Nitride Semiconductor Devices

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Nitride Semiconductor Devices: Principles and Simulation 2007

Edited by Joachim Piprek

WILEY-VCH Verlag GmbH & Co. KGaA

Contents
Preface XV
List of Contributors XVII
Part 1 Material Properties 1
1 Introduction 3
Joachim Piprek
1.1 A Brief History 3
1.2 Unique Material Properties 4
1.3 Thermal Parameters 5
References 10
2 Electron Bandstructure Parameters 13
Igor Vurgaftman and Jerry R. Meyer
2.1 Introduction 13
2.2 Band Structure Models 14
2.3 Band Parameters 17
2.3.1 GaN 19
2.3.2 AlN 25
2.3.3 InN 28
2.3.4 AlGaN 30
2.3.5 InGaN 32
2.3.6 InAlN 34
2.3.7 AlGaInN 34
2.3.8 Band Offsets 35
2.4 Conclusions 36
References 37
3 Spontaneous and Piezoelectric Polarization: Basic Theory vs.
Practical Recipes 49
Fabio Bernardini
3.1 Why Spontaneous Polarization in III-V Nitrides? 49
3.2 Theoretical Prediction of Polarization Properties in AlN, GaN and
InN 51
3.3 Piezoelectric and Pyroelectric Effects in III-V Nitrides
Nanostructures 54
3.4 Polarization Properties in Ternary and Quaternary Alloys 58
3.5 Orientational Dependence of Polarization 64
References 67
4 Transport Parameters for Electrons and Holes 69
Enrico Bellotti and Francesco Bertazzi
4.1 Introduction 69
4.2 Numerical Simulation Model 70
4.2.1 Scattering in the Semi-Classical Boltzmann Equation 72
4.3 Analytical Models for the Transport Parameters 76
4.4 GaN Transport Parameters 79
4.4.1 Electron Transport Coefficients 79
4.4.2 Hole Transport Coefficients 81
4.5 AlN Transport Parameters 84
4.5.1 Electron Transport Coefficients 84
4.5.2 Hole Transport Coefficients 86
4.6 InN Transport Parameters 87
4.6.1 Electron Transport Coefficients 88
4.6.2 Hole Transport Coefficients 89
4.7 Conclusions 91
References 91
5 Optical Constants of Bulk Nitrides 95
Rüdiger Goldhahn, Carsten Buchheim, Pascal Schley, Andreas Theo
Winzer, and Hans Wenzel
5.1 Introduction 95
5.2 Dielectric Function and Band Structure 95
5.2.1 Fundamental Relations 95
5.2.2 Valence Band Ordering, Optical Selection Rules and Anisotropy 97
5.3 Experimental Results 99
5.3.1 InN 99
5.3.2 GaN and AlN 102
5.3.3 AlGaN Alloys 105
5.3.4 In-rich InGaN and InAlN Alloys 107
5.4 Modeling of the Dielectric Function 108
5.4.1 Analytical Representation of the Dielectric Function 109
5.4.2 Calculation of the Dielectric Function for Alloys 111
5.4.3 Influence of Electric Fields on the Dielectric Function 112
References 114
6 Intersubband Absorption in AlGaN/GaN Quantum Wells 117
Sulakshana Gunna, Francesco Bertazzi, Roberto Paiella, and Enrico
Bellotti
6.1 Introduction 117
6.2 Theoretical Model 118
6.2.1 Spontaneous and Piezoelectric Polarization 122
6.3 Numerical Implementation 123
6.3.1 Achieving Self-consistency: The Under-RelaxationMethod 127
6.3.2 Predictor–Corrector Approach 128
6.4 Absorption Energy in AlGaN-GaN MQWs 129
6.4.1 Numerical Analysis of Periodic AlGaN-GaN MQWs 130
6.4.2 Numerical Analysis of Non-periodic AlGaN-GaN MQWs and
Comparison with Experimental Results 138
6.5 Conclusions 141
References 142
7 Interband Transitions in InGaN Quantum Wells 145
Jörg Hader, Jerome V. Moloney, Angela Thränhardt, and Stephan W.
Koch
7.1 Introduction 145
7.2 Theory 146
7.2.1 Bandstructure andWavefunctions 146
7.2.2 Semiconductor Bloch Equations 149
7.2.3 Semiconductor Luminescence Equations 151
7.2.4 Auger Recombination Processes 152
7.3 Theory–Experiment Gain Comparison 154
7.4 Absorption/Gain 156
7.4.1 General Trends 156
7.4.2 Structural Dependence 159
7.5 Spontaneous Emission 161
7.6 Auger Recombinations 164
7.7 Internal Field Effects 164
7.8 Summary 166
References 167
8 Electronic and Optical Properties of GaN-based Quantum Wells with
(10¯10) Crystal Orientation 169
Seoung-Hwan Park and Shun-Lien Chuang
8.1 Introduction 169
8.2 Theory 170
8.2.1 Non-Markovian gain model with many-body effects 175
8.3 Results and Discussion 177
8.4 Summary 188
References 189
9 Carrier Scattering in Quantum-Dot Systems 191
Frank Jahnke
9.1 Introduction 191
9.2 Scattering Due to Carrier–Carrier Coulomb Interaction 193
9.2.1 Formulation of the Problem and Previous Developments 193
9.2.2 Kinetic Equation and Scattering Rates 195
9.2.3 Results for Carrier–Carrier Scattering 198
9.3 Scattering Due to Carrier–Phonon Interaction 200
9.3.1 Perturbation Theory Versus Polaron Picture 200
9.3.2 Polaron States and Kinetics 202
9.3.3 Results for Carrier Scattering Due to LO-phonons 204
9.4 Summary and Outlook 207
References 208
Part 2 Devices 211
10 AlGaN/GaN High Electron Mobility Transistors 213
Tomás Palacios and Umesh K. Mishra
10.1 Introduction 213
10.2 Physics-based Simulations 216
10.2.1 Basic Material Properties 217
10.2.2 Polarization 218
10.2.3 Surface States 222
10.2.4 Electron Mobility 224
10.2.5 Breakdown Voltage 227
10.2.6 Energy Balance Models 228
10.3 Conclusions 230
References 231
11 Intersubband Optical Switches for Optical Communications 235
Nobuo Suzuki
11.1 Introduction 235
11.2 Physics of ISBT in Nitride MQWs 236
11.2.1 Dipole Moment 236
11.2.2 Rate Equations 236
11.2.3 Absorption 238
11.2.4 Relaxation Time 239
11.2.5 Dephasing Time and Spectral Linewidth 240
11.3 Calculation of Absorption Spectra 242
11.3.1 TransitionWavelength and Built-In Field 242
11.3.2 Absorption Spectra 243
11.4 FDTD Simulator for GaN/AlGaN ISBT Switches 244
11.4.1 Model 245
11.4.2 Saturation of Absorption 246
11.4.3 Temporal Response 248
11.4.4 Future Applications 249
References 251
12 Intersubband Electroabsorption Modulator 253
Petter Holmström
12.1 Introduction 253
12.2 Modulator Structure 256
12.2.1 Multiple-Quantum-Well Structure 256
12.2.2 Waveguide and Contacting 259
12.3 Model 261
12.3.1 Conduction Band Potential and Active Layer Biasing 261
12.3.2 Intersubband Transitions 263
12.3.3 Optical Mode and the Plasma Effect 265
12.4 Results 266
12.4.1 Electroabsorption 266
12.4.2 Chirp Parameter 269
12.4.3 Electrical Properties 270
12.4.4 Figure of Merit 271
12.4.5 Absorption Saturation 272
12.4.6 Thermal Properties and Current 273
12.4.7 Significance of the Linewidth 275
12.5 Summary 276
References 276
13 Ultraviolet Light-Emitting Diodes 279
Yen-Kuang Kuo, Sheng-Horng Yen, and Jun-Rong Chen
13.1 Introduction 279
13.2 Device Structure 281
13.3 Physical Models and Parameters 282
13.3.1 Band Structure 283
13.3.2 Polarization Effects 285
13.3.3 Carrier Transport Model 287
13.3.4 Thermal Model 288
13.3.5 Spontaneous Emission 288
13.3.6 Ray Tracing 290
13.4 Comparison Between Simulated and Experimental Results 291
13.5 Performance Optimization 293
13.5.1 Optimal Aluminum Composition in p-AlGaN Electron Blocking
Layer 293
13.5.2 Optimal Number of QuantumWells 294
13.5.3 Lattice-matched AlInGaN Electron Blocking Layer 296
13.6 Conclusion 299
References 300
14 Visible Light-Emitting Diodes 303
Sergey Yu. Karpov
14.1 Introduction 303
14.2 Simulation Approach and Materials Properties 304
14.3 Device Analysis 309
14.3.1 Band Diagrams, Carrier Concentrations, and Partial Currents 310
14.3.2 Internal Quantum Efficiency and Carrier Leakage 312
14.3.3 Emission Spectra 315
14.3.4 Polarity Effects 317
14.4 Novel LED Structures 320
14.4.1 LED with Indium-free Active Region 320
14.4.2 Hybrid ZnO/AlGaN LED 321
14.5 Conclusion 323
References 324
15 Simulation of LEDs with Phosphorescent Media for the Generation of
White Light 327
Norbert Linder, Dominik Eisert, Frank Jermann, and Dirk Berben
15.1 Introduction 327
15.2 Requirements for a Conversion LED Model 328
15.3 Color Metrics for Conversion LEDs 330
15.4 Phosphor Model 332
15.4.1 Phosphor Materials 332
15.4.2 Luminescence and Absorption of Phosphor Particles 334
15.4.3 Scattering of Phosphor Particles 335
15.4.4 Determination of Material Parameters 341
15.4.5 LED Ray Tracing Model 344
15.5 Simulation Examples 346
15.6 Conclusions 350
References 350
16 Fundamental Characteristics of Edge-Emitting Lasers 353
Gen-ichi Hatakoshi
16.1 Introduction 353
16.2 Basic Equations for the Device Simulation 354
16.2.1 Electrical and Optical Simulation 354
16.2.2 Simulation Model for Thermal Analysis 357
16.3 Simulation for Electrical Characteristics and Carrier Overflow
Analysis 359
16.4 Perpendicular TransverseMode and Beam Quality Analysis 366
16.5 Thermal Analysis 370
16.6 Conclusions 378
References 378
17 Resonant Internal Transverse-Mode Coupling in InGaN/GaN/AlGaN
Lasers 381
Gennady A. Smolyakov and Marek Osi ´ nski
17.1 Introduction 381
17.2 Internal Mode Coupling and the Concept of “Ghost Modes” 382
17.3 Device Structure and Material Parameters 384
17.4 Calculation Technique 385
17.5 Results of Calculations 386
17.5.1 Resonant Conditions 386
17.5.2 Spatial Characteristics of Laser Emission under the Resonant
Internal Mode Coupling 391
17.5.3 Spectral Effects of the Resonant Internal Mode Coupling 394
17.5.4 Carrier-Induced Resonant Internal Mode Coupling 396
17.6 Discussion and Conclusions 399
References 401
18 Optical Properties of Edge-Emitting Lasers: Measurement and
Simulation 405
Ulrich T. Schwarz and Bernd Witzigmann
18.1 Introduction 405
18.2 Waveguide Mode Stability 406
18.3 Optical Waveguide Loss 412
18.4 Mode Gain Analysis 417
18.5 Conclusion 420
References 422
19 Electronic Properties of InGaN/GaN Vertical-Cavity Lasers 423
Joachim Piprek, Zhan-Ming Li, Robert Farrell, Steven P. DenBaars, and
Shuji Nakamura
19.1 Introduction to Vertical-Cavity Lasers 423
19.2 GaN-based VCSEL Structure 424
19.3 Theoretical Models and Material Parameters 425
19.3.1 Carrier Transport 426
19.3.2 Electron Band Structure 429
19.3.3 Built-In Polarization 432
19.3.4 Photon Generation in the QuantumWells 434
19.3.5 Optical Mode 436
19.4 Simulation Results and Device Analysis 437
19.4.1 Current Confinement 438
19.4.2 Polarization Effects 438
19.4.3 Threshold Current 440
19.4.4 AlGaN Doping 442
19.4.5 AlGaN Composition 443
19.5 Summary 443
References 443
20 Optical Design of Vertical-Cavity Lasers 447
Włodzimierz Nakwaski, Tomasz Czyszanowski, and Robert P. Sarzała
20.1 Introduction 447
20.2 The GaN VCSEL Structure 449
20.3 The Scalar Optical Approach 453
20.4 The Vectorial Optical Approach 454
20.5 The Self-consistent Calculation Algorithm 458
20.6 Simulation Results 460
20.7 Discussion and Conclusions 464
References 465
21 GaN Nanowire Lasers 467
Alexey V. Maslov and Cun-Zheng Ning
21.1 Introduction 467
21.2 Nanowire Growth and Characterization 469
21.3 Nanowire Laser Principles 470
21.4 Anisotropy of Material Gain 471
21.5 Guided Modes 475
21.5.1 Guided Modes, Dispersions, and Mode Spacing 476
21.5.2 Reflection from Facets 479
21.5.3 Far-field Pattern 481
21.5.4 Confinement Factors for Anisotropic Nanowires 483
21.5.5 Spontaneous Emission Factors 486
21.6 Modal Gain and Threshold 488
21.7 Conclusion 489
References 490
Index 493

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