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 |  موضوع: كتاب MicroSystem Design الأحد 16 مايو 2021, 1:29 am | |
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أخوانى فى الله
أحضرت لكم كتاب
MicroSystem Design
Stephen D. Senturia
Massachusetts Institute of Technology
و المحتوى كما يلي :
Contents
Foreword
Preface
Acknowledgments
xvii
xxi
xxv
Part I GETTING STARTED
INTRODUCTION
What are they?
How are they made?
What are they made of?
How are they designed?
Microsystems vs. MEMS
Markets for Microsystems and MEMS
Case Studies
Looking Ahead
AN APPROACH TO MEMS DESIGN
2.1
2.2
2.3
2.4
Design: The Big Picture
2.1.1
2.1.2
2.1.3
Device Categories
High-Level Design Issues
The Design Process
Modeling Levels
2.2.1
2.2.2
Analytical or Numerical?
A Closer Look
Example: A Position-Control System
Going Forward From Here
MICROFABRICATION
3.1
3.2
Overview
Wafer-Level Processes
3.2.1
3.2.2
Substrates
Wafer Cleaningviii MICROSYSTEM DESIGN
Oxidation of Silicon
Local Oxidation
Doping
Thin-Film Deposition
Wafer Bonding
3.3
3.4
Pattern Transfer
Optical Lithography
Design Rules
Mask Making
Wet Etching
Dry Etching
Additive Processes: Lift-Off
Planarization
Conclusion
4. PROCESS INTEGRATION
A Bulk-Micromachined Diaphragm Pressure Sensor
A Surface-Micromachined Suspended Filament
Moving On
Sample Process Flows
Developing a Process
A Simple Process Flow
The Self-Aligned Gate: A Paradigm-Shifting Process
Basic Principles of Process Design
From Shape to Process and Back Again
Process Design Issues
Part II MODELING STRATEGIES
LUMPED MODELING
Introduction
Conjugate Power Variables
One-Port Elements
5.3.1
5.3.2
5.3.3
5.3.4
Ports
The Variable-Assignment Conventions
One-Port Source Elements
One-Port Circuit Elements
5.4.1 Kirchhoff’s Laws
Circuit Connections in the Convention
Formulation of Dynamic Equations
5.5.1
5.5.2
Complex Impedances
State Equations
Transformers and Gyrators
5.6.1
5.6.2
ImpedanceTransformations
The Electrical Inductor
5.
6. ENERGY-CONSERVING TRANSDUCERSContents ix
Part III DOMAIN-SPECIFIC DETAILS
8.
7. DYNAMICS
Introduction
The Parallel-Plate Capacitor
Charging the Capacitor at Fixed Gap
Charging the Capacitor at Zero Gap, then Lifting
The Two-Port Capacitor
Electrostatic Actuator
Charge Control
Voltage Control
Pull-In
Adding Dynamics to the Actuator Model
The Magnetic Actuator
Equivalent Circuits for Linear Transducers
The Position Control System – Revisited
Introduction
Linear System Dynamics
Direct Integration
System Functions
Fourier Transform
Sinusoidal Steady State
Eigenfunction Analysis
Nonlinear Dynamics
Fixed Points of Nonlinear Systems
Linearization About an Operating Point
Linearization of the Electrostatic Actuator
Transducer Model for the Linearized Actuator
Direct Integration of State Equations
Resonators and Oscillators
And Then There’s Chaos...
ELASTICITY
Introduction
Constitutive Equations of Linear Elasticity
Stress
Strain
Elastic Constants for Isotropic Materials
Other Elastic Constants
Isotropic Elasticity in Three Dimensions
Plane Stress
Elastic Constants for Anisotropic Materials
Thermal Expansion and Thin-Film Stress
Other Sources of Residual Thin-Film Stress
Selected Mechanical Property Data
Material Behavior at Large Strainsx MICROSYSTEM DESIGN
8.5.1 Plastic Deformation
9. STRUCTURES
Overview
Axially Loaded Beams
Beams With Varying Cross-section
Statically Indeterminate Beams
Stresses on Inclined Sections
Bending of Beams
Types of Support
Types of Loads
Reaction Forces and Moments
Pure Bending of a Transversely Loaded Beam
Differential Equation for Beam Bending
Elementary Solutions of the Beam Equation
Anticlastic Curvature
Bending of Plates
Plate in Pure Bending
Effects of Residual Stresses and Stress Gradients
Stress Gradients in Cantilevers
Residual Stresses in Doubly-Supported Beams
Buckling of Beams
Plates With In-Plane Stress
What about large deflections?
ENERGY METHODS
Elastic Energy
The Principle of Virtual Work
Variational Methods
Properties of the Variational Solution
Rayleigh-Ritz Methods
Estimating Resonant Frequencies
Extracting Lumped-Element Masses
11. DISSIPATION AND THE THERMAL ENERGY DOMAIN
Dissipation is Everywhere
Electrical Resistance
Charging a Capacitor
Dissipative Processes
Large Deflections of Elastic Structures
A Center-Loaded Doubly-Clamped Beam
Combining Variational Results with Simulations
The Uniformly Loaded Doubly-Clamped Beam
Residual Stress in Clamped Structures
Elastic Energy in Plates and Membranes
Uniformly Loaded Plates and Membranes
Membrane Load-Deflection BehaviorContents xi
The Thermal Energy Domain
The Heat-Flow Equation
Basic Thermodynamic Ideas
Lumped Modeling in the Thermal Domain
Self-Heating of a Resistor
Temperature Coefficient ofResistance
Current-source drive
Voltage-source drive
A Self-Heated Silicon Resistor
Other Dissipation Mechanisms
Contact Friction
Dielectric losses
Viscoelastic losses
Magnetic Losses
Diffusion
Irreversible Thermodynamics: Coupled Flows
Thermoelectric Power and Thermocouples
Thermoelectric Heating and Cooling
Other Coupled-Flow Problems
Modeling Time-Dependent Dissipative Processes
12.
13.
LUMPED MODELING OF DISSIPATIVE PROCESSES
Overview
The Generalized Heat-Flow Equation
The DC Steady State: The Poisson Equation
Finite-Difference Solution of the Poisson Equation
12.4.1 Temperature Distribution in a Self-Heated Resistor
Eigenfunction Solution of the Poisson Equation
Transient Response: Finite-Difference Approach
Transient Response: Eigenfunction Method
One-Dimensional Example
Equivalent Circuit for a Single Mode
Equivalent Circuit Including All Modes
FLUIDS
What MakesFluids Difficult?
Basic Fluid Concepts
Viscosity
Thermophysical Properties
SurfaceTension
Conservation of Mass
Time Rate of Change of Momentum
The Navier-Stokes Equation
Energy Conservation
Reynolds Number and Mach Number
Incompressible Laminar Flow
Couette Flow
xii MICROSYSTEM DESIGN
Poiseuille Flow
Development Lengths and Boundary Layers
Stokes Flow
Squeezed-Film Damping
13.4.1 Rigid Parallel-Plate Small-Amplitude Motion
Electrolytes and Electrokinetic Effects
Ionic Double Layers
Electroosmotic Flow
Electrophoresis
Diffusion Effects
Pressure Effects
Mixing
Modeling of Electrokinetic Systems
Part IV CIRCUIT AND SYSTEM ISSUES
14. ELECTRONICS
Introduction
Elements of Semiconductor Physics
14.2.1
14.2.2
Equilibrium Carrier Concentrations
Excess Carriers
The Semiconductor Diode
The Diffused Resistor
The Photodiode
The Bipolar Junction Transistor
The MOSFET
Large-Signal Characteristics of the MOSFET
MOSFET Capacitances
Small-Signal Model of the MOSFET
MOSFET Amplifiers
The CMOS Inverter
Large-Signal Switching Speed
The Linear-Gain Region
Other Amplifier Configurations
Operational Amplifiers
14.10 Dynamic Effects
14.11
14.12
Basic Op-Amp Circuits
InvertingAmplifier
Short Method for Analyzing Op-Amp Circuits
Noninverting Amplifier
TransimpedanceAmplifier
Integrator
Differentiator
Charge-Measuring Circuits
14.12.1
14.12.2
Differential Charge Measurement
Switched-Capacitor Circuits397
Contents xiii
15.
16.
FEEDBACK SYSTEMS
Introduction
Basic Feedback Concepts
Feedback in Linear Systems
Feedback Amplifiers
Example: The Position Controller
PID Control
The Effect of Amplifier Bandwidth
Phase Margin
Noise and Disturbances
Stabilization of Unstable Systems
Controllability and Observability Revisited
15.4 Feedback in Nonlinear Systems
15.4.1 Quasi-static Nonlinear Feedback Systems
15.5 Resonators and Oscillators
Simulink Model
The (Almost) Sinusoidal Oscillator
Relaxation Oscillation
NOISE
Introduction
The Interference Problem
16.2.1
16.2.2
16.2.3
Shields
Ground Loops
Guards
Characterization of Signals
16.3.1 Amplitude-Modulated Signals
Characterization of Random Noise
16.4.1
16.4.2
16.4.3
16.4.4
16.4.5
Mean-Square and Root-Mean-Square Noise
Addition of Uncorrelated Sources
Signal-to-Noise Ratio
Spectral Density Function
Noise in Linear Systems
Noise Sources
16.5.1
16.5.2
16.5.3
16.5.4
16.5.5
Thermal Noise
Noise Bandwidth
Shot Noise
Flicker Noise
Amplifier Noise
Example: A Resistance Thermometer
16.6.1
16.6.2
16.6.3
Using a DC source
Modulation of an AC Carrier
CAUTION: Modulation Does Not Always Work
Driftsxiv MICROSYSTEM DESIGN
Part V CASE STUDIES
PACKAGING
Introduction to the Case Studies
Packaging, Test, and Calibration
An Approach to Packaging
A Commercial Pressure-Sensor Case Study
Device Concept
System Partitioning
Interfaces
Details
A Final Comment
A PIEZORESISTIVE PRESSURE SENSOR
Sensing Pressure
Piezoresistance
Analytic Formulation in Cubic Materials
Longitudinal and Transverse Piezoresistance
Piezoresistive Coefficients of Silicon
Structural Examples
Averaging over Stress and Doping Variations
A Numerical Example
The Motorola MAP Sensor
Process Flow
Details of the Diaphragm and Piezoresistor
Stress Analysis
Signal-Conditioning and Calibration
Device Noise
Recent Design Changes
Higher-Order Effects
A CAPACITIVE ACCELEROMETER
Introduction
Fundamentals of Quasi-Static Accelerometers
Position Measurement With Capacitance
Circuits for Capacitance Measurement
Demodulation Methods
Chopper-Stabilized Amplifiers
Correlated Double Sampling
Signal-to-Noise Issues
A Capacitive Accelerometer Case Study
Specifications
Sensor Design and Modeling
Fabrication and Packaging
Noise and Accuracy
Position Measurement With Tunneling Tips
ELECTROSTATIC PROJECTION DISPLAYSContents xv
Introduction
Electromechanics of the DMD Device
Electrode Structure
Torsional Pull-in
Electromechanics of Electrostatically Actuated Beams
M-Test
The Grating-Light-Valve Display
Diffraction Theory
Device Fabrication and Packaging
Quantitative Estimates of GLV Device Performance
A Comparison
A PIEZOELECTRIC RATE GYROSCOPE
Introduction
Kinematics of Rotation
The Coriolis Rate Gyroscope
Sinusoidal Response Function
Steady Rotation
Response to Angular Accelerations
Generalized Gyroscopic Modes
Piezoelectricity
The Origin of Piezoelectricity
Analytical Formulation of Piezoelectricity
Piezoelectric Materials
Piezoelectric Actuation
Sensing with Piezoelectricity
A Quartz Rate Gyroscope Case Study
Electrode Structures
Lumped-Element Modeling of Piezoelectric Devices
QRS Specifications and Performance
A Quantitative Device Model
The Drive Mode
Sense-Mode Displacement of the Drive Tines
Coupling to the Sense Tines
Noise and Accuracy Considerations
Closing Comments
DNA AMPLIFICATION
Introduction
Polymerase Chain Reaction (PCR)
Elements of PCR
Specifications for a PCR System
Microsystem Approaches to PCR
BatchSystem
PCR Flow System
Thermal Model of the Batch Reactor
Control Circuit and Transient Behaviorxvi MICROSYSTEM DESIGN
Thermal Model of the Continuous Flow Reactor
A Comparison
23. A MICROBRIDGE GAS SENSOR
Overview
System-Level Issues
First-Order Device and System Models
Filament Characteristics
Resistance-Control System
A Practical Device and Fabrication Process
Creating the Filament
High-Temperature Bond Pads
Catalyst Coating
Sensor Performance
Demonstration of Hydrogen Detection
Mass-Transport-Limited Operation
Reaction-Rate-Limited Operation
Advanced Modeling
Epilogue
Appendices
A– Glossary of Notation
B– Electromagnetic Fields
Introduction
Quasistatic Fields
Elementary Laws
Electroquasistatic Systems
Magnetoquasistatic Systems
C– Elastic Constants in Cubic Material
References
IndexForeword
Index
Accelerometer
accuracy, 523
Analog Devices, 513
automotive, 18, 22
electromechanics of, 518
fabrication, 520
force-feedback, 398
lumped element model, 499
monolithic, 10
noise, 523, 528
offset, 524
packaged with ASIC, 458
piezoresistive, 474
process for, 87
selection of process for, 86
table of specifications, 516
Acceptor, 354
ionization of, 355
Activation energy, 41
Actuator
electrostatic, 130, 149, 173, 531
magnetic, 139
piezoelectric, 575
Adhesion
loss of in stressed film, 191
unwanted, see Stiction
work of, 287
Adhesives, 88
Air
bulk modulus, 319
viscosity, 350
Airbag, 18
Alignment marks, 94
Aluminum, 11, 83
eutectic with silicon, 44
mechanical properties of, 196
stress, 554
Aluminum nitride, 43
Ammonium hydroxide, 34
Amplifier
bandwidth in feedback system, 407
chopper-stabilized, 510
general properties, 372
operational, 381
Amplitude modulation, 431
Angular momentum, 113
Angular acceleration, 564
Angular velocity, 113
of rotating body, 562
Anneal
drive-in, 40, 81
post-deposition, 45
post-implant, 40
Annealing
in PCR, 607
Anodic bonding, 49, 464
Anticlastic curvature, 218
Antimony, 38
Application-specific integrated circuit (ASIC),
87, 458
Argon, 68
Armature, 139
Arsenic, 38, 39
Ashing, 68
Attractor, 415
Base region, 365
Baseband 1/f noise, 447
Baseband signal, 430
Basin of attractor, 415
Beam
axially loaded, 201
bending of, 207
buckling of, 232
buckling stress, 235
cantilever, see Cantilever
differential equation for, 214
doubly-clamped
variational analysis, 245, 249
doubly-supported, 207678 MICROSYSTEM DESIGN
leveraged bending, 543
nonlinear expression for curvature, 215
pure bending of, 211
statically indeterminate, 203
stress-dominated behavior, 256
stress-stiffening, 544
with varying cross-section, 203
Beam equation
Euler, 228
solution of, 216
Beam support
built-in, 207
clamped, 207
fixed, 207
pinned, 207
pinned on rollers, 207
simple, 207
Bending
produced by piezoelectric film, 577
Bending-dominated behavior, 253
Biaxial modulus, 191, 225
measurement of, 260
Biaxial stress, 190
Bipolar junction transistor (BJT), 31, 365
Black’s formula, 399
Bode plot, 159
Body effect, 369
Body force, 184
on fluid, 324
Body of MOSFET, 366
Boltzmann’s constant, 41, 291
Bond pads
for high temperature, 642
Boron, 38, 81
Boundary conditions
Dirichlet and Neumann, 301
for beam equation, 216
Boundary layer, 332
Boundary-element method, 20
Breakdown voltage of diode, 360
Brittle material, 196
Brownian motion noise, 437
Buckling
of beam, 232
of heated filament, 640
of interim structures, 90
Buffer amplifier, 388
Buffer solution, 345
Built-in potential of diode, 358
Bulk modulus, 189, 191
CAD, 19, 21, 86
Calibration, 24
costs, 454
golden units, 467
of pressure sensor, 490, 492
shifts after packaging, 462
with EPROM, 465
Cantilever, 207, 575
bent by stress gradient, 222
maximum deflection of, 217
tip height due to bending, 227
with deposited stressed film, 224
Capacitance, 111
across transformer, 426
gate-to-drain, 84
junction, 362
of MOSFET, 371
of tilted-plate capacitor, 539
oxide in MOSFET, 368
Capacitance measurement
circuits for, 502
Capacitor, 18
differential, 501
energy when charging, 269
for position measurement, 501
generalized, 110
parallel-plate, 111
parallel-plate actuator, 149, 173, 543
two-port, 129
with moving plate, 125
Capillary, 321
Carrier concentration
equilibrium, 354
Cascode, 381
Catalyst, 12
Channel of MOSFET, 365
Channel-length modulation, 370
Channeling of implanted ion, 40
Chaos, 178
Charge control of actuator, 131
Charge in diffuse double layer, 342
Charge-measurement circuit, 391
Chemical mechanical polishing (CMP), 75
Chemical vapor deposition, 44
low-presssure (LPCVD), 44
plasma-enhanced (PECVD), 45
selective, 640
Chopper-stabilized amplifier, 510
Chromium
electroplating of, 45
Chromium in photomasks, 55
Circuit elements, 103
one-ports, 109
sources, 108
table of conventions, 107
two-ports, 129, 143
Circuit models
rules for constructing, 114
CMOS inverter, 373
Co-energy, 113
of two-port capacitor, 132
of capacitor, 110
of inductor, 123Index 679
of magnetic actuator, 140
Coefficient of friction, 286
Coefficient of thermal expansion, 204, 639
Coercive force, 290
Collector region, 365
Combustible gas sensor, 12
control circuit, 634
fabrication, 639
finite-difference model, 646
packaging, 632
system architecture, 631
Common-mode signal, 427
Competition, 16
Complex impedance, 116
Compliance of spring, 112
Computer-aided design, see CAD
Concentration
of combustible gas, 644
of ionic species, 339
relation to potential, 292
Conductance, 303
Conduction band, 353
Conductivity
electrical, 268
thermal, 274
Conjugate power variables, 104
table of, 105
Conservation of mass, 322
Contact angle, 321
Contacts, 83
to back side of wafer, 80
to silicon diode, 358
Contamination, 88
Continuity equation, 299
for excess carriers, 356
for fluids, 322
for heat, 273
Controllable mode, 164
Controller, 24, 398
Convection, 274
in PCR system, 622
Convolution, 157, 301
Copper, 88
electroplating of, 45
Coriolis force, 563
Correlated double sampling, 511
Correlation of noise sources, 434
Costs, 454
Couette flow, 327, 519
Counter-doping, 38
Critical damping, 156
Cross-axis sensitivity, 525
CrSi alloy, 465
Crystal growth
Czochralksi, 32
float zone, 32
Current density, 268
CVD, see Chemical vapor deposition
Damping constant, 25, 155
Darcy friction factor, 331
Dashpot, 137
Deal-Grove model, 35
Debye length, 340, 348
Decibel, 435
Deep reactive ion etching (DRIE), 69
Demodulation methods, 507
Densification of CVD films, 45
Density
of fluid, 319
of selected materials, 196
Depletion approximation, 358
Design
high-level issues, 18, 26
market-driven, 17, 18
technology-driven, 17, 18
Design issues, 16
Design rules, 54
Development length, 331
Device geometry, 19
Diaphragm, 9, 575
Diaphragm thickness
control of, 92, 482
Die attach, 80, 461, 464
Die separation, 91
for accelerometer, 523
Dielectric loss, 287
Differential control, 405
Differential equations
ordinary, 19
partial, 20
Differential pair, 381
Differentiator circuit, 390
Diffraction theory, 544
Diffusion, 290
dopant, 41
Dt product, 42
effects on electrophoretic separation, 347
magnetic, 289
numerical example, 42
Diffusion constant, 291
dopants in silicon, 41
temperature dependence, 41
Diffusion equation, see Heat-flow equation
Diffusion length, 357
Diffusivity, 300
Diode
circuit symbol, 358
noise model, 440
process for, 79
semiconductor, 357
Dirichlet boundary condition, 301
Displacement
generalized, 105, 112
virtual, 243680 MICROSYSTEM DESIGN
Display
diffractive, 11, 533
projection, 18
reflective, 532
Dissipation, 267
Dissipativeeffects
table of, 272
Distributed load, 207
Disturbance, 24, 398, 409
DMD display, 532
DNA, 12, 606
Donor, 354
ionization of, 355
Doping, 38, 354
averaging over variations of, 477
net, 355
Double helix, 607
Double layer, 340
diffuse, 341
Doxyribonucleic acid, see DNA
Drain, 83, 365
Drift-diffusion equation, 291, 356
Drifts as 1/f noise, 447
Ductile material, 196
Eddy currents, 289
Effort, 105
Eigenfunctions, 216
lumped-element model for, 309
of Euler beam equation, 232
of heat flow equation, 305, 616
Eigenvalue, 161
Eigenvector, 161
Einstein relation, 292, 356
Elastic constants
of anisotropic materials, 191
of cubic material, 192
of isotropic material, 186
of selected materials, 196
of silicon, 192
Elastomer, 197
Electric field, 268, 288
at semiconducor junction, 357
in tilted-plate capacitor, 539
Electrodeposition, 45
Electrokinetic effects, 339
Electroless plating, 46
Electrolyte, 339
Electromagnetic fields, 657
Electromechanical coupling coefficient
piezoelectric, 589
Electromechanical coupling constant, 145
Electromechanics
of beams, 541
of DMD display, 536
Electron concentration
equilibrium, 354
excess, 356
Electron-volt, 354
Electronic charge, 268
Electrons, 38
Electroosmotic flow, 343
Electrophoresis, 344
in electroosmotic flow, 345
Electroplating, 45
Electrostatic potential, 268
Emissivity, 274
Emitter region, 365
Energy
bending, 250
conservation of, 275
elastic, 240, 552
in generalized inductor, 112
in inductor, 123
internal, 275
kinetic, 113
Energy conservation in fluid, 324
Energy density, 240
electrostatic, 242
in plates and membranes, 256
magnetic, 242
strain, 241
Energy domains, 106
thermal, 272
Energy gap, 353
Entrance length, 331
Entropy, 276
Epitaxy, 44
of silicon, 92
Epoxy resin, 50, 464
EPROM, 465
Equivalent circuit, see Lumped-element model
Error in feedback system, 24, 398
Etch stop
dielectric, 67
electrochemical, 66, 92, 483
p+ layer, 67
Etch-rate data source, 58
Etchants
table, 58
Etching, 5
deep reactive ion (DRIE), 69
plasma, 68
table of gases for, 68
reactive-ion, 69
vapor, 68
wet anisotropic, 61
wet isotropic, 57
Ethylene diamine pyrochatecol (EDP), 61
convention, 106, 114
Euler beam equation, 228, 541
Euler buckling limit, 235
Eulerian method for fluids, 322
Evaporation, 42Index 681
Excess carriers, 355
generation in space-charge layer, 360
generation of, 356
Extension during PCR cycle, 608
Fabrication technologies, 27
Faraday’s law, 289
Feed-forward compensation, 406
Feedback, 24, 27
differential, 406
in nonlinear system, 411
integral, 405
Feedback amplifiers, 399
Feedback system
block diagram, 397
for control of PCR reactor, 619
Field-emission tip fabrication, 74
Finite-difference method, 20, 301
Finite-element method, 20, 245
Fixed point, 416
of nonlinear system, 164
Flexural rigidity, 221
Flicker noise, 440
Flow, 105
Couette, 327
electroosmotic, 343
plug, 344
Poiseuille, 328
pressure-driven, 328
Flow stress, 197
Force on walls bounding a flow, 330
Forced response of system, 156
Foundries, 455
Fourier transform, 216
connection to Laplace transform, 157
Fourier’s Law of heat conduction, 274
Fracture, 197
Fracture mechanics, 287
Fraunhofer diffraction, 547
Frequency modulation, 430
Frequency response of linear system, 159
Friction
contact, 286
Coulomb, 287
convention, 107
Gallium arsenide, 30
Gas constant, 319
Gate, 83
self-aligned polysilicon, 84
Gate oxide, 83, 365
Glass, 11
thermal conductivity, 624
Glass-frit bonding, 49, 464
Global fixed point, 164
Glossary of notation, 651
GLV display, 533, 544
fabrication, 548
packaging, 549
Gold, 88, 642
electroplating of, 45
eutectic with silicon, 44
thermocompression bonding of, 50
Grating light valve display, see GLV display
Gravity body force on fluid, 324
Gray scale
of DMD display, 532
of GLV display, 534
Green’s function, 301
Ground loop, 428
Grounds
potentials between, 427
Guard ring, 430
Guards, 429
Gyrator, 118
in model of electrical inductor, 122
Gyroscope, see Rate gyroscope
Hardening at large strains, 197
Hardware-description language (HDL), 26
HDL convention, 108
Heat capacity, 273
Heat conduction
Fourier’s Law, 274
Heat energy, 272
Heat flux, 273
Heat of reaction, 644
of combustible gas, 637
Heat-flow equation, 275, 299
Helmholtz planes, 341
High-Aspect-Ratio Microstructures (HARM),
46
Hole concentration
equilibrium, 354
excess, 356
Holes, 38, 354
Holes through a wafer, 67
with DRIE, 71
Homogeneous solution, 216
of Euler beam equation, 233
Hooke’s Law, 112, 189
Huygen’s Principle, 545
Hydraulic diameter, 331
Hydroflouric acid, 34, 58, 61, 642
buffered, 97
Hydrogen
detection of, 643
sensing of, 632
Hydrogen peroxide, 34
Hysteresis
in catalytic reactions, 646
magnetic, 289
Impedance parameters for transducer, 144
Impedance transformation682 MICROSYSTEM DESIGN
with transformers and gyrators, 119
Impedance transformation factor, 144
Implant dose, 82
Impulse function, 157, 247
Impulse response, 157, 301
of heat-flow equation, 307
Incompressible laminar flow, 326
Incompressible material, 189
Inductance of electrical inductor, 123
Inductor
electrical, 120
generalized, 112
Inertance, 112
Information in signal, 430
Injection of minority carriers, 359
Ink-jetprinting, 18
Insulation of metal layers, 45
Integral control, 405
Integrator circuit, 389
Interconnect
two-level, 549
Interfering signals, 425
Internal energy, 275
Intrinsic carrier concentration, 354
Inversion layer, 366
Inverting amplifier, 384
Ion dose, 38
Ion implantation, 38
Ion milling, 68
Irreversible process, 271
Jacobian, 166, 171
Johnson noise, 437
Joule heating, 269
lumped model, 634
of filament, 632
of silicon resistor, 282
Junction, 357
Junction depth, 42, 82
Junction isolation, 363
Kinematic viscosity, 318
Kinetic energy, 243
from trial solution, 261
Kirchhoff’s Laws, 114
Known good die, 455
Knudsen number, 333, 558
L-U factorization, 303
Lamé constants, 188
Laminar flow, 325
Laplace equation, 269, 339
Laplace transform, 116, 152, 216, 307
connection to Fourier transform, 157
of impulse response, 336
Laser trimming, 465
Lattice, 30
Lead zirconate titanate (PZT), 46
Lift-off, 71
LIGA, 46
Limit cycle, 150, 178, 414
Limiter, 416
Linear system dynamics, 150
Linear transducer two-port model, 143
Linearization, 142, 145, 165
Lithography, 5
double-sided, 56
effect of misalignment, 55
electron-beam, 55
misalignment, 84
optical, 50
proximity, 52
scanning projection, 53
soft, 56
step-and-repeat projection, 52
systematic errors in, 53
Load-deflection behavior, 249
of beam with residual stress, 255
of doubly-clamped beam, 253, 254
of membrane, 259
of plate, 257
LOCOS, 37
Loop transmission, 408
Loss factor, 288
Lumped elements, 104
one-ports, 109
two-port, 118
Lumped-element model
accelerometer, 498
Couette flow, 328
for heat-flow problems, 311
linear transducer, 144
of heated filament, 634
PCR batch reactor, 618
PCR continuous-flow system, 623
piezoelectric rate gyroscope, 588
Poiseuille flow, 330
thermal domain, 278
values for PCR batch reactor, 618
M-Test, 544, 552
Mach number, 326
Macro-model, 20
Magnetic circuit, 121
Magnetic diffusion, 289
Magnetic field, 121
Magnetic flux, 121
in magnetic actuator, 140
Magnetic hysteresis, 290
Magnetic materials, 290
Magnetic permeability, 121
Magnetomotive force, 121
Majority carrier, 268
Manifold Absolute Pressure Sensor(MAP), 460,
481Index 683
specifications, 460
Manufacturing, 16
Maple, 13, 248
Market, 16
automotive, 18
development of, 17
starving, 17
Mask alignment targets, 90
Mask polarity, 82
Masks, 19, 50
curved features in, 56
fabrication of, 55
for anisotropic etching, 62
for diode, 80
for pressure sensor, 95
low-cost method for, 56
Mass, 25
from variational solution, 263
of actuator, 137
Material derivative, 323
Material properties, 19
dependence on process conditions, 45
Materials, constitutive properties, 7
MATLAB, 13, 21, 303
MATLAB commands
bode,160
eig, 161
freqs, 160
ode, 173
rlocus, 401
roots,167
Mean free path, 558
Mean-square noise, 434
Mechanical properties of selected materials, 196
Membrane, 236
Membrane equation
solution of, 236
MEMCAD, 86
MEMS, see Microsystems
Meniscus, 321
Mesh, 245
Mesh refinement, 247, 304
Metal
evaporation of, 42
insulation of, 45
sputtering of, 43
Metal-Oxide Field-Effect Transistor, see MOSFET
Metallization, 83
Microelectromechanical systems, see Microsystems
Microfabrication, 5
Micromachining, 5
bulk, 9, 11, 29, 59, 92, 481, 578, 612
of glass, 614
surface, 10, 11, 29, 60, 97, 520, 548
material systems for, 60
Microrocket, 317
Microsystems, 3
categories, 15
design of, 7
examples, 9
fabrication, 5
integrated, 6
markets, 8
materials, 6
Microturbine, 71
Microturbomachinery, 317
Miller indices, 30
Minority carrier lifetime, 356
Minority carriers, 356
Mirror, 18
Mixed boundary conditions, 301
Mixing
in fluid channel, 348
Mobility, 268
electron, 356
electrophoretic, 344
Modeling, 18, 19, 22, 86
lumped-element, 103
Modeling levels, 19, 23, 27
device, 20, 26
physical, 20, 21
process, 19
system, 19
Models
algebraic, 21
analytical, 21
in support of design, 19
Modulation methods for noise reduction, 446
Molecular weight, 319
Moment, 184, 208
due to deposited film, 225
Momentum, 113
generalized, 105
MOS technology, 31
MOSFET, 83
circuit symbols, 366
incremental model, 371
large-signal characteristics, 367
Navier-Stokes equation, 324
with electric field, 343
Negative resistance, 269
Neumann boundary condition, 301
Neutral axis, 212
Newtonian fluid, 318
Nickel
electroplating of, 45
No-slip boundary condition, 329, 343
Noise, 24, 27
1/f, 440
accelerometer, 439, 450
amplifier, 441
Brownian motion, 500684 MICROSYSTEM DESIGN
current, 440
diffusion, 450
impact on system design, 466
in bipolar transistors, 444
in diode, 440
in feedback system, 398, 409
in linear system, 435
in MOSFET, 441
in pressure sensor, 492
in rate gyroscope, 602
in resistor, 437
on capacitor, 439
random, 425
Noise bandwidth, 438
Noise factor, 442
Noise figure, 442
Noninverting amplifier, 387, 400
Nonsaturation of MOSFET, 368
Normalization
of eigenvector, 161
Notation
glossary, 651
symbol conflicts, 106, 114
npn transistor, 365
Nucleic acid, 606
Nucleotide, 606
Numerical prototyping, 21
Numerical simulation, 253
Observable mode, 164
Offset of pressure sensor, 491
Offset voltage of op-amp, 383
Ohm’s Law, 110, 267, 289
Ohmic contacts, 80
Onsager relations, 293
Operating point, 164
Operational amplifier
frequency response, 383
input offset voltage, 383
short method for analyzing, 387
symbol, 381
transfer function, 382
Optoelectronic devices, 30
Ordinary differential equations, see Differential
equations, ordinary
Oscillation, 150, 164
Oscillator, 178, 413
SIMULINK model of, 417
marginal, 419
relaxation, 420
to drive rate gyroscope, 597
Overdamped system response, 156
Overlap capacitance, 371
Overshoot of step response, 156
Oxidation
dry, 35
local, 37
numerical example, 36
wet, 36
Oxygen plasma, 68
Packaging, 22, 87
at wafer level, 91, 455
costs, 454
guidelines, 455
next-level, 466
two-chip, 88
wafer-level, 464
Paradigm shift, 16, 17
Parallel connection of circuit elements, 114
Partial differential equations, see Differential
equations, partial
Particular solution, 216
Partitioning, 86
of process, 88
system, 87, 457, 461
two-chip, 458
Passivation
electrochemical, 66
PCR, 11, 606
batch reactor, 611
continuous flow reactor, 614
cycle time, 611
system specifications, 610
PDMS, 56
Peak detector, 507
Peel force, 191
Pellistor, 629
Peltier coefficient, 293
Pendulum, 165
Permalloy
electroplating of, 45
Permanent magnets, 290
Phase angle, 159
Phase margin, 408
Phase modulation, 430
Phosphine, 640
Phosphorus, 38, 39, 81
Photoconductivity, 364
Photocurrent, 364
Photodiode, 364
Photolithography, see Lithography
Photomasks, see Masks
Photoresist
as masking layer for implant, 38
deposition of, 50
electron-beam, 56
negative, 52
positive, 52
removal of, 68
spin casting of, 46
SU-8, 76
Physical vapor deposition, 42
PID control, 405
Piezoelectric bimorph, 577Index 685
Piezoelectric coefficients, 572
Piezoelectric materials
table of properties, 573
Piezoelectricity, 11
analytical formulation, 571
origin of, 570
Piezoresistance
in cubic materials, 471
in polysilicon, 475
nonlinearity of, 471
numerical example, 480
physical origin, 470
Piezoresistive coefficients
general, 472
longitudinal, 473
silicon, 473
transverse, 473
Piezoresistive tensor, 472
Piezoresistors, 9, 48, 92
picture frame design, 493
placement on diaphragm, 476
self-heating of, 282
Xducer, 481
Pirhana, 34
Planar technology, 29
Planarization, 74
with polymers, 76
with resist etchback, 76
Plane stress, 190
Plane wave, 545
Plant, 397
Plasma, 42
Plastic deformation, 197
Plate modulus, 220
Plates
bending of, 219
with in-plane stress, 235
Platinum, 12
as catalyst, 640, 642
Plug flow, 344
PMMA, 56
pn junction, 42
pnp transistor, 365
Point load, 207
Poiseuille flow, 328
Poisson equation, 300, 339
finite-difference solution, 301
Poisson ratio, 187
of selected materials, 196
Polarization
dielectric, 288, 570, 657
Pole of system function, 116, 155
Pole-zero diagram, 156
poly(phenylene sulfide) (PPS), 464
poly(dimethylsiloxane) (PDMS), 56
Polyimide, 46, 50, 76
biaxial modulus, 195
thermal expansion coefficient, 195
Polymer, 46
in DRIE process, 69
Polymerase, 610
Polymerase chain reaction, see PCR
Polymers, 88
poly(methylmethacrylate) (PMMA), 56
Polysilicon, 12, 97
mechanical properties of, 196
temperature coefficient of resistance, 636
thermal conductivity, 636, 649
Port
of lumped element, 106
sign conventions, 107
Position control system, 24, 145, 498
as feedback system, 400
Position measurement, 500
with tunneling tips, 525
Position sensor, 24
Potassium hydroxide, 61, 92
Potential energy
from trial solution, 261
total, 244
Potential energy stored in capacitor, 110
Power dissipation
in Couette flow, 328
in fluid, 318
Joule heating, 269
Pressure, 208
due to surface tension, 320
effective on bent stressed beam, 228
sensing methods for, 469
Pressure sensor
circuit for, 488
improvements in, 493
integrated, 9
monolithic, 10, 458
Piezoresistive, 483
process for, 92, 481
stress analysis of, 485
trim procedure, 490
Primer
in PCR, 607
Principal axes, 190
Principle of Virtual Work, 243
Process, 19
additive, 42, 71
back side of wafer, 87
back-end, 88
design principles, 79, 85
for accelerometer, 520
for combustible gas sensor, 639
for diode, 80
for grating light valve display, 548
for PCR batch reactor, 614
for PCR continuous flow reactor, 614
for pressure sensor, 92, 481686 MICROSYSTEM DESIGN
front-end, 88
lift-off, 71
subtractive, 57
thermal constraints, 88
Process bias, 54, 90
Projected range, 38
in photoresist, 39
in silicon dioxide, 39
standard deviation of, 40
Proof mass, 10, 218
Proportional control, 405
Pull-in, 134, 168
torsional, 537
Pull-in voltage, 135
of beam, 543
of DMD display, 540
Pyrex, 49
Quality factor, 156
Quartz, 11, 30
amorphous, 55
anisotropoic wet etching of, 61
cuts of, 34
mechanical properties of, 196
piezoelectric coefficients, 574
stiffness matrix, 574
table of properties, 573
Radiation, 274
Radius of curvature, 212
of cantilever-film composite, 226
Rate control, 405
Rate gyroscope, 11, 150
coupling to sense mode, 599
disk, 567
model parameters, 594
principle of, 563
quartz, 578
specifications for, 593
tuning fork, 567
wine glass, 568
with angular acceleration, 567
with steady rotation, 566
Rayleigh-Ritz method, 261, 551
RCA cleans, 34
Reaction force, 205, 208
Reaction moment, 209
Reaction rate
mass-transport limited, 644
reaction-rate limited, 645
Reciprocal transducer, 144
Recombination, 356
in space-charge layer, 360
Reduced-order model, 20
Release etch, 60
Reliability, 458
testing for, 467
Reluctance, 121
Remanent flux density, 290
Residual stress, 196, 222, 226
in clamped structures, 255
measurement of, 259
of GLV beam, 551
of selected materials, 196
Resistance
electrical, 267
of fluid channel, 345
of resistor, 268
temperature coefficient (TCR), 279
Resistance thermometer
for combustible gas sensor, 630
noise in, 442
Resistor
diffused, 363
generalized, 109
self-heating, 278
trimmable, 465
Resonant frequency
damped, 156
from Rayleigh-Ritz method, 261
of doubly-clamped beam, 262
shift from squeezed-film damping, 338
undamped, 155
Resonator, 178, 413
Reynolds equation, 333
linearized, 335
Reynolds number, 325
Reynolds transport theorem, 323
Ringing in system response, 156
Root locus, 401
Root mean-square noise, 434
Rotation
kinematics of, 561
of rigid body, 185
Rotation rate, 562
Routh test, 403
Rubber, 197
s-plane, 116
Sacrificial layer, 60
Saturation of MOSFET, 368
Second-order system, 117
Seebeck coefficient, 293
Self-assembled monolayer, 56
Self-heating, 278
finite-difference example, 303
in combustible gas sensor, 630
numerical example, 285
of piezoresistor, 282
with current-source, 279
with voltage source, 281
Semiconductor conductivity, 268
Semiconductor diode, 357
Sensitivity analysis, 90
Separation by electrophoresis, 344Index 687
Series connection of circuit elements, 114
Set point, 24, 398
Shape memory
in viscoelastic materials, 198
Shear force, 209
in fluid, 318
Shear modulus, 188
Shear strain, 188
Shear stress, 188
at wall, 328
Shield
electrostatic, 427
magnetic, 428
Shift invariance, 157
Shot noise, 439
Sidebands
due to angular acceleration, 567
of AM modulated waveform, 431
Signal-to-noise ratio, 434
in accelerometers, 500
in capacitance measurement, 512
Silica
fused, see Quartz, amorphous
Silicon, 5, 9
anisotropic wet etching of, 61
boron-doped as etch mask, 65
charge carriers in, 38
CVD of, 44
density of, 283
elastic constants, 192
electron mobility, 356
energy gap, 354
epitaxy of, 45
etch rate of p+ in KOH, 65
etch rates in KOH, 65
heat capacity of, 283
hole mobility, 356
intrinsic carrier concentration, 354
mechanical properties of, 196
oxidation of, 34
p-type, 38
permittivity, 358
piezoresistive coefficients, 473
polycrystalline, see Polysilicon
resistivity of, 282
single-crystal, 30
specific heat, 636
TCR of, 283
thermal expansion coefficient, 195, 639
Silicon dioxide, 35, 58, 92, 640
as masking layer for implant, 38
captured, 97
CVD of, 44, 97
etch rate in KOH, 65
mechanical properties of, 196
permittivity, 368
sputtering of, 43
thickness increase, 37
voids in, 45
Silicon nitride, 11, 58, 640
as etch mask for KOH, 92
as etch stop, 67
as masking layer for implant, 38
CVD of, 44
etch rate in KOH, 65
mechanical properties of, 196
silicon-rich, 60, 67
stress, 554
Silicon on insulator, 48
Silicone, 50
Silicone gel, 461, 464, 465
Silicone rubber, 56
Simulation, 20
of fluid damping, 520
SIMULlNK, 13, 21, 24, 26
model of electrostatic actuator, 173
CMOS inverter, 377
Sinter of aluminum, 83
Sinusoidal steady state, 158
Sol-gel deposition, 46
Solder, 50, 467
Source, 83
Source follower, 381
Source region, 365
Space-charge layer, 358
Sparse matrices, 303
Spectral density function, 435
Spectrum of amplitude modulated signal, 433
Spherical wave, 545
SPICE, 26, 304
Spin casting, 46
Spin-on glass, 46
Spindt process, 74
Spring, 25, 112
Duffing, 253, 254
torsional, 537
Spring constant
of axially loaded beam, 202
of cantilever, 217
of doubly-supported beam, 230
of GLV beam, 551
of membrane, 237
with pressure load, 542
Spring-mass-dashpot system, 25, 26, 114
Spring-softening, 168
Squeeze number, 337
Squeezed-film damping, 137, 332, 520
cutoff frequency, 337
damping constant, 337
equivalent circuit, 337
of GLV display, 557
transfer function for, 335
Stability
of feedback system, 403688 MICROSYSTEM DESIGN
of fixed point, 165, 166
of interim structures, 90
Stability analysis, 134
State equations, 19, 117
direct integration of, 151
of linear system, 151
State variables, 19, 117
Static equilibrium, 184
of differential beam element, 211
Steady state
DC, 116
sinusoidal, 158
Stefan-Boltzmann constant, 274
Stiction, 60, 287
Stiffness coefficients, 192
Stiffness of spring, 112
Stokes flow, 332
Strain
axial, 202
bending, 246, 251
biaxial, 190
definition, 185
in bent beam, 212
in bent cantilever, 217
shear, 188
thermal, 204
uniaxial, 185
Strain energy
bending, 246
definition, 241
of bent beam, 252
Stress
averaging over variations of, 477
axial, 202, 204
balance of thin-film, 92
biaxial, 190
buckling threshold of beam, 235
control of in thin films, 47
definition, 184
flow, 197
in bent beam, 212
in bent cantilever, 217
in doubly-supported beam, 226
in thin films, 195
normal, 184
shear, 184
thermal, 204
thin-film, 87, 89
yield, 197
Stress concentration, 191
Stress gradient, 222
Stretching contribution to energy, 250
Stretching-dominated behavior, 253
Stringer, 74
Subsystem, 22
Sulfuric acid, 34
Superposition, 157
SUPREM, 39, 42
Supttering, 42
Surface concentration, 82
Surface tension, 320
Suspended filament
process for, 97
Switched-capacitor circuit, 393
Switching speed
of CMOS inverter, 376
Synchronous demodulator, 507
System
dissipative, 164
linear, 149
linear time-invariant, 157
nonlinear, 149
dynamics of, 164
time-invariant, 157
System architecture, 22, 26
System function
poles and zeros of, 155
System interfaces, 458
System partitioning, 22, 26, 457, 461
Technology, 16
development of, 17
Technology CAD (TCAD), 19
Temperature coefficient of resistance (TCR), 279
Temperature compensation
of offset, 492
of span, 490
Tension, 229
TEOS, 640
Terminals
of circuit elements, 103
Test costs, 454
Tetramethyl ammonium hydroxide (TMAH), 61
Thermal conductivity, 274
Thermal convention, 108, 277
Thermal energy domain, 272
Thermal expansion, 193
Thermalexpansioncoefficient
of selected materials, 196
Thermal noise, 436
Thermal stress, 226
Thermal time constant
of PCR batch reactor, 617
of PCR continuous-flow reactor, 621
Thermal voltage, 292
Thermistor, 279
Thermocouples, 293
Thermodynamics
First Law, 271, 275
irreversible, 291
Second Law, 271, 276
Thermoelectric heating and cooling, 295
Thermoelectric power, 293
Thermometer
resistance, 442Index 689
Thermoplastic, 464
Thin-film deposition, 5, 42
Threshold voltage of MOSFET, 366
Titanium, 642
Titanium nitride, 83, 642
Titanium-tungsten alloy, 83
Torque, 184
Tough material, 197
Transconductance, 371
Transducer model
of linearized actuator, 169
Transducers, 125
energy-conserving, 144
linear, 142
Transduction methods, 26
Transfer function, 116
Transformer, 118
Transient response
lumped model for
from eigenfunctions, 307
from finite difference method, 307
Transimpedance amplifier, 388
Transistor circuit symbols, 365
Translation of rigid body, 186
Trial solution, 216
for membrane equation, 236
in variational method, 244
Trim, see Calibration
Trim technology, 465
Triode region of MOSFET, 368
Tungsten, 44
thermal expansion, 639
Turbulent flow, 326
Uncontrollable mode, 163
Undercut of mask feature, 57, 63
Underdamped system response, 156
Unit cell, 30
silicon, 31
Unobservable mode, 163
Unstable system
stabilization with feedback, 410
Valence band, 353
Variational methods, 244
accuracy of, 247, 249
Velocity of sound, 326
Verification, 21, 23
Vias, 83
Vibration, 24
Virtual work, 243
Viscoelasticity, 198, 288
Viscosity, 318
of gas, 558
Voids, 45
from interdiffusion, 83
Voltage control of actuator, 132
Voltage follower, 388
Wafer architecture, 91
Wafer bonding, 5, 47
of glass, 11
with adhesive layers, 49
with glass frit, 49
with sealed cavities, 48
Wafer cleaning, 34
Wafer sizes, 30
Wafers
identification by flats, 34
quartz, 34
specifications of, 32
Wall charge, 342, 344
Water
bulk modulus, 319
coefficient of thermal expansion, 319
mass density, 617
specific heat, 617
surface tension, 322
thermal conductivity, 617
viscosity, 350
Wheatstone bridge, 449
of piezoresistors, 477
Wire bonding, 80, 461, 465
Xducer, 481
Xenon diflouride, 61, 68, 548
Yield stress, 197
Young’s modulus, 187
for composite structure, 226
of selected materials, 196
Zero of system function, 116, 155
Zero-input response, 153
Zero-state response, 153
Zeta potential, 342
Zinc oxide, 43
piezoelectric coefficients, 575
stiffness matrix, 574
table of properties, 573
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