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CHAPTER 1 The Crystal Structure of Solids1

Preview1

1.1 Semiconductor Materials1

1.2 pes of Solids2

1.3 Space Lattices3

1.3.1 Primitive and Unit Cell3

1.3.2 Basic Crystal Structures4

1.3.3 Cstal Planes and Miller Indices5

1.3.4 The Diamond Structure9

1.4 Atomic Bonding11

1.5 Imperfections and Impurities in Solids13

1.5.1 Imperfections in Solids13

1.5.2 Impurities in Solids15

1.6 Growth of Semiconductor Materials16

1.6.1 Growth from a Melt16

1.6.2 Epitazial Growth18

1.7 Summa19

Problems21

CHAPTER 2 Introduction to Quantum Mechanics24

Preview24

2.1 Principles of Quantum Mechanics25

2.1.1 Energy Quanta25

2.1.2 Wave Particle Duality26

2.1.3 The Uncertain Principle29

2.2 Schrodinger's Wave Equation30

2.2.1 The Wave Equation30

2.2.2 Physical Meaning of the WaveFunction32

2.2.3 Bounda Conditions32

2.3 Applications of Schrodinger's WaveEquation33

2.3.1 Electn in Free Space33

2.3.2 The Infinite Potential Well34

2.3.3 The Step Potential Function38

2.3.4 The Potential Barrier42

2.4 Extensions of the Wave Theo to Atoms45

2.4.1 The One-Electn Atom45

2.4.2 The Periodic Table48

2.5 Summary50

Problems51

CHAPTER 3 Introduction to the Quantum Theoryof Solids56

Preview56

3.1 Allowed and Forbidden Energy Bands57

3.1.1 Formation of Energy Bands57

3.1.2 The Knig-Penney Model61

3.1.3 The k-Space Diagram66

3.2 Electrical Conduction in Sods70

3.2.1 The Energy Band and the Bond Model70

3.2.2 Drift Current72

3.2.3 Electron Eective mass73

3.2.4 Concept of the Hole76

3.2.5 Metals, Insulators, andSemiconductors78

3.3 Extension to Three Dimensions80

3.3.1 The k-Space Diagrams of Si and GaAs81

3.3.2 Additional Effective Mass Concepts82

3.4 Densi of States Function83

3.4.1 Maatheutical Derivation83

3.4.2 Extension to Semiconductors86

3.5 Statistical Mechanics88

3.5.1 Statistical Laws88

3.5.2 The Fermi-Dirac Pbabili Function89

3.5.3 The Distribution Function and theFermi Energy91

3.6 Summa96

Problems98

CHAPTER 4 The Semiconductor in Equilibrium103

Preview103

4.1 Charge Carriers in Semiconductors104

4.1.1 Equilibrium Distribution of Electnsand Holes104

4.1.2 The no and po Equations106

4.1.3 The Intrinsic Carrier Concentration110

4.1.4 The Intrinsic Fermi-LevelPosition113

4.2 Dopant Atoms and Energy Levels115

4.2.1 Qualitative Description115

4.2.2 Ionization Energy117

4.2.3 Gup 111-V Semiconductors119

4.3 The Extrinsic Semiconductor120

4.3.1 Equilibrium Distribution of Electnsand Holes121

4.3.2 The nopo Product124

4.3.3 TheFermi Dirac Integl125

4.3.4 Degenerate and Nondegenterate. Semiconductors127

4.4 Statistics of Donors and Acceptors128

4.4.1 Pbability Function128

4.4.2 Complete Ionizauion and Feze-Out129

4.5 Charge Neutrality132

4.5.1 Compensated SenuConduetois133

4.5.2 Equilibrium Electron and HoleConcentrations133

4.6 Position of Fermi Energy Level139

4.6.1 Mhematical Derivation139

4.6.2 Variation of Ef withDaping Concentrationand Temperatune142

4.6.3 Relevance of the Fermi Energy144

4.7 Summa145

Problems148

CHAPTER 5 Carrier ansport Phenomena154

Preview154

5.1 Carrier Drift154

5.1.1 Drift Current Densi155

5.1.2 Mobili Effects157

5.1.3 Conductivi162

5.1.4 Veloci Saturation167

5.2 Carrier Diusion169

5.2.1 Diusion Current Densi170

5.2.2 Total Curnt Densi173

5.3 Graded Impuri Distribution173

5.3.1 Induced Electric Field174

5.3.2 The Einstein Relation176

5.4 The Hall Effect177

5.5 Summa180

Problems182

CHAPTER 6 Nonequilibrium Excess Carriersin Semiconductors189

Preview189

6.1 Carrier Generation and Recombination190

6.1.1 The Semiconductor in Equilibrium190

6.1.2 Excess Carrier Generationand Recombination191

6.2 Characteristics of Excess Carriers194

6.2.1 Continui Equations195

6.2.2 Time-Dependent DiusionEquations196

6.3 Ambipolar Transpo197

6.3.1 Derivation of the AmbipolarTransport Equation198

6.3.2 Limits of Extrinsic Dopingand Low Injection200

6.3.3 Applications of the AmbipolarTransport Equation203

6.3.4 Dielectric Relaxation Time Constant211

6.3.5 Hayneshockley Experiment213

6.4 AQuasi-Fertni Energy Levels216

6.5 Excess-Carrier Lifetime218

6.5.1 Shockley-Read-Hall Theoof Recombination219

6.5.2 Limits of Extrinsic Dopingand Low Injection222

6.6 Surface Effects224

6.6.1 Surface States224

6.6.2 Surface Recombination Veloci226

6.7 Summa229

Problems231

CHAPTER 7 The pn Junction238

Preview238

7.1 Basic Structure of the pn Junction238

7.2 Zero Applied Bias240

7.2.1 Built-in Potential Barrier240

7.2.2 Electric Field242

7.2.3 Space Charge Width246

7.3 Reverse Applied Bi247

7.3.1 Space Charge Width and ElectricField248

7.3.2 Junction Capacitance251

7.3.3 One-Sided Junctions253

7.4 Nonuniforny Doped Junctions255

7.4.1 Linearly Graded Junction255

7.4.2 Hyperabrupt Junctions258

7.5 Summa260

Problems262

CHAPTER 8 The pn Junction Diode268

Preview268

8.1 pn Junction Current269

8.1.1 Qualitative Description of Charge Flowin a pn Junction269

8.1.2 Ideal Current-Voltage Relationship270

8.1.3 Bounda Conditions271

8.1.4 Minori Carrier Distribution275

8.1.5 Ideal pn Junction Current277

8.1.6 Summa of Physics281

8.1.7 Temperature Eects284

8.1.8 The “Short” Diode284

8.2 Small-Signal Model of the pn Junction286

8.2.1 Diffusion Resistance286

8.2.2 Small-Signal Admittance288

8.2.3 Equivalent Circuit295

8.3 Generation-Recombination Currents297

8.3.1 Reverse-Bias Generation Current297

8.3.2 Forward-Bias Recombination Current300

8.3.3 Total Forward-Bias Current303

8.4 Junction Breakdown305

8.5 Charge Storage and Diode Transients309

8.5.1 The Tu—— Transient309

8.5.2 The Tu-on Transient312

8.6 The Tunnel Diode313

8.7 Summa316

Problems318

CHAPTER 9 Metal-Semiconductor and SemiconductorHeterojunctions326

Preview326

9.1 The Schottky Barrier Diode326

9.1.1 Qualitative Characteristics327

9.1.2 Ideal Junction Properties329

9.1.3 Nonideal Eects on the Barrier Height333

9.1.4 Current-Voltage Relationship337

9.1.5 Comparison of the Schooky Barrier Diodeand the pn Junction Diode341

9.2 Metal-Semiconductor Ohmic Contacts344

9.2.1 Ideal Nonctifying Barriers345

9.2.2 Tunneling Barrier346

9.2.3 Specific Contact Resistance348

9.3 Heterojunctions349

9.3.1 Heterojunction Materials350

9.3.2 Energy-Band Diagrams350

9.3.3 Two-Dimensional Electron Gas351

9.3.4 Equilibum Electrostatics354

9.3.5 Curnt-Voltage Charactestics359

9.4 Summa359

Problems361

CHAPTER 10 The Bipolar Transistor367

Preview367

10.1 The Bipolar Transistor Action368

10.1.1 The Basic Principle of operation369

10.1.2 Simplified Transistor CurrentRelations370

10.1.3 The Modes of Operation374

10.1.4 Amplification with BipolarTransistors376

10.2 Minori Carrier Distribution377

10.2.1 Forward-Active Mode378

10.2.2 Other Modes of Operation384

10.3 Low-Frequency Common-BaseCurrent Gain385

10.3.1 Contributing Factors386

10.3.2 Mathematical Derivation of CurrentGain Factors388

10.3.3 Summa392

10.3.4 Example Calculations of theGain Factors393

10.4 Nonideal Effects397

10.4.1 Base Width Modulation397

10.4.2 High Injection401

10.4.3 Emier Bandgap Narwing403

10.4.4 Current Cwding405

10.4.5 Nonuniform Base Doping406

10.4.6 Breakdown Voltage408

10.5 Equivalent Circuit Models413

10.5.1 Ebers Moll Model414

10.5.2 Gummel-Poon Model416

10.5.3 Hybd-Pi Model418

10.6 Frequency Limitations422

10.6.1 Time-Delay Factors422

10.6.2 Transistor Cutoff Frequency424

10.7 Large-Signal Switching427

10.7.1 Switching Characteristics427

10.7.2 The Schonky-Clamped Transistor429

10.8 Other Bipolar Transistor Structures430

10.8.1 Polysilicon EmierBJT430

10.8.2 Silicon-Germanium Base Transistor431

10.8.3 Hetejunction Bipolar Transistors434

10.9 Summa435

Problems438

CHAPTER 11 Fundamentals of the Metal-Oxide-Semiconductor Field-Effect Transistor449

Preview449

11.1 The Two-Terminal MOS Structure450

11.1.1 Energy-Band Diagrams450

11.1.2 Depletion Layer Thickness455

11.1.3 Work Function Dierences458

11.1.4 Ft-Band Voltage462

11.1.5 Threshold Voltage465

11.1.6 Charge Distribution471

11.2 Capacitance-Voltage Characteristics474

11.2.1 Ideal C-V Characteristics474

11.2.2 Frequency Effects479

11.2.3 Fixed Oxide and InterfaceCharge Eects480

11.3 The Basic MOSFET Operation483

11.3.1 MOSFET Structures483

11.3.2 Current-Voltage Retionship—Concepts486

11.3.3 Current-Voltage Relationship—Mathematical Derivation490

11.3.4 Transconductance498

11.3.5 Substrate Bias Effects499

11.4 Frequency Limitations502

11.4.1 Small-Signal Equivalent Circuit502

11.4.2 Frequency Limitation Factorsand Cuto Frequency504

11.5 The CMOS Technology507

11.6 Summa509

Problems513

CHAPTER 12 Metal-Oxide--Semiconductor Field-EffectTransistor: Additional Concepts523

Preview523

12.1 Nonideal Effects524

12.1.1 Subthreshold Conduction524

12.1.2 Channel Length Modulation526

12.1.3 Mobili Variation530

12.1.4 Velocity Saturation532

12.1.5 Ballistic Transport534

12.2 MOSFET Scaling534

12.2.1 Constant-Field Scaling534

12.2.2 Threshold Voltage—FirstAppximations535

12.2.3 Generalized Scaling536

12.3 Threshold Voltage Modications537

12.3.1 Short-Channel Eects537

12.3.2 Narrow-Channel Eects541

12.4 Additional Electcal Charactestics543

12.4.1 Breakdown Voltage544

12.4.2 The Lightly Doped DrainTransistor550

12.4.3 Threshold Adjustment by IonImplantation551

12.5 Radiation and Hot-Electron Effects554

12.5.1 Radiation-Induced Oxide Charge555

12.5.2 Radiation-Induced Interface States558

12.5.3 Hot-Electn Charging Eects560

12.6 Summa561

Problems563

CHAPTER 13 The Junction Field-Effect Transistor570

Preview570

13.1 gET Concepts571

13.1.1 Basic pn JFET Operation571

13.1.2 Basic MESFET Operation575

13.2 The Device Characteristics577

13.2.1 Internal Pincho Voltage, PinchoVolge, and Drain-to-SourceSaturation Voltage577

13.2.2 Ideal DC Current-Voltage RelationshipDepletion Mode JFET582

13.2.3 Transconductance587

13.2.4 The MESFET588

13.3 Nonideal Eects593

13.3.1 Channel Length Modulation594

13.3.2 Veloci Saturation Eects596

13.3.3 Subthreshold and Gate CurrentEects596

13.4 Equivalent Circuit and FrequencyLimitations598

13.4.1 Small-Signal Equivalent Circuit598

13.4.2 Frequency Limitation Factorsand Cuto Frequency600

13.5 High Electron Mobili Transistor602

13.5.1 Quantum Well Structures603

13.5.2 Transistor Performance604

13.6 Summa609

Problems611

CHAPTER 14 Optical Devices617

Preview617

14.1 Optical Absorption618

14.1.1 Photon Absorption Coecient618

14.1.2 Electron-Hole Pair GenerationRate621

14.2 Solar Cells623

14.2.1 The pn Junction Solar Cell623

14.2.2 Conversion Eficiency and SolarConcentration626

14.2.3 Nonuniform Absorption Eects628

14.2.4 The Hetejunction Solar Cell628

14.2.5 Amorphous Silicon Solar Cells630

14.3 Photodetectors631

14.3.1 Photoconductor632

14.3.2 Photodiode634

14.3.3 PIN Photodiode639

14.3.4 Avalanche Photodiode640

14.3.5 Phototransistor641

14.4 Photoluminescence andElectroluminescence642

14.4.1 Basic Transitions643

14.4.2 Luminescent Eciency645

14.4.3 Materials645

14.5 Light Emitting Diodes647

14.5.1 Generation of Light648

14.5.2 Internal Quantum Efficiency648

14.5.3 External Quantum Efciency649

14.5.4 LED Devices651

14.6 Laser Diodes653

14.6.1 Stimulated Emission and PopulationInversion654

14.6.2 Optical Cavity656

14.6.3 Threshold Current657

14.6.4 Device Structures andCharacteristics658

14.7 Summa661

Problems663

CHAPTER 15 Semiconductor Power Devices668

Preview668

15.1 Power Bipolar Transistors668

15.1.1 Vertical Power Transistor Structure669

15.1.2 Power Transistor Characteristics670

15.1.3 Darlington Pair Configuration674

15.2 Power MOSFETs676

15.2.1 Power Transistor Structures676

15.2.2 Power MOSFET Characteristics678

15.2.3 Parasitic BJT682

15.3 Heat Sinks and JunctionTemperature683

15.4 The Thyristor686

15.4.1 The Basic Characteristics686

15.4.2 Triggering the SCR689

15.4.3 SCR Tu-Of692

15.4.4 Device Structus692

15.5 Summa696

Problems699

APPENDIX A Selected List of Symbols730

APPENDIX B and General Constants711

APPENDIX C The Periodic Table715

APPENDIX D The Error Function717

APPENDIX E “Derivation” ofSchrodiogr'sWaveEquation719

APPENDIX F Unit of Energy——The Electron-Volt721

APPENDIX G Answers to Selected Problems723

Index731