Design, Modeling, and Testing of High Performance RF Bistable Magnetic Actuators A Dissertation ...

286 Pages·2005·4.65 MB·English

Design, Modeling, and Testing of High Performance RF Bistable Magnetic Actuators

A Dissertation
Presented to
The Academic Faculty

by

Gary D. Gray, Jr.

In Partial Fulfillment
Of the Requirements for the Degree
Doctor of Philosophy in Chemical Engineering

Georgia Institute of Technology
December, 2004
Design, Modeling, and Testing of High Performance RF Bistable Magnetic Actuators

Approved by:
Dr. Paul A. Kohl, Advisor Dr. Pete Ludovice
School of Chemical & Biomolecular School of Chemical & Biomolecular
Engineering Engineering
Georgia Institute of Technology Georgia Institute of Technology

Dr. Dennis Hess Dr. Ronald Rousseau
School of Chemical & Biomolecular School of Chemical & Biomolecular
Engineering Engineering
Georgia Institute of Technology Georgia Institute of Technology

Dr. Peter Hesketh Dr. Joseph Schork
School of Mechanical Engineering School of Chemical & Biomolecular
Georgia Institute of Technology Engineering
Georgia Institute of Technology

Date Approved: December 2004
ACKNOWLEDGEMENT

There are many who have contributed to my success in graduate school, and first
among them is my Ph.D. advisor, Dr. Paul Kohl, who led me to a project well suited for
my interests, gave me the freedom to direct my progress, and challenged me throughout
this process. I am also very appreciative of the trust and confidence he showed in
permitting me to pursue coursework outside of chemical engineering. I also thank my
project sponsor, Superconductor Technologies, Inc. located in Santa Barbara, California.
In particular I am grateful to Eric Prophet, with whom I worked in design of devices and
who shared many valuable discussions into this research topic.

I also wish to acknowledge the entire Kohl research group at Georgia Tech and the
Microelectronics Research Center cleanroom facilities in which the device fabrication
was performed. In particular, I wish to recognize the extraordinary contributions from
the following individuals: Lingbo Zhu, of the Kohl research group, who worked with me
to develop the processing steps for the devices presented in this thesis and who worked
fabricating many of the magnetic actuators presented in Chapter 5; Matthew Morgan, of
the Kohl research group, who performed much of the testing of the electrostatic actuators
discussed in Chapter 3; Eric Prophet, of STI, who provided RF performance data of
completed devices; Joel Pikarsky, of the MIRC, who helped assemble devices by means
of a flip chip bonding device; and Charlie Suh, of the MIRC, who expertly diced
completed wafers.

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In addition, I wish to thank my father, who encouraged me to pursue this graduate
work, my mother, whose pride in me is always felt, and my entire family, always
impressed with what I have accomplished. Thanks especially to my wife, Diane, whose
patience has endured my countless evenings reading, stressing over coursework, and my
repeated need to find pen and paper to scribble some calculation. Finally, I value the
friendships I have made during my days at Georgia Tech, as they have often eased the
difficult times. Thanks to David Vener, friend and best man, whose success has always
motivated me to achieve more. Thanks to Stephen Lewis, a friend who shared hobbies,
lunch, and many physics text; Hollie Kelleher, who always was willing to listen, as well
as answer detailed thesis questions; and thanks to Kevin Doyle, who lightened the
atmosphere with his humor and friendship.

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TABLE OF CONTENTS

Acknowledgement iii

List of Tables x

List of Figures xi

List of Symbols xvii

Summary xxvi

Chapter 1 Introduction 1

Chapter 2 Experimental 15

2.1 Microelectronic Processing 15

2.1.1 Metallization 15
2.1.2 Lithography 16
2.1.3 Etch 16
2.1.4 Electroplating 17

2.2 Analysis 19

2.3 Modeling 20

2.4 Electrostatic Actuator Testing 21

2.5 Magnetic Actuator Testing 25

Chapter 3 Improvements to CVC Tuning Range

3.1 Theory 29

3.2 Electrostatic Actuator Fabrication 36

3.3 Results 41

3.3.1 Device Testing and Measurements: Hinge and Tip Variations 42

3.3.1.1 Double-Hinged Ellipse 42

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3.3.1.2 Double-Hinged Rectangle 44
3.3.1.3 Fully-Hinged Rectangle 46
3.3.1.4 Double-Hinged Square 47

3.3.2 Hysteresis 51

3.4 Modeling 53

3.4.1 Finite Element Modeling 53
3.4.2 Comparison to Experimental Results 58
3.4.3 Pull-in Analysis 60
3.4.4 Beam and Tip Geometry 62
3.4.5 Capacitance Modeling 63

3.5 Temperature Effects 65

3.6 Summary 68

Chapter 4 Ultra-Low Switching Energy and Modeling 70

4.1 Design Criterion 77

4.1.1 Mechanical Design 77
4.1.2 Magnetic Element Design 81
4.1.3 Coil Design 84

4.2 Establishing the Design Space 87

4.3 Optimized Designs 92

4.4 Contact Force Modeling 93

4.5 Results 94

4.6 Discussion 101

4.6.1 Minimum Latching Field 101
4.6.2 Minimum Switching Field/Current 102
4.6.3 Switching Dynamics 103
4.6.4 Contact Force 108
4.6.5 Minimum Latching Field 110
4.6.6 Switching Speed and Energy 111

4.7 Summary 115

Chapter 5 Assembly and Performance 116

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5.1 Theory 117

5.2 Magnetic Actuator Fabrication 120

5.2.1 Top Substrate Processing 120
5.2.2 Bottom Substrate Processing 122

5.3 Results 127

5.3.1 Modeling Comparison 134
5.3.2 Measured Device Switching 141
5.3.3 Contact Resistance 145
5.3.4 Cycling and Lifetime Tests 146
5.3.5 Contact Force 148
5.3.6 Overdriving 151

5.4 Discussion 151

5.4.1 Applications 153

5.5 Summary 159

Chapter 6 Magnetic MEMS Wiping Actuator 160

6.1 Theory 160

6.2 Results and Discussion 167

6.2.1 Dynamic Behavior 172
6.2.2 Static Limit 172
6.2.3 Friction 177

6.3 Summary 180

Chapter 7 Conclusions 181

7.1 Summary of Work 181

7.2 Comparison of Electrostatic and Magnetostatic Actuation 183

Chapter 8 Recommendations 191

8.1 Mechanical Bistability 192

8.1.1 Principle of Operation 192
8.1.2 Gold Bridges 195

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8.1.3 Processing 196
8.1.4 Nanoindentation 198

Appendix A: Magnetics 202

A.1 Forces and Torques on Magnetic Dipoles 202

A.2 Magnetic Materials 204

A.2.1 Diamagnetism 204
A.2.2 Paramagnetism 205
A.2.3 Ferromagnetism 206

A.3 H-M Curve 211

A.4 Hard and Soft Magnetic Materials 214

A.5 Effects of Demagnetization on M-H Loop 216

Appendix B: Calculations 218

B.1 Demagnetization Field and Demagnetization Factors 218

B.2 Equilibrium Solution 224

B.2.1 Type-3 Actuator in 10-mT Field 225
B.2.2 Type-1 Actuator in 10-mT Field 228

B.2.2.1 Type-1 and Type-3 Actuator in 25-mT Field 229

B.2.3 Type-2 Actuator in 25-mT Field 231

B.2.3.1 Type-2 Actuator in 50-mT Field 232

B.3 Changes in Hinge Projection onto X-Axis 233

B.4 2nd Derivative of Equation of Constraint 236

B.5 2/3rd Rule for Electrostatic Actuation 237

B.6 Calculation of Coil Resistance 242

B.7 Time to Electroplate 243

B.8 Coil Operating Power 245

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B.9 Calculation of Switching Field from Coil 246
B.10 Euler Lagrange Calculations 247

B.11 Stiffness of Beams 249

B.11.1 Fixed/Free Beam 249
B.11.2 Fixed/Guided Beam 251

B.12 Calculation of ∆B 253
coil

References 255

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LIST OF TABLES

Table 1.1 Comparison of performance of RF MEMS, PIN-Diode, and FET
technologies for RF applications. 5

Table 3.1 Comparison of pull-in voltage, initial deflection and tuning range
for four different devices, depending on the coverage of the
stressed hard gold. 50

Table 4.1 Geometries of three candidate devices. 95

Table 4.2 Minimum external coil current for onset of switching and contact
force for different configurations. 107

Table 4.3 Modeled minimum switching times and energies for each design. 108

Table 5.1 Comparison of modeled and experimental data for minimum
conditions. 142

Table 6.1 Geometrical description of magnetically actuated MEMS device. 169

Table 7.1 Three cases for comparison of electrostatic and magnetic
actuation. 186

Table B.1 Demagnetization factors for common geometries. 221

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