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CHAPTER 1 The Crystal Structure of Solids 1

Preview 1

1.1 Semiconductor Materials 1

1.2 pes of Solids 2

1.3 Space Lattices 3

1.3.1 Primitive and Unit Cell 3

1.3.2 Basic Crystal Structures 4

1.3.3 Cstal Planes and Miller Indices 5

1.3.4 The Diamond Structure 9

1.4 Atomic Bonding 11

1.5 Imperfections and Impurities in Solids 13

1.5.1 Imperfections in Solids 13

1.5.2 Impurities in Solids 15

1.6 Growth of Semiconductor Materials 16

1.6.1 Growth from a Melt 16

1.6.2 Epitazial Growth 18

1.7 Summa 19

Problems 21

CHAPTER 2 Introduction to Quantum Mechanics 24

Preview 24

2.1 Principles of Quantum Mechanics 25

2.1.1 Energy Quanta 25

2.1.2 Wave Particle Duality 26

2.1.3 The Uncertain Principle 29

2.2 Schrodinger's Wave Equation 30

2.2.1 The Wave Equation 30

2.2.2 Physical Meaning of the WaveFunction 32

2.2.3 Bounda Conditions 32

2.3 Applications of Schrodinger's WaveEquation 33

2.3.1 Electn in Free Space 33

2.3.2 The Infinite Potential Well 34

2.3.3 The Step Potential Function 38

2.3.4 The Potential Barrier 42

2.4 Extensions of the Wave Theo to Atoms 45

2.4.1 The One-Electn Atom 45

2.4.2 The Periodic Table 48

2.5 Summary 50

Problems 51

CHAPTER 3 Introduction to the Quantum Theoryof Solids 56

Preview 56

3.1 Allowed and Forbidden Energy Bands 57

3.1.1 Formation of Energy Bands 57

3.1.2 The Knig-Penney Model 61

3.1.3 The k-Space Diagram 66

3.2 Electrical Conduction in Sods 70

3.2.1 The Energy Band and the Bond Model 70

3.2.2 Drift Current 72

3.2.3 Electron Eective mass 73

3.2.4 Concept of the Hole 76

3.2.5 Metals, Insulators, andSemiconductors 78

3.3 Extension to Three Dimensions 80

3.3.1 The k-Space Diagrams of Si and GaAs 81

3.3.2 Additional Effective Mass Concepts 82

3.4 Densi of States Function 83

3.4.1 Maatheutical Derivation 83

3.4.2 Extension to Semiconductors 86

3.5 Statistical Mechanics 88

3.5.1 Statistical Laws 88

3.5.2 The Fermi-Dirac Pbabili Function 89

3.5.3 The Distribution Function and theFermi Energy 91

3.6 Summa 96

Problems 98

CHAPTER 4 The Semiconductor in Equilibrium 103

Preview 103

4.1 Charge Carriers in Semiconductors 104

4.1.1 Equilibrium Distribution of Electnsand Holes 104

4.1.2 The no and po Equations 106

4.1.3 The Intrinsic Carrier Concentration 110

4.1.4 The Intrinsic Fermi-LevelPosition 113

4.2 Dopant Atoms and Energy Levels 115

4.2.1 Qualitative Description 115

4.2.2 Ionization Energy 117

4.2.3 Gup 111-V Semiconductors 119

4.3 The Extrinsic Semiconductor 120

4.3.1 Equilibrium Distribution of Electnsand Holes 121

4.3.2 The nopo Product 124

4.3.3 TheFermi Dirac Integl 125

4.3.4 Degenerate and Nondegenterate. Semiconductors 127

4.4 Statistics of Donors and Acceptors 128

4.4.1 Pbability Function 128

4.4.2 Complete Ionizauion and Feze-Out 129

4.5 Charge Neutrality 132

4.5.1 Compensated SenuConduetois 133

4.5.2 Equilibrium Electron and HoleConcentrations 133

4.6 Position of Fermi Energy Level 139

4.6.1 Mhematical Derivation 139

4.6.2 Variation of Ef withDaping Concentrationand Temperatune 142

4.6.3 Relevance of the Fermi Energy 144

4.7 Summa 145

Problems 148

CHAPTER 5 Carrier ansport Phenomena 154

Preview 154

5.1 Carrier Drift 154

5.1.1 Drift Current Densi 155

5.1.2 Mobili Effects 157

5.1.3 Conductivi 162

5.1.4 Veloci Saturation 167

5.2 Carrier Diusion 169

5.2.1 Diusion Current Densi 170

5.2.2 Total Curnt Densi 173

5.3 Graded Impuri Distribution 173

5.3.1 Induced Electric Field 174

5.3.2 The Einstein Relation 176

5.4 The Hall Effect 177

5.5 Summa 180

Problems 182

CHAPTER 6 Nonequilibrium Excess Carriersin Semiconductors 189

Preview 189

6.1 Carrier Generation and Recombination 190

6.1.1 The Semiconductor in Equilibrium 190

6.1.2 Excess Carrier Generationand Recombination 191

6.2 Characteristics of Excess Carriers 194

6.2.1 Continui Equations 195

6.2.2 Time-Dependent DiusionEquations 196

6.3 Ambipolar Transpo 197

6.3.1 Derivation of the AmbipolarTransport Equation 198

6.3.2 Limits of Extrinsic Dopingand Low Injection 200

6.3.3 Applications of the AmbipolarTransport Equation 203

6.3.4 Dielectric Relaxation Time Constant 211

6.3.5 Hayneshockley Experiment 213

6.4 AQuasi-Fertni Energy Levels 216

6.5 Excess-Carrier Lifetime 218

6.5.1 Shockley-Read-Hall Theoof Recombination 219

6.5.2 Limits of Extrinsic Dopingand Low Injection 222

6.6 Surface Effects 224

6.6.1 Surface States 224

6.6.2 Surface Recombination Veloci 226

6.7 Summa 229

Problems 231

CHAPTER 7 The pn Junction 238

Preview 238

7.1 Basic Structure of the pn Junction 238

7.2 Zero Applied Bias 240

7.2.1 Built-in Potential Barrier 240

7.2.2 Electric Field 242

7.2.3 Space Charge Width 246

7.3 Reverse Applied Bi 247

7.3.1 Space Charge Width and ElectricField 248

7.3.2 Junction Capacitance 251

7.3.3 One-Sided Junctions 253

7.4 Nonuniforny Doped Junctions 255

7.4.1 Linearly Graded Junction 255

7.4.2 Hyperabrupt Junctions 258

7.5 Summa 260

Problems 262

CHAPTER 8 The pn Junction Diode 268

Preview 268

8.1 pn Junction Current 269

8.1.1 Qualitative Description of Charge Flowin a pn Junction 269

8.1.2 Ideal Current-Voltage Relationship 270

8.1.3 Bounda Conditions 271

8.1.4 Minori Carrier Distribution 275

8.1.5 Ideal pn Junction Current 277

8.1.6 Summa of Physics 281

8.1.7 Temperature Eects 284

8.1.8 The “Short” Diode 284

8.2 Small-Signal Model of the pn Junction 286

8.2.1 Diffusion Resistance 286

8.2.2 Small-Signal Admittance 288

8.2.3 Equivalent Circuit 295

8.3 Generation-Recombination Currents 297

8.3.1 Reverse-Bias Generation Current 297

8.3.2 Forward-Bias Recombination Current 300

8.3.3 Total Forward-Bias Current 303

8.4 Junction Breakdown 305

8.5 Charge Storage and Diode Transients 309

8.5.1 The Tu—— Transient 309

8.5.2 The Tu-on Transient 312

8.6 The Tunnel Diode 313

8.7 Summa 316

Problems 318

CHAPTER 9 Metal-Semiconductor and SemiconductorHeterojunctions 326

Preview 326

9.1 The Schottky Barrier Diode 326

9.1.1 Qualitative Characteristics 327

9.1.2 Ideal Junction Properties 329

9.1.3 Nonideal Eects on the Barrier Height 333

9.1.4 Current-Voltage Relationship 337

9.1.5 Comparison of the Schooky Barrier Diodeand the pn Junction Diode 341

9.2 Metal-Semiconductor Ohmic Contacts 344

9.2.1 Ideal Nonctifying Barriers 345

9.2.2 Tunneling Barrier 346

9.2.3 Specific Contact Resistance 348

9.3 Heterojunctions 349

9.3.1 Heterojunction Materials 350

9.3.2 Energy-Band Diagrams 350

9.3.3 Two-Dimensional Electron Gas 351

9.3.4 Equilibum Electrostatics 354

9.3.5 Curnt-Voltage Charactestics 359

9.4 Summa 359

Problems 361

CHAPTER 10 The Bipolar Transistor 367

Preview 367

10.1 The Bipolar Transistor Action 368

10.1.1 The Basic Principle of operation 369

10.1.2 Simplified Transistor CurrentRelations 370

10.1.3 The Modes of Operation 374

10.1.4 Amplification with BipolarTransistors 376

10.2 Minori Carrier Distribution 377

10.2.1 Forward-Active Mode 378

10.2.2 Other Modes of Operation 384

10.3 Low-Frequency Common-BaseCurrent Gain 385

10.3.1 Contributing Factors 386

10.3.2 Mathematical Derivation of CurrentGain Factors 388

10.3.3 Summa 392

10.3.4 Example Calculations of theGain Factors 393

10.4 Nonideal Effects 397

10.4.1 Base Width Modulation 397

10.4.2 High Injection 401

10.4.3 Emier Bandgap Narwing 403

10.4.4 Current Cwding 405

10.4.5 Nonuniform Base Doping 406

10.4.6 Breakdown Voltage 408

10.5 Equivalent Circuit Models 413

10.5.1 Ebers Moll Model 414

10.5.2 Gummel-Poon Model 416

10.5.3 Hybd-Pi Model 418

10.6 Frequency Limitations 422

10.6.1 Time-Delay Factors 422

10.6.2 Transistor Cutoff Frequency 424

10.7 Large-Signal Switching 427

10.7.1 Switching Characteristics 427

10.7.2 The Schonky-Clamped Transistor 429

10.8 Other Bipolar Transistor Structures 430

10.8.1 Polysilicon EmierBJT 430

10.8.2 Silicon-Germanium Base Transistor 431

10.8.3 Hetejunction Bipolar Transistors 434

10.9 Summa 435

Problems 438

CHAPTER 11 Fundamentals of the Metal-Oxide-Semiconductor Field-Effect Transistor 449

Preview 449

11.1 The Two-Terminal MOS Structure 450

11.1.1 Energy-Band Diagrams 450

11.1.2 Depletion Layer Thickness 455

11.1.3 Work Function Dierences 458

11.1.4 Ft-Band Voltage 462

11.1.5 Threshold Voltage 465

11.1.6 Charge Distribution 471

11.2 Capacitance-Voltage Characteristics 474

11.2.1 Ideal C-V Characteristics 474

11.2.2 Frequency Effects 479

11.2.3 Fixed Oxide and InterfaceCharge Eects 480

11.3 The Basic MOSFET Operation 483

11.3.1 MOSFET Structures 483

11.3.2 Current-Voltage Retionship—Concepts 486

11.3.3 Current-Voltage Relationship—Mathematical Derivation 490

11.3.4 Transconductance 498

11.3.5 Substrate Bias Effects 499

11.4 Frequency Limitations 502

11.4.1 Small-Signal Equivalent Circuit 502

11.4.2 Frequency Limitation Factorsand Cuto Frequency 504

11.5 The CMOS Technology 507

11.6 Summa 509

Problems 513

CHAPTER 12 Metal-Oxide--Semiconductor Field-EffectTransistor: Additional Concepts 523

Preview 523

12.1 Nonideal Effects 524

12.1.1 Subthreshold Conduction 524

12.1.2 Channel Length Modulation 526

12.1.3 Mobili Variation 530

12.1.4 Velocity Saturation 532

12.1.5 Ballistic Transport 534

12.2 MOSFET Scaling 534

12.2.1 Constant-Field Scaling 534

12.2.2 Threshold Voltage—FirstAppximations 535

12.2.3 Generalized Scaling 536

12.3 Threshold Voltage Modications 537

12.3.1 Short-Channel Eects 537

12.3.2 Narrow-Channel Eects 541

12.4 Additional Electcal Charactestics 543

12.4.1 Breakdown Voltage 544

12.4.2 The Lightly Doped DrainTransistor 550

12.4.3 Threshold Adjustment by IonImplantation 551

12.5 Radiation and Hot-Electron Effects 554

12.5.1 Radiation-Induced Oxide Charge 555

12.5.2 Radiation-Induced Interface States 558

12.5.3 Hot-Electn Charging Eects 560

12.6 Summa 561

Problems 563

CHAPTER 13 The Junction Field-Effect Transistor 570

Preview 570

13.1 gET Concepts 571

13.1.1 Basic pn JFET Operation 571

13.1.2 Basic MESFET Operation 575

13.2 The Device Characteristics 577

13.2.1 Internal Pincho Voltage, PinchoVolge, and Drain-to-SourceSaturation Voltage 577

13.2.2 Ideal DC Current-Voltage RelationshipDepletion Mode JFET 582

13.2.3 Transconductance 587

13.2.4 The MESFET 588

13.3 Nonideal Eects 593

13.3.1 Channel Length Modulation 594

13.3.2 Veloci Saturation Eects 596

13.3.3 Subthreshold and Gate CurrentEects 596

13.4 Equivalent Circuit and FrequencyLimitations 598

13.4.1 Small-Signal Equivalent Circuit 598

13.4.2 Frequency Limitation Factorsand Cuto Frequency 600

13.5 High Electron Mobili Transistor 602

13.5.1 Quantum Well Structures 603

13.5.2 Transistor Performance 604

13.6 Summa 609

Problems 611

CHAPTER 14 Optical Devices 617

Preview 617

14.1 Optical Absorption 618

14.1.1 Photon Absorption Coecient 618

14.1.2 Electron-Hole Pair GenerationRate 621

14.2 Solar Cells 623

14.2.1 The pn Junction Solar Cell 623

14.2.2 Conversion Eficiency and SolarConcentration 626

14.2.3 Nonuniform Absorption Eects 628

14.2.4 The Hetejunction Solar Cell 628

14.2.5 Amorphous Silicon Solar Cells 630

14.3 Photodetectors 631

14.3.1 Photoconductor 632

14.3.2 Photodiode 634

14.3.3 PIN Photodiode 639

14.3.4 Avalanche Photodiode 640

14.3.5 Phototransistor 641

14.4 Photoluminescence andElectroluminescence 642

14.4.1 Basic Transitions 643

14.4.2 Luminescent Eciency 645

14.4.3 Materials 645

14.5 Light Emitting Diodes 647

14.5.1 Generation of Light 648

14.5.2 Internal Quantum Efficiency 648

14.5.3 External Quantum Efciency 649

14.5.4 LED Devices 651

14.6 Laser Diodes 653

14.6.1 Stimulated Emission and PopulationInversion 654

14.6.2 Optical Cavity 656

14.6.3 Threshold Current 657

14.6.4 Device Structures andCharacteristics 658

14.7 Summa 661

Problems 663

CHAPTER 15 Semiconductor Power Devices 668

Preview 668

15.1 Power Bipolar Transistors 668

15.1.1 Vertical Power Transistor Structure 669

15.1.2 Power Transistor Characteristics 670

15.1.3 Darlington Pair Configuration 674

15.2 Power MOSFETs 676

15.2.1 Power Transistor Structures 676

15.2.2 Power MOSFET Characteristics 678

15.2.3 Parasitic BJT 682

15.3 Heat Sinks and JunctionTemperature 683

15.4 The Thyristor 686

15.4.1 The Basic Characteristics 686

15.4.2 Triggering the SCR 689

15.4.3 SCR Tu-Of 692

15.4.4 Device Structus 692

15.5 Summa 696

Problems 699

APPENDIX A Selected List of Symbols 730

APPENDIX B and General Constants 711

APPENDIX C The Periodic Table 715

APPENDIX D The Error Function 717

APPENDIX E “Derivation” ofSchrodiogr'sWaveEquation 719

APPENDIX F Unit of Energy——The Electron-Volt 721

APPENDIX G Answers to Selected Problems 723

Index 731