Physics of Semiconductor Devices

Contents

Contents of Volume 1

1.0 Introduction, 1
1.1 Bandgap Width, 6
1.2 Fermi-Dirac and Maxwell-Botzmann Distributions, 9
1.3 Carrier Concentrations, 16: 1.3.1 The pn Product at Equilibrium, 16; 1.3.2 Charge Neutrality, 21
1.4 Fermi Level, 36: 1.4.1 Quasi-Fermi and Electrostatic Potentials, 45
1.5 Carrier Transport, 49: 1.5.1 Drift and Diffusion Currents, 50; 1.5.2 Drift Mobility and Diffusion Coefficient, 53; 1.5.3 Electrical Conductivity and Resistivity, 58
1.6 Recombination Processes, 71: 1.6.1 Direct Recombination, 71; 1.6.1 Recombination through Traps, 72; 1.6.2 Surface Recombination, 81
1.7 Basic Equations for Semiconductor Device Operation, 83: 1.7.1 Poisson Equation, 83; 1.7.2 Transport Equations, 86; 1.7.3 Continuity Equations, 91
1.8 Non-Homogeneous Semiconductors, 105
1.9 Heavy Doping Effects, 112: 1.9.1 Bandgap Narrowing, 112; 1.9.2 Transport Equations in Degenerate Semiconductors, 114
1.10 Basic Device Technology, 118: 1.10.1 Solid-State Diffusion, 121; 1.10.2 Ion Implantation, 135
Supplementary Problems, 139: Solutions to Supplementary Problems, 144

2. p-n Junction Diode, 147

2.0 Introduction, 147
2.1 Built-in Potential, 148
2.2 Depletion Region: Potential and Electric Field Distributions, 153
2.3 Depletion Region Capacitance, 166
2.4 Current-Voltage Characteristics, 176: 2.4.1 Shockley Equation, 176; 2.4.2 Influence of Built-in Field, 212; 2.4.3 Influence of Heavy-Doping Effects, 216
2.5 Small-Signal Dynamic Characteristics, 218: 2.5.1 Small-Signal Resistance, 218; 2.5.2 Excess Minority Carrier Charge, 226; 2.5.3 Diffusion Admittance and Diffusion Capacitance, 234
2.6 Transient Behavior, 248
Supplementary Problems, 258: Solutions to Supplementary Problems, 267

Appendix A: Finding Roots of Equations by Method of Successive Approximations, 273

Appendix B: Solutions of Diffusion Equations, 276

Diffusion from Unlimited Source, 277

Diffusion from Limited Source, 277

Appendix C: Complementary Error Function, 279

List of References, 281

Crossectional view of a junction p-n diode

3. Bipolar Transistor, 1

3.0 Introduction, 1
3.1 Static Characteristics, 6: 3.1.1 Regions of Operation, 6; 3.1.2 Currents Flowing in Transistor, 7; 3.1.3 Emitter Eficiency, Base Transport Factor and Current Gain, 38; 3.1.4 Ebers-Moll Equations, 55; 3.1.5 Input and Output Characteristics, 61
3.2 Influence of Doping Distribution on Emitter Eficiency and Base Transport Factor, 83: 3.2.1 Transport Through Non-Uniform Doped Base, 83; 3.2.2 Emitter Eficiency of a Transistor with Non-Uniform Impurity Doping, 96; 3.2.3 Influence of Surface Recombination, 100; 3.2.4 Heavy-Doping Effects, 104
3.3 Characteristics of Real Transistors, 115: 3.3.1 High Injection, 115; 3.3.2 Spatial Current Distribution, 116; 3.3.3 Series Resistances, 119; 3.3.4 Base-Width Modulation (Early Effect), 127
3.4 Dynamic Characteristics, 142: 3.4.1 Ebers-Moll Model, 142; 3.4.2 Small-Signal h-Equivalent Circuit, 150; 3.4.3 Hybrid-pi Equivalent Circuit, 169
3.5 High-Frequency Characteristics, 174: 3.5.1 Cutoff Frequencies, 181; 3.5.2 High-Frequency Hybrid-pi Equivalent Circuit, 202
3.6 Transient Behavior, 206: 3.6.1 Charge Control Model, 207
Supplementary Problems, 226: Solutions to Supplementary Problems, 241

Appendix A: Proof of Ebers-Moll Model Reciprocity, 249

List of References, 255

Ebers-Moll model of an npn transistor