G_O'Brien PhD Dissertation

Design and Fabrication of MEMS Angular Rate and
Angular Acceleration Sensors with CMOS Switched
Capacitor Signal Conditioning
by
Gary J. O’Brien
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
(Electrical Engineering)
in The University of Michigan
2004
Doctoral Committee:
Professor Khalil Najafi, Chair
Professor Richard B. Brown
Professor Noel C. Perkins
Professor Kensall D. Wise
Dr. David J. Monk, Sensor Development Engineering Manager,
Sensor Products Division, Motorola Inc.

©
ReservedRightsAll
BrienO'J.Gary
2004

ii
DEDICATION
This dissertation is dedicated to my wife Pamela and son Connor whose
unyielding love, support, and encouragement have enriched my soul and inspired me to
pursue and complete this research.

iii
ACKNOWLEDGMENTS
I would like to express my gratitude and appreciation for the guidance and support
given by my research advisor Professor Khalil Najafi. I also would like to thank
Professors Wise, Brown, and Perkins for their interest in my research. Many thanks to
Professor Perkins for discussions on rotating body dynamics.
I would also like to express my sincere gratitude to Dr. David Monk, Sensor
Development Engineering Manager, Motorola Sensor Products Division. Dave was able
to provide me with technical guidance, vision, and focus while functioning as both my
manager at Motorola and as my PhD industrial research advisor. Demetre Kondylis
supported this research through direct funding in his former role as Operations Manager,
Motorola Sensor Products Division. I will be forever grateful to Demetre for his
passionate and loyal support without whom none of this research would have been
possible. Brett Richmond continued to support my research efforts after taking the
leadership helm as General Manager, Motorola Sensor Products Division. I would like to
take this opportunity to thank Brett for his continued support and leadership in addition to
being a fellow Georgia Tech alumni (“GO Jackets”).
I want to thank my inertial sensor research group members, past and present, Arvind
Salian, Jun Chae, Hsiao Chen, Fatih Kocer, Haluk Kulah, and Jason Weigold for all their
help and friendship. I would especially like to thank both Arvind and Ark Wong for the
many interesting discussions regarding design and operation of MEMS devices while
working many late hours in the Solid State Electronics Lab.

iv
Mike McCorquodale, Ruba Borno, T. J. Harpster, Stefan Nikles, and Joseph Potkay,
all welcomed and allowed me to virtually live at their Ann Arbor apartment on multiple
occasions during my last year and a half of research for which I will be forever grateful.
Near honorable mention is in order for Brian Stark who was the source and sink of much
humor during my years in Ann Arbor; I wish him the best of luck in his future virtual
engineering endeavors.
I also wish the best of luck to the spring/2004 wave of Michigan PhD graduates who I
was fortunate enough to take classes with in addition to spending many hours in the
SSEL clean room including Andy DeHennis, T-Roy Olsson, Brian Stark, Mike
McCorquodale, Keith Kraver, and T.J. Harpster (who was kind enough to bring
donuts/drinks to my final defense for PhD committee and audience members).
I would also like to thank my sister Kathy and parents Jane and Donald O’Brien for
their love, support and encouragement. Both my grandmothers passed away during the
course of this research and I would like to sincerely thank both Lillian Brennen-O’Brien
and Alberta Nelson-Smith for all their love, support, and fond memories which I will
forever cherish.
This dissertation is dedicated to my wife Pamela Okamoto-O’Brien and son Connor
whose unyielding love, support, and encouragement have enriched my soul and inspired
me to both pursue and complete this research.
Finally, I would like to thank all my past Michigan MEMS research professors,
friends, and alumni with a loud and clear cheer; “GO BLUE”.

v
TABLE OF CONTENTS
DEDICATION................................................................................................................... ii
ACKNOWLEDGEMENTS ............................................................................................ iii
LIST OF FIGURES......................................................................................................... ix
LIST OF TABLES...........................................................................................................xv
LIST OF APPENDICES ............................................................................................... xvi
CHAPTER
1. INTRODUCTION.........................................................................................1
1.1 Automotive Accelerometer Evolution.............................................2
1.2 MEMS Linear Axis Accelerometers................................................4
1.2.1 Piezoelectric Inertial Sensor Transduction ...................................7
1.2.2 Piezoresistive Inertial Sensor Transduction..................................8
1.2.3 Tunneling Inertial Sensor Transduction......................................11
1.2.4 Thermal Inertial Sensor Transduction ........................................13
1.2.5 Capacitive Inertial Sensor Transduction.....................................15
1.3 MEMS Angular Acceleration and Rate Sensors............................17
1.4 Thesis Outline................................................................................19
2. VIBRATORY RATE GYROSCOPE PRINCIPLES ..............................21
2.1 Foucault Pendulum History ...........................................................22
2.2 Foucault Pendulum Properties.......................................................24
2.3 Pendulum Physical Properties........................................................27

vi
2.4 Pendulum Normal Mode Model ....................................................29
2.5 Open Loop Normal Mode Model ..................................................32
2.6 Closed Loop Normal Mode Model................................................33
2.7 Summary of Angular Rate Sensor Principles ................................34
3. VIBRATORY RATE GYROSCOPE TYPES..........................................35
3.1 Prismatic Beam Vibratory Gyroscopes..........................................35
3.2 Tuning Fork Vibratory Gyroscopes...............................................37
3.3 Linear Axis Accelerometer Vibratory Gyroscopes........................39
3.4 Torsion Mode Vibratory Gyroscopes ............................................42
3.5 Vibrating Shell Gyroscopes...........................................................45
3.6 Automotive Gyroscope Classification and Performance...............49
3.7 Vibratory Gyroscope Performance Summary................................51
4. SURFACE MICROMACHINED DUAL ANCHOR
GYROSCOPE .............................................................................................53
4.1 Dual Anchor Gyroscope Basic Design and Performance
Goals ..............................................................................................53
4.2 Angular Rate Sensor Operation .....................................................54
4.3 Basic Angular Rate Sensor Configuration.....................................57
4.4 Angular rate Sensor Design Enhancements...................................59
4.4.1 Anti-Stiction Beam Tip Anchors ................................................60
4.4.2 Dual Anchor Attach....................................................................63
4.4.3 Z-Axis Overtravel Stop...............................................................69
4.4.4 Dual Beam Torsion Spring .........................................................73
4.4.5 Differential Dual Electrode Sense Ring Capacitance.................75
4.5 Angular Rate Sensor Resonant Frequency Models .......................80
4.6 Angular Rate Sensor Empirical Results.........................................82

vii
4.7 Angular Rate Sensor FEA Simulation Results ..............................83
4.8 Brownian Noise .............................................................................85
4.9 Angular Rate Sensor Summary......................................................85
5. DUAL ANCHOR ANGULAR ACCELERATION SENSOR ................88
5.1 Angular Acceleration Sensor Fundamentals..................................88
5.2 Angular Acceleration Sensor Applications....................................91
5.3 Angular Rate Sensor and Angular Acceleration Sensor
Design Comparison........................................................................92
5.4 Surface Micromachined Angular Accelerometer Basic
Operation........................................................................................94
5.4.1 Surface Micromachined Angular Accelerometer Resonant
Frequencies ...............................................................................105
5.5 Angular Accelerometer Surface Micromachined to SOI
Design Conversion.......................................................................112
5.5.1 SOI Angular Accelerometer Basic Operation...........................119
5.5.2 SOI Angular Accelerometer Basic Signal Conditioning
C-V Conversion ........................................................................127
5.5.3 SOI Angular Accelerometer Finite Element Analysis
Simulation Results ....................................................................130
5.6 Angular Acceleration Sensor Summary.......................................133
6. CMOS SWITCHED CAPACITOR SIGNAL CONDITIONING........137
6.1 Front End Architecture ................................................................137
6.2 Front End Capacitive Sensor Charge Redistribution...................140
6.3 Theoretical Calculation and SPICE Simulation Comparison......143
6.4 CMOS Control Chip Top Level Overview..................................145
6.5 CMOS Signal Conditioned Angular Accelerometer Electrical
Output ..........................................................................................147
6.6 CMOS Signal Conditioned Angular Acceleration Sensor
Summary......................................................................................149

viii
7. SENSOR FABRICATION PROCESS FLOWS ....................................152
7.1 SOI Sensor Mechanical Anchor Fabrication Fundamentals........153
7.2 Short SOI Process Flow...............................................................154
7.2.1 Clear Field Sensor Perimeter Fabrication.................................156
7.2.2 Dark Field Sensor Perimeter Fabrication..................................157
7.3 Integrated SOI Process Flow .......................................................159
7.3.1 Substrate Anchor Trench Refill Etch Stop Process Example...160
7.4 SOI Process Flow Summary........................................................166
8. SUMMARY AND FUTURE WORK......................................................168
APPENDICES................................................................................................................173
BIBLIOGRAPHY..........................................................................................................241

ix
LIST OF FIGURES
Figure 1.1 Electromechanical event accelerometer used 1990’s automobiles.................2
Figure 1.2 Simple mass-spring accelerometer with acceleration along z-axis.................5
Figure 1.3 Piezoresistive strain-gage based silicon accelerometer. ...............................10
Figure 1.4. Tunneling tip accelerometer with electrostatic force feedback loop ............12
Figure 1.5 Thermal accelerometer isometric view.........................................................13
Figure 1.6 Thermal accelerometer cross section............................................................14
Figure 1.7 Thermal accelerometer differential temperature profile versus x-axis.........14
Figure 1.8 Capacitive sensor configuration cases ..........................................................16
Figure 1.9 Capacitive accelerometer sandwiched between two glass wafers................17
Figure 2.1 Foucault pendulum located at north pole......................................................24
Figure 2.2 Foucault pendulum path as interpreted by earth bound observer .................25
Figure 2.3 Rotation of Foucault pendulum as a function of latitude..............................26
Figure 2.4. Foucault pendulum rotation coupling at different locations on earth...........26
Figure 2.5 Simple pendulum and mass-spring system oscillators..................................27
Figure 2.6 Foucault pendulum normal mode model ......................................................30
Figure 2.7 Open loop angular rate sense operation........................................................32
Figure 3.1 Rectangular beam vibrating rate gyroscope..................................................35
Figure 3.2 Murata Gyrostar triangular beam gyroscope ................................................36
Figure 3.3 Tuning fork y-axis drive and x-axis Coriolis coupling about z-axis ............38
Figure 3.4 Dual accelerometer isometric view and cross section ..................................40
Figure 3.5 Dual accelerometer linear acceleration signal rejection ...............................41
Figure 3.6 Prismatic beam torsion decoupled mode vibratory gyroscope .....................42
Figure 3.7 Two axis vibrating disc gyroscope ...............................................................43

x
Figure 3.8 Polysilicon vibrating disc gyroscope Coriolis induced rotation ...................44
Figure 3.9 Top and side view of decoupled torsion mode vibratory gyroscope ............44
Figure 3.10 Wine glass shaped hemispherical resonator gyroscope................................46
Figure 3.11 Node precession of the HTG with externally applied angular rate...............47
Figure 3.12 Micromachined vibrating ring gyroscope drive and sense modes................48
Figure 4.1 Angular rate sensor Coriolis force diagram..................................................55
Figure 4.2 Basic angular rate sensor cross section.........................................................57
Figure 4.3 Basic polysilicon angular rate sensor configuration.....................................58
Figure 4.4 Centrally anchored polysilicon beam springs...............................................58
Figure 4.5 Simple torsion beam spring outer mass coupling suspension.......................59
Figure 4.6 Enhanced anchor parallel plate electrostatic sense-actuation arrays ............60
Figure 4.7 Centrally anchored electrostatic array vertical stiction.................................61
Figure 4.8 Standard and split central drive disc designs................................................61
Figure 4.9 Electrostatic beam array cross section with tip anchors ...............................62
Figure 4.10 Tip anchor electrical isolation on nitride passivated substrate .....................62
Figure 4.11 Fixed electrode parallel plate array substrate electrode interconnect ...........63
Figure 4.12 Dual anchor angular rate sensor suspension.................................................64
Figure 4.13 Folded beam and torsion post equivalent spring constant model .................64
Figure 4.14 Folded beam equivalent spring constant model............................................65
Figure 4.15 Z-axis mechanical over-travel stop...............................................................69
Figure 4.16 Mechanical over-travel stop tilted view........................................................70
Figure 4.17 Sub-micron mechanical over-travel stop-gap...............................................71
Figure 4.18 Enhanced angular rate sensor decoupled mode suspension..........................74
Figure 4.19 Dual torsion beam coupling spring...............................................................74
Figure 4.20 Dual torsion beam coupling spring stress concentration simulation ...........75

xi
Figure 4.21 Angular rate sense ring capacitance electrode configuration ......................76
Figure 4.22 Tilted view of differential electrode capacitor..............................................76
Figure 4.23 Differential capacitor support post detail......................................................77
Figure 4.24 Drive disc displacement and velocity at sense ring inner radius (rin)...........78
Figure 4.25 Angular rate coupled Coriolis force sense ring displace simulation.............78
Figure 4.26 Sense ring z-axis displacement electrode capacitance and schematic..........79
Figure 4.27 Sense mode resonant frequency measurement test configuration ................82
Figure 4.28 Sense mode resonant peak @44.96kHz, Q=225...........................................83
Figure 4.29 Angular rate sensor measurement data .........................................................83
Figure 5.1 Description of rigid body rotation using a fixed particle point reference.....89
Figure 5.2 Example of rate table excited with 15 deg. displacement 2Hz sinusoid.......89
Figure 5.3 Angular rate sensor and angular acceleration sensor comparison ................92
Figure 5.4 Angular acceleration sensor capacitive parallel plate beam arrays ..............93
Figure 5.5 Capacitive angular acceleration sensor bond pad electrical schematic ........93
Figure 5.6 Angular accelerometer disc configuration....................................................94
Figure 5.7 Capacitive array radial dimensions referenced from center of rotation........95
Figure 5.8 Angular accelerometer dual beam spring suspension attach points..............97
Figure 5.9 Outer connected spring constant directed along x-y plane...........................98
Figure 5.10 Inner connected spring constant directed along x-y plane............................98
Figure 5.11 Interleaved folded beam spring design .........................................................99
Figure 5.12 Lateral spring constant theoretical model and FEA simulation results ......100
Figure 5.13 %ΔC/C0 Vs beam spring length (L) and outer disc radius (R2). .................101
Figure 5.14 Outer connected spring constant directed along z-axis...............................102
Figure 5.15 Inner connected spring constant directed along z-axis ...............................102
Figure 5.16 Model of z-axis surface tension sensor displacement Vs thickness ...........104

xii
Figure 5.17 Torsion mode frequency Vs spring length and outer disc radius................107
Figure 5.18 Modal z-axis frequency for 2μm thick proof mass disc .............................108
Figure 5.19 Modal z-axis frequency for 20μm thick proof mass disc ...........................108
Figure 5.20 Modal z-axis frequency ratio for 2μm thick proof mass disc.....................109
Figure 5.21 Modal z-axis frequency ratio for 20μm thick proof mass disc...................110
Figure 5.22 Angular acceleration sensor design conversion from polysilicon to SOI...112
Figure 5.23 Centrally anchored folded beam spring array with solid central hub.........113
Figure 5.24 Beam spring substrate anchor and central hub detail..................................114
Figure 5.25 DRIE trench defined SOI suspension BOX anchor cross section ..............115
Figure 5.26 Angular acceleration sensor interleaved inner and outer radial anchors ....116
Figure 5.27 Angular acceleration sensor identical spring dual radius interleave...........117
Figure 5.28 SOI 20μm thick angular accelerometer ΔC/C0 sensitivity @α=100r/s2
....118
Figure 5.29 Angular acceleration sensor and bond pad schematic ................................119
Figure 5.30 SOI angular accelerometer capacitive array radial dimensions..................120
Figure 5.31 Sensor capacitance Vs applied angular acceleration (α) ............................121
Figure 5.32 Linearized sensor capacitance Vs applied angular acceleration (α)...........122
Figure 5.33 Capacitive sensor C-V plot test equipment configuration..........................124
Figure 5.34 Capacitance-Voltage plot theoretical comparison to empirical data ..........125
Figure 5.35 Self-Test capacitance array (N=10 electrodes)...........................................125
Figure 5.36 Self-Test capacitance array applied voltage Vs angular acceleration(α) ...126
Figure 5.37 Simplified switched capacitor front end .....................................................128
Figure 5.38 Control chip voltage output Vs applied angular acceleration (α)...............129
Figure 5.39 Angular accelerometer two-chip interconnection top view........................130
Figure 5.40 ANSYS angular acceleration sensor meshed solid model..........................131
Figure 5.41 Displacement simulation of proof mass using z-axis linear acceleration...132

xiii
Figure 5.42 Beam spring displacement due to angular acceleration about z-axis .........133
Figure 6.1 Switched capacitor front end top level schematic.......................................138
Figure 6.2 Phases 0-2 front end charge distribution.....................................................141
Figure 6.3 Transmission gate charge re-distribution clock phase detail......................142
Figure 6.4 Basic transmission gate schematic sub-circuit (T-gate7)............................143
Figure 6.5 First stage capacitance to voltage (C to V) transconduction slope .............144
Figure 6.6 Front end sample-and-hold voltage output for a 1%ΔC/C0 ........................144
Figure 6.7 CMOS control chip functional block diagram............................................145
Figure 6.8 CMOS control chip analog signal path top level schematic.......................146
Figure 6.9 CMOS control chip interfaced to capacitive angular accelerometer ..........147
Figure 6.10 CMOS control chip output voltage reference (Noise=4.3VRMS) ................148
Figure 6.11 Output voltage measurement for a sinusoidal 40r/s2
input.........................148
Figure 6.12 Angular rate table test equipment configuration.........................................149
Figure 6.13 Eccentric cam sinusoidal arm linkage with motor driven transmission .....149
Figure 7.1 Typical SOI MEMS mechanical BOX attached anchor .............................153
Figure 7.2 Short SOI process flow DRIE trench defined Box anchor cross section....155
Figure 7.3 Short SOI process flow released device and bond pad cross section .........155
Figure 7.4 Clear field perimeter SOI short process flow angular accelerometers .......156
Figure 7.5 Bond pad interconnect beam anchor electrical isolation from substrate ....157
Figure 7.6 Bond pad metal and interconnect beam detail............................................157
Figure 7.7 Dark field perimeter SOI short process flow angular accelerometer..........158
Figure 7.8 Dark field SOI electrical short to bond pad with substrate contact plate....159
Figure 7.9 SOI anchor perimeter etch-stop process flow.............................................160
Figure 7.10 SOI anchor trench refill perimeter etch-stop example ...............................161
Figure 7.11 Polysilicon trench refill substrate electrical contact process flow..............162

xiv
Figure 7.12 Polysilicon trench refill substrate electrical contact cleaved sample..........162
Figure 7.13 Substrate polysilicon electrical contact bond pad interconnection.............163
Figure 7.14 Substrate electrical contact cross section and electrical schematic ............164
Figure 7.15 Silicon dopant density (cm-3
) Vs resistivity (Ω-cm)...................................165
Figure 8.1 Fully inner hub connected folded beam spring suspension ........................170
Figure 8.2 Fully inner hub connected folded beam spring suspension detail ..............170
Figure 8.3 1200μm angular accelerometer with extra beam spring folds....................171
Figure 8.4 1200μm angular accelerometer beam spring fold detail.............................172

xv
LIST OF TABLES
TABLE
1.1 Inertial Sensor Transduction Types and Mechanisms ....................................7
1.2 Common MEMS transducer piezoelectric materials and properties ..............8
1.3 Typical piezoresistance coefficients for n- and p-type silicon.....................10
3.1 Multiple classes of gyroscope performance..................................................49
3.2 Commercial automotive gyroscope performance comparison ....................51
4.1 Angular rate sensor model comparison results............................................84
4.2 ANSYS sense ring moment of inertia simulation results ............................84
5.1 Angular accelerometer specification data....................................................92
5.2 Angular accelerometer SOI model verification results..............................130
5.3 ANSYS modal frequency simulation results.............................................132
5.4 Commercial/research prototype angular accelerometer performance ........135
6.1 Simulated Vs theoretical sample and hold stage output voltage................143

xvi
LIST OF APPENDICES
APPENDIX
A. Electrostatic Latch and Release of MEMS Cantilever Beams....................173
B. Super Critical CO2 Chamber Design and Operation...................................193
C. Deep Reactive Ion Etch Tool Characterization ..........................................206
D. Switched Capacitor Low Pass Filter/Amplifier..........................................225
E. Stiction Assisted Substrate Contact Design and Operation........................230
F. Integrated SOI Process Flow ......................................................................236

1
CHAPTER 1
INTRODUCTION
Inertial sensing is typically categorized into three distinct sensor system types
represented by linear axis acceleration, angular rate (gyroscopes), and angular
acceleration. The development and commercialization of high volume low cost silicon
surface micromachined linear axis accelerometers [1-3] has been the predominant micro-
electromechanical system (MEMS) based sensor application realized by the automotive
market over the past decade. However, due to rapid advances in MEMS fabrication
technology made over the past several years, design efforts have been recently re-focused
in the development of low cost automotive micromachined gyroscopes. Currently, the
primary automotive gyroscope applications are active vehicle traction control, roll over
detection, and stabilization systems [4-7]. The target resolution for automotive angular
rate sensors used to detect vehicle roll-over is typically less than 2deg/s in a 40Hz
bandwidth with a (+/-)300deg/s full scale span. Active vehicle control applications [6]
typically require a target resolution of less than 1deg/s in a 50Hz bandwidth with a (+/-)
100deg/s full scale span. The target cost is between $10 and $20 per sensor, with single
customer orders typically ranging in millions of units per year [8]. Angular acceleration
sensors are currently used as feedback elements for computer hard drive read/write head
positioning algorithm applications [9, 10] in commercial volumes [11] with target costs
typically ranging from $5 to $9 per sensor. Although automotive angular acceleration
crash detection applications have been proposed [12] they have not yet been realized in
the commercial domain due to the poor sensitivity and resolution of low cost MEMS
sensors currently commercially available. Applications such as hand held camera
stabilization and active vehicle control [6] may also benefit from the use of low cost

2
lightweight angular accelerometers as closed loop feedback elements, provided sensors
with higher sensitivity and resolution can be provided in commercial volumes.
1.1 Automotive Accelerometer Evolution
The Intermodal Surface Transportation Efficiency Act (ISTEA), signed into law
during 1991, ensured that 100% of production automobiles sold in the United States were
to be equipped with occupant safety airbags by 1998. Electromechanical accelerometers
used for automotive crash detection and subsequent air bag deployment in the early
1990’s consisted of a roller anchored via a flat spring band [13] as shown in the top view
of Figure 1.1.
A B
A B
Constant
Velocity
(0 acceleration)
Motion
Large deceleration
(>6g) upon impact
R1
RAB = ∞ Ω
RAB ≅ R1Ω
Metal
Cover
Baseplate
Backstop Roller Electrical
Contact
Spring
Band
Electrical
Resistor
R1
Proof mass roller completes electrical contact circuit for >6g acceleration
A B
A B
Constant
Velocity
(0 acceleration)
Motion
Large deceleration
(>6g) upon impact
R1
RAB = ∞ Ω
RAB ≅ R1Ω
Metal
Cover
Baseplate
Backstop Roller Electrical
Contact
Spring
Band
Electrical
Resistor
R1
Proof mass roller completes electrical contact circuit for >6g acceleration
Figure 1.1 Electromechanical event accelerometer used in early 1990’s automobiles.

3
Sufficient deceleration experienced during a crash event, typically in excess of 6g’s
(where 1g = 9.81m/s2
), caused the roller to displace from its zero-acceleration position
until the electrical contact was closed as shown in the bottom view of Figure 1.1.
Electrical resistance measured at the accelerometer’s connections A and B provided the
airbag control system with discrete event detection where an open/short circuit
represented less/greater than 6g’s respectively. Three of the electromechanical discrete
event accelerometers were used in the early airbag control system loops to evaluate the
severity of a crash regarding discrimination of intentional activation/deployment. Two of
the accelerometers were placed in the vehicle’s front crush zone typically located on the
frame behind the front bumper or on the lower portion of the radiator supports [14]. The
remaining accelerometer was placed in the occupant zone either in or near the passenger
compartment often referred to as a “safing sensor”. Deceleration values experienced in
the crush and occupant zones are separated by both magnitude and phase (time).
Although the crush zone accelerometers provided both earlier crash warning and larger
deceleration magnitudes they were not able to discriminate actual acceleration values
occurring along the vehicle’s major axis. The “safing sensor” was added as a redundant
crash event verification accelerometer to prevent inadvertent airbag deployment should
both crush zone accelerometers either malfunction or experience a shock not correlated to
an actual crash event.
Micromachined electromechanical capacitive accelerometers [1-3] were a logical
replacement since these analog sensors provided sufficient bandwidth, sensitivity, and
resolution to facilitate adequate single point testing when located in the vehicle’s
occupant zone. MEMS capacitive accelerometers were initially available for less than $8
per device in production quantities. This represented a significant cost reduction over the
electromechanical event detection accelerometers supplied by Breed and TRW at a target
cost of $15 per device [14] where three devices were required per automobile. In

4
addition, wiring harness costs were reduced using the single point MEMS accelerometer
approach. The MEMS accelerometers were less expensive, more reliable, provided a
continuous analog signal output, and were smaller than their electromechanical switch
counterparts.
A typical MEMS accelerometer currently used in the automotive airbag market is the
MMA3201D manufactured by Motorola. The MMA3201D accelerometer exhibits a
bandwidth of 0-400Hz, sensitivity of 50mV/g, span of (+/-) 40g, and resolution of 0.06g.
The continuous analog output of this type of MEMS accelerometer significantly
enhanced automotive inertial sensing control applications. Modern airbag deployment
control loops were quickly adapted in the mid 1990’s to recognize and discriminate front,
side, and rear vehicle crash signatures using rule based and/or fast Fourier transform
algorithms evaluated via electronic modules. The electronic modules consisted of
application specific integrated circuits coupled with embedded microprocessors.
Typically, the accelerometer was incorporated directly onto the electronic module’s
printed circuit board providing both electrical interconnection and mechanical support.
The front, side, and rear acceleration crash signatures of an automobile are model specific
requiring automotive manufacturers to tailor and qualify airbag crash detection
algorithms based on deceleration data acquired from intentionally crashed vehicles
whenever a new product line is introduced.
1.2 MEMS Linear Axis Accelerometers
Virtually all inertial MEMS sensors exhibit electromechanical transduction
components which can be modeled as simple linear or rotational acceleration. As a
result, inertial MEMS models contained in this thesis expand and exploit this relationship
wherever applicable.

5
Linear accelerometers measure acceleration directed along a specific axis of desired
sensitivity. Typically the accelerometer consists of a mechanically suspended proof
mass-spring system as shown in Figure 1.2.
Spring
Anchor
Fixed Electrode
Movable Proof-mass z0
z0 - Δz
KZ
M
K
f Z
π2
1
0 =
M = mass
KZ = spring constant
aZ = acceleration
FZ = acceleration force
Resonant Frequency
QM
fTfK
a Z
Brownian
Δ
= 08π
Brownian Noise
Equivalent Acceleration
KZ
x
y
z
Zero Acceleration Proof Mass Position
Non-Zero Acceleration Proof Mass Displacement
T = temperature
Δf = bandwidth
Q = quality factor
Spring
Anchor
Fixed Electrode
Movable Proof-mass z0
z0 - Δz
KZ
M
K
f Z
π2
1
0 =
M = mass
KZ = spring constant
aZ = acceleration
FZ = acceleration force
Resonant Frequency
QM
fTfK
a Z
Brownian
Δ
= 08π
Brownian Noise
Equivalent Acceleration
KZ
x
y
z
x
y
z
Zero Acceleration Proof Mass Position
Non-Zero Acceleration Proof Mass Displacement
T = temperature
Δf = bandwidth
Q = quality factor
T = temperature
Δf = bandwidth
Q = quality factor
Figure 1.2 Simple mass-spring accelerometer with acceleration along z-axis.
An externally applied z-axis acceleration causes the movable proof-mass to translate
location as referenced to the initial gap (z0) between the proof-mass and fixed reference
electrode. The movable proof-mass experiences a mechanical force proportional to the
block’s mass (M) multiplied by the externally applied acceleration (aZ) as given by
Newton’s second law of motion in Eq. 1.1. The relationship between the mechanical

6
spring constant (KZ) and proof-mass translation distance (ΔZ) due to an externally applied
force results in spring elongation described by Hooke’s law as given in Eq. 1.2.
ZZ MaF = (1.1)
ZZZ KF Δ= (1.2)
The relationship between applied acceleration and proof-mass displacement is
described by combining equations 1.1 and 1.2 as given in Eq. 1.3.
Z
Z
Z a
K
M
=Δ (1.3)
Therefore, the proof-mass displacement (Δz) is directly proportional to the applied
external acceleration (aZ) and scaled by the ratio of mass (M) to the system’s mechanical
spring constant (KZ) for small linear deflections.
The proof-mass displacement as a function of applied external acceleration from the
zero-acceleration position is converted into an electrical signal using electronics
interfaced to the sensor. The electronic circuit configuration is dictated by the type of
acceleration sensor used. Inertial MEMS sensor interface circuits have been previously
demonstrated as compatible with capacitive [1-3], piezoelectric [15, 16], piezoresistive
[17-19], tunneling [20-25], and thermal [26] sensor transduction types as listed in Table
1.1.

7
Table 1.1 Inertial Sensor Transduction Types and Mechanisms
Sensor Type DC/Low Freq AC/High Freq Limit Transduction Mechanism
Piezoelectric >5 Hz >100kHz (4-40kHz typical) compression of spring redistrubutes charge
Piezoresistive 0 Hz <10kHz (0.4-5kHz typical) stress in spring changes resistance
Tunneling 0 Hz <1kHz (4-400Hz typical) tunneling currrent due to tip/electrode proximity
Thermal 0 Hz <100Hz (30-40Hz typical) thermal transport delay of heat pulse in N2 gas
Capacitive 0 Hz >100kHz (1-20kHz typical) capacitive sense gap between mass/electrode
1.2.1 Piezoelectric Inertial Sensor Transduction
Crystalline materials in which an applied mechanical stress produces an electric
polarization, and reciprocally, an applied electric field generates a mechanical strain are
referred to as piezoelectric. Piezoelectric sensors are classified as “self generating” since
the electric field resulting from an applied mechanical stress generates a differential
voltage signal. However, a key potential limitation of this transduction mechanism is that
while the piezoelectric effect produces a DC charge polarization it will not sustain a DC
current [27, 28]. Therefore, piezoelectric transducers are inherently incapable of
providing a DC response. The limited low frequency response of piezoelectric
transducers is primarily due to parasitic charge leakage paths in the non-centrosymmetric
crystal materials under constant mechanical strain.
The piezoelectric differential voltage signal is easily signal conditioned using typical
low noise voltage amplification circuits [15]. Although silicon is not a piezoelectric
material, thin piezoelectric films such as PZT (lead zirconate titanate) or BaTiO3 (barium
titanate) can be deposited onto silicon substrates to form MEMS based sensors and
actuators. Several common piezoelectric materials and properties are listed in Table 1.2
[29].

8
Table 1.2 Common MEMS transducer piezoelectric materials and properties.
Material ZnO Quartz AlN BaTiO3 PZT Units
Piezoelectric coefficient (d33) 246 2.3 3.9 190 130 [pC/N]
Relative dielectric constant (εr) 1400 4.5 8.5 4100 1000 εr ε0 [F/m]
Piezoelectric materials exhibit charge leakage under constant strain and eventually the
electric field providing the sensor differential voltage will decrease towards zero [30].
As a result, low frequency sensor operation at values less than 10Hz have been difficult
to demonstrate using piezoelectric transducer materials [14]. An example of a constant
mechanical strain would be to orient the accelerometer’s sense axis in line with the
earth’s gravitational field.
Piezoelectricity, pyroelectricity, and ferroelectricity share properties inherent to the
electrical polarization vector associated with the non-centrosymmetric crystals which
comprises the sensor bulk material. If a material is piezoelectric, in most cases it will
also be pyroelectric and ferroelectric with very few exceptions of exotic materials [29]
outside the scope of typical MEMS processing/research. The pyroelectric behavior limits
the use of these materials in automotive applications since most suitable piezoelectric
sensor materials exhibit considerable temperature sensitivity requiring some form of an
integrated sensor [15] or signal conditioned analog/digital compensation technique. The
increase in sensor interface complexity to compensate for pyroelectric effects coupled
with the lack of DC operation make piezoelectric sensing a less attractive technology
regarding automotive applications where large temperature spans and static operation are
key system requirements. While quartz has proven to be an excellent material regarding
negligible aging effects, this attribute does not describe thin film PZT deposited by
sputter or SOLGEL lanthanum doping techniques [31]. Creep and depoling of the
ferroelectric PZT material domains have been identified as possible material degradation
effects responsible for an observed 5% drop in displacement amplitude of a piezoelectric

9
micromechanical resonator tested over a 100 hour period [32]. Delaminations have been
observed at the PZT-Pt interface [33], suggesting that these films may be susceptible to
interfacial failure with repeated bending which raises significant concern as to the long
term reliability of piezoelectric thin film deposition based sensors and actuators. The Pt
electrode may be replaced by other materials such as doped polysilicon with respect to
PZT film deposition and annealing which desirably developed a random polycrystalline
perovskite phase, but were also subject to tensile cracking [34]. Film integrity at the PZT
electrode film interface may require significant process innovation before this technology
can guarantee the high degree of reliability required for automotive safety applications
where a 10year operational device lifetime is a typical requirement.
1.2.2 Piezoresistive Inertial Sensor Transduction
Crystalline materials in which an applied mechanical strain produces a change in the
electrical resistance are piezoresistive. Many crystalline materials exhibit a change in the
mobility or the number of charge carriers as a function of volume deformation due to
applied mechanical stress [35]. The deformed volume affects the energy gap between the
valence and conduction bands resulting in a change in the number of available carriers
responsible for bulk electrical resistivity in semiconductor materials with additional
effects modeled by Herring [36]. Monocrystalline silicon exhibits a large piezoresistivity
[37] combined with excellent mechanical properties making this material a good
candidate for potential sensor applications regarding mechanical strain measurement [38-
40]. The use of dopant diffusion techniques in the fabrication of piezoresistive sensors
for stress, strain, and pressure was initially proposed by Pfann and Thurston [41] in 1961.
Thin single crystal silicon dopant diffused membranes were used to form a pressure
sensor fabricated by Tufte et al [42] in 1962 . The first micromachined piezoresistive
strain gage accelerometer was demonstrated by Roylance and Angell [17] in 1979 for use
in biomedical implants to measure heart wall accelerations. The accelerometer was

10
fabricated from a silicon wafer sandwiched between two anodically bonded 7740 Pyrex
glass wafers to provide hermetic operation as shown in Figure 1.3.
Pyrex
Glass
Pyrex
Glass
Silicon
Movable
Proof Mass
Cantilever Beam Diffused Piezoresistor
Device Cross-section
Cavity
Anodic
Bonds
Figure 1.3 Piezoresistive strain-gage based silicon accelerometer.
Strain gage accelerometers are fabricated by placing either deposited polycrystalline
silicon or diffused single crystal silicon resistors onto the proof mass suspension at areas
of peak stress [43]. The sensitivity of single crystal silicon is highly orientation
dependent based on πXX coefficients [37, 44] as shown in Table 1.3.
Table 1.3 Typical piezoresistance coefficients for n- and p-type silicon.
Dopant Resistivity Concentration π11 π12 π44
n-type 11.7 3*1014
-102.2 53.4 -13.6
p-type 7.8 2*1015
6.6 -1.1 138.1
Units Ω-cm cm-3
10-11
Pa-1
10-11
Pa-1
10-11
Pa-1
Therefore, mask misalignment rotation errors during photolithography steps with the
wafer flat can result in some reduction in piezoresistive sensitivity. Polycrystalline
silicon is more tolerant of mask alignment rotation errors regarding piezoresistance, but is
less sensitive than single crystal material. Also, polycrystalline silicon piezoresistance is
strongly influenced by grain size. Large grain polycrystalline silicon can approach 60-

11
70% the piezoresistance of single crystal silicon [45]. However, the piezoresistance of
small grain polysilicon is approximately seven times less than single crystal silicon [46].
Piezoresistance coefficients depend strongly on dopant type, n-type or p-type, and are
weak functions of doping levels for values less than 1019
cm-3
, but then decrease
significantly as doping is increased. The piezoresistive coefficients also decrease with
increasing temperature, falling to 70% at 150C as compared to room temperature
operation. The piezoresistive temperature dependence is nonlinear which is compounded
with the need to compensate for the large temperature coefficient of resistivity due to
typically low dopant concentrations used [37, 44]. A Wheatstone bridge configuration
can be used to optimize the output sensitivity over temperature without the typical large
nonlinearity error due to temperature coefficients of resistance associated with other
compensation techniques such as increased voltage gain [47-49]. Doping can also be
increased at the cost of decreased piezoreistance sensitivity to compensate for undesirable
temperature coefficient of resistance effects.
1.2.3 Tunneling Inertial Sensor Transduction
Electron tunneling is used between a sharp conductive tip and electrode in near
contact suspended via a mechanical spring to form an accelerometer [21]. The tunneling
current (IT) is a function of the applied bias voltage (VB) and tip to proof-mass separation
(dT) where constants are used for the quantum mechanical barrier height (Φ = 0.2eV) and
αI = 1.025 Å-1
eV-0.5
. A feedback control loop is used to maintain a relatively constant
tunneling current (IT) by controlling the feedback voltage (VF) providing the electrostatic
force to maintain the movable proof-mass and tunneling tip separation (dT) as shown in
Figure 1.4.

12
Anchor
Movable Proof Mass
Tunneling Tip
+
-
Silicon Substrate
IT VF
Suspension
Spring
Dielectric
(SiXNY)
dT
TI d
BT eVI
Φ−
∝
α
VB
+
-
Anchor
Movable Proof Mass
Tunneling Tip
+
-
Silicon Substrate
IT VF
Suspension
Spring
Dielectric
(SiXNY)
dT
TI d
BT eVI
Φ−
∝
α
VB
+
-
Figure 1.4 Tunneling tip accelerometer with electrostatic force feedback loop.
The tunneling tip bias voltage is typically less than 1 volt for separations on the order
of 10 angstroms between the tip and proof-mass. The separation distance is typically
fabricated much larger than the 10 angstrom operating gap where the electrostatic force
provided by the feedback loop is used to reduce and maintain the gap during operation.
The feedback loop voltage is typically on the order of 20 volts [50]. Mechanical shocks
experienced during normal device operation will inevitably result in undesirable tip to
proof-mass contact referred to as tip-crashing due to the small operating separation
distance. The accelerometer control electronics must also include current limiting during
tip-crashing to preclude destruction of the conductive tip [51]. The tunneling current
exhibits a 1/f noise spectrum with a noise floor on the order of 20nano-g/√Hz reported in
a 5Hz-1.5kHz bandwidth [52].
While tunneling accelerometers have proven to be extremely sensitive they have been
difficult to manufacture due to large device to device variation. Tunneling
accelerometers are not yet as repeatable as capacitive sensors regarding both their basic
sensitivity and noise characteristics [53].

13
1.2.4 Thermal Inertial Sensor Transduction
The operating principle of a thermal accelerometer is based on the effect of
acceleration with respect to the free convection heat transfer of a hot gas bubble inside a
sealed cavity. A single-axis thermal accelerometer consisting of a central heater located
between two temperature coefficient of resistance (TCR) based polysilicon temperature
sensors suspended over an etched cavity, to provide thermal isolation to the silicon
substrate, has been previously demonstrated [26] as shown in Figure 1.5.
Silicon Substrate
Etched Cavity Bottom
Oxide
Heater
Temp Sensor2Temp Sensor1
X
YZ
X
YZ
Figure 1.5 Thermal accelerometer isometric view.
The two suspended temperature sensors, temperature sensor1 (TS1) and temperature
sensor2 (TS2), are located at equal distances symmetric about the central heater as shown
in Figure 1.6. The temperature profile in the proximity of the central heater is symmetric
when no external acceleration is applied. However, the symmetry is disturbed when a
non-zero acceleration is applied as shown by dotted lines in Figure 1.7.

14
Bottom
Oxide
Sidewall
Oxide Polysilicon
Nickel
Silicon Substrate
Heater
Temp
Sensor1
Temp
Sensor2
Etched Cavity
X
Z
Figure 1.6 Thermal accelerometer cross section.
Temperature
X Axis
Location
Zero X Axis Acceleration-X Axis Acceleration
X
T
+X Axis Acceleration
X
T
ΔT ΔT
HTRTS1 TS2HTRTS1 TS2 HTRTS1 TS2
Figure 1.7 Thermal accelerometer differential temperature profile versus x-axis.
The temperature coefficient of resistance of the lightly-doped polysilicon is used to
measure the differential temperature as a function of acceleration. The thermal time
constant of the temperature sensors, with their polysilicon coefficient of thermal
resistance controlled via doping concentration to approximately 2000ppm/C, are coupled
with the thermal properties of the sealed cavity gas as a multi-pole control system with
the first pole located at approximately 20 Hz [26]. A sensor bandwidth extension
technique has been described to extend the thermal accelerometer to 160Hz [54] by
increasing the analog system gain as a function of frequency matched with the initial
mechanical pole at 20dB/decade. This electrical-zero/mechanical-pole matching

15
technique increases the apparent system bandwidth at the cost of significantly degraded
signal to noise ratio beyond the initial mechanical pole frequency. As a result, it may
prove difficult for this technology to achieve the 400Hz bandwidth typically required for
automotive accelerometer applications. In addition, the central heater consumes power
on the order of 20mW which must also be regulated, to maintain a constant heater
temperature versus an automotive ambient temperature swing of -40C to 85C, using
closed loop electronics which consume additional power. As a result, this method
consumes a significant amount of power and may prove difficult to implement in either
automotive or battery powered commercial applications where capacitive linear axis
accelerometers are currently available with lower power drain and wider signal
bandwidth.
1.2.5 Capacitive Inertial Sensor Transduction
An important advantage of capacitive accelerometers is that, as opposed to the
piezoresistive accelerometers, there is a very small degree of inherent temperature
sensitivity [55]. Changes in capacitance over temperature, for devices operated at
constant low pressures, are primarily attributed to the thermal expansion/contraction of
sensor electrodes causing a change in the effective dielectric gap. However, the
temperature coefficient for the dielectric constant of air, maintained at a constant pressure
of 1-atmosphere and normalized to 20°C, has been identified as 2ppm/°C for dry air and
7ppm/C for moist air [56]. Although non-zero, this capacitive temperature dependence is
typically orders of magnitude less than piezoresistive devices.
Capacitive sensors are typically integrated using a combination of fixed and movable
electrodes which sense mechanical displacement. The inherent nonlinearity associated
with several types of capacitive sensor operation is often overshadowed by their

16
simplicity and very small temperature coefficients. Several potential capacitive sensor
configurations [57, 58] are illustrated in Figure 1.8.
a
b
c
a
c
Δz
Δz
Parallel
Plate
Differential
C1
C2
z0 z0
C1
a
c
Δx
z0C1
a
Δx
z0C1 C2
a
c
z0
Δx
εr
Dielectric
b c
zz
A
C
Δ−
=
0
0
1
ε
zz
A
C
Δ−
=
0
0
1
ε
zz
A
C
Δ+
=
0
0
2
ε
0
10
1
z
yW
C
ε
=
Overlap
Area
xyA =
xxW Δ−=1
0
10
1
z
yW
C
ε
=
0
20
2
z
yW
C
ε
=
xxW Δ+=2
Differential
Overlap Area
Movable
Dielectric
0
10
1
z
yW
C
ε
=
0
20
2
z
yW
C rεε
=
21 CCCtotal +=
Case 1 Case 2 Case 3 Case 4 Case 5
a
b
c
a
c
Δz
Δz
Parallel
Plate
Differential
C1
C2
z0 z0
C1
a
c
Δx
z0C1
a
Δx
z0C1 C2
a
c
z0
Δx
εr
Dielectric
b c
zz
A
C
Δ−
=
0
0
1
ε
zz
A
C
Δ−
=
0
0
1
ε
zz
A
C
Δ+
=
0
0
2
ε
0
10
1
z
yW
C
ε
=
Overlap
Area
xyA =
xxW Δ−=1
0
10
1
z
yW
C
ε
=
0
20
2
z
yW
C
ε
=
xxW Δ+=2
Differential
Overlap Area
Movable
Dielectric
0
10
1
z
yW
C
ε
=
0
20
2
z
yW
C rεε
=
21 CCCtotal +=
Case 1 Case 2 Case 3 Case 4 Case 5
Figure 1.8 Capacitive sensor configuration cases.
The parallel plate capacitor has been used to measure a spring suspended proof mass
displacement as a function of the separation between the proof mass and a fixed reference
electrode [59]. Interface circuits to convert the parallel plate sensor capacitance to an
output voltage signal have been previously demonstrated [60].
Differential capacitance accelerometers with a vertical out of plane displacement have
been demonstrated in bulk silicon [61], as shown in Figure 1.9, and surface
micromachined polysilicon [1, 3]. Lateral displacement in the wafer plane has also been
demonstrated using a differential capacitance interdigitated finger scheme [2]. The
maximum displacement of these devices is typically limited to 10% the initial gap due to
the non-linear capacitance relationship.

17
Glass
Glass
Silicon
Movable
Electrode (b)
Fixed Metal Electrode (c)
Fixed Metal Electrode (a) a
b
c
Cantilever Beam
SchematicDevice Cross-section
Figure 1.9 Capacitive accelerometer sandwiched between two glass wafers.
Interdigitated comb drives, which utilize electrode area overlap, can be used to sense
lateral [62] and vertical [63] proof mass displacement via linear capacitance changes.
However, this technique is typically used only for large travel electrostatic displacement
actuation due to its lower inherent sensitivity to the proof mass displacement .
Capacitive sensing is currently the default transduction mechanism for MEMS based
mass/spring accelerometers used in the automotive market [1-3] primarily due to its
relatively low temperature sensitivity.
1.3 MEMS Angular Acceleration and Rate Sensors
Angular accelerometers [10-12, 64] typically employ a capacitive inertial sensor
interface similar to the linear accelerometer described in the previous section. These
angular accelerometers complete the desired mapping of 6 degrees of freedom with
respect to accelerations directed along (linear x,y,z) and about (angular x,y,z) the x,y,z
axes. The major difference between a linear and angular accelerometer is in the proof
mass suspension mode coupling with all other aspects remaining virtually identical. As a
result, significant reuse of technology can be incorporated to fabricate angular
acceleration devices as described in Chapters 4 and 5 of this thesis.

18
Gyroscopes measure angular rate optically or mechanically using either the Sagnac or
Coriolis effects [65], respectively. Currently, the performance of both ring laser and fiber
optic gyroscopes is far superior to that of their mechanical counterparts, but their high
manufacturing cost and size prohibits their use in low cost automotive applications even
in high volume production quantities [66]. As a result, mechanical Coriolis effect
gyroscopes currently dominate 100% of the automotive angular rate sensor market
During the past decade a great deal of research has been performed on MEMS based
vibratory rate gyroscopes (VRG) for intended use in automotive applications. Angular
rate sensors (gyroscopes) have been implemented using vibrating rings [67-69], prismatic
beams [70-74], tuning forks [75-77], and torsion [78, 79] oscillation.
Micromachined processing technologies capable of producing gyroscopes can be
categorized as piezoelectric quartz [6, 7], electroplated nickel [4, 68, 75], bulk silicon
[73, 80], surface micromachined polysilicon [1-3, 5, 8, 76-79], polysilicon trench refill
[63, 69], and silicon on insulator (SOI) [81-83]. Our research is focused on aspects of
both surface and SOI micromachining as these technologies represent the current trend to
fabricate the sensor and CMOS interface integrated circuitry in the same facility. Also,
single chip fusion comprised of sensor and integrated circuitry can be eventually realized
using this methodology.
1.4 Thesis Outline
Chapter 2 introduces the Foucault pendulum as a model for vibratory rate
gyroscopes. The normal mode model is described and several modes of gyroscope
operation are identified. Open and closed loop (force feedback) operation address the
trade-off between angular rate resolution and sensor bandwidth respectively.

19
Chapter 3 describes the various classes and types of vibratory gyroscopes. Examples
from each class are presented with advantages and disadvantages compared from each
configuration. A list of desirable characteristics is presented as a set of design rules for
an enhanced surface micromachined gyroscope.
Chapter 4 introduces the surface micromachined dual anchor gyroscope as a means
to solve many of the challenges listed in Chapter 2. The desire for low cost surface
micromachined gyroscopes required several design and process innovations to increase
both device performance and yield. Device cross sections, process flow, and
characterization results are included. Device models specific to the dual anchor
gyroscope are presented with verification results simulated using ANSYS finite element
analysis (FEA) software.
Chapter 5 describes basic operation of angular accelerometers and provides a model
and characterization results of a surface micromachined dual anchor angular
accelerometer. Model results suggest thicker substrates are required to achieve angular
acceleration sensitivities to satisfy the computer hard disk and automotive markets. This
argument is used as a rationale to develop high aspect ratio angular acceleration sensors
in thick silicon on insulator (SOI) substrates. Characterization results are compared to
theoretical models and finite element analysis (FEA) simulation where applicable.
Chapter 6 describes the capacitive MEMS angular accelerometer and gyroscope
switched capacitor CMOS front end electronic signal conditioning architecture. Noise
rejection at the sensor interface is addressed at the initial capacitance to voltage (C-V)
stage by sampling the differential sensor capacitance values in parallel using a sample

20
and hold technique. Switched capacitor transient simulations are compared to theoretical
transfer functions summarized in this thesis.
Chapter 7 describes the angular accelerometer fabricated in an SOI process flow.
Design enhancements made possible using SOI with a polysilcion/nitride trench refill
process are demonstrated.
Chapter 8 briefly summarizes the body of research included in this thesis and
suggests potential improvements to the demonstrated angular rate and acceleration sensor
designs.

21
CHAPTER 2
VIBRATORY RATE GYROSCOPE PRINCIPLES
Vibrating elastic bodies, like the Foucault pendulum [84], can be used to measure
rotation. The vast majority of micromachined gyroscopes use vibrating mechanical
elements to sense rotation. These vibrating rate gyroscopes (VRG) are angular rate
sensing devices which have no unidirectional rotating parts that would require bearings
and as a result can be easily miniaturized and batch fabricated using micromachining
techniques [85]. Vibratory gyroscopes are based on the transfer of energy between two
normal operating modes of a structure described by Coriolis acceleration. Coriolis
acceleration, named after the French scientist and engineer G. G. de Coriolis (1792-
1843), is an apparent acceleration that arises in a rotating reference frame which is
proportional to the frame’s rate of rotation. MEMS vibratory gyroscopes which utilize
Coriolis acceleration to measure angular rate are typically categorized into one of several
basic classes; vibrating rings [67-69], prismatic beams [71-74], tuning forks [75-77],
and torsion [78, 79] oscillation.
This chapter describes the principles of vibratory gyroscope rotation measurement
using the Foucault pendulum as a reference model. The Foucault pendulum model is
referenced throughout this dissertation providing a consistent explanation as to how
vibratory gyroscopes work and as a comparison between the multiple classes listed
above. The normal mode model provides the theoretical basis to understand and predict
the performance of typical MEMS vibratory gyroscopes. As a result, the normal mode
model will be applied to multiple vibratory gyroscope classes, throughout the remainder
of this thesis, in order to predict angular rate sensitivity and compare different design
implementations.

22
2.1 Foucault Pendulum History
Jean Bernard Leon Foucault (1819-1868), the inventor of the gyroscope in 1852,
demonstrated during the 1851 World's Fair that a pendulum could track the rotation of
the Earth. This work began in 1848 while Leon Foucault was setting up a long and
slender metal rod in his shop lathe. Foucault “twanged" the free end of the singly
clamped rod with an impulse, similar to a strike of a tuning fork, causing it to vibrate at
its natural frequency in a vertical direction. Foucault then slowly rotated the lathe chuck
by 90 degrees and observed no change in the vibration pattern vertical alignment.
Serendipity allowed Leon Foucault to analyze the physical implications of the
vibrating rod oscillation plane, observed to be independent of the lathe chuck base
rotation, and construct a second experiment to test his hypothesis. Subsequently, he set
up a small pendulum in his drill press, started the pendulum into oscillation by hand, and
then rotated the drill press about the earth’s gravity acceleration vector direction. Once
again, the pendulum kept swinging in its original oscillation plane independent of the fact
that its mounting point reference was rotating.
Foucault then spent the next several months constructing a 2 meter long wire
suspended pendulum with a 5 kilogram ball in his cellar workshop. Before the amplitude
of the swing was fully damped he observed that the weight on the end of the pendulum
appeared to rotate clockwise, as noted in Foucault’s journal at exactly two o'clock in the
morning on January 6, 1851 [86]. Foucault hypothesized that the rotation of the earth
must be responsible for the clockwise rotation of the pendulum pattern by analogy to the
rotating drill press in his previous experiment. Now convinced of the rotating reference
frame principle, Foucault constructed a second pendulum with an 11 meter wire in the
Paris Observatory and it also rotated clockwise as predicted due to the earth’s rotation.

23
Foucault publicly demonstrated a 67-meter tall pendulum at the 1851 Paris Exhibition
in the Pantheon - a Parisian church. A stylus was placed under the 28 kg cannon ball
proof mass with sand scattered in a circular pattern to record the pendulum trace over
multiple oscillations. The cannon ball was pulled to one side and held fixed in place with
a string. With much ceremony, the string was ignited and the ball began to describe a
straight (non-elliptical) path in the sand. Within a few minutes, the pendulum had begun
to swing slightly clockwise and the previous narrow straight-line in the sand had widened
to look like a twin-bladed propeller. Foucault described to the crowd of invited guests
and formally trained scientists that the earth rotated "under" his pendulum. As a result,
he provided the empirical evidence for rotation of the earth that had been unsuccessfully
attempted by Copernicus, Kepler, Descartes, Galileo, and Newton during the preceding
three centuries.
In the following year, during 1852, Foucault repeated his pendulum experiment with
a massive spinning weight which he called the gyroscope [87]. He showed that the
gyroscope, just like the pendulum, ignored the local effect of earth rotation.
Foucault’s gyroscope used the relatively constant inertia of a large unidirectional
spinning mass, analogous to the sinusoidal inertia of the pendulum, to maintain the initial
proof mass oscillation plane independent of the earth’s rotating reference frame.
An object will remain either at rest or in uniform motion along a straight line unless
compelled to change its state by the action of an external force. This is normally taken as
the definition of inertia as described by Newton’s first law of motion. Inertia is the
physical property responsible for maintaining the oscillation plane of both the Foucault
pendulum and gyroscope fixed in space while the earth rotates beneath them.

24
2.2 Foucault Pendulum Properties
MEMS vibratory rate gyroscopes do not exhibit the gyroscope property of constant
inertia due to a proof mass spinning with a constant rotation rate. It is therefore
unfortunate that MEMS angular rate sensors are referred to as vibratory rate gyroscopes.
Instead, MEMS vibratory rate gyroscopes operate very similar to the Foucault pendulum
based on their shared properties of bi-directional proof mass oscillation coupled with
displacement angles much smaller than 2π radians.
The Foucault pendulum can be most easily understood by considering a pendulum
that is set into motion at the earth’s north pole. To an observer, who is fixed in space
above the north pole, it appears that the plane of the pendulum swing remains stationary
while the earth rotates [88]. However, an observer standing on the earth at the north pole
would perceive that pendulum precession is occurring at the rotation rate of the earth (Ω
= 360°/day). The apparent force causing the pendulum to precess in a clockwise
direction, as viewed by the observer standing at the north pole, is described by the
Coriolis acceleration vector as shown in Figure 2.1.
North Pole
North Pole
South Pole Fixed Space View Above North Pole
Earth
Rotation
Pendulum
Pendulum
aCoriolis
North Pole
North Pole
South Pole Fixed Space View Above North Pole
Earth
Rotation
Pendulum
Pendulum
aCoriolis
Figure 2.1 Foucault pendulum located at north pole.

25
The periodic path of the pendulum can be used to calculate the earth’s rotation rate
(Ω) via the measured period (τ) and the angular separation between complete precession
cycles (θ) as shown in Figure 2.2. In this mode of operation, called whole angle mode
[89], the pendulum operates as a rate integrating gyroscope.
North Pole
View Above North Pole at t=0
Earth
Rotation
Pendulum
bob
1
2
3
4
5
6
7
θ
8
View observed standing at north pole as
earth rotates from t = 0-2τ, where τ = tB-tA
Pendulum
path
Pendulum
bob
A
B
Ω
Ω×= vaCoriolis 2
τ
θ
=Ω
North Pole
View Above North Pole at t=0
Earth
Rotation
Pendulum
bob
1
2
3
4
5
6
7
θ
8
View observed standing at north pole as
earth rotates from t = 0-2τ, where τ = tB-tA
Pendulum
path
Pendulum
bob
A
B
Ω
Ω×= vaCoriolis 2
τ
θ
=Ω
Observer
Figure 2.2 Foucault pendulum path as interpreted by earth bound observer.
The coupling of the earth’s rotation with the Foucault pendulum, a strong function of
latitude, is based on the magnitude of the Coriolis acceleration. The Coriolis acceleration
vector magnitude and direction are defined by the cross products of the proof mass
velocity vector (v) and rotation rate vector (Ω) of the earth. The 0° latitude at the equator
orients the maximum velocity vector of the pendulum proof mass and the rotation vector
of the earth along a parallel direction resulting in a zero magnitude Coriolis acceleration
vector cross product. The maximum velocity vector of the pendulum proof mass is
tangent to the earth’s surface assuming an idealized uniform gravitational field at sea
level for all latitudes. The coupling of the Foucault pendulum, neglecting surface altitude
and gravitational deviations [90], as a function of latitude is described by the function
plotted in Figure 2.3.

26
Equator
Pendulum
North Pole
South Pole
0 10 20 30 40 50 60 70 80 90
0
90
180
270
360
Pendulumrotation[°/day]
Latitude location of pendulum
Lat 90° N
Lat 0°
Lat 90° S
)sin(
360
latitude
day
=θ
Equator
Pendulum
North Pole
South Pole
0 10 20 30 40 50 60 70 80 90
0
90
180
270
360
Lat 90° N
Lat 0°
Lat 90° S
Equator
Pendulum
North Pole
Equator
Pendulum
North Pole
South Pole
0 10 20 30 40 50 60 70 80 90
0
90
180
270
360
Lat 90° N
Lat 0°
Lat 90° S
)sin(
360
latitude
day
=θ
Figure 2.3 Rotation of Foucault pendulum as a function of latitude.
The coupling of earth’s rotation and the Foucault pendulum produces a clockwise
(CW) and counterclockwise (CCW) rotation as witnessed by a local observer in the
northern and southern hemispheres respectively, as shown in Figure 2.4.
San Francisco
~225°/day CW
Mexico City
~120°/day CW
Ann Arbor
~242°/day CW
Chandler, AZ
~196°/day CW Equator
0°/day
North Pole
360°/day CW
Cape Canaveral
~175°/day CW
South Pole
360°/day CCW
Rio de Janeiro
~120°/day CCW
CW = Clockwise
CCW = Counterclockwise
San Francisco
~225°/day CW
Mexico City
~120°/day CW
Ann Arbor
~242°/day CW
Chandler, AZ
~196°/day CW Equator
0°/day
North Pole
360°/day CW
Cape Canaveral
~175°/day CW
South Pole
360°/day CCW
Rio de Janeiro
~120°/day CCW
CW = Clockwise
CCW = Counterclockwise
Figure 2.4 Foucault pendulum rotation coupling at different locations on earth.

27
2.3 Pendulum Physical Properties
The simple pendulum is described by an idealized model consisting of a proof mass
suspended by a mass-less string of fixed length in a uniform gravitational field. When
the proof mass is pulled to one side of its straight down equilibrium position and
subsequently released it will oscillate along a semicircular path isochronously.
Although the pendulum is not truly a simple harmonic oscillator, enhanced insight
and overall model simplification is afforded by direct comparison to the operation of a
simple mass-spring system. The initial step requires defining the mechanical restoring
forces of the pendulum (FT) and mass-spring (Fx) systems, as shown in Figure 2.5, and
given by Eq. 2.1 and Eq. 2.2 respectively.
m
m
TF
mg
T
θ L
2
xK
2
xKx
xKF xx −=
x
y
1 Degree of freedom pendulum 1 Degree of freedom mass-spring
)sin(θmgFT −=
m
Kx
x =ϖ
Spring
Cartesian
System
Polar
System
r
θ
Equilibrium
position
m
m
TF
mg
T
θ L
2
xK
2
xKx
xKF xx −=
x
y
)sin(θmgFT −=
m
Kx
x =ϖ
Spring
Cartesian
System
Polar
System
r
θ
m
m
TF
mg
T
θ L
2
xK
2
xKx
xKF xx −=
x
y
)sin(θmgFT −=
m
Kx
x =ϖ
Spring
Cartesian
System
Polar
System
r
θ
Equilibrium
position
Figure 2.5 Simple pendulum and mass-spring system oscillators.
)sin()( θθ mgFT −= (2.1)
xKxF xx −=)( (2.2)

28
The pendulum mechanical restoring force is non-linear in nature. However, if the
maximum angle (θ) is small, the small angle approximation can be used to linearize the
pendulum model mechanical restoring force as given by Eq. 2.3.
θθ mgFT −≅)( (2.3)
The pendulum mechanical restoring force can then be converted to linear terms in x
using the relationship θ = x/L as given by Eq. 2.4.
x
L
mg
xFT −≅)( (2.4)
The linearized mechanical restoring force of the pendulum is defined by equating Eq.
2.2 and Eq. 2.4 while solving for Kx as given by Eq. 2.5.
L
mg
Kx ≅ (2.5)
The resonant frequency of a simple mass-spring system is given by Eq. 2.6.
m
Kx
=ϖ (2.6)
As a final step, we substitute Eq. 2.5 into Eq. 2.6 to represent the resonant frequency
of the pendulum in terms of a linearized simple mass-spring system as given by Eq. 2.7.
L
g
≅ϖ (2.7)

29
The period of the linearized pendulum model is then dependent upon the length (L)
and gravity (g) defined by Eq. 2.8.
g
L
πτ 2≅ (2.8)
This results in the familiar relationship that a pendulum’s period (τ) is independent of
mass. This relationship approximates the pendulum motion as simple harmonic and is
valid only for small angle displacements. The linearized simple harmonic model error,
as compared to the accurate non-linear model regarding prediction of τ, is less than 0.5%
for an angular displacement of +/-15 degrees as measured from the pendulum equilibrium
position [91]. Therefore, the approximation is useful where small angle displacements
are prescribed.
All vibratory gyroscopes are based on the transfer of energy between two resonant
modes as a function of Coriolis acceleration. Although the Foucault pendulum is one of
the simplest vibratory gyroscopes, its basic operating principles can be applied to all
Coriolis acceleration based devices. As a result, the following section will address the 2-
D simple harmonic oscillation model of the Foucault pendulum.
2.4 Pendulum Normal Mode Model
Mathematically, the precession of the Foucault pendulum can be modeled as a
function of its normal mode model. The normal mode model consists of a central proof
mass suspended with linear mechanical springs oriented about the x and y axes as shown
in Figure 2.6.

30
m
2
xK
2
xK
Spring
2
yK
2
yK
x
y
z
Ωz
x
y
m
Ω×= vaCoriolis 2
mm
2
xK
2
xK
Spring
2
yK
2
yK
x
y
z
Ωz
x
y
m
Ω×= vaCoriolis 2
Figure 2.6 Foucault pendulum normal mode model.
Vibration theory provides a methodology from which any arbitrary vibration mode of
an elastic body can be modeled in terms of its normal modes [92]. These normal modes
of vibration are uncoupled in the absence of a rotating reference frame. The normal
mode model orients the drive and sense normal modes along the x and y axes
respectively which significantly simplifies the pendulum analysis. The coupled equations
of motion for the Foucault pendulum in the x-y plane [93] are given by Eq. 2.9 and 2.10,
where x(t) and y(t) represent the displacement amplitudes directed along the principal x
and y axes of vibration respectively.
0)(
)(
2
)( 2
2
2
=+Ω− tx
dt
tdy
dt
txd
z ϖ (2.9)
0)(
)(
2
)( 2
2
2
=+Ω+ ty
dt
tdx
dt
tyd
z ϖ (2.10)
The solution to this system of equations is given by Eq. 2.11 and Eq. 2.12.

31
)sin()cos()( ttAtx z ϖΩ= (2.11)
)sin()sin()( ttAty z ϖΩ−= (2.12)
These normal mode solutions predict that the Foucault pendulum will transfer energy
between modes at a precession rate equal to the applied rotation rate about the z-axis.
This analysis assumes that the spring constant for both the x and y axes are equal forcing
the normal mode frequency (ω) to equivalent values for all possible solutions in the x-y
plane. Asymmetries due to variation in spring constant (Kx, Ky), distributed among
individual springs, are neglected in the normal mode model analysis.
Energy transfer in the normal mode model assumes no damping present in the system.
The damping coefficient (b) will be introduced in Chapter 3 as a parametric measurement
of energy loss in the system extracted from the quality factor (Q) which describes the
ratio of the normal mode energy storage/dissipation while excited at resonance (ω).
In a practical system, where the damping coefficient (b) is non-zero, energy must be
continually introduced into the system to maintain a constant drive mode amplitude at, or
near, resonance to compensate for energy dissipation. Damping can be attributed to
multiple factors including viscous damping of the ambient gas surrounding the resonating
proof mass [94], acoustic radiation of energy through the anchor supports [67], and
intrinsic energy dissipation in the resonator structural materials [95] where polysilicon,
single crystal silicon, and quartz represent several typical examples.

32
2.5 Open Loop Normal Mode Model
Applying an excitation signal to maintain drive mode displacement amplitude while
simultaneously monitoring the sense mode displacement amplitude to measure the
angular rate signal is described as the open loop mode [89, 96] as shown in Figure 2.7.
2
xK
2
xKSpring
2
yK
2
yK
x
y
m
x-axis drive
signal applied to
maintain fixed
amplitude at
resonance
y-axis displacement signal
used as parametric
measurement of angular rate
ω
z
Q
x
y Ω
= 2
2
xK
2
xKSpring
2
yK
2
yK
x
y
m
x-axis drive
signal applied to
maintain fixed
amplitude at
resonance
y-axis displacement signal
used as parametric
measurement of angular rate
ω
z
Q
x
y Ω
= 2
Figure 2.7 Open loop angular rate sense operation.
The quality factor (Q) is a function of the proof mass (m), the resonant frequency (ω),
and the damping coefficient (b) as given by Eq. 2.13.
b
m
Q ω= (2.13)
The ratio of x to y axis displacement amplitudes has been modeled as a function of
angular rate for a normal mode gyroscope with damping [96] and is given by Eq. 2.14.
ω
z
Q
x
y Ω
= 2 (2.14)

33
This relationship implies that the secondary mode is amplified by the quality factor
(Q) and inversely proportional to the resonant drive frequency (w). However, when the
pendulum based vibratory gyroscope is operated in open loop mode there is a lag time
associated between the application of an external angular rate and the corresponding y-
axis secondary mode to reach its steady state amplitude [96], as given by Eq. 2.15.
ω
τ
Q2
= (2.15)
The lag time between the externally applied angular rate signal and amplitude build-
up in the y-axis sense direction is the significant bandwidth limiting factor of the open
loop mode. However, the bandwidth can be significantly extended by using forced
feedback to null displacement of the sense mode [89, 96] similar to closed loop
accelerometer operation [2, 97].
2.6 Closed Loop Normal Mode Model
This mode of operation is similar to open loop operation with the additional
constraint that the y-axis amplitude is maintained at zero displacement. As a result, the
long time period (t) required to increase the sense axis amplitude over multiple drive
cycles at resonance (ω) is not required. This method potentially extends the sensor
bandwidth to the resonant drive frequency (ω) where an appropriate force feedback
signal is applied as given by Eq. 2.16.
ω
z
xy QFF
Ω
= 2 (2.16)

34
However, the application of the force feedback signal to null sense mode
displacement causes a control loop oscillation which introduces more system noise than
is observed for the open loop mode. This design trade-off results in an increased sensor
bandwidth with decreased angular rate resolution.
2.7 Summary of Angular Rate Sensor Principles
MEMS based vibratory rate gyroscopes utilize some aspect of the Foucault pendulum
normal mode model with very few potentially noteworthy exceptions [98]. This normal
mode model applies across the macro to micro domains where economy of scale can be
exploited in the latter [94]. Most vibratory rate gyroscope designs use quality factor
amplification to boost the coupled mode angular rate signal. Design trade-offs must be
evaluated dependent upon which method of angular rate measurement is employed. The
methods of angular rate measurement include whole angle, open loop, or closed loop
forced feedback. Typically, MEMS vibratory rate gyroscopes are operated in the open or
closed loop modes. Open loop mode sensing provides a simple and high resolution
measurement technique at the cost of significantly reduced bandwidth. As the quality
factor (Q) increases, angular rate sensitivity increases while bandwidth is decreased. The
closed loop forced feedback mode addresses the bandwidth problem by extending the
usable sensor bandwidth theoretically to near resonant operation frequencies. However,
this technique causes the proof mass to oscillate about the zero displacement position
which introduces intrinsic noise into the detection scheme. As a result, the closed loop
forced feedback technique provides a larger bandwidth, at the expense of reduced angular
rate resolution, when compared to an open loop implementation with identical sensor
configurations. Chapter 3 will describe previously introduced angular rate sensor
designs. Development of design trade-offs with respect to the vibratory rate gyroscope
designed, fabricated, and characterized as a function of this thesis work will be
documented in chapter 4.

35
CHAPTER 3
VIBRATORY RATE GYROSCOPE CLASSES
Vibrating elastic bodies, similar to the Foucault pendulum [84], can be used to
measure rotation. Vibratory rate gyroscopes are based on the transfer of energy between
two normal operating modes of a structure described by Coriolis acceleration. MEMS
vibratory gyroscopes which utilize Coriolis acceleration to measure angular rate are
typically categorized into one of several basic classes; vibrating rings [67-69], prismatic
beams [70-74], tuning forks [75-77], and torsion [78, 79] oscillation.
3.1 Prismatic Beam Vibratory Gyroscopes
A basic MEMS gyroscope can be described by a vibrating rectangular cantilever
beam with identical drive and sense vibratory modes [71, 99] as shown in Figure 3.1.
Drive mode
piezoelectric
transducer
Sense mode
piezoelectric
transducer
ΩzRotation Rate
Sense mode
(Coriolis
response)
vibration
Drive mode vibration
Cantilever beam
substrate anchor
Drive mode
piezoelectric
transducer
Sense mode
piezoelectric
transducer
ΩzRotation Rate
Sense mode
(Coriolis
response)
vibration
Drive mode vibration
Cantilever beam
substrate anchor
Figure 3.1 Rectangular beam vibrating rate gyroscope.

36
The beam dimensions for the drive and sense modes are closely matched to define a
system almost identical to the Foucault pendulum normal mode model. As a result, the
analysis and description of this system is straight forward using an input signal to drive a
fixed amplitude while measuring the secondary mode.
A variation of the rectangular beam gyroscope has been demonstrated using
triangular vibrating beams [74]. Excitation voltage is used to drive the beam into
resonance via a piezoelectric electrode located on one of the three triangular beam faces.
Energy radiated in the form of mechanical displacement to two non-normal modes is
sensed by the remaining two piezoelectric electrodes as a differential voltage signal with
unequal displacement amplitudes representing a non-zero angular rate input, as shown in
Figure 3.2.
Isometric view of beam
Top view in a zero rotation rate field
Drive C
Sense A Sense B Ωz
Sense A Sense B
Rotation rate(t)=B(t)-A(t)
Top view in a non-zero rotation rate field
Energy transfer from drive to sense
modes of triangular beam used to
measure angular rate input signal
Piezoelectric electrodes
Displacement
Drive C
Displacement
B(t)-A(t)=0
Isometric view of beam
Top view in a zero rotation rate field
Drive C
Sense A Sense B Ωz
Sense A Sense B
Rotation rate(t)=B(t)-A(t)
Top view in a non-zero rotation rate field
Energy transfer from drive to sense
modes of triangular beam used to
measure angular rate input signal
Piezoelectric electrodes
Displacement
Drive C
Displacement
B(t)-A(t)=0
Figure 3.2 Murata Gyrostar triangular beam gyroscope.

37
Characterization results of this device, commercially available from Murata,
produced a relatively large change in angular rate sensitivity versus ambient temperature
[100], primarily due to the pyroelectric behavior of piezoelectric materials.
Prismatic beam vibratory rate gyroscopes typically exhibit several additional
problems inherent to the design which significantly limit device performance [65]. These
problems include acoustic energy loss at the beam/substrate anchor interface [67] and the
inability to discriminate between linear axis acceleration, oscillating at or near the sense
mode frequency, and an actual rotation rate signal. Automotive applications typically
experience environmental vibrations in the form of spurious linear axis accelerations up
to 5kHz in frequency. Undesirable linear axis acceleration sensitivity can be reduced by
increasing the vibratory gyroscope’s resonant frequency well beyond the intended sensor
application environment noise frequency range [65].
3.2 Tuning Fork Vibratory Gyroscopes
A design technique to reduce linear acceleration sensitivity of prismatic vibratory
gyroscopes is described by integrating two vibrating prismatic beams driven with anti-
phase displacement amplitude to form a differential Coriolis based angular rate sensor. A
further enhancement is achieved by mounting the vibrating beams to a common base to
form a tuning fork. Tuning forks form a balanced oscillator where no net torque is
transferred to the common base, referred to as the stem, under a zero rotation rate input
[101]. A non-zero angular rate causes Coriolis force induced sinusoidal anti-phase
displacement of the sense tines orthogonal to the drive mode vibration. The angular rate
signal can be measured as a function of differential tine displacement [102], or as a
torsion vibration of the tuning fork stem [103], as shown in Figure 3.3.

38
Ωz Ωz
Drive
Mode
Coriolis
Force
Drive
Mode
Coriolis
Force
Tuning Fork Stem Torque CW Tuning Fork Stem Torque CCW
x
y
z
Ωz Ωz
Drive
Mode
Coriolis
Force
Drive
Mode
Coriolis
Force
Tuning Fork Stem Torque CW Tuning Fork Stem Torque CCW
x
y
z
Figure 3.3 Tuning fork with y-axis drive and x-axis Coriolis coupling about z-axis.
The balanced tuning fork gyroscope is theoretically less sensitive to undesired linear
axis accelerations than the prismatic beam designs, at least to a first order analysis.
However, this design is more susceptible to angular accelerations directed about the input
axis. As a result, tuning fork gyroscope designs are typically operated at a resonant drive
frequency an order of magnitude higher than the application environmental noise to
reduce angular rate sensing errors [104].
When the drive and sense modes of a tuning fork are matched, the normal mode
model describes an increase in the angular rate sensitivity multiplied directly by the
quality factor (Q). However, variation due to wafer processing photolithography and etch
steps typically result in slightly mismatched mass centers with respect to the individual
tines. This mass center variation can manifest itself as a resonant frequency mismatch
between the individual tines [65, 94]. Since unmatched tines exhibit different resonant
frequencies they will require either mass addition/removal near the mass center [105,
106] or electromechanical compensation to ensure anti-phase displacement at a given
drive frequency near resonance. This mode mismatch problem may also be further

39
exacerbated by dependence of resonant frequency upon ambient temperature, typically
ranging from –40C to 125C for automotive applications. As a result, many tuning fork
designs are not based upon matched drive and sense resonant vibration modes.
3.3 Linear Axis Accelerometer Vibratory Gyroscopes
A single linear axis accelerometer can be configured to operate as a vibratory
gyroscope similar in operation to the prismatic beam devices described in section 3.1.
The accelerometer is driven at, or near, resonance along a primary drive axis while an
orthogonal secondary sense mode is used to measure the Coriolis based angular rate
signal.
Single linear accelerometer vibratory gyroscopes have been previously described with
orthogonal drive and sense modes [76, 107] using polysilicon as the resonator structural
material. However, these sensors are unable to discriminate between angular rate and
linear acceleration input signals. Dual accelerometer vibratory gyroscope designs,
similar to the dual tine tuning fork, are able to reject linear acceleration inputs at the
sensor making them better suited for automotive applications.
A dual linear accelerometer vibratory gyroscope design was fabricated by Draper
Labs with nickel as the structural resonator material with metal electrodes formed on a
glass substrate used to drive and measure displacement capacitively [75]. A second
generation of the Draper Labs dual accelerometer tuning fork gyroscope was fabricated
using single crystal silicon as the structural resonator material [108] bonded to the
underlying glass substrate and subsequently released using ethylene diamine
pyrocatechol (EDP) based on the dissolved wafer process [109].

40
Multiple electrostatic comb drives [62] were used to both excite and measure the
primary drive mode frequency of each individual proof mass displaced parallel to the
wafer substrate. Closed loop electrostatic feedback was used to maintain a constant drive
mode displacement amplitude (a0). An external rotation rate (Ω) applied normal to the
drive mode plane causes a Coriolis force based displacement (aCoriolis) of each proof mass
in opposite directions [104] as given by Eq. 3.1.
)sin(2 0 taaCoriolis ωΩ= (3.1)
The Coriolis force based displacement is measured via the parallel plate capacitance
as a function of separation between the proof mass and metal electrodes deposited on the
quartz substrate, as shown in Figure 3.4.
Quartz Substrate
Electrode 1 Electrode 2
Proof
Mass 1
Proof
Mass 1
Z0 Z0
Silicon Silicon
A
A
View A-A: Sensor Cross SectionNickel Sensor Isometric View
AnchorSuspension
Spring
Proof
Mass 1
Proof
Mass 2
Comb
Drive
0
0
0
Z
A
C
ε
=
ZZ
A
C
Δ−
=
0
0εΩ
Ω=0
Drive
Quartz Substrate
Proof
Mass 1
Proof
Mass 1
Z0 Z0
Silicon Silicon
A
A
View A-A: Sensor Cross SectionNickel Sensor Isometric View
AnchorSuspension
Spring
Proof
Mass 1
Proof
Mass 2
Comb
Drive
0
0
0
Z
A
C
ε
=
ZZ
A
C
Δ−
=
0
0εΩ
Ω=0
Drive
Figure 3.4 Dual accelerometer isometric view with capacitive sensor cross section.
First order rejection of linear acceleration is realized by configuring the dual proof
mass capacitance measurement as differential. This differential capacitance
configuration can also be signal conditioned to simultaneously measure both linear

41
acceleration and angular rate signals which may be desirable in many inertial navigation
and automotive applications. A comparison of differential capacitance values
experienced by the dual accelerometer vibratory gyroscope for both angular rate and
linear acceleration inputs is shown in Figure 3.5.
Angular Rate Signal Response
Ω
Ω=0Z1 Z2
a
Z0
Quartz Substrate Quartz Substrate
Linear Acceleration Signal Rejection
2121 CCZZ <⇒>
12 CCC −=Δ
2121 CCZZ =⇒=
0=ΔC
n
n
Z
A
C 0ε
=Center
Position
Mass 1 Mass 2 Mass 1 Mass 2
12 CCC −=Δ
0≠ΔC
Z2Z1
Angular Rate Signal Response
ΩΩ
Ω=0Z1 Z2
a
Z0
Quartz Substrate Quartz Substrate
Linear Acceleration Signal Rejection
2121 CCZZ <⇒>
12 CCC −=Δ
2121 CCZZ =⇒=
0=ΔC
n
n
Z
A
C 0ε
=Center
Position
Mass 1 Mass 2 Mass 1 Mass 2
12 CCC −=Δ
0≠ΔC
Z2Z1
Figure 3.5 Dual accelerometer linear acceleration signal rejection.
Drive mode closed loop electrostatic feedback is typically required to compensate for
signal error due to geometric differences in either the proof mass magnitudes or
suspension spring constants. Mechanical spring coupling can also be used to better
match the dual proof mass displacements. Bosch has demonstrated a dual accelerometer
tuning fork vibratory gyroscope with a mechanical coupling spring between each mass
and its suspension springs [77]. This device was driven into oscillation using Lorentz
forces resulting from an electric current loop located within the magnetic field of a
permanent magnet suspended above the proof masses.
A silicon bulk micromachined gyroscope has been demonstrated by JPL using four
proof masses suspended above a glass wafer substrate by a single support post [110].

42
The major components of this device include the silicon clover leaf shaped vibrating
structure, a quartz baseplate with metal electrodes used to excite and measure proof mass
displacement, and a metal post which is manually epoxy bonded to both the proof mass
and underlying glass substrate [111]. An improvement over this manually epoxy
assembled bulk micromachined gyroscope utilized a two sided anisotropic etch to release
the clover leaf set of four proof masses while simultaneously forming a single crystal
silicon support post [112].
3.4 Torsion Mode Vibratory Gyroscopes
Torsion mode vibratory gyroscopes operate similar to the normal mode model where
energy is transferred from a primary drive mode to a secondary sense mode as a function
of applied angular rate excitation. An early micromachined example was demonstrated
by Draper Labs using a gimbal structure [73]. The gyroscope was driven into torsion at a
frequency of 3 kHz with constant amplitude along a single axis as shown in Figure 3.6.
Ω
Driven
Vibratory
Axis
Sense Vibratory Axis
Fixed Electrodes
Rotation Signal Input Axis
Gyro Element
Ω
Driven
Vibratory
Axis
Sense Vibratory Axis
Fixed Electrodes
Rotation Signal Input Axis
Gyro Element
Figure 3.6 Prismatic beam torsion decoupled mode vibratory rate gyroscope.

43
A two axis surface micromachined gyroscope has been demonstrated using a disc
resonator driven about the z-axis [78]. The disc resonator is suspended above two pairs
of electrodes by four beam springs anchored to the wafer substrate as shown in Figure
3.7.
A A
X-Axis
Electrode
X-Axis
Electrode
y
y
Y-Axis
Electrodes
Ωx
Z-Axis
Resonant
Drive
z
Substrate
Anchors
Z-Axis Torsion
Disc Resonator
Disc
Resonator
Top View of Torsion Disc Resonator View A-A
x
A A
X-Axis
Electrode
X-Axis
Electrode
y
y
Y-Axis
Electrodes
Ωx
Z-Axis
Resonant
Drive
z
Substrate
Anchors
Z-Axis Torsion
Disc Resonator
Disc
Resonator
Top View of Torsion Disc Resonator View A-A
x
Figure 3.7 Two-axis vibrating disc gyroscope.
Capacitive electrodes are used to measure the disc z-axis separation. The electrodes
are oriented in differential pairs along both the x and y axes. An input rotation rate signal
about the x-axis induces a Coriolis acceleration causing the disc to oscillate about the y-
axis as shown in Figure 3.8. Similarly, an input rotation rate signal about the y-axis
induces a Coriolis acceleration causing the disc to oscillate about the x-axis. Different
sense modulation frequencies were used for each of the two sense axes. However, small
micromachined wafer process variations [113] produced devices with well-matched sense
modes with low noise but degraded cross-axis rejection while poorly-matched modes
produced an increase in noise with improved cross-axis rejection. A proposed method to
avoid the trade-off nature of noise versus cross-axis sensitivity was to employ a closed
loop electrostatic feedback loop in future designs.

44
z
x
y
Ωx
z
x
y
Ωx
Coriolis Force
Couple CW
Coriolis Force
Couple CCW
Z-Axis Drive CW Vibration Phase
Z-Axis Drive CCW Vibration Phase
y
y
z
x
y
Ωx
z
x
y
Ωx
z
x
y
Ωx
Coriolis Force
Couple CW
Coriolis Force
Couple CCW
Z-Axis Drive CW Vibration Phase
Z-Axis Drive CCW Vibration Phase
y
y
Figure 3.8 Polysilicon vibrating disc gyroscope Coriolis induced tilt oscillation.
A mechanically decoupled mode torsion vibratory gyroscope has been demonstrated
with improved cross axis rejection. The mechanical sensor consists of an inner drive
wheel, anchored to the substrate with beam springs radiating from a central post,
connected to an outer proof mass by two torsion springs [79] as shown in Figure 3.9.
Substrate
Torsion Primary Drive Mode Torsion Secondary Sense Mode
Dielectric
Sense Electrodes
Anchor
Post
Comb
Drives
Beam
Springs
Coriolis Force Couple
for CCW Drive Phase
Gap
Ωx
x
y
x
z
Torsion Beam
Proof
Mass
Substrate
Dielectric
Sense Electrodes
Anchor
Post
Comb
Drives
Beam
Springs
for CCW Drive Phase
Gap
Ωx
x
y
x
z
Torsion Beam Substrate
Dielectric
Sense Electrodes
Anchor
Post
Comb
Drives
Beam
Springs
for CCW Drive Phase
Gap
Ωx
x
y
x
y
x
z
x
z
Torsion Beam
Proof
Mass
Figure 3.9 Top and side view of decoupled torsion mode vibratory gyroscope.

45
Electrostatic comb drives [62] are used to excite the torsion drive mode about the z-
axis inner disc. Coriolis forces produce a torque in the torsion beam suspended outer
proof mass. The torque displacement is sensed capacitively as a function of separation
between the surface micromachined thick polysilicon proof mass [114] and fixed
substrate electrodes.
3.5 Vibrating Shell Gyroscopes
Tuning fork vibratory gyroscopes utilize the transfer of energy between two normal
modes of operation. These normal modes, although frequency matched, are typically not
identical such as tuning fork tine bending versus stem torsion. Dual accelerometer
designs also exhibit different mode properties in the primary and secondary modes
independent of the matched resonant frequency values. The primary and secondary mode
resonant frequencies may be matched at room temperature while large excursions from
these values may occur, which typically do not track with each other, as temperature is
swept over a –40C to 90C temperature range. In contrast, vibrating shell gyroscopes
transfer energy between two identical primary and secondary vibration modes avoiding
temperature stability problems experienced by tuning fork designs.
Vibrating shell gyroscopes typically have a bell-like structure and may be shaped
either like a wine glass [96, 115], cylinder [116], or ring [68]. The Delco wine glass
shaped hemispherical resonator gyroscope (HRG) was fabricated in fused quartz
suspended by a fixed stem with the vibrating shell rim encapsulated by concentric drive
and sense electrodes as shown in Figure 3.10.

46
Drive
Electrodes
Sense
Electrodes
Node
Anti-nodeRim
Support
Stem
Hemispherical
Resonator
Hemispherical
Resonator
Rim
Fixed
Outer Hermetic
Enclosure
Side View of HRG Resonator Top View of HRG Rim and Fixed Electrodes
Drive
Electrodes
Sense
Electrodes
Node
Anti-nodeRim
Support
Stem
Hemispherical
Resonator
Hemispherical
Resonator
Rim
Fixed
Outer Hermetic
Enclosure
Side View of HRG Resonator Top View of HRG Rim and Fixed Electrodes
Figure 3.10 Wine glass shaped quartz hemispherical resonator gyroscope.
The metal plated HRG shell is excited electrostatically at the resonator natural
frequency by a sinusoidal signal applied to the outer case fixed electrodes. A closed loop
servo is used to maintain the resonator rim amplitude during operation. The cavity
pressure is maintained at near vacuum to avoid both damping and mechanical coupling
between the resonator with respect to the inner and outer case surfaces. The reported
quality factor (Q) for the HRG was greater than 6x106
, with time constants on the order
of 17 minutes in duration. As a result, it is possible to excite the HRG with intermittent
drive signals applied to the shell with 10-15 minute intervals between bursts.
The nodes of a wine glass resonator do not remain stationary in space as compared to
the Foucault pendulum. Instead, the nodal pattern of a vibrating shell will rotate in the
direction of fixed case rotation with a displacement angle coupling of 0.3 times the case
rotation angle [117], as shown in Figure 3.11. As a result, precession of the nodal pattern
relative to the fixed case electrodes can be used to measure the externally applied angular
rate signal.

47
Static Operation of HRG Node Precession of CW Rotated HRG Body
Case Index Point
Case
RotationVibration
Pattern Nodal
Rotation θ
θ3.0
Static Operation of HRG Node Precession of CW Rotated HRG Body
Case Index Point
Case
RotationVibration
Pattern Nodal
Rotation θ
θ3.0
Figure 3.11 Node precession of the HRG with externally applied angular rate signal.
Researchers at General Motors and the University of Michigan have developed a
nickel vibrating ring gyroscope suspended by semicircular beam springs anchored to the
silicon substrate wafer at a common central point [68]. Symmetry considerations require
that at least eight replicated springs are included to balance the device with two identical
drive and sense flexural modes that exhibit near equal natural frequencies [89].
Electrodes were located along the outer perimeter of the resonating ring to provide drive,
sense, and mode tuning capability of the natural frequencies. The ring is electrostatically
excited into an elliptical shaped drive mode vibration pattern with a fixed amplitude.
When subjected to an external rotation rate about its normal axis, Coriolis acceleration
causes energy to be transferred from the primary drive to secondary sense mode as shown
in Figure 3.12. The capacitively monitored sense mode amplitude is proportional to the
applied external angular rate signal. This normal mode gyroscope sensitivity is
proportional to the resonating ring quality factor with values reported greater than 2000.
A polysilicon version of the ring gyroscope demonstrated significant increases in quality
factor and angular rate sensitivity [69].

G_O'Brien PhD Dissertation

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