the contact force. The probe is excited at the mechanical resonance
ωp '25 kHz with approximately 25-nm oscillation amplitude.
is very sensitive. A large change in phase and amplitude response is measured using
a small contact force. The resonance frequency ωp is stable, such that we have never
needed to readjust the excitation frequency for our tests.
We use the contact detection method for finding the reticle’s edge. The time plot
for an experiment, where we use contact detection, is shown in Figure 5-8. As shown
in the top subplot, the piezoelectric actuator approaches the reticle, and the contact detection system is activated at the same time. The contact detection system’s
phase measurement is shown in the bottom subplot. When activated, the phase measurement goes through a 1-ms transient. The phase measurement is a steady-state
response, and thus it is valid after the transients have disappeared. After the 1-ms
transient, contact is detected as the phase measurement raising above zero degrees.
The resulting contact forces are shown in the middle subplot. Once the reticle edge
is detected, the actuator retracts back. The detected edge location is shown in the
top subplot.
156
Approach
Contact
Retract
2
S
Sr
Strain [μm]
1.5
1
Edge
0.5
0
450
452
454
456
458
460
time [ms]
462
464
466
468
470
452
454
456
458
460
time [ms]
462
464
466
468
470
452
454
456
458
460
time [ms]
462
464
466
468
470
3
Force [N]
2
1
0
-1
450
∠ Yp @ ωb [deg]
60
40
20
0
-20
-40
450
Figure 5-8: Self-sensing contact detection is used to detect the reticle’s edge. The time
plots of actuator’s strain (top), contact force (middle), and phase response (bottom)
are shown. In the top plot, the signals Sr , S, and Edge indicate the reference, the
measured strain, and the registered edge location, respectively.
157
5.4
Application to Atomic Force Microscope
Application of the self-sensing contact detection method has been inspired by operation of self-sensing atomic force microscopes (AFM). In this section, we describe
our high-accuracy atomic force microscope (HAFM), which uses a self-sensing probe
[83]. We provide background information on the HAFM project, describe the HAFM
design, instrumentation and control, and provide experimental results.
5.4.1
Background
The HAFM has been designed to be integrated with the sub-atomic measuringmachine (SAMM) positioning stage and be used for dimensional metrology with
nanometer-scale accuracy. The project is a joint effort by researchers at MIT and
UNC-Charlotte. The SAMM has been designed in the doctoral thesis of Holmes [33],
and has more recently undergone extensive upgrades in measurement systems and
control as described in [64]. HAFM’s mechanical design was completed in the master
thesis of Ljubicic [49]. The HAFM’s electronics, instrumentation, and control were
completed as a part of this thesis. The HAFM has been transferred and integrated
with the SAMM stage at UNC-Charlotte. It is being used for dimensional metrology
with nanometer accuracy over a measurement volume of 25 mm × 25 mm × 0.1
mm. Similar large-range AFMs have been designed for dimensional metrology by
other institutes, such as Physikalisch-Technische Bundesanstalt (PTB) [17], National
Institute of Standards and Technology (NIST) [45], National Metrology Institute of
Japan (NMIJ) [57], and National Research Council of Canada (NRCC) [21].
A CAD model of the SAMM with the HAFM is shown in Figure 5-9. The subatomic measuring machine consists of two parts: an oil chamber and a metrology
chamber. The platen is neutrally buoyant in fluorosilicone oil. The platen can be actuated in six degrees of freedom (DOF) by the four levitation linear motors. A sample
holder, which carries the sample being measured, is in the metrology chamber and is
fixed to the platen using support bars. The position of the sample holder is measured
relative to the Zerodur metrology frame using laser interferometers for the in-plane
158
Borescope
AFM Head
Sample Holder
Metrology
Chamber
Metrology Frame
Platen
Oil
Chamber
Magnet Array
Linear Motor
Figure 5-9: CAD drawing of the subatomic measuring machine (SAMM) with the
high-accuracy atomic force microscope (HAFM) installed as its metrology probe.
DOFs (x, y, and θz ) and using capacitive displacement sensors for the out-of-plane
DOFs (z, θx , and θx ). The HAFM is installed on the SAMM’s metrology frame and
measures and tracks the sample in the z-direction. A bore scope passes through the
center of the HAFM and is used for visually locating features on the substrate to be
measured.
5.4.2
High-Accuracy Atomic Force Microscope
The assembled HAFM and its cross-sectioned CAD model are shown in Figure 510. The AFM probe is fixed to the bottom of the moving stage. The moving stage
is constrained by the guide flexure to motion in the Z-direction only. The moving
stage is driven by a piezo stack actuator with a range of 20 µm. The actuator is
159
x
y
Probe
Borescope
Piezoelectric
Actuator
Coupling
Flexure
Capacitive
S
Sensor
Kinematic
Mount
Guide
Flexure
Moving
Stage
i
Probe
Figure 5-10: Photo of the assembled HAFM (right) and cross-sectioned CAD model
of the HAFM (left).
connected to the moving stage using a coupling flexure. The coupling flexure is
designed to be rigid only in the Z-direction in order to transfer only the Z-motion
of the piezoelectric actuator, while attenuating its error motion. The position of the
moving stage is measured using three capacitive displacement sensors symmetrically
arranged around the moving stage. The center axis of the HAFM is left free for a
borescope to pass through. More details on the HAFM’s mechanical design can be
found in the Master’s thesis of Ljubicic [49].
A simplified block diagram of the HAFM control system is shown in Figure 511. Here, we use a self-sensing Akiyama probe. The preamplifier buffer and the
self-resonance control electronics are used to amplify the probe’s signals and set it in
controlled-amplitude self-resonance. We use the probe in the period-measuring mode.
The tracking controller uses the probe’s self-resonance period as feedback and drives
the piezoelectric actuator to track the sample surface. We implement the tracking
controller using an FPGA device. The real-time computer is used for logging the
image data and controlling the SAMM stage.
160
AFM Head
DAC
16
bits
Piezo
Driver
ADC
20
bits
Capacitive
Sensor Box
Real-Time
Controller
Akiyama
Probe
Sample
X-Y Scanner
(S.A.M.M.)
ie
Image
Data
Logging
X-Y Scan
Control
Processor
ve
FPGA
Pre-Amp.
Board
2ve
Self-Res
Control
CLKSR
vm
Period
Estimatio
n
TSR
Tracking
Control
Figure 5-11: Simplified block diagram of the HAFM system.
161
vP
-6
Admittance [M
Mho]
10
-7
10
-8
10
48.1
48.2
48.3
48.4
Frequency [Hz]
48.5
100
Phase [deg]
50
0
-50
-100
-150
Experimental
Fit
Compensated
48 1
48.1
48.2
48
2
48 3
48.3
48 4
48.4
Frequency [Hz]
48 5
48.5
Figure 5-12: An Akiyama probe’s admittance frequency response shown based on our
experimental data (blue), the analytical fit(green), and the compensated analytical
function (red).
5.4.3
Self-Sensing Probe
Conventional AFM systems use an optical-lever for sensing the probe’s oscillation.
To achieve a compact design, which can be more easily integrated with the SAMM,
we use a self-sensing probe that eliminates the need for the optical-lever mechanism.
We use a commercially available self-sensing Akiyama probe3 . The Akiyama probe
consists of a cantilever symmetrically attached to the ends of a tuning fork’s prongs.
Applying a voltage to the piezoelectric tuning fork creates an in-plane motion of the
tuning fork prongs, which results in an out-of-plane tapping motion of the cantilever
tip. The probe has been invented by Akiyama [2].
The Akiyama probe can be used for self-sensing contact detection as described in
Section 5.2. The probe’s admittance frequency response is shown in Figure 5-12 near
3
The Akiyama probe is a product of NANOSENSORST M . Pictures of the Akiyama probe are a
courtesy of NANOSENSORS, and are used with permission (http://www.nanosensors.com).
162
its first resonance frequency of about 48.3 kHz. The experimentally captured probe
admittance consists of the parallel combination of a capacitive admittance (Yc ) and a
piezoelectric admittance (Yp ). An analytical model is fitted to the frequency response
using (5.4) with the added low-pass dynamics of the measurement buffer as
Yt (s) = [
p2 s
1
+ Cs]
,
2
ms + bs + k
τs + 1
(5.26)
where τ is the time-constant of the measurement buffer. The values for the fitted
model are
m/p2 = 1.372 × 104 [H]
b/p2 = 2.867 × 106 [Ω]
k/p2 = 1.265 × 101 5 [F−1 ]
C = 0.99 [pF]
τ = 2.59 × 10−6 [s].
The close agreement between the experimental data and the fitted model shown
in Figure 5-12 confirms the validity of the model developed in Section 5.2.
To obtain the symmetric resonance corresponding to the mechanical resonance of
the probe, we cancel the capacitive current as will be described in Section 5.4.5. The
compensated piezoelectric admittance is shown in Figure 5-12 in red. As can be seen,
the piezoelectric admittance peaks at a slightly higher frequency and is symmetric.
For maximum sensitivity, we use the probe’s compensated piezoelectric admittance
frequency response at its resonance frequency.
5.4.4
Frequency Measuring AFM
Due to its tuning fork design, the Akiyama probe’s first mechanical resonance has a
high quality factor of approximately 1000 in air. A high quality factor means a sharper
resonance peak with more sensitivity to contact. However, a high quality factor
163
P(s)
Φ(s)
P(s): probe
Φ(s): rest of the loop
K: variable gain
K
Figure 5-13: Simplified block diagram of the AFM self-resonance loop
resonator also dissipates less energy per cycle, which means any transient lasts longer
before it disappears. This can reduce a probe’s bandwidth if used in the amplitude
or phase measuring mode, where it is excited at a fixed frequency and the changes in
phase and amplitude are used as feedback for tracking the sample surface. Albrecht
introduced the frequency-measuring AFM mode, which addresses this problem and
eliminates the limit set on the detection bandwidth by the high quality factor [3].
Albercht uses constructive feedback, with an actively controlled feedback gain, to
set the cantilever in controlled-amplitude self-resonance at its mechanical resonance
frequency. In this configuration, the frequency of self-resonance shifts with the probe’s
mechanical resonance frequency, and thus can be used as feedback to track the sample.
Atia uses this method with a near-field scanning optical microscope [11].
A simplified block diagram of a self-resonance loop, which consists of the probe
P (s), variable gain K, and the rest of the loop Φ(s), is shown in Figure 5-13. In order
for this loop to self-resonate with a constant amplitude, it must have an imaginary
pole pair on the imaginary axis, and hence, s=jωm must be a solution to the loop’s
characteristic equation:
−P (s)Φ(s)K + 1|s=jωm = 0
⇒ P (s)Φ(s)|s=jωm = 1/K

 |P (s)Φ(s)|
s=jωm = 1/K
⇒
 6 P (s)|
= −6 Φ(s)|
s=jωm
s=jωm
Amplitude Condition
Phase Condition
(5.27)
,
For the loop to self-resonate at ωm , the loop-transmission frequency response
must satisfy the phase and amplitude conditions of (5.27). The phase response of
the rest of the loop (Φ) is manually set, such that the phase condition is satisfied at
164
5
x 10
3
5
x 10
1
2
0
0
-1
-2
-2
-1000
0
…
-3
-3
-2
-1
0
Real Axis
1
2
1000
…
Imaginary Axis
2
3
5
x 10
Figure 5-14: Root locus plot of the self-resonance loop
the probe’s mechanical resonance frequency (ωm ). This ensures that self-resonance
occurs at the probe’s mechanical resonance frequency. The amplitude condition is
satisfied by the amplitude controller, which actively varies the feedback gain K. The
amplitude controller changes K to increase or decrease the loop gain to make the
oscillation amplitude grow or decay respectively. The self-resonance control can also
be analyzed using the root-locus plot shown in Figure 5-14. Increasing or decreasing
the loop gain will shift the poles between the right- and left-half plane, resulting in the
oscillation envelope to grow or decay respectively. Setting the phase for the rest of the
loop (Φ) changes the departure angle of locus from the imaginary pole pair. We set
the phase such that the locus for a positive feedback gain departs horizontally toward
the imaginary axis. In this way, the probe will self-resonate at the same frequency as
the mechanical resonance’s imaginary pole pair. More information on modeling and
controlling self-resonance can be found in [70, 83].
Setting the probe in self-resonance results in the probe oscillating at the frequency
where it satisfies the phase condition in (5.27). As a result, Albercht’s frequency165
Self-Resonance Frequency (kHz)
47
22 nA
24 nA
29 nA
34 nA
38 nA
56 nA
46.9
46.8
46 7
46.7
46.6
46.5
0
200
400 600 800
Z-Position (nm)
1000 1200
Figure 5-15: Experimentally obtained sense curves for an Akiyama probe under test
at different oscillation amplitudes.
measuring method can also be implemented by measuring the probe’s phase response
at its mechanical resonance and changing its excitation frequency to control the measured phase response. Edwards [20] and Rychen [71] measure the probe’s phase
response and control it by changing the excitation frequency. They use the varying
excitation frequency as feedback to track the sample surface. This implementation
of frequency-measuring AFM requires a phase-locked-loop and a variable-frequency
excitation source. However, it provides more flexibility and can potentially achieve a
better resolution if used with a locked-in amplifier.
We use the frequency-measuring method for our AFM. Similar to Albercht’s implementation, we set the probe in constant amplitude self-resonance and use the probe’s
self-resonance frequency as feedback to track the sample surface. More details on the
implementation of the self-resonance controller is provided in Section 5.4.5. The sense
curves for the Akiyama probe, which is set in self-resonance, are shown in Figure 515. As the probe approaches the sample, the self-resonance frequency increase from
46646 Hz, when free in air, to 46938 Hz when completely in contact with the sample.
At a smaller oscillation amplitude, for a given approach distance, the probe spends
166
Table 5.1: Table of the probe sensitivity at different oscillation amplitudes
Electrical
Estimated Mechanical
Sensitivity
Amplitude (nA)
Amplitude (nm)
(Hz/nm)
22
376
0.777
24
442
0.661
29
527
0.554
34
616
0.474
38
702
0.416
56
1074
0.272
a longer portion of its oscillation period in contact with the sample. As a result, the
probe’s sensitivity increases as the oscillation amplitude is decreased. A list of the
probe’s sensitivity at different oscillation amplitudes is provided in table 5.1. The
mechanical oscillation amplitude is estimated as the length of Z-position range over
which the frequency changes. As the probe approaches the sample, it takes a distance
equal to the amplitude of oscillation to go from having no contact to having contact
throughout the oscillation cycle. There is a minimum oscillation amplitude, below
which stable oscillation cannot be sustained perhaps due to the small scale of the
signals and pour signal-to-noise ratio. That minimum amplitude limit is found to be
22 nA, which is equivalent to approximately 376 nm tip oscillation amplitude.
5.4.5
Probe Electronics
Following the method introduced by Albercht [3], we set the probe in controlledamplitude self-resonance using analog electronics. The electronics are adapted, with
some modification, from the technical guide provided for the Akiyama probe [60].
We use a preamplifier board to amplify the small piezoelectric current close to the
probe. A self-resonance control board is used to set the probe in controlled-amplitude
self-resonance.
A schematic of the preamplifier board is shown in Figure 5-16. The preamplifier
board has a transformer for interfacing the drive signal (VE ) from the self-resonance
control board to the probe. Using a transformer prevents ground loops by providing
167
an AC coupled link, where the boards do not share a common ground. In this way,
the ground nets of the preamplifier (CMP A ) and the self-resonance controller (CMSR )
boards are not connected in DC. A transformer with a center tap is used to obtain a
signal opposite to the driving signal, which can be used for compensating the probe’s
capacitive current. The signal is used to drive a variable capacitor (VarC) and inject
a current that cancels the probe’s capacitive current. We tune the variable capacitor
by minimizing the compensated probe current at a frequency well above the first
resonance mode, for example at 100kHz, where the capacitive current is dominant.
The circuit uses a transimpedance buffer for converting the piezoelectric current into a
voltage measurement. The voltage signal is amplified again by another voltage buffer
with a closed-loop gain of approximately five. The probe’s current signal is very
sensitive to noise. We use a miniaturized coaxial cable to shield the signal, as shown
in the schematic. The circuit is designed, such that the shield and the current signal
are at the same voltage. In this way, the shield’s parasitic capacitance does not affect
the current measurement, and the shield prevents stray electric field coupling. The
transimpedance buffer’s design keeps the connection to the probe at virtual ground.
To ensure that the shield and signal voltages match, the shield is connected directly
to the ground at the operational amplifier’s non-inverting terminal.
A key part of the electronic design is the preamplifier’s transimpedance buffer. It
is important that the buffer has a high current to voltage gain, is stable, and has a
high bandwidth. In order to achieve a relatively high crossover frequency, we use a
de-compensated OP338, which is not unity-gain stable. Because the feedback resistor
is large, the feedback at the cross-over is dominated by the capacitive voltage-divider
formed by the feedback capacitor C1 = 1 pF and the parasitic capacitance between
the op-amp’s inverting and non-inverting terminals. The parasitic capacitance consists of the op-amp’s input capacitance as well as the shield and the circuit board’s
stray capacitance. With the parasitic capacitance being larger than the feedback capacitance, the capacitive voltage-divider’s gain is significantly smaller than unity and
can stabilize the de-compensated op-amp.
The schematic design of the self-resonance control board is shown in Figures 5168
2VE
CMPA
SP-67
CMSR
+
VE
Akiyama Probe
IvarC
Ip
VI
CMPA
CMPA
OPA627
CMPA
Figure 5-16: Schematic design of the preamplifier board. The picture of the Akiyama
probe is courtesy of NANOSENSORST M . Shield connections are shown at input
terminals of operational amplifier OP 1.
17 and 5-18. As shown in Figure 5-17, we use a fully differential input buffer to
measure and filter the amplified current measurement (VI ) from the preamplifier
board. We convert the buffered differential signal (UP and UN ) into a single ended
signal (UI ) using an analog adder-subtractor buffer. We measure the period of the selfresonance using an FPGA device. An AD790 precision comparator is used to convert
the differential current measurement signals (UP and UN ) into a digital square-wave
signal that can be read by the FPGA’s digital input.
As shown in Figure 5-18, we use a precision rectifier and a low-pass filter to estimate the self-resonance signal’s amplitude. We use an analog amplitude-controller
consisting of an integrator and a lead-lag filter. The controller’s proportional gain
can be tuned using the POT2 potentiometer. The reference voltage can be adjusted
using the POT3 potentiometer. The amplitude-control loop is nonlinear. We apply
a resistor-capacitor (RC) low-pass filter (R30 and C18 ) to the reference amplitude to
ensure that rapid changes in the reference do not destabilize the nonlinear amplitude
control system. The amplitude controller works by changing the feedback gain. We
use an analog multiplier to apply the changing feedback gain to the current measurement. We use an all-pass filter to adjust the feedback phase and make sure that the
169
differential to single ended buffer
fully differential buffer
1
UP
VI
UI
CMPA
UN
precision comparator
UP
CLKSR
UN
Figure 5-17: Schematic design of the self-resonance control board showing the fullydifferential input buffer and precision comparator module used to digitize the selfresonance signal.
170
precision rectifier
amplitude controller
UI
gain
CMSR
CMSR
CMSR
multiplier
all-pass filter
scaling buffer
gain
UI
2VE
CMSR
CMSR
Figure 5-18: Schematic design of the self-resonance control board showing the control
blocks consisting of amplitude measurement, loop gain control, and phase shifting.
phase-condition, given by (5.27), is satisfied at the mechanical resonance frequency.
Finally, we use an additional analog buffer for scaling and low-pass filtering the feedback signal. The feedback signal must be low-pass filtered to avoid exciting the higher
resonance modes of the probe.
5.4.6
Tracking Controller
We design a tracking controller, which uses the probe’s self-resonance period as feedback to move the probe normal to the sample surface in order to track the surface.
We have designed the tracking controller using loop-shaping. The frequency response
of the tracking plant from the piezo amplifier’s reference voltage to the change in the
171
Magnitude [arb.]
M
2
10
0
10
open-loop
-2
10
compensated
1
Phase [deg]
10
2
3
10
10
4
10
0
-100
-200
-300
1
10
2
10
3
10
Frequency [Hz]
4
10
Figure 5-19: Bode plot of the tracking control system’s open-loop and compensatedloop frequency responses.
self-resonance period is shown in Figure 5-19. The two resonance peaks are believed
to be due to the AFM head’s structural modes. The probe has nearly flat response
up to the resonance peaks. The compensated loop-return-ratio is also shown in Figure 5-19. The compensated loop has a unity cross-over frequency of 100 Hz with 65◦
of phase margin. Relatively large phase margin is helpful for keeping this nonlinear
loop stable through large-signal transitions.
The control law consists of an integrator, a low-pass filter, and two notch filters
at 1.5 kHz and 2.3 kHz. The integrator provides loop gain below the cross-over
frequency and a slope of -20dB/decade for achieving a robust cross-over point. We
use a low-pass filter to attenuate the controller gain at frequencies higher than the
loop cross-over frequency. We use two notch filters to mask the structural modes. A
block diagram of the discrete control law is shown in Figure 5-20.
As shown in Figure 5-21, the period estimation and the tracking controller are
implemented on a National Instrument’s NI-PXI-7813R FPGA card. We detect the
edges of the self-resonance signal using digital logic. We use a 200-MHz counter
as the time reference. At every edge, we store the counter’s value in a FIFO. The
172
TSR
Plant
VP
Tracking Controller
TRef
+
−
integrator
low-pass
notch
notch
z +1
z −1
212 z
28 z − 240
1.5kHz
2.3kHz
Q=0.4
Q=0.3
TSR
Plant
VP
Figure 5-20: The tracking controller’s discrete time control law. The controller will
be sampled at two times the probe’s resonance frequency; i.e. sampling is synchronous with the edges of the square wave CLKSR , and thus sampling is at about
2 × 46.8 kHz = 93.6 kHz where the exact value varies with the tip-sample engagement.
time-stamps are read from the FIFO within the slower running while-loop, where the
change in the time stamp is calculated and is used as a measurement of the selfresonance period. The tracking controller uses this period measurement as feedback
to follow the sample surface. The controller loop reads a new time-stamp as soon as a
new value is written to the FIFO. Because there are two edges (falling and rising) per
oscillation cycle, the controller samples at two times the self-resonance frequency. As
will be explained in Section 5.4.7, sampling the controller synchronous to the tapping
motion improves the tracking noise.
The tracking controller’s step response is shown in Figure 5-22 at 100-Hz and
1-kHz measurement bandwidths. As can be seen with the 1-kHz measurement bandwidth, the HAFM’s structural vibration modes are excited and are present in the
tracking response. This is expected because the controller does not control the vibration modes. The notch filters only mask the modes, so that they are not visible to
the controller and do not affect the system’s stability. The step response with 100-Hz
measurement bandwidth filters out the response due to the vibration modes and is
much less noisy.
The HAFM’s noise, when tracking a stationary sample, is measured using the
capacitive displacement probes and is shown in Figure 5-23 at 100-Hz and 1-kHz
measurement bandwidths. The loop bandwidth remains at 100 kHz for both of these
173
0.5
0
1000 Hz
Axxial Position [nm]
1
0.5
0
100 Hz
NI PXI-7813R FPGA Card
-0
0.5
5
0
2
Time [s]
-0.5
0.5
-1
4
0
clock
manager
if true
V
Z-1
2
4
Time [s] counter
200
MHz
FIFO
single-cycle timed-loop
while-loop
+
TSR
−
FIFO
tracking
controller
vP
Z-1
40
MHz
Axxial Position [nm]
-1
CLKSR
100
80
Figure 5-21: The implementation
of period estimation and tracking controller on the
FPGA device. The controller
within
the while-loop is updated at every rising or
60
falling edge of CLKSR , when a new value is written to the FIFO.
40
1-kHz meas. b.w.
100 Hz meas
100-Hz
meas. b
b.w.
w
20
0
0
Axial Position [n
nm]
Axxial Position [nm]
1
5
10
Time [ms]
15
20
100
80
60
40
1-kHz meas. b.w.
100-Hz meas. b.w.
20
0
0
5
10
Time [ms]
15
20
Figure 5-22: The step response of the HAFM’s closed loop tracking system viewed at
100-Hz and 1-kHz measurement bandwidth.
174
1
Axxial Position [nm]
Axxial Position [nm]
1
0.5
1000 Hz
0
-0.5
05
-1
0
2
Time [s]
0.5
0
-0 5
-0.5
-1
4
100 Hz
0
2
4
Time [s]
Figure 5-23: The HAFM’s noise when tracking a stationary sample surface, viewed
at 100-Hz and 1000-Hz measurement bandwidths.
measurements. The tracking noise is 0.12 nm and 0.24 nm RMS over five seconds at
100-Hz and 1000-Hz measurement bandwidths. The capacitive displacement sensors
are the major contributors to the measured noise.
5.4.7
Tapping-Synchronous Controller Sampling
The probe’s self-resonance period is used as feedback by the tracking controller. The
period measurement updates at the zero-crossing edges of the self-resonance signal.
There is a non-integer mismatch between the control and measurement update rates if
the controller is sampled at a fixed rate in time. Such non-integer sampling mismatch
within a control loop can introduce low-frequency aliased components, which will
significantly degrade the controller’s performance. We thus sample the controller
synchronously with the zero-crossings of probe’s self-resonance signal [5]. In this way,
the measurement and control sampling rates will be identical and there will be no
non-integer sampling rate mismatch.
Figure 5-24 shows the block diagram of the tracking control loop. The transfer
function M(s) represents the HAFM actuation dynamics from the reference piezo
voltage vP to probe motion z. We model the probe as a constant gain p representing
the probe’s sensitivity in Hertz per nanometer. We use a probe sensitivity of 0.5
Hz/nm, which corresponds to the probe oscillating with a current amplitude of 34
nA. Measuring the period as the time between zero crossings of the signal is equivalent
175
vP
Mech. Sys.
z
M( )
M(s)
Probe
P
Mvg. Avg.
f SR
f SR′
Inverse
1/X
TSR′
ZOH
f CTRL
e
−
C(z)
+
TREF
ZOH
+
TSR
−
Quantiz.
Tracking Controller
+
+
−
Z-1
Time Estimation
Figure 5-24: Block diagram of the HAFM’s tracking control loop including the
discrete-time measurement and control sampling. The dashed line indicates the frequency at which the blocks are updated.
to applying a moving average filter, with an averaging window width equal to half of
a self-resonance period, to the probe’s frequency and inverting the average frequency
0
0
). The value of the period is sampled at the
) to obtain the period estimate (TSR
(fSR
zero-crossings of the self-resonance signal. We use a 200-MHz clock incrementing a
digital counter to estimate the self-resonance period, which provides a resolution of
±2.5 ns. This is modeled using a quantization block (Quantiz.) with a step size of
5 ns. Any timing gain or loss from this quantization in one period measurement is
added to the next period measurement. In other words, the accumulated timing error
due to time discretization is limited to ±2.5 ns and the average period is correctly
measured. The tracking controller compares the self-resonance period to a reference
period to calculate the error, which is passed to the tracking control law (C(s)). The
diagram shows the controller being sampled at fCT RL .
Within the control loop, sampling occurs at two points: probe oscillation period
measurement at fSR and tracking control at fCT RL . Sampling a signal creates replicas
of the frequency content shifted by integer multiples of the sampling frequency [63].
If the two sampling rates are integer multiples, the shifts will fold back on each
other. However, if a non-integer mismatch exists, the frequency content can be mixed.
This is particularly bad if high frequency measurement noise is mixed into the low176
1
f CTRL
+
−
trig
1
P
s
+
t
z
z-11
Controller
vP
M(s)
−
+
Time
TREF
Mech.
Sys.
Probe
f SR
Triggered
Control Block
Selected
S
CLK
+
+
+
n
C(z)
−
+
+
z-1
−
TSR
Triggered Time Estimation Block
Figure 5-25: Diagram of the model used for simulating the tracking control loop in
MATLAB Simulink.
frequency range, where the controller has enough bandwidth to respond and follow
the noisy signal. Lu describes this issue in the case of using a digital quadrature
optical encoder’s feedback for position control. He addresses the problem by using a
position estimator [50].
We test the significance of the non-integer sampling mismatch using a simulation
model of the tracking controller in MATLAB Simulink. A block diagram of the model
is shown in Figure 5-25.
As shown in Figure 5-25, the simulation uses Simulink’s triggered blocks to model
sampling. To efficiently generate the zero-crossings edges, we integrate in time the
frequency of oscillation multiplied by two. Half of an oscillation period is completed
and a new edge arrives when the integrator reaches the value one. We use this as a
trigger for executing the triggered simulation blocks and for resetting the integrator.
With this model, we can choose to sample the controller synchronous to the probe
(fSR ) or at a fixed sampling rate (fCT RL ). The simulation also allows us to add noise
(n) to the time measurement in order to model the effect of measurement noise, in
addition to the time-discretization error. The noise sequence (n) is white noise, is randomly generated prior to simulation, and is loaded with time during simulation. The
noise magnitude is equivalent to a signal-to-noise ratio of 100 for the self-resonance
177
-1
0.05
0.1 0.15
time [s]
0
-1
-2
0
0.2
2
2
1
1
0
-1
-2
0
0.05
0.1 0.15
time [[s]]
0.2
0.05
0.1 0.15
time [s]
0.2
0.05
0.1 0.15
time [[s]]
0.2
NOISY
0
CLEA
AN
1
Position [nm]
1
-2
0
Position [nm]
FIXED
2
Position [nm]
Position [nm]
SYNCH.
2
0
-1
-2
0
Figure 5-26: Simulated step responses for synchronous or fixed rate sampling with
(noisy) or without (clean) measurement noise.
signal.
We use the simulation model to test and compare the HAFM’s tracking noise
for synchronous and fixed rate sampling with and without measurement noise (n).
The HAFM’s simulated 1-nm step response is shown in Figure 5-26. Note that the
synchronously sampled controller’s response is significantly less noisy than the fixed
time sampling rate controller. With synchronous sampling, the measurement noise
and the time discretization error remain at high frequency and are not mixed into the
low frequency content, and thus they can be effectively filtered out by the tracking
system’s low-pass dynamics.
As another test, the root-mean-square (RMS) tracking noise of the HAFM is
shown in Figure 5-27 versus the reference period for synchronous and fixed rate controller sampling and with or without added measurement noise. As can be seen,
178
Noisy Synch
1
Noisy Fixed
Clean Synch
Clean Fixed
0.9
Tracking Error [nm RMS]
0.8
0.7
0.6
0.5
0.4
0.3
02
0.2
0.1
0
2136.5
37.5
2136.75
2137.0
2137.25
TREF [Ticks @ 200MHz]
2137.5
Figure 5-27: The HAFM’s simulated RMS tracking noise for synchronous and fixed
rate control with and without measurement noise.
synchronous sampling performs significantly better than fixed rate sampling. In the
center, where Tr ef = 2137 ticks, fixed-rate sampling performs well only if the signal
is noise free because, in this special case, the fixed rate sampling is synchronous to
the probe’s oscillation. However, in presence of measurement noise, the RMS error
is almost independent of the reference period and synchronous sampling performs
significantly better than fixed rate sampling.
5.4.8
Experimental Results
Prior to transferring the HAFM to UNC-Charlotte, the HAFM was tested at MIT
for imaging. We integrated the HAFM with a Veeco Multimode-E piezo-tube scanner which moved the sample to provide the XY raster scans. The HAFM provides
the z-tracking. Resulting images of TGX01 and TGZ01 standard gratings manu179
TGX 01
TGX‐01
TGZ 01
TGZ‐01
µm
nm
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
Figure 5-28: Images of the TGX01 (left) and the TGZ01 (right) standard gratings
captured using the HAFM integrated with the Veeco Scanner at 10µm/s and 5µm/s
scan speeds respectively.
factured by Mikromasch are shown in Figure 5-28. The TGX01 grating is a 1-µm
high checkerboard grating. The grating has sharp edged flat tops, which can be used
for extracting the geometry of the AFM tip. The TGZ01 grating has 25.5±0.1 nm
peak-to-valley height. A histogram of the measured height across the TGZ01 grating
is shown in Figure 5-29, which indicates an average to peak-valley height of 25.6 nm.
Trace and retrace scans of the TGZ01 grating are shown in Figure 5-30 for different
scan speeds. The line scan undershoots on the left side of the step. The undershoot is
the same regardless of the scan direction. This makes us believe that the undershoot
is a result of an actual tip-sample interaction, and it is not due to controller right
half-plane zeros.
Once its performance was confirmed, the HAFM was transferred to UNC-Charlotte,
where it was integrated with the SAMM and is now being used for metrology. Figure 5-31 shows the HAFM installed on the SAMM’s metrology frame. Figure 5-32
shows an image of a triangular grating captured using the HAFM by Jerald Overcash
at UNC-Charlotte. The grating has been manufactured using optical interference
lithography using a tool created Mark Schattenburg at MIT, as described in [44].
The triangular grating has a pitch of 200 nm and a height of 30 nm. The image
consists of 256 lines and is captured at a scan speed of 195 nm/s over 22 minutes and
180
25.6
[nm]
Probability
0 15
0.15
0.1
0.05
Probability
0.15
0
15
0
25.6
[nm]
0
10
0.1
20
30
Height [nm]
40
Figure 5-29: Histogram of height over the HAFM’s image of TGZ01 grating.
0.05
0
Z Measure
ement [nm]
Z Measure
ement [nm]
30
20
0
10
20
30
Height [nm]
40
10
1.2 μm/s T
30
0
1.2 μm/s R
20
-10
12 μm/s T
12 μm/s R
10 0
1
2
(← R) Fast Axis1.2
[μm]
(T →
T )
μm/s
0
1.2 μm/s R
-10
12 μm/s T
12 μm/s R
0
1
2
(← R) Fast Axis [μm] (T →)
3
3
Figure 5-30: Trace and retrace line scans of the TGZ01 grating at different scan
speeds.
181
Figure 5-31: Image of the HAFM installed on the SAMM’s metrology frame at UNCCharlotte.
is plotted with no additional filtering or image correction.
5.5
Application to Magnetic Self-Sensing Imager
In this section, we present a magnetic macro-scale imager, which uses the self-sensing
contact detection method. The imager uses a novel self-sensing and self-actuating
electromagnetic probe. The design of the instrument has been inspired by the operation of AFMs. More details on the imager design, implementation, and control are
provided in the following subsections.
5.5.1
Background
We have designed the macro-scale magnetic imager to be used in the teaching lab for
Mechatronics (2.737), a graduate level course offered by the Mechanical Department
182
Z Position AFM (nm)
40
35
30
25
20
30 nm
15
10
5
0
‐5
‐200
0
‐100
‐200
‐300
‐400
‐500
‐100
100
0
200
300
400
500
600
Figure 5-32: The HAFM’s image of a saw tooth grating captured by Jerald Overcash
using the HAFM and the SAMM at UNC-Charlotte.
at MIT. We have developed a set of eight new labs for this course based upon the
imager hardware. The instrument is suitable for teaching because it is observable
by the naked eye and can be touched and heard. It is rugged, easy to build, and
very inexpensive. To the best of our knowledge the instrument is the first magnetic
self-sensing self-actuating probe. It can also be scaled to a smaller size and be used
as an inexpensive AFM.
5.5.2
Macro-Scale Magnetic AFM Probe
The self-sensing self-actuating probe consists of simply a metallic cantilever, a coil,
and a permanent magnet. A CAD model of the probe is shown in Figure 5-33. The
probe’s support bracket is machined using a section of an L-shaped extruded aluminum bar. The cantilever is cut using water-jet out of a 0.008-inch thick sheet of
Phosphorous Bronze Alloy 510. The cantilever is 1.5-inch long and 0.25-inch wide.
The cantilever tip is created by bending down the sharp end of the cantilever. The
cantilever is attached to the stator using a clamping piece bolted to the stator. The
clamping piece has edges for a well defined and rigid contact. A solid clamp is nec183
connector
coil
magnet
cantilever
Figure 5-33: Assembled macro-scale self-sensing and self-actuating magnetic probe
(top left), its CAD model (top right), and detailed side view showing the clamp design
(bottom right).
essary for achieving a low-loss resonator. A magnet is attached to the end of the
cantilever using a high-strength epoxy adhesive. The magnet is magnetized vertically. A coil, with 30 turns, is mounted onto the stator, and is positioned above the
magnet. The coil is held by an adapter piece made out of Delrin and filled with
epoxy. The adapter piece is bolted onto the stator. The coil’s end wires connect to
a barrel connector on the stator, which connects to the power amplifier. To exclude
the connector’s resistance from the coil voltage measurements, we use a four wire
connection with the measurement buffer’s input lines directly soldered to the coil.
The setup also includes a micrometer-head. We use the micrometer head for
testing and calibrating the probe. The micrometer’s anvil is used as a movable surface
for interaction with the probe. By turning the micrometer, we can move the anvil
up or down and thereby calibrate the probe. In this way, the probe can be tested
without an actual scanner to move the sample under the probe.
5.5.3
Self-Actuation
Applying a current to the coil creates a Lorentz force acting between the coil and the
magnet. We use this force to bend the cantilever up or down to follow the sample
184
surface. The actuation constant can be calibrated for each probe using the micrometer
head. The probe under test is found to have an actuation constant of 0.5 mm/A.
Considering our power amplifier’s current limit of ±2 A, the probe thus has a tracking
range of ±1 mm.
5.5.4
Self-Sensing
The magnetic probe is a mechanical resonator. The resonator’s resonance frequency
shifts to a slightly higher frequency as a result of contact. The resonator’s mechanical
dynamics reflect into the coil’s electrical impedance response and can be measured.
As a result, contact can be detected by monitoring the electrical signals of the coil.
The probe can be modeled and used for self-sensing as described in Section 5.2.2. The
probe’s impedance frequency response is shown in Figure 5-34 based on experimental
data as well as a fitted analytical model. When free in air, the probe’s resonance
peak is at 35.2 Hz. The probe’s total impedance (Zt ) can be modeled using (5.8).
The following parameters are obtained by fitting this model to the probe’s frequency
response:
m = 0.6 × 10−3 [kg]
b = 3.2 × 10−4 [Ns/m]
k = 29.3[N/m]
p = 0.0118 [N/A]
R = 0.057 [Ω]
L = 4 [µH].
The magnetic impedance’s (Zm ) resonance is visible within the total impedance
(Zt ) frequency response and peaks out of the passive impedance (ZRL ). For imaging,
it is desired to compensate for the passive impedance (ZRL ) and obtain the magnetic
impedance (ZM ), which corresponds directly to the mechanical resonance. Unlike
the total impedance (Zt ), the magnetic impedance’s gain approaches zero away from
185
the resonance and its phase has a one-to-one relationship with frequency. Using the
magnetic impedance makes the resonance controller more robust and also improves
the noise performance of the probe. We obtain the probe’s magnetic voltage (vm ) by
estimating the voltage across the passive impedance (R and L in series) and subtracting that estimate from the measured probe voltage. In this way we can compensate
the probe and obtain the magnetic impedance (Zm ) frequency response shown in red
in Figure 5-34. Given the low frequency of resonance, we perform the compensation inside the real-time controller sampling at 5-kHz. Close to the resonance, the
inductive voltage is negligible compared to the resistive voltage and can be ignored
for compensation purposes, and thus only the resistance is compensated. We apply a
low-pass filter to the compensated impedance response to filter the inductive voltage
and the probe’s other modes at higher frequencies.
5.5.5
Control System
To use the compensated probe for self-sensing contact detection, we set it in controlledamplitude self-resonance at its natural mechanical resonance frequency. We use the
changes in the self-resonance frequency as feedback to detect contact and follow the
sample surface. A block diagram of the probe’s control system is shown in Figure 535. The control system consists of compensation, self-resonance control, and tracking
subsystems.
The voltage measured across the coil (ve ) is compensated by subtracting the estimate of the resistive and inductive voltages to obtain an estimate of the magnetic voltage (v̂m ). The self-resonance control branch feeds back this voltage as a self-resonance
current (iSR ) excitation to set the probe in self-resonance. The self-resonance controller changes the feedback gain r via the multiplier to control the amplitude of
oscillation. We feed forward the gain r0 which is the expected required gain for
constant-amplitude self-resonance when oscillating freely in air. The amplitude of
oscillation is measured by first band-pass filtering, then by taking the absolute value
of the compensated voltage, and then by applying a moving average filter. We set
the width of the moving average filter to five oscillation cycles of the probe. Using
186
0
|Z| [V/A]
10
-1
10
-2
10
33
33.5
34
34.5
35
f [Hz]
35.5
36
37
Zt EXP
90
Zm EXP
Zt AN
45
∠ Z [deg]
36.5
Zm AN
0
-45
-90
33
33.5
34
34.5
35
f [Hz]
35.5
36
36.5
37
Figure 5-34: Experimental impedance frequency response of the magnetic probe
shown before (Zt EXP) and after (Zm EXP) compensation for coil resistance as well
as their corresponding analytical fits (Zt AN & Zm AN).
187
Resistor
λ̂LF
Probe
p2s
ms 2 + bs + k
ie
vm
ve
+
R + Ls
Comp.
+
iSR
itrack
r
+
+
Δr
Ca (s)
Ct ( s )
−
vˆm
Self-Res Ctrl
Aref
r0
+
)
R + Lˆ s
Â
Mvg
Avg
−
−
fˆ
+
Abs
BPF
Frequency
Estimation
Track Ctrl
f ref
Figure 5-35: Block diagram of the probe’s control system showing the compensation, self-resonance control, and tracking control subsystems. For the low resonance
frequency, we let L̂ = 0
188
a width equal to an integer multiple of the oscillation period sets the discrete filter’s
notches at the fundamental oscillation frequency and its harmonics. This makes it
more effective at filtering the amplitude measurement ripples. For imaging, we use a
reference oscillation amplitude of Aref = 1.9 mV peak-to-peak. We use a proportional
integral amplitude controller with the following transfer function:
Ca (s) = Kp
s+1
s + ωi
= 200000
s
s
(5.28)
The experimentaly measured and analytically fitted frequency responses of the
amplitude control system’s plant and its compensated-loop are shown in Figure 5-36.
The experimental data is provided for the probe oscillating freely in air and locked
to the sample using a reference frequency of 36 Hz. The analytical fit is based on the
model of resonance amplitude control presented in [70] and a model of the discrete
moving average filter. The compensated loop is shown based on the analytical fit
and an amplitude controller given by (5.28). The loop is designed for a unity crossover frequency of 1-Hz and a phase margin of 56◦ . Experiments show that a more
conservative amplitude controller with Kp = 50000 and a lower cross-over frequency
can result in less noisy images and a more robust control system. We have successfully
imaged samples using amplitude control gains in range of 50000 to 200000.
The probe’s self-resonance frequency shifts in response to tip-sample contact. The
tracking controller Ct (s) uses this as a feedback to follow the sample surface. We use
a reference self-resonance frequency of 35.7 Hz, which is 0.5 Hz above the free air
resonance frequency. This results in a light tapping contact between the sample and
the probe. The self-resonance frequency is estimated by measuring the time between
the zero crossings of the resonance signal. The tracking controller consists of an
integrator term and a high-frequency roll-off filter:
Ct (s) =
Ki ωr
2 20π
=
s s + ωr
s s + 20π
(5.29)
189
0
|A/Δr| [V]
10
-5
10
-10
10
0
1
10
10
f [Hz]
0
∠ A/Δr [deg]
-100
-200
-300
-400
in air
locked @ f=36Hz
theoretical
compensated loop
0
1
10
10
f [Hz]
Figure 5-36: Experimental and analytically fitted frequency responses of the amplitude control system’s plant and compensated-loop.
190
2
Magnitude ||
10
0
10
-2
10
0
1
10
10
f [Hz]
Phase ∠ [deg]
200
0
-200
-400
Plant fSR/it(s) [Hz/A]
Compensated-Loop fSR/it(s) × Ct(s)
-600
0
10
1
10
f [Hz]
Figure 5-37: Experimentally obtained frequency responses of the plant and the compensated loop of the tracking control system.
The tracking control system’s plant and compensated-loop frequency responses are
shown in Figure 5-37. The tracking controller achieves a unity cross-over frequency
of 1 Hz with 89◦ of phase margin. Given the non-linear nature of the probe, it is
important to use a simple and robust controller which is not too sensitive to the
changes in the plant frequency response. We have successfully imaged samples using
an integral gain (Ki ) of 0.5 to 2. Increasing the gain increases the probe’s bandwidth
but also increases its tracking noise.
5.5.6
Scanner Hardware
To image a sample, the imager needs a scanner to raster scan the sample under the
probe. The scanner hardware for the imager is shown in Figure 5-37. The scanner
consists of a voice coil position stage for the fast scan axis and a stepper positioning
191
Stepper
Voice Coil
Stage
Probe
Voice Coil
Stage
Stepper
Motor
Figure 5-38: The imager’s scanner hardware (left) and CAD design (right).
stage for the slow scan axis. We use the VCS14-020-BS-01SC-MCS voice coil stage
and the SCS-05-08-1H stepper stage by H2W-Tech4 . The position of the voice coil
stage is measured using a MicroE Mercury 1000 sine-cosine encoder with a grating
pitch of 20 µm. Interpolating this signal using the LabVIEW FPGA, we have achieved
a stage position control resolution of better than 50 nm. The stepper stage realizes
the slow scan axis by using a stepper with 200 full-steps per revolution and a leadscrew with 1-in pitch. By driving the stepper using 16 sub steps, we can achieve a
positioning resolution of 1.6 µm.
The imager’s hardware also includes a printed circuit board. The board has an
instrumentation amplifier for amplifying the coil voltage by 50 times before measuring it using the controller’s analog inputs. A sense resistor on the board is used for
measuring the probe’s current. The board also has buffers and comparators for am4
H2W Technologies Inc.: www.h2wtech.com
192
Figure 5-39: Macro AFM measuring a penny (right) and the captured image (left).
plifying and digitizing the encoder’s analog sine and cosine signals, so that they can
be measured by the controller’s analog and digital inputs.
5.5.7
Experimental Results
We have used the imager to capture images of several different samples. Figure 5-39
shows the probe imaging a penny and the captured image. Figure 5-40 shows the
probe imaging an MIT key chain. An image of a quarter captured using the probe is
shown in Figure 5-41. The images have all been captured at a scan speed of 1mm/s.
5.6
Summary
We reviewed prior art self-sensing methods. We introduced a self-sensing contact
detection method which can be used with actuated systems to precisely detect contact
between the actuated system and a work piece. This method has been inspired by
self-sensing atomic force microscopy. We presented the application of this method
to the reticle assist device for detecting contact between the assist device and the
reticle. By precisely detecting contact between the reticle and the assist device, we
can control the piezo’s extension in reference to the reticle edge. In this chapter, we
also showed this method being used with two AFM systems: the HAFM which is
193
Figure 5-40: Macro AFM measuring an MIT key chain and the scanned image (top
right).
430
430µm
0µm
Figure 5-41: Images of a quarter captured using macro AFM visualized in 3D (left)
and 2D (right).
194
designed for metrology, and the Macro AFM which is built as a lab instrument for
teaching.
In the next chapter, we present the reticle assist device’s control system design
and the results of the reticle assist experiments. The control system utilizes the
self-sensing contact detection method as well as the new VQV charge amplifier with
HHC.
195
196
Chapter 6
Reticle-Assist Device Control and
Experimental Results
6.1
Control System Design
Using the reticle assist device, we can compensate more than 95% of the simulated
reticle inertial forces. In this chapter, we describe the reticle assist device’s control
system. We explain the operation of the assist device and how a state-machine design
is used to automate the system. We describe two possible architectures for controlling
the motion and the forces: using strain sensor’s feedback and sensorless operation.
We describe how we calibrate and control the reticle assist device’s output force. We
present the methods used for controlling the reticle assist device’s motion. Finally,
we briefly describe how we use self-sensing contact detection to detect the reticle’s
edge.
6.1.1
State-Machine Design
The reticle assist device’s operation can be summarized as the following four steps:
1 Coarse-Adjustment: before a reticle exchange, a coarse-retract occurs. Once
the new reticle is placed, a coarse-approach preloads the piezo actuator against
the reticle. Once the piezo actuator is extended by the desired gap size, the
197
coarse-clamp is activated. In this way, we can position the piezo and approximately achieve the desired gap size.
2 Fine-Actuation: Fine-actuation is used to exert a pushing force on the reticle
to cancel its inertial load. The fine-actuation consists of the following states:
2.1 Approach: prior to a simulated acceleration, the piezo approaches the
reticle and finds its edge.
2.2 Push: the piezo stays at the reticle’s edge and extends to push and cancel
the simulated inertial loads.
2.3 Retract: the piezo retracts back to avoid contacting and disturbing the
reticle during the sensitive exposure interval.
The coarse-adjustment occurs only once a new reticle is loaded. The fine-actuation
occurs once per die exposure. We tested and confirmed the effectiveness of the coarseadjustment method using a manual pressure regulator. We used a state-machine
design to automate the fine-actuation process. A block diagram of the state-machine
is shown in Figure 6-1. The different states as well as the coarse adjustment step are
described in the following subsections.
Coarse-Adjustment
To test the coarse adjustment mechanism, we place the assist device such that the
reticle’s edge is within 0.5 mm of piezo actuator’s tip. We extend the piezo actuator
by 1 µm. Next, we manually adjust the pressure regulator’s output from 0 to approximately 20 psi. The bellow extends and preloads the piezo actuator’s tip against
the reticle. Then we activate the coarse-clamp by applying vacuum to the pressure
pocket. Finally, we retract the piezo back to its original length. In this way, we are
able to create a gap of approximately 1 µm. The limited stiffness of the piezo-reticle
contact causes the gap to be slightly less than 1µm. The created gap size also depends
on the precision of the clamping mechanism and how much the clamp displaces the
coarse stage as it is activated.
198
AM
Machine
Reference
Edge
Piezo
Control
IM
SREF
IM
Self-Sensing
Contact
Detection
AM
QM
ON
Enter:
EN_PUSH=1;
Edge=QREF;
[CD 1]
[CD=1]
[cmd=3]
Exit:
EN_PUSH=0;
PUSH
Enter:
EN_APP=1;
EN_CD=1;
[cmd=2]
Enter:
EN_RET=1;
Exit:
EN_RET=0;
Exit:
EN_APP=0;
EN_CD=0;
APPROACH
RETRACT
[cmd=0]
[cmd=1]
Enter:
EN_APP=0;
EN_RET=0;
EN_PUSH=0;
EN_CD=0;
OFF
Figure 6-1: Reticle assist device’s state-machine design used for automating the fineactuation process.
199
Approach
While in the approach state, the piezo moves towards the reticle until it detects the
reticle’s edge. The state-machine enters the approach state when an input command
of cmd = 2 is received. The command is issued 20 ms before the occurrence of the
simulated inertial load. Once the machine enters the approach state, contact detection
is enabled and the piezo starts to move towards the reticle at a speed of 150 nm/ms.
Once the reticle’s edge is detected, the contact detection method is disabled and the
machine enters the push state. The contact detection subsystem excites the probe at
its resonance. Because the excitation disturbs the reticle, we enable contact detection
during the approach state only. In our implementation, the edge location is detected
for every acceleration cycle. Although frequent edge detection is not necessary, it can
be used as diagnostic tool for confirming the operation of the assist device.
Push
During the push state, the piezo is held at the reticle’s edge and extends to push on the
reticle to cancel the simulated inertial force. The pushing state can be entered from
the approach state once contact is detected. Once the machine enters the push state,
the reticle’s edge location register is updated and the pushing method is enabled. To
push on the reticle, the piezo is extended relative to the edge location. A calibrated
look-up-table of the extension versus the pushing force is used to calculate the required
extension based on the value of the simulated inertial force. The force calibration and
control methods are described in Section 6.1.3. The pushing state is exited, when the
acceleration cycle is finished and the pusher needs to retract back. We exit the
pushing state and enter the retract state by issuing a command cmd = 3.
Retract
During the the retract state, the piezo moves back to 1.5 µm away from the reticle’s
edge. The retract state can be entered from the push state by issuing a command
cmd = 3. Once the machine enters the retract state, it starts to move back at a
200
speed of 400 nm/ms and stops 1.5 µm away from the edge. When the assist device is
enabled, it enters the retract state by default. The state machine can exit the retract
state and enter the approach state if a command cmd=2 is given.
6.1.2
System Architecture Designs
In this section, we describe two system architectures for controlling the device’s pushing force. The first design uses the strain sensor’s feedback to control the piezo’s
motion. The second design does not use any sensors. Instead, it uses open-loop
charge-control. The designs are described with more detail in the following subsections.
Strain-Controlled Operation
The design of the control system, when using the strain sensor’s feedback, is shown
in Figure 6-2. The design of the state machine was described in the previous section.
A reference calculation block calculates the piezo’s reference position based on the
state of the device, edge location, and the required output force. In the retract and
approach states, the block changes the reference signal to move the piezo away or
toward the reticle at the specified retract or approach speeds respectively. During
the push state, the block calculates the piezo extension relative to the reticle’s edge
required for creating the desired pushing force. The extension is calculated using a
calibrated look-up-table of extension versus pushing force. Force control and calibration are described in Section 6.1.3. A strain controller is used for following the piezo
reference (SREF ) position in closed-loop using the strain sensor’s feedback (S). The
strain controller is described in Section 6.1.4. The strain controller drives the piezo
using the VQV charge amplifier which was presented in Chapter 4. Using charge
control eliminates hysteresis and the phase lag resulting from it. Self-sensing contact
detection is used to detect contact. In this configuration, contact is detected as the
shift in the phase response from piezo voltage (VM ) to the piezo strain (S) when excited at the actuator’s resonance frequency. Application of self-sensing to the reticle
201
PM
F
CMD
PM
Contact
Detection
i
VM
F
State
Machine
State
Edge
Calculate
Reference
SREF
SREF
+
Strain
Control
−
VREF
VQV
Amplifier
Using HHC
Q
VM
S
Piezo
S
PM
Self-Sensing
g
Contact
Detection
VM
S
Figure 6-2: Simplified block diagram of the control system design using strain sensor’s
feedback for controlling the piezo’s extension. Variable s is the strain gauge output;
signal P M is the phase measurement from the Contact Detection block.
assist device was described in Chapter 5.
Sensorless Charge-Controlled Operation
The configuration described in the previous subsection required a strain sensor measurement. In this subsection, we describe a sensorless configuration, which does not
require any sensor feedback. This architecture is based on charge control. Figure 6-3
shows a simplified block diagram of the charge-controlled architecture. In this configuration, the strain controller is replaced by charge control. In this configuration, the
edge location and the required piezo extension are specified in terms of the charge
amplifier’s reference signal (VREF ). The Calculate Reference block uses a calibrated
look-up-table of the pushing force versus the piezo extension. We drive the piezo using
the VQV charge amplifier. We use hybrid hysteresis compensation, which eliminates
the charge amplifier’s transient and enables linear control of the piezo’s extension
even at low frequencies. Any remaining transient is compensated for by updating
the edge location before every acceleration cycle. In this configuration, self-sensing
202
F
Q
F
CMD
State
Machine
PM
State
Edge
Calculate
Reference
VREF
VQV
Amplifier
Using HHC
VM
IM
Piezo
VREF
Self-Sensing
Contact
Detection
i
PM
IM
VM
Figure 6-3: Simplified block diagram of the control system design using charge control
for open-loop
control of the piezo’s extension.
F
F
State Calculate SREF
State
Machine
Reference
contact PM
detection
is performed
the piezo’s current (IM ) and voltage (VM ) meaEdgeusing
CMD
surements.
SREF
+
6.1.3
Strain
Control
VREF
Force
− Calibration and
VQV
Amplifier
Using HHC
Control
Q
VM
S
Piezo
S
The reticle assist device controls its output force by controlling the deformation of
its mechanical force-loop stiffness. The stiffness
VM of the device’s mechanical force loop
Self-Sensing
g
AM be used for open-loop force control. We use an experimentally
is repeatable and can
Contact
S
Detection
calibrated look-up-table of the
pushing force versus the piezo’s extension to control
the force. The contact force (F) versus the piezo strain (S) is shown in Figure 6-4
based on the experimental data and an analytical fitted model. The experimental
measurement and calibration methods are presented in Section 6.2.2.
A model of the mechanical loop is shown in Figure 6-5. The mechanical force
loop’s stiffness consists of the reticle clamp (kR ), piezo to reticle contact (kH ), piezo
stack (kP ), and the assist device clamp (kC ). All of the elements are modeled as a
constant stiffness, except for the contact, which has a non-linear stiffness changing
with the contact force F. We model the contact stiffness using the Hertz contact model
[76]. Based on this model the contact force (F) and deformation (δ) are related as
the following, where c is a constant whose value depends on the Young’s modulus and
203
80
70
60
10 cycles
50
1 cycle
Fit
Force [N]
ST
40
30
20
10
0
0
2
4
Strain [μm]
6
8
Figure 6-4: Experimental plot of the pushing force versus piezo strain with an overlaid
least-squared fit based on the analytical model.
½ kR
½ kC
F
Piezo
Reticle
FI
Clamp
kp
kH
S
½ kR
Contact
FI
kR
½ kC
F
kH
kC
F
S
Virtual
Ground
kP
Figure 6-5: A simplified lumped stiffness model of the reticle assist device and the
reticle.
204
curvature of the contacting parts:
2
δH = cF 3 .
(6.1)
The calibration map is the pushing force (F) versus the extension of the piezo (S)
relative to the point of contact with the reticle edge. The calibration map is dependent
on the reticle edge displacement. However, for successful operation of the assist device,
the net force (inertial load minus the assist force) on the reticle is almost zero, and
thus the reticle edge displacement is approximately zero as well. With the reticle
being stationary, its clamp stiffness can be neglected when analyzing the mechanical
force loop to create a model that can be fitted to the force calibration data. The piezo
stiffness also does not affect the model because piezo’s extension is measured across
the piezo stack. Therefore, only the the contact and assist device clamp stiffness
must be included in the model. The measured piezo strain is equal to the sum of the
contact deformation (δH ) and the assist device’s clamp deformation (δC ):
2
S = δh + δc = cF 3 +
F
kC
(6.2)
where F is the force in Newtons, S is the piezo’s extension in µm, kC is the assist
device clamp stiffness in N/µm, c is the constant used in (6.1) for defining the contact
stiffness. The analytical model of (6.2) is fitted to the experimental data using a leastsquare fit method. The fitted parameters values are as the following:
c = 0.256
µm/N2/3
kC = 31.0
N/µm.
Please note that the value obtained for the stiffness of the clamp includes the stiffness
of the assist device clamp structure in series with the stiffness of the surface plate
holding the setup together. For a description of the mechanical design please refer to
Chapter 3.
205
6.1.4
Motion Control
For the operation of the reticle assist device we require to control the position of
the piezo’s tip. In this section, we describe the two methods which we have used
to control the piezo’s motion: closed-loop extension control using the strain gauge
feedback and open-loop extension control using charge-control.
Strain Feedback
The control system design shown in Figure 6-2 uses a closed-loop strain controller,
which controls the piezo’s extension based on the strain gauge feedback. We have designed a strain controller using the loop-shaping technique. The frequency response of
the strain control system’s plant, controller, and compensated loop transmission are
shown in Figure 6-6. The plant frequency response is shown from amplifier reference
voltage to the strain gauge measurement buffer output voltage. The plant frequency
response is flat up to approximately 5 kHz, where a pole is intentionally added to the
amplifier’s reference input for protecting the piezo from being over excited at its resonance and also for low-pass filtering the input noise. The plant’s frequency response
also shows two resonances at 27 kHz and 31 kHz due to the mechanical vibration
modes of the actuator. For our controller we use a double integrator, high-frequency
roll-off filters, and two notch filters to attenuate the loop gain at the mechanical resonances. The resulting compensated loop frequency response shows a unity cross-over
frequency of 2.5 kHz and a phase margin of 100 degrees.
We use double integrator to make sure that the strain controller can follow a ramp
reference signal with zero steady-state error. The inertial loads typically increase as
a ramp. As a result, the piezo reference signal is also approximately a ramp. Using
a double integrator improves the piezo’s ability to track the reference signals. To
avoid large delays resulting from a slow sampling rate, we implement the controller
using discrete-time transfer functions on a LabVIEW PXI-7854R FPGA card. The
controller is sampled at 312.5 kHz. The controller transfer function in continuous
206
1
10
Magnitude
0
10
-1
10
-2
10
3
4
10
10
Frequency [Hz]
200
OL
C
LT
100
Phase [deg]
0
-100
-200
-300
-400
-500
3
4
10
10
Frequency [Hz]
Figure 6-6: Frequency responses of the strain control system’s plant (OL), controller
(C), and compensated loop transmission (LT).
207
time is
C(s) = [
ωc
ωc α2
ωc
ωc α1
+
]×[
+
] × N1 (s) × N2 (s) × Kp .
s + ωc α1 α1s
s + ωc α2 α2 s
(6.3)
The transfer functions N1 and N2 are notch filters at ω1 =27 kHz and ω2 =31 kHz
respectively. By adding a low-pass filter and an integrator, we can obtain the integrator and the roll-off filters separated by a factor α2 around the desired unity cross-over
frequency (ωc ). The controller is discretized using the MATLAB c2d function for
implementation on the FPGA. The following are the controller parameter values:
ωc = 2500 × 2π
rad/s
(6.4)
Kp = 2.3
V/V
(6.5)
α1 = 3
(6.6)
α2 = 6
s + 2 × 0.2/5/ω1 s + ω12
N1 = 2
s + 2 × 0.2 × 5/ω1 s + ω12
s2 + 2 × 0.3/5/ω2 s + ω22
N2 = 2
.
s + 2 × 0.3 × 5/ω2 s + ω22
(6.7)
2
(6.8)
(6.9)
Charge Control
For sensorless operation, we control the piezo’s motion using charge-control. We use
the VQV amplifier with hybrid hysteresis compensation (HHC). The amplifier design
and the hysteresis compensation algorithm are described in Chapter 4. Using the
HHC method enables linear and repeatable control of the piezo at low frequencies as
well as the high frequencies. This is important because the piezo’s reference signal
includes a quasi-static component, which cannot be precisely followed in open-loop
using a conventional charge amplifier without the HHC method.
208
6.1.5
Self-Sensing Contact Detection
The application of the self-sensing contact detection method to the reticle assist device is described in detail in Chapter 5. We use the shift in the phase response of
the probe near its mechanical resonance to detect contact between the tip and the
sample. Piezo’s mechanical and electrical dynamics are coupled and both can be used
for self-sensing. In the architecture shown in Figure 6-2, we use the probe’s mechanical dynamics and perform self-sensing using the strain and voltage measurements.
For the sensorless configuration shown in Figure 6-3, we use the probe’s electrical
dynamics and perform self-sensing contact detection using the probe’s voltage and
current measurements.
6.2
Experimental Results
In this section, we introduce the experiments used for testing the effectiveness of the
reticle assist device. In the first section, we present the experimental hardware. Next,
we present the experimental methods used for testing and measuring the performance
of the assist device. Finally, we present the experimental results of the reticle-assist
experiments. The results are presented for both the strain-controlled and sensorless
operation of the assist device.
6.2.1
Experimental Setup
A picture of the experimental setup is shown in Figure 6-7. We use the setup for
calibrating and testing the reticle assist device.
The mechanical hardware includes the reticle assist device, a reticle assembly, and
displacement measurement sensors. The setup is mounted on a 1-in thick Aluminum
plate. The design of the reticle assist device was described in Chapter 3. The reticle
assembly includes a reticle, its mount, and a force actuator. The reticle’s force actuator is used to simulate the inertial loads by exerting a force on the reticle. The reticle
assembly has been provided to us by ASML. The experimental setup also includes
209
Surface
Plate
Reticle
Assist
Device
Disp
Disp.
Sensor
Figure 6-7: Experimental setup used for calibrating and testing the reticle-assist
device.
210
Figure 6-8: Picture of the strain gauge measurement circuit board.
capacitive displacement sensors for measuring the displacement of the assist device’s
vacuum clamp and the reticle relative to the surface plate.
For driving the assist device’s piezoelectric actuator, the experimental setup uses
the VQV charge amplifier, which was described in Chapter 4. We drive the reticle
assembly’s force actuator using a current-controlled power amplifier, which has been
designed in our lab around a APEX PA-12 power device. Details on the power amplifier design can be found in [61]. We use our own Wheatstone bridge circuit to
measure the changes in the strain gauge’s resistance. A picture of the strain gauge
measurement circuit is shown in Figure 6-8. The circuit uses an AD624 instrumentation amplifier and a REF5050 reference voltage regulator. Information on the design
and measurement of piezo-resistive sensors can be found in [65].
The setup uses four capacitive displacement sensors. Two ADE 2805-S capacitive
displacement probes measure the displacement of the assist device’s clamp in the force
direction. The ADE 2805-S probes have a range of ±50 µm and are used with the
ADE 3800 probe drivers. Two Microsense AD2823 capacitive displacement sensors
are used to measure the displacement of reticle’s edge in the force direction. The
Microsense AD2823 probes have a range of ±10 µm and are used with Microsense
211
8810 probe drivers.
The vacuum for the clamps is created using a Laybold Trivac D8B vacuum pump.
We use two manual ball valves for switching the vacuum supplied to the reticle clamp
and the assist device clamp. The pressure for actuating the bellow is provided using
a manual pressure regulator operating on the 100-psi wall supply.
6.2.2
Experimental Methods
To test the effectiveness of the reticle assist device, we simulate the inertial loads on
the reticle using the reticle assembly’s force actuator. The force actuator applies a
force equal to the expected inertial load. At the same time, the reticle assist device
attempts to exert the exact opposite force onto the reticle’s edge. In this way, the
simulated inertial load is carried by the assist device. Depending on the assist device’s
force compensation accuracy, a net force remains, which is carried by the reticle clamp.
The following are the main steps for testing the reticle-assist device:
1. Use the reticle assembly’s force actuator to simulate an inertial load corresponding to a practical motion profile.
2. Use the pusher to create the exact opposite force on the reticle to cancel the
simulated inertial force.
3. Use capacitive displacement sensors to sense the displacement of the reticle’s
edge as a measure of the remaining net force.
Reticle slip can be measured as the displacement of the reticle’s edge relative to
its original position after the forces are removed. The force compensation inaccuracy
of the assist device is measured as the displacement of the reticle in response to the
simulated force during the test. The following subsections provide more detail on
how forces and displacements are estimated. We also explain how the assist device is
calibrated.
212
Force Measurement
The reticle clamp deforms as a result of the remaining net force not compensated
by the assist device. We measure this deformation using the capacitive displacement
sensors. The reticle clamp has a constant stiffness with a linear force versus displacement behavior. Therefore, the reticle clamp’s deformation can be used to estimate
the residual force. With this setup, we can measure the displacement of the reticle’s
edge. Assuming that no slip occurs between the reticle and the clamp, the clamp’s
deformation can be measured as the displacement of the reticle’s edge. We estimate
the residual forces as the displacement of the reticle’s edge times the stiffness of the
reticle clamp. This measurement method is accurate below the first resonant mode
of the reticle assembly, where the inertial force is negligible compared to the elastic
forces. Given the first resonance frequency of the reticle assembly, this method provides us with sufficient measurement bandwidth. Knowing the residual force and the
reticle actuator force, the assist device’s output force can be estimated.
Displacement Measurement
Using the capacitive displacement sensors, we can measure the displacement of the
reticle edge and the assist device’s clamp relative to the surface plate. The strain
gauge sensor measures the piezo’s extension.
The displacement of the reticle’s edge includes the deformation of the reticle
clamp, slip at the reticle-clamp interface, and thermally-induced size variations of the
reticle. Using the assist device, slip can be avoided. The thermally-induced changes
are slow, and thus, over short periods, are negligible or can be separated from the
measurement data. With no slip and negligible thermal variations, the reticle clamp
deformation can be estimated as the displacement of the reticle edge. At the same
time, slip can be detected as any displacement of the reticle edge, which is not recovered when the forces are removed. The force actuator, which is attached to the
reticle, can heat up. The reticle has a very low coefficient of thermal expansion and
does not expand significantly from the added heat. However, the reticle is deformed
213
by the expansion of the part of the force actuator attached to it.
All of the measurements are referenced to the surface plate. The surface plate is
also a part of the mechanical force-loop. The pushing forces deform and excite the
vibration modes of the surface plate. The excited vibration modes of the plate continue after the forces are removed. The plate vibration appears on our displacement
measurements. This can be mitigated if the setup is designed such that the forces
are on the support structure’s neutral axis. Alternatively, the surface plate’s stiffness
can be increased if it is bolted to a thicker plate, such as the surface top of an optical
table. We use a vibration damping pad underneath the surface plate to faster damp
out its vibrations.
Force Calibration
We experimentally calibrate the reticle-assist device’s output force versus the piezo
extension. The extension can be expressed as the piezo’s strain for the control architecture using the strain gauge feedback, and can be expressed in terms of the reference
charge amplifier voltage for the sensorless control system design.
The forces can be estimated using the method described in Section 6.2.2. However,
the method requires that the reticle does not slip. This can be achieved if an initial
approximation of the force versus extension calibration map exists. For obtaining the
first calibration map, we switch the role of the assist device and the force actuator.
We extend the assist device to push on the reticle. At the same time, we drive the
reticle’s force actuator in closed-loop to keep the reticle’s edge at a fixed position. In
this way, the reticle does not slip, and the pushing force can measured as the force
actuator’s effort plus the stiffness of the clamp multiplied by any error in regulating
the reticle’s edge location. Using this method, we can accurately calibrate the assist
device.
We only need to perform this once to obtain a calibration map. Once a good
approximation of the calibration map exist, the assist device can operate effectively
and can prevent reticle slip. Form this point on, the experimental test data can be
used to update the force versus extension calibration map.
214
6.2.3
Strain-Controlled Reticle Assist Experiment
In this section, we present the results of the reticle assist experiment for the straincontrolled assist device. Time plots of the experimental results for 10 consecutive
simulated acceleration cycles are shown in Figure 6-9. The same plots for the single
acceleration cycle between the times 0.3 and 0.4 seconds are shown in Figure 6-10.
The top plot shows the simulated inertial load, which is applied to the reticle using
the reticle assembly’s force actuator. For the experiments we use a simulated inertial
load profile with a 60-N peak and a 6.4-N/ms maximum rate of change. The topmiddle plot shows the displacement of the reticle’s edge measured using the capacitive
displacement sensors. The reticle’s edge displacement is limited to 25 nm. With a
reticle clamp stiffness of 100 N/µm this is equivalent to 2.5 N of residual force. This
shows that the reticle assist device has compensated about 96% of the simulated
inertial load. The bottom-middle plot shows the piezo actuator’s reference extension,
actual extension, and the extension corresponding to the reticle edge location. The
bottom plot shows the contact detection method’s phase response. Contact is defined
as the point where the phase response at the resonance from voltage to strain rises
above zero degrees. Contact detection is enabled during the approach state. When
initially enabled, the contact detection methods goes through a transient where its
output is not reliable. For this reason, the contact detection logic ignores the phase
response for the first 2 ms.
Figure 6-11 shows the motion of the piezo actuator versus time with the state of
the assist device marked on the plot. As can be seen, during the retract state, the
piezo stands 1.5 µm away from the edge. The state switches from retract to approach
20 ms before the simulated inertial load is applied. The piezo extends toward the
reticle edge at a speed of 1.5 µm/s until contact is detected. The state switches to
push as soon as contact is detected. In the push state, the piezo changes its extension
based on the force versus extension calibration map to follow the reference force input.
As soon as the simulated inertial force is applied, the piezo extends and pushes on
the reticle. At the end of the acceleration profile, the state switches from push to
215
60
Force [N]
40
20
Reticle Displacement [nm]
0
0
0.2
0.4
0.6
0.8
1
time [s]
1.2
1.4
1.6
1.8
2
0
0.2
0.4
0.6
0.8
1
time [s]
1.2
1.4
1.6
1.8
2
30
20
10
0
-10
-20
-30
Piezo Strain [μm]
6
S
Sref
4
edge
2
0
-2
0
0.2
0.4
0.6
0.8
1
time [s]
1.2
1.4
1.6
1.8
2
0
0.2
0.4
0.6
0.8
1
time [s]
1.2
1.4
1.6
1.8
2
C.D. Phase [deg]
100
50
0
-50
-100
Figure 6-9: Time plot of the reticle-assist experiment for a strain-controlled reticle
assist device showing 10 acceleration cycles with a corresponding peak inertial load
of 60 N.
216
Force [N]
60
40
20
Reticle Displacement [nm]
0
0.3
0.31
0.32
0.33
0.34
0.35
time [s]
0.36
0.37
0.38
0.39
0.4
0.31
0.32
0.33
0.34
0.35
time [s]
0.36
0.37
0.38
0.39
0.4
30
20
10
0
-10
-20
-30
0.3
Piezo Strain [μm]
6
S
S
4
ref
edge
2
0
0.3
0.31
0.32
0.33
0.34
0.35
time [s]
0.36
0.37
0.38
0.39
0.4
0.31
0.32
0.33
0.34
0.35
time [s]
0.36
0.37
0.38
0.39
0.4
C.D. Phase [deg]
60
40
20
0
-20
-40
0.3
Figure 6-10: Time plot of the reticle-assist experiment for a strain-controlled reticle
assist device showing a single acceleration cycles with a corresponding peak inertial
load of 60 N.
217
retract
approach
push
retract
6
S
Sref
5
Piezo Strrain [ μm]
edge
4
3
2
1
0
0.3
0.31
0.32
0.33
0.34
0.35
time [s]
0.36
0.37
0.38
0.39
0.4
Figure 6-11: Time plot of the reticle assist device’s piezo motion shown for one
acceleration cycle with the state-machine’s state marked on the plot.
retract, and the piezo moves back to a position 1.5 µm away from the reticle edge.
The plot of the reticle displacement in Figure 6-9 shows a slow drift in the reticle’s
position. This drift is due to forced expansion of the reticle resulting from the thermal
expansion for the force actuator part attached to the reticle. Figure 6-12 shows the
reticle edge displacement over a longer period of 10 seconds. As can be seen, the
initial drift in the reticle position is recovered as the force actuator’s temperature
decreases with time.
6.2.4
Charge-Controlled Reticle Assist Experiment
Here, we present the results of the reticle assist experiment for the charge-controlled
assist device. Time plots of the experimental results for 10 consecutive simulated
acceleration cycles are shown in Figure 6-13. The same plots for the single acceleration cycle between the times 0.3 and 0.4 seconds are shown in Figure 6-14. The top
plot shows the simulated inertial load, which is applied to the reticle using the reticle
assembly’s force actuator. For the experiments we use a simulated inertial load profile
218
30
Reticle Displacement [nm]
20
10
0
-10
-20
-30
0
1
2
3
4
5
time [s]
6
7
8
9
10
Figure 6-12: Time plot of the reticle edge displacement for the assist experiment
shown over a longer period of 10 seconds.
with a 60-N peak force and a 6.4-N/ms maximum rate of change. The top-middle plot
shows the displacement of the reticle’s edge measured using the capacitive displacement sensors. The reticle’s edge displacement is limited to 30 nm, which assuming a
reticle clamp stiffness of 100 N/µm is equivalent to 3 N of residual force. This shows
that the reticle assist device has compensated about 95% of the simulated inertial
load. The bottom-middle plot shows the piezo actuator’s charge reference extension,
measured charge, HHC compensation charge, and the charge corresponding to the
reticle edge location. The bottom plot shows the contact detection method’s phase
response. Contact is defined as the point where the phase response at the resonance
from the peizo’s voltage to its current rises above zero degrees. Contact detection
is enabled during the approach state. When initially enabled, the contact detection
methods goes through a transient where its output is not reliable. For this reason,
the contact detection logic ignores the phase response for the first 2 ms.
As can be seen, the charge-controlled assist device is as effective as the straincontrolled assist device. We can successfully compensate 95% of the inertial load
without using any sensors, by controlling piezo’s charge and measuring its current and
219
Force [N]
60
40
20
Reticle Displacement [nm]
0
0
0.2
0.4
0.6
0.8
1
time [s]
1.2
1.4
1.6
1.8
2
0
0.2
0.4
0.6
0.8
1
time [s]
1.2
1.4
1.6
1.8
2
30
20
10
0
-10
-20
-30
Piezo Extension [V]
60
Q
M
40
QREF
Q
C
20
edge
0
-20
0
0.2
0.4
0.6
0.8
1
time [s]
1.2
1.4
1.6
1.8
2
0
0.2
0.4
0.6
0.8
1
time [s]
1.2
1.4
1.6
1.8
2
C.D. Phase [deg]
100
50
0
-50
-100
Figure 6-13: Time plot of the reticle-assist experiment for a charge-controlled reticle
assist device showing 10 acceleration cycles with a corresponding peak inertial load
of 60 N.
220
Force [N]
60
40
20
Reticle Displacement [nm]
0
0.3
0.31
0.32
0.33
0.34
0.35
time [s]
0.36
0.37
0.38
0.39
0.4
0.31
0.32
0.33
0.34
0.35
time [s]
0.36
0.37
0.38
0.39
0.4
30
20
10
0
-10
-20
-30
0.3
60
Q
Piezo Strain [V]
M
QREF
40
Q
C
edge
20
0
0.3
0.31
0.32
0.33
0.34
0.35
time [s]
0.36
0.37
0.38
0.39
0.4
0.31
0.32
0.33
0.34
0.35
time [s]
0.36
0.37
0.38
0.39
0.4
C.D. Phase [deg]
60
40
20
0
-20
-40
0.3
Figure 6-14: Time plot of the reticle-assist experiment for a charge-controlled reticle
assist device showing a single acceleration cycles with a corresponding peak inertial
load of 60 N.
221
voltage. As explained in the previous section, the slow drift in the reticle edge position
is a result of thermally induced deformations in the reticle and will be recovered as
the force actuator’s temperature decreases with time. The charge-controlled assist
device uses the same state-machine design as the strain-controlled device.
6.2.5
Additional Experimental Results
In this section, we present additional experimental data related to the operation of
the assist device.
Force vs. Extension Calibration Map
Figure 6-15 shows the assist device’s output force versus the piezo’s charge and extension. The force versus charge plot is shown for the charge amplifier with and without
the hybrid hysteresis compensation (HHC) method. As can be seen, the force versus
charge plot without the HHC method is not repeatable and drifts as a result of the
charge amplifier’s transient. The drift reduces the assist device’s force compensation
accuracy. Using the HHC method, we can significantly attenuate the drift and obtain a repeatable force versus charge relationship, which can be accurately used as
a calibration map for force compensation. The results presented in Section 6.2.4 are
obtained using a charge-controlled device, which utilizes the HHC method and a force
versus charge calibration map the same as the blue curve shown in Figure 6-15. The
results provided in Section 6.2.3 are obtained using a strain-controlled device, which
uses a force versus strain calibration map similar to the red curve in Figure 6-15.
Self-Sensing
Figure 6-16 shows the self-sensing method’s phase response versus the contact force.
The phase response is calculated at the piezo’s first resonance frequency from the
piezo’s current to its voltage. We define contact as the point where the phase rises
above zero degrees. Precise determination of the contact point is important to accurate force control. Detecting contact allows us to relate the piezo’s extension to the
222
70
70
w/ HHC
fit
no HHC
60
50
40
Force [N]
Force [N]
50
60
30
20
40
30
20
10
10
0
0
-10
0
20
40
Charge Reference [V]
60
-10
0
2
4
6
Strain [μm]
Figure 6-15: Assist device’s output force plotted versus the piezo’s charge (left) and
extension (right). The piezo’s force versus charge is shown for the charge amplifier
with and without the hybrid hysteresis compensation (HHC) method.
deformation of the mechanical loop, which we use to control the pushing force.
Assist Device Clamp
The assist device uses a vacuum clamp. The clamp’s force versus displacement behavior is shown in Figure 6-16. The clamp has hysteresis in the its pre-sliding regime.
This is due to non-uniform distribution of compliance over the vacuum surface. Elements of the surface are linked to the load through mechanical links with different
compliances. The clamp’s pre-sliding behavior can be modeled using the Maxwell
slip model. We fit a Maxwell slip mode to the clamp’s virgin curve. The virgin curve
is the clamp’s behavior, when starting from a state where all surface asperities are
relaxed. We can set the asperities to their relaxed state and obtain the virgin curve
by turning the clamp off and then back on. The model follows the clamp’s overall
behavior. However, the experimental data shows a slow drift with time, which is not
captured by the model. The drift may be due to mechanical creep or thermal drift.
223
60
e
∠Ye(s) | ω=ω [deg]
50
40
30
20
10
10 cycles
1 cycle
0
-10
-20
0
20
40
Contact Force [N]
60
80
Figure 6-16: The self-sensing method’s phase response versus the piezo extension.
The phase response is calculated from piezo voltage to piezo current at the piezo’s
resonance frequency.
224
60
Exp
Virgin Curve
Poly Fit
Break Points
GMS Model
50
Force [N]
40
30
20
10
0
-10
-0.2
0
0.2
0.4
0.6
0.8
Pusher Clamp Disp. [μm]
1
1.2
Figure 6-17: Assist device vacuum clamp’s force versus displacement behavior within
the pre-sliding regime. The plot shows the experimental data (blue), a fitted Maxwell
slip model (circles), and the model’s simulated output (black).
6.3
Summary
We presented the reticle assist device’s control system design. We described the statemachine design which is used for automating the device’s operation. We also showed
two possible system architecture designs: a configuration that uses a strain gauge for
closed-loop piezo position control and a sensorless configuration that uses the VQV
charge amplifier with HHC for open-loop piezo position control. We introduced the
pre-calibrated extension to force map, which is used by the device to control its output
force. This map is based on the piezo extension past the reticle edge. We showed
how the self-sensing contact detection method is used to register the piezo’s extension
in reference to the edge. We performed reticle assist experiments, where the assist
device canceled better than 95% of the inertial loads and prevented reticle slip. The
experimental setup, methods, and results were provided.
225
226
Chapter 7
Conclusions and Suggestions for
Future Work
7.1
Conclusion
This thesis provides the design and the enabling control techniques for a high-force
density sensorless reticle assist device. By completely eliminating the reticle slip problem in lithography scanners, the device allows a faster stage acceleration and can improve the manufacturing throughput. We designed and experimentally demonstrated
successful operation of the reticle assist device. When tested with a simulated inertial
force profile with 60-N peak force and 6400-N/s force rate, the device compensated
better than 95% of the inertial forces and prevented reticle slip. The results of the
reticle assist experiments are provided in Chapter 6, Section 6.2.
We designed and manufactured a piezoelectric solid-state assist device with a low
mass, good dynamics, and a large force output. As an alternative, we also presented
the detailed design of a novel thermally-balanced magnetostrictive assist device. The
mechanical designs are described in Chapter 3. We developed a novel charge amplifier
design with a more robust feedback circuit and a method for hysteresis compensation
at low frequencies. We experimentally demonstrated the amplifier eliminating piezo’s
hysteresis at all frequencies. Analogous to the charge amplifier, we also designed a
magnetic flux controller, which can be utilized for linearizing the force output of nor227
mal flux (reluctance type) electromagnetic actuators. We tested the magnetic flux
amplifier by applying it to a electromagnetically actuated linear positioning stage.
The charge amplifier and the magnetic flux controller are presented in Chapter 4. In
Chapter 5, we presented a self-sensing contact detection method, which is inspired
by atomic force microscopy. We applied this method to the assist device for contact
detection and to two AFM systems (HAFM and Macro AFM) for imaging. Utilizing
the novel charge amplifier and the self-sensing contact detection method, we implemented a control system which compensates better than 95% of the simulated inertial
loads without using any sensors. The design of this control system is presented in
Chapter 6.
The following list outlines the main contributions of this thesis:
1. Designed and implemented a high-force density reticle assist device consisting
of a coarse approach mechanism and a fine actuation mechanism.
2. Designed a novel thermally balanced magnetostrictive actuator as an alternative
actuation method for the assist device.
3. Invented a charge amplifier with better robustness and hysteresis compensation
in DC.
(a) Designed and implemented a charge-controlled amplifier with 100-W power,
140-V rail-to-rail voltage, and 100-kHz small signal bandwidth.
(b) Introduced a new charge control feedback circuit, referred to as VQVcontrol, for improved amplifier controller robustness to added series load
impedance.
(c) Invented a method, referred to as hybrid hysteresis compensation (HHC),
for compensating conventional charge amplifiers’ hysteresis at low frequencies.
4. Applied a self-sensing contact detection method, which has been inspired by
atomic force microscopy, to a piezoelectric stack actuator. Demonstrated precise
contact detection using the piezo’s current and voltage measurements.
228
5. Experimentally demonstrated the effectiveness of the reticle assist device at
eliminating reticle slip. When tested with a simulated force profile with 60-N
peak force and 6400-N/s force rate of change, the device compensated better
than 95% of the inertial load.
6. As a part of this thesis, the self-sensing contact detection was applied to a
piezoelectric self-sensing high-accuracy AFM and a macro-scale electromagnetic
profiler:
(a) Developed the electronics and control for a piezoelectric self-sensing highaccuracy AFM (HAFM). Helped with integration of the HAFM with the
SAMM metrology stage at UNC-Charlotte. Confirmed the operation of
the AFM by performing imaging tests at MIT.
(b) Designed and built a novel macro-scale self-sensing magnetic profiler. Performed imaging tests to confirm the operation of the profiler.
7. Developed and tested techniques for electromagnetic reluctance actuator linearization, which were analogous to the methods used for linearization of piezos
through charge control.
7.2
Suggestions for Future Work
The following sections outline suggested future work.
7.2.1
Design for Integration and Scan Testing
The reticle assist device was designed for experimental confirmation of the technology.
The device was designed for easy manufacturing and operation. For integration with
the lithography scanners, the reticle assist device can be re-packaged into a more
compact design. In the current design, the bellow, the clamp, and the piezo actuator
are stacked in series. The device can be made more compact if the piezo actuator and
229
the bellow are nested within the clamp. The clamp’s size can be reduced by switching
to a pressurized clamp. The re-packaged design can be tested on a scanner.
7.2.2
Charge Amplifier Automation
The hybrid hysteresis compensator (HHC) is tuned manually by the operator. The
tuning process can be automated. The electronics required for automatic tuning and
implementation of the HHC can be added in the form of a micro-controller to the
charge amplifier. Additionally, the micro-controller can also be used for adjusting
the amplifier’s feedback circuit. In this way, the amplifier can be used with piezo
actuators having different capacitance values.
7.2.3
Macro-Scale AFM
The Macro-scale AFM was described in Section 5.5. The following subsections discuss
the potential to improve the macro AFM.
Low Cost Macro-Scale AFM
As described in Section 5.5, the macro-scale atomic force microscope uses our selfsensing electromagnetic probe design which can be produced at a low cost. However,
the XY stage, which is used for raster scanning the sample, is purchased off-the-shelf
and is expensive. The development of a low-cost XY stage can significantly reduce
the cost of the macro-scale AFM and makes this instrument much more accessible.
Higher Resolution Macro-Scale AFM
The macro AFM has a resolution in the order of 1µm. Future efforts can focus
on improving the resolution of the macro AFM. The resolution can potentially be
improved by reducing the probe size, which results in a more sensitive probe, by
using a coil with more turns, which results in a larger coil voltage, and by using a
higher resolution frequency estimation method, which reduces the feedback noise.
230
Longer Tracking Range Macro-Scale AFM
The macro-scale AFM uses self-actuates the probe for tracking the sample. The
probe has a limited actuation range of ±0.5 mm. The limited tracking range prevents
imaging of samples with large features. The macro AFM’s range can be improved if
a separate actuator with a longer range is used for the tracking axis.
7.2.4
Thermally-Balanced Magnetostrictive Actuator
The design of a novel thermally balanced magnetostrictive actuator was presented
in Section 3.4 as a potential alternative for building solid-state assist devices. The
actuator was not selected for this application due its larger mass compared to the
the piezoelectric stack actuators. However, such an actuator can have applications
in other areas, such as fuel injectors. As future work, a thermally-balanced magnetostrictive actuator can be manufactured and experimentally tested.
231
232
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