Advanced Theory Of Semiconductor Devices Book
CONTENTS
Preface
Acknowledgments
Chapter 1 A Brief Review of the Basic Equations 1
1.1 The Equations of Classical Mechanics, Application
to Lattice Vibrations 2
1.2 The Equations of Quantum Mechanics 9
Chapter 2 The Symmetry of the Crystal Lattice
2.1 Crystal Structures of Silicon and GaAs
2.2 Elements of Group Theory 22
2.2.1 Point Group 22
2.2.2 TranslationalInvariance 26
2.3 Bragg Reflection 29
19
19
Chapter 3 The Theory of Energy Bands in Crystals 33
3.1 Coupling Atoms 33
3.2 Energy Bands by Fourier Analysis 34
3.3 Equations of Motion in a Crystal 42
3.4 Maxima of Energy Bands-Holes 46
3.5 Summary of Important Band-Structure
Parameters 50
3.6 Band Structure of Alloys 50
Chapter 4 Imperfections of Ideal Crystal Structure 57
4.1 Shallow Impurity Levels-Dopants 58
4.2 Deep Impurity Levels 60
4.3 Dislocations, Surfaces, and Interfaces 62
vii
viii Contents
Chapter 5 Equilibrium Statistics for Electrons and Holes 67
5.1 Density of States 67
5.2 Probability of Finding Electrons in a State 73
5.3 Electron Density in the Conduction Band 75
Chapter 6 Self-Consistent Potentials and Dielectric
Properties 81
6.1 Screening and the Poisson Equation in One
Dimension 82
6.2 Self-Consistent Potentials and the Dielectric
Function 83
Chapter 7 Scattering Theory
7.1 General Considerations-Drude Theory 89
7.2 Scattering Probability from the Golden
Rule 94
7.2.1 Impurity Scattering 94
7.2.2 Phonon Scattering 96
7.2.3 Scattering by a S-ShapedPotential 102
7.3 Important Scattering Mechanisms in Silicon and
Gallium Arsenide 103
89
Chapter 8 The Boltzmann Transport Equation 109
8.1 Derivation 109
8.2 Solutions of the Boltzmann Equation in the
Relaxation Time Approximation 114
8.3 Distribution Function and Current Density 121
8.4 Effect of Temperature Gradients and Gradients of
the Band Gap Energy 125
8.5 Ballistic and Quantum Transport 127
8.6 The Monte Carlo Method 129
Chapter 9 Generation-Recombination 135
9.1 Important Matrix Elements 135
9.1.1 RadiativeRecombination 135
9.1.2 Auger Recombination 139
9.2 Quasi-Fermi Levels (Imrefs) 139
9.3 Generation-RecombinationRates 140
9.4 Rate Equations 144
Chapter 10 The HeteroJunction Barrier 147
10.1 Thermionic Emission of Electrons over
Barriers 147
Contents ix
10.2 Free Carrier Depletion of Semiconductor
Layers 151
10.3 Connection Rules for the Potential at an
Interface 153
10.4 Solution of Poisson's Equation in the Presence of
Free Charge Carriers 154
10.4.1 Classical Case 154
10.4.2 Quantum Mechanical Case 157
10.5 Pronounced Effects of Size Quantization and
Heterolayer Boundaries 162
Chapter 11 The Device Equations of Shockleyand Stratton 167
11.1 The Method of Moments 167
11.2 Moment for the Average Energy and Hot
Electrons 170
11.2.1 Steady-StateConsiderations 171
11.2.2 VelocityTransients and Overshoot 175
11.2.3 Equation of Poisson and Carrier Velocity 176
Chapter 12 Numerical Device Simulations 181
12.1 General Considerations 181
12.2 Numerical Solution of the Shockley
Equations 184
12.2.1 Numerical Simulation Beyond the Shockley
Equations 188
Chapter 13 Diodes
13.1 Schottky Barriers-ohmic Contacts 194
13.2 The p-n Junction 201
13.2.1 Introduction and Basic Physics 201
13.2.2 Basic Equations for the Diode Current 207
13.2.3 Steady-State Current in Forward Bias 211
13.2.4 AC Carrier Concentrations and Current in Forward
Bias 213
13.2.5 Short Diodes 215
13.2.6 Recombinationin Depletion Region 216
13.2.7 Extreme Forward Bias 219
13.2.8 Asymmetric Junctions 221
13.2.9 Effects in Reverse Bias 223
13.3 High-Field Effects in Semiconductor
Junctions 226
13.3.1 Role of Built-In Fields in Electron Heating and p-n
Junction Currents 226
193
x Contents
13.3.2 Impact Ionization in p-n Junctions 229
13.3.3 Zener Tunneling 236
13.3.4 Real Space Transfer 240
13.4 Negative Differential Resistance and
Semiconductor Diodes 241
Chapter 14 Laser Diodes 247
14.1 Basic Geometry and Equations for Quantum Well
Laser Diodes 248
14.2 Equations for Electronic Transport 250
14.3 Coupling of Carriers and Photons 253
14.4 Numerical Solutions of the Equations for Laser
Diodes 257
Chapter 15 Transistors 265
15.1 Simple Models 266
15.1.1 Bipolar Transistors 266
15.1.2 Field Effect Transistors 272
15.2 Effects of Reduction in Size, Short Channels
278
15.2.1 Scaling Down Devices 278
15.2.2 Short Gates and Threshold Voltage 279
15.3 HotElectron Effects 281
15.3.1 Mobility in Small MOSFETs 281
15.3.2 Impact Ionization, Hot Electron Degradation
284
Chapter 16 Future Semiconductor Devices 291
16.1 New Types of Devices 291
16.1.1 Extensions of ConventionalDevices 291
16.1.2 Future Devices for Ultrahigh Integration 293
16.2 Challenges in Nanostructure Simulation 295
16.2.1 Nanostructures in Existing Semiconductor
Devices 296
16.2.2 Quantum Dots 297
16.2.3 Structural, Atomistic, and Many-Body
Effects 297
Appendix A Tunneling and the Golden Rule
Appendix B The One Band Approximation
Appendix C Temperature Dependence of the Band Structure 307
Appendix 0 Hall Effect and Magnetoresistance 309
Appendix E The Power Balance Equation 311
Appendix F The Self-Consistent Potential at a Heterojunction
315
Appendix G Schottky Barrier Transport 317
Index 321
About the Author 333
