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عدد المساهمات : 19001 التقييم : 35505 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| 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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