Advanced Theory Of Semiconductor Devices
Karl Hess
University of Illinois at Urbana-Champaign
CONTENTS
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
>>>>>TO<<<<<
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
301
305
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
