Microtransducer CAD

Computer-aided-design (CAD) of semiconductor microtransducers is relatively new in contrast to their counterparts in the integrated circuit world. Integrated silicon microtransducers are realized using microfabrication techniques similar to those for standard integrated circuits (ICs). Unlike IC devices, however, microtransducers must interact with their environment, so their numerical simulation is considerably more complex. While the design of ICs aims at suppressing "parasitic" effects, microtransducers thrive on optimizing the one or the other such effect. The challenging quest for physical models and simulation tools enabling microtransducer CAD is the topic of this book. The book is intended as a text for graduate students in Electrical Engineering and Physics and as a reference for CAD engineers in the microsystems industry.

Contenu

1. Introduction.- 1.1 Modeling and Simulation of Microtransducers.- 1.2 Illustrative Example.- 1.2.1 Thermal Flow Sensor.- 1.2.2 Thermal Sensors and Actuators.- 1.2.3 Goals and Benefits of Modeling and Simulation.- 1.3 Progress in Microtransducer Modeling.- 1.4 References.- 2 Basic Electronic Transport.- 2.1 Poisson's Equation.- 2.2 Continuity Equations.- 2.3 Carrier Transport in Crystalline Materials and Isothermal Behavior.- 2.3.1 Transport Relations.- 2.3.2 Carrier Concentrations.- 2.3.3 Doping-Induced Band Gap Narrowing.- 2.3.4 Temperature-Dependence of Band Gap Energy.- 2.3.5 Carrier Mobility and Matthiessen's Rule.- 2.3.6 Generation-Recombination.- 2.4 Electrical Conductivity and Isothermal Behavior in Polycrystalline Materials.- 2.4.1 Doping-Dependence.- 2.4.2 Temperature-Dependence.- 2.5 Electrical Conductivity and Isothermal Behavior in Metals.- 2.6 Boundary and Interface Conditions.- 2.6.1 Ohmic Contacts.- 2.6.2 Schottky Contacts.- 2.6.3 Insulators and Interfaces.- 2.6.4 Outer Boundaries.- 2.7 The External Fields - What Do They Influence?.- 2.8 References.- 3 Radiation Effects on Carrier Transport.- 3.1 Reflection and Transmission of Optical Signals.- 3.1.1 Single- and Multi-Layer Thin Film Systems.- 3.2 Modeling Optical Absorption in Intrinsic Semiconductors.- 3.2.1 Band-to-Band Transitions.- 3.2.2 Absorption Coefficient.- 3.3 Absorption in Heavily-Doped Semiconductors.- 3.3.1 Band-to-Band Absorption Coefficient.- 3.3.2 Free Carrier Absorption Coefficient.- 3.4 Optical Generation Rate and Quantum Efficiency.- 3.5 Low Energy Interactions with Insulators and Metals.- 3.5.1 Refractive Index and Extinction Coefficient.- 3.6 High Energy Interactions and Monte Carlo Simulations.- 3.6.1 Photoelectric Effect, Compton Scattering, and Pair Production.- 3.6.2 Ionization Yield.- 3.6.3 Photon Attenuation Coefficients.- 3.6.4 Monte Carlo Simulations.- 3.7 Model Equations for Radiant Sensor Simulation.- 3.8 Illustrative Simulation Example - Color Sensor.- 3.9 References.- 4 Magnetic Field Effects on Carrier Transport.- 4.1 Galvanomagnetic Transport Equation.- 4.1.1 Galvanomagnetic Effects.- 4.2 Galvanomagnetic Transport Coefficients.- 4.2.1 Magnetic Field Dependence.- 4.2.2 Electric Field Dependence.- 4.3 Equations and Boundary Conditions for Magnetic Sensor Simulation.- 4.3.1 Unipolar Analysis.- 4.3.2 Bipolar Analysis.- 4.4 Illustrative Simulation Example - Micromachined Magnetic Vector Probe.- 4.5 References.- 5 Thermal Non-Uniformity Effects on Carrier Transport.- 5.1 Non-Isothermal Effects.- 5.1.1 The Seebeck, Peltier, and Thomson Effects.- 5.1.2 Wiedemann-Franz Law.- 5.2 Electrothermal Transport Model.- 5.2.1 Governing Equations.- 5.2.2 Boundary Conditions.- 5.3 Electrical and Thermal Transport Coefficients.- 5.3.1 The Seebeck Coefficient in Semiconductors and Metals.- 5.3.2 Thermal Conductivity in Semiconductors, Metals, and Dielectrics.- 5.3.3 Specific Heat in Semiconductors, Metals, and Dielectrics.- 5.4 Electro-Thermo-Magnetic Interactions.- 5.5 Heat Transfer in Thermal Microstructures.- 5.5.1 Governing Equations for Convective Heat Transfer.- 5.5.2 Zero Flow Two-Dimensional Heat Transfer Coefficient.- 5.5.3 Thermal Conductivity of Gases.- 5.5.4 Radiative Heat Transfer.- 5.5.5 Model Simplification for Quasi Three-Dimensional Analysis.- 5.6 Summary of Equations and Computational Procedure.- 5.7 Illustrative Simulation Example - Micro Pirani Gauge.- 5.8 References.- 6 Mechanical Effects on Carrier Transport.- 6.1 Piezoresistive Effect.- 6.1.1 Piezoresistance Coefficients in Monocrystalline Semiconductors.- 6.1.2 Doping- and Temperature-Dependence of Piezoresistance Coefficients.- 6.1.3 Non-Linear Piezoresistance Coefficients.- 6.1.4 Piezoresistance Coefficients in Polycrystalline Semiconductors.- 6.2 Strain and Electron Transport.- 6.2.1 Conduction Band.- 6.2.2 Electron Mobility and Piezoresistance.- 6.3 Strain and Hole Transport.- 6.3.1 Valence Band.- 6.3.2 Hole Mobility and Piezoresistance.- 6.4 Piezojunction Effect.- 6.5 Effects of Stress Gradients.- 6.5.1 Electron Transport.- 6.5.2 Hole Transport.- 6.5.3 Phonon Transport and Heat Flux.- 6.5.4 Thermodynamic Consideration of Electro-Thermo-Mechanical Interactions.- 6.6 Galvano-Piezo-Magnetic Effects.- 6.6.1 Piezo-Hall Coefficients.- 6.7 The Piezo Drift-Diffusion Transport Model.- 6.7.1 Transport Relations.- 6.7.2 Complete System and Summary of Model Equations.- 6.7.3 Discretization Scheme.- 6.7.4 Solution Scheme.- 6.7.5 Evaluation of Terminal Currents.- 6.8 Illustrative Simulation Example - Stress Effects on Hall Sensors.- 6.9 References.- 7 Mechanical and Fluidic Signals.- 7.1 Definitions.- 7.1.1 Transformations.- 7.1.2 Forces.- 7.1.3 Stress.- 7.1.4 Strain and Thermal Expansion.- 7.1.5 Strain-Rate.- 7.2 Model Equations for Mechanical Analysis.- 7.2.1 Governing Equations and Constitutive Relations.- 7.2.2 Simplified Analysis for Single- and Multi-Layer Diaphragms.- 7.2.3 Material Parameters and Extraction.- 7.3 Model Equations for Analysis of Fluid Transport.- 7.3.1 Constitutive Properties.- 7.3.2 Governing Equations.- 7.3.3 Fluidic Damping.- 7.4 Illustrative Simulation Example - Analysis of Flow Channels.- 7.4.1 Model Equations in Vorticity-Stream Function Formulation.- 7.4.2 Rotated Finite Difference Numerical Scheme.- 7.4.3 Computed Flow Profiles.- 7.5 References.- 8 Micro-Actuation.- 8.1 Transduction Principles.- 8.2 State-of-the-Art and Preview.- 8.3 Electrostatic Actuation.- 8.3.1 Electrostatic Analysis.- 8.4 Thermal Actuation.- 8.4.1 Electrothermal Analysis.- 8.4.2 Shape Memory Actuation.- 8.5 Magnetic Actuation.- 8.5.1 Magnetostriction Analysis.- 8.5.2 Electrodynamic Analysis.- 8.5.3 Electromagnetic Drive Analysis.- 8.6 Piezoelectric Actuation.- 8.6.1 Piezoelectric Analysis.- 8.6.2 Electro-Thermo-Mechanical Interactions and Coupling Coefficients.- 8.7 Electroacoustic Transducers.- 8.7.1 Acoustic Wave Propagation in Solids.- 8.7.2 Interactions with Ambient Fluid.- 8.8 Computational Procedure and Coupling.- 8.9 Illustrative Example - CMOS Micromirror.- 8.10 References.- 9 Microsystem Simulation.- 9.1 Electrical Analogues for Mixed-Signals and Historical Developments.- 9.2 Circuit Modeling and Implementation Considerations.- 9.2.1 Multi-Variate Polynomial Dependent Sources.- 9.2.2 Synthesis from Multi-Dimensional Field Equations.- 9.3 Lumped Analysis: Illustrative Example - Electrostatic Micromirror.- 9.3.1 Capacitance and Torque Modeling.- 9.3.2 Verification Using the Panel Method.- 9.3.3 SPICE Simulation.- 9.4 Distributed Analysis: Illustrative Example - Flow Microsensor.- 9.4.1 Model Equations and Circuit Synthesis.- 9.4.2 SPICE Simulation.- 9.5 References.