9780792372462

Microsystem Design

by
  • ISBN13:

    9780792372462

  • ISBN10:

    0792372468

  • Format: Hardcover
  • Copyright: 2000-11-01
  • Publisher: Kluwer Academic Pub

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Summary

The goal of this book is to bring together into one accessible text the fundamentals of the many disciplines needed by today's engineer working in the field of microelectromechanical systems (MEMS). The subject matter is wide-ranging: microfabrication, mechanics, heat flow, electronics, noise, and dynamics of systems, with and without feedback. Because it is very difficult to enunciate principles of 'good design' in the abstract, the book is organized around a set of Case Studies that are based on real products, or, where appropriately well-documented products could not be found, on thoroughly published prototype work. The Case Studies were selected to sample a multidimensional space: different manufacturing and fabrication methods, different device applications, and different physical effects used for transduction. The Case Study subjects are: the design and packaging of a piezoresistive pressure sensor, a capacitively-sensed accelerometer, a quartz piezoelectrically-driven and sensed rate gyroscope, two electrostatically-actuated optical projection displays, two microsystems for the amplification of DNA, and a catalytic sensor for combustible gases. This book is used for a graduate course in 'Design and Fabrication of Microelectromechanical Devices (MEMS)' at the Massachusetts Institute of Technology. It is appropriate for textbook use by senior/graduate courses in MEMS, and will be a useful reference for the active MEMS professional. Each chapter is supplemented with homework problems and suggested related reading. In addition, the book is supported by a web site that will include additional homework exercises, suggested design problems and related teaching materials, and software used in the textbook examples and homework problems.

Table of Contents

Foreword xvii
Preface xxi
Acknowledgments xxv
Part I GETTING STARTED
Introduction
3(12)
Microsystems vs. MEMS
3(5)
What are they?
3(2)
How are they made?
5(1)
What are they made of?
6(1)
How are they designed?
7(1)
Markets for Microsystems and MEMS
8(1)
Case Studies
9(3)
Looking Ahead
12(3)
An Approach to MEMS Design
15(14)
Design: The Big Picture
15(4)
Device Categories
15(1)
High-Level Design Issues
16(1)
The Design Process
17(2)
Modeling Levels
19(5)
Analytical or Numerical?
21(1)
A Closer Look
22(2)
Example: A Position-Control System
24(2)
Going Forward From Here
26(3)
Microfabrication
29(50)
Overview
29(1)
Wafer-Level Processes
30(20)
Substrates
30(4)
Wafer Cleaning
34(1)
Oxidation of Silicon
34(3)
Local Oxidation
37(1)
Doping
38(4)
Thin-Film Deposition
42(5)
Wafer Bonding
47(3)
Pattern Transfer
50(27)
Optical Lithography
50(4)
Design Rules
54(1)
Mask Making
55(2)
Wet Etching
57(10)
Dry Etching
67(4)
Additive Processes: Lift-Off
71(3)
Planarization
74(3)
Conclusion
77(2)
Process Integration
79(24)
Developing a Process
79(6)
A Simple Process Flow
79(4)
The Self-Aligned Gate: A Paradigm-Shifting Process
83(2)
Basic Principles of Process Design
85(6)
From Shape to Process and Back Again
85(1)
Process Design Issues
86(5)
Sample Process Flows
91(7)
A Bulk-Micromachined Diaphragm Pressure Sensor
92(5)
A Surface-Micromachined Suspended Filament
97(1)
Moving On
98(5)
Part II MODELING STRATEGIES
Lumped Modeling
103(22)
Introduction
103(1)
Conjugate Power Variables
104(2)
One-Port Elements
106(8)
Ports
106(1)
The Variable-Assignment Conventions
106(2)
One-Port Source Elements
108(1)
One-Port Circuit Elements
109(5)
Circuit Connections in the e→V Convention
114(2)
Kirchhoff's Laws
114(2)
Formulation of Dynamic Equations
116(2)
Complex Impedances
116(1)
State Equations
117(1)
Transformers and Gyrators
118(7)
Impedance Transformations
119(1)
The Electrical Inductor
120(5)
Energy-Conserving Transducers
125(24)
Introduction
125(1)
The Parallel-Plate Capacitor
125(4)
Charging the Capacitor at Fixed Gap
126(1)
Charging the Capacitor at Zero Gap, then Lifting
127(2)
The Two-Port Capacitor
129(1)
Electrostatic Actuator
130(9)
Charge Control
131(1)
Voltage Control
132(2)
Pull-In
134(3)
Adding Dynamics to the Actuator Model
137(2)
The Magnetic Actuator
139(3)
Equivalent Circuits for Linear Transducers
142(3)
The Position Control System - Revisited
145(4)
Dynamics
149(34)
Introduction
149(1)
Linear System Dynamics
150(14)
Direct Integration
151(1)
System Functions
152(5)
Fourier Transform
157(1)
Sinusoidal Steady State
158(2)
Eigenfunction Analysis
160(4)
Nonlinear Dynamics
164(19)
Fixed Points of Nonlinear Systems
164(1)
Linearization About an Operating Point
165(1)
Linearization of the Electrostatic Actuator
166(3)
Transducer Model for the Linearized Actuator
169(4)
Direct Integration of State Equations
173(5)
Resonators and Oscillators
178(1)
And Then There's Chaos...
178(5)
Part III DOMAIN-SPECIFIC DETAILS
Elasticity
183(18)
Introduction
183(1)
Constitutive Equations of Linear Elasticity
184(9)
Stress
184(1)
Strain
185(1)
Elastic Constants for Isotropic Materials
186(2)
Other Elastic Constants
188(1)
Isotropic Elasticity in Three Dimensions
189(1)
Plane Stress
190(1)
Elastic Constants for Anisotropic Materials
191(2)
Thermal Expansion and Thin-Film Stress
193(3)
Other Sources of Residual Thin-Film Stress
195(1)
Selected Mechanical Property Data
196(1)
Material Behavior at Large Strains
196(5)
Plastic Deformation
197(4)
Structures
201(38)
Overview
201(1)
Axially Loaded Beams
201(6)
Beams With Varying Cross-section
203(1)
Statically Indeterminate Beams
203(2)
Stresses on Inclined Sections
205(2)
Bending of Beams
207(11)
Types of Support
207(1)
Types of Loads
207(1)
Reaction Forces and Moments
208(3)
Pure Bending of a Transversely Loaded Beam
211(2)
Differential Equation for Beam Bending
213(3)
Elementary Solutions of the Beam Equation
216(2)
Anticlastic Curvature
218(1)
Bending of Plates
219(3)
Plate in Pure Bending
220(2)
Effects of Residual Stresses and Stress Gradients
222(13)
Stress Gradients in Cantilevers
222(4)
Residual Stresses in Doubly-Supported Beams
226(5)
Buckling of Beams
231(4)
Plates With In-Plane Stress
235(2)
What about large deflections?
237(2)
Energy Methods
239(28)
Elastic Energy
240(3)
The Principle of Virtual Work
243(1)
Variational Methods
244(5)
Properties of the Variational Solution
247(2)
Large Deflections of Elastic Structures
249(11)
A Center-Loaded Doubly-Clamped Beam
249(4)
Combining Variational Results with Simulations
253(1)
The Uniformly Loaded Doubly-Clamped Beam
254(1)
Residual Stress in Clamped Structures
255(1)
Elastic Energy in Plates and Membranes
256(1)
Uniformly Loaded Plates and Membranes
257(2)
Membrane Load-Deflection Behavior
259(1)
Rayleigh-Ritz Methods
260(7)
Estimating Resonant Frequencies
260(3)
Extracting Lumped-Element Masses
263(4)
Dissipation and the Thermal Energy Domain
267(32)
Dissipation is Everywhere
267(1)
Electrical Resistance
267(2)
Charging a Capacitor
269(2)
Dissipative Processes
271(1)
The Thermal Energy Domain
272(6)
The Heat-Flow Equation
275(1)
Basic Thermodynamic Ideas
275(2)
Lumped Modeling in the Thermal Domain
277(1)
Self-Heating of a Resistor
278(8)
Temperature Coefficient of Resistance
279(1)
Current-source drive
279(2)
Voltage-source drive
281(1)
A Self-Heated Silicon Resistor
282(4)
Other Dissipation Mechanisms
286(5)
Contact Friction
286(1)
Dielectric losses
287(1)
Viscoelastic losses
288(1)
Magnetic Losses
289(1)
Diffusion
290(1)
Irreversible Thermodynamics: Coupled Flows
291(5)
Thermoelectric Power and Thermocouples
293(2)
Thermoelectric Heating and Cooling
295(1)
Other Coupled-Flow Problems
296(1)
Modeling Time-Dependent Dissipative Processes
296(3)
Lumped Modeling of Dissipative Processes
299(18)
Overview
299(1)
The Generalized Heat-Flow Equation
299(1)
The DC Steady State: The Poisson Equation
300(1)
Finite-Difference Solution of the Poisson Equation
301(4)
Temperature Distribution in a Self-Heated Resistor
303(2)
Eigenfunction Solution of the Poisson Equation
305(2)
Transient Response: Finite-Difference Approach
307(1)
Transient Response: Eigenfunction Method
307(1)
One-Dimensional Example
308(1)
Equivalent Circuit for a Single Mode
309(2)
Equivalent Circuit Including All Modes
311(6)
Fluids
317(36)
What Makes Fluids Difficult?
317(1)
Basic Fluid Concepts
318(8)
Viscosity
318(1)
Thermophysical Properties
319(1)
Surface Tension
320(2)
Conservation of Mass
322(1)
Time Rate of Change of Momentum
323(1)
The Navier-Stokes Equation
324(1)
Energy Conservation
324(1)
Reynolds Number and Mach Number
325(1)
Incompressible Laminar Flow
326(6)
Couette Flow
327(1)
Poiseuille Flow
328(3)
Development Lengths and Boundary Layers
331(1)
Stokes Flow
332(1)
Squeezed-Film Damping
332(7)
Rigid Parallel-Plate Small-Amplitude Motion
334(5)
Electrolytes and Electrokinetic Effects
339(14)
Ionic Double Layers
340(3)
Electroosmotic Flow
343(1)
Electrophoresis
344(3)
Diffusion Effects
347(1)
Pressure Effects
348(1)
Mixing
348(1)
Modeling of Electrokinetic Systems
349(4)
Part IV CIRCUIT AND SYSTEM ISSUES
Electronics
353(44)
Introduction
353(1)
Elements of Semiconductor Physics
353(4)
Equilibrium Carrier Concentrations
354(1)
Excess Carriers
355(2)
The Semiconductor Diode
357(6)
The Diffused Resistor
363(1)
The Photodiode
364(1)
The Bipolar Junction Transistor
365(1)
The MOSFET
365(7)
Large-Signal Characteristics of the MOSFET
367(4)
MOSFET Capacitances
371(1)
Small-Signal Model of the MOSFET
371(1)
MOSFET Amplifiers
372(9)
The CMOS Inverter
373(3)
Large-Signal Switching Speed
376(3)
The Linear-Gain Region
379(2)
Other Amplifier Configurations
381(1)
Operational Amplifiers
381(2)
Dynamic Effects
383(1)
Basic Op-Amp Circuits
384(7)
Inverting Amplifier
384(3)
Short Method for Analyzing Op-Amp Circuits
387(1)
Noninverting Amplifier
387(1)
Transimpedance Amplifier
388(1)
Integrator
389(1)
Differentiator
390(1)
Charge-Measuring Circuits
391(6)
Differential Charge Measurement
391(2)
Switched-Capacitor Circuits
393(4)
Feedback Systems
397(28)
Introduction
397(1)
Basic Feedback Concepts
397(1)
Feedback in Linear Systems
398(13)
Feedback Amplifiers
399(1)
Example: The Position Controller
400(5)
PID Control
405(2)
The Effect of Amplifier Bandwidth
407(1)
Phase Margin
408(1)
Noise and Disturbances
409(1)
Stabilization of Unstable Systems
410(1)
Controllability and Observability Revisited
411(1)
Feedback in Nonlinear Systems
411(2)
Quasi-static Nonlinear Feedback Systems
412(1)
Resonators and Oscillators
413(12)
Simulink Model
417(1)
The (Almost) Sinusoidal Oscillator
418(2)
Relaxation Oscillation
420(5)
Noise
425(28)
Introduction
425(1)
The Interference Problem
426(4)
Shields
427(1)
Ground Loops
428(1)
Guards
429(1)
Characterization of Signals
430(3)
Amplitude-Modulated Signals
431(2)
Characterization of Random Noise
433(3)
Mean-Square and Root-Mean-Square Noise
434(1)
Addition of Uncorrelated Sources
434(1)
Signal-to-Noise Ratio
435(1)
Spectral Density Function
435(1)
Noise in Linear Systems
436(1)
Noise Sources
436(6)
Thermal Noise
436(2)
Noise Bandwidth
438(1)
Shot Noise
439(1)
Flicker Noise
440(1)
Amplifier Noise
441(1)
Example: A Resistance Thermometer
442(5)
Using a DC source
445(1)
Modulation of an AC Carrier
446(1)
Caution: Modulation Does Not Always Work
447(1)
Drifts
447(6)
Part V CASE STUDIES
Packaging
453(16)
Introduction to the Case Studies
453(1)
Packaging, Test, and Calibration
454(1)
An Approach to Packaging
455(4)
A Commercial Pressure-Sensor Case Study
459(10)
Device Concept
461(1)
System Partitioning
461(1)
Interfaces
462(1)
Details
463(4)
A Final Comment
467(2)
A Piezoresistive Pressure Sensor
469(28)
Sensing Pressure
469(1)
Piezoresistance
470(11)
Analytic Formulation in Cubic Materials
471(1)
Longitudinal and Transverse Piezoresistance
472(1)
Piezoresistive Coefficients of Silicon
473(1)
Structural Examples
474(3)
Averaging over Stress and Doping Variations
477(3)
A Numerical Example
480(1)
The Motorola MAP Sensor
481(16)
Process Flow
481(2)
Details of the Diaphragm and Piezoresistor
483(2)
Stress Analysis
485(3)
Signal-Conditioning and Calibration
488(4)
Device Noise
492(1)
Recent Design Changes
493(1)
Higher-Order Effects
494(3)
A Capacitive Accelerometer
497(34)
Introduction
497(1)
Fundamentals of Quasi-Static Accelerometers
498(2)
Position Measurement With Capacitance
500(13)
Circuits for Capacitance Measurement
502(5)
Demodulation Methods
507(3)
Chopper-Stabilized Amplifiers
510(1)
Correlated Double Sampling
511(1)
Signal-to-Noise Issues
512(1)
A Capacitive Accelerometer Case Study
513(12)
Specifications
516(2)
Sensor Design and Modeling
518(2)
Fabrication and Packaging
520(3)
Noise and Accuracy
523(2)
Position Measurement With Tunneling Tips
525(6)
Electrostatic Projection Displays
531(30)
Introduction
531(5)
Electromechanics of the DMD Device
536(5)
Electrode Structure
536(1)
Torsional Pull-in
537(4)
Electromechanics of Electrostatically Actuated Beams
541(3)
M-Test
544(1)
The Grating-Light-Valve Display
544(14)
Diffraction Theory
544(4)
Device Fabrication and Packaging
548(2)
Quantitative Estimates of GLV Device Performance
550(8)
A Comparison
558(3)
A Piezoelectric Rate Gyroscope
561(44)
Introduction
561(1)
Kinematics of Rotation
561(2)
The Coriolis Rate Gyroscope
563(7)
Sinusoidal Response Function
565(1)
Steady Rotation
566(1)
Response to Angular Accelerations
567(1)
Generalized Gyroscopic Modes
567(3)
Piezoelectricity
570(8)
The Origin of Piezoelectricity
570(1)
Analytical Formulation of Piezoelectricity
571(2)
Piezoelectric Materials
573(2)
Piezoelectric Actuation
575(2)
Sensing with Piezoelectricity
577(1)
A Quartz Rate Gyroscope Case Study
578(27)
Electrode Structures
579(3)
Lumped-Element Modeling of Piezoelectric Devices
582(10)
QRS Specifications and Performance
592(2)
A Quantitative Device Model
594(1)
The Drive Mode
595(3)
Sense-Mode Displacement of the Drive Tines
598(1)
Coupling to the Sense Tines
599(3)
Noise and Accuracy Considerations
602(1)
Closing Comments
602(3)
DNA Amplification
605(24)
Introduction
605(1)
Polymerase Chain Reaction (PCR)
606(5)
Elements of PCR
606(4)
Specifications for a PCR System
610(1)
Microsystem Approaches to PCR
611(5)
Batch System
611(3)
PCR Flow System
614(2)
Thermal Model of the Batch Reactor
616(5)
Control Circuit and Transient Behavior
618(3)
Thermal Model of the Continuous Flow Reactor
621(4)
A Comparison
625(4)
A Microbridge Gas Sensor
629(21)
Overview
629(1)
System-Level Issues
630(2)
First-Order Device and System Models
632(7)
Filament Characteristics
632(2)
Resistance-Control System
634(5)
A Practical Device and Fabrication Process
639(4)
Creating the Filament
639(2)
High-Temperature Bond Pads
641(1)
Catalyst Coating
642(1)
Sensor Performance
643(3)
Demonstration of Hydrogen Detection
643(1)
Mass-Transport-Limited Operation
644(1)
Reaction-Rate-Limited Operation
645(1)
Advanced Modeling
646(2)
Epilogue
648(2)
Appendices 650(15)
A- Glossary of Notation
651(6)
B- Electromagnetic Fields
657(6)
B.1 Introduction
657(1)
B.2 Quasistatic Fields
657(1)
B.3 Elementary Laws
657(1)
B.4 Electroquasistatic Systems
658(1)
B.5 Magnetoquasistatic Systems
659(4)
C- Elastic Constants in Cubic Material
663(2)
References 665(12)
Index 677

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