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Full Description
Complete coverage of the field of silicon-based photonic devices, including a chapter on nonlinear silicon photonics
Silicon Photonics discusses the physics, technology, and device operation of photonic devices using silicon, Group IV semiconductors, and their alloys. The book delivers an optimal combination of background information about photonic structures with description of up-to-date results and trends in silicon photonics. This Second Edition includes a new chapter on nonlinear silicon photonics as well as numerous updates to existing content.
Readers will find information on the role of silicon in photonics and its advantages and disadvantages as well as the properties of these alloys. Subsequent chapters in Silicon Photonics explore topics including:
Quantum structures, covering quantum wells, wires, and dots, superlattices, Si-based quantum structures, and effects of electric fields
Optical processes, covering absorption processes in semiconductors, intervalence band absorption, free-carrier absorption, and recombination and luminescence
Si light modulators, covering electrorefraction, thermo-optic effects, modulators, and optical and electrical structures
Raman lasers, covering Raman scattering, the Raman effect in silicon, the Raman gain coefficient, and continuous-wave Raman lasers
Principles of planar waveguide devices, covering directional couplers and distributed Bragg reflectors
Silicon Photonics is an excellent resource on the subject for materials scientists, applied physicists, electrical engineers, and postgraduate students working in Si photonics.
Contents
Preface xi
Volume 1
1. Introduction to Silicon Photonics 1
1.1 Introduction 1
1.2 VLSI: Past, Present, and Future Roadmap 3
1.3 The Interconnect Problem in VLSI 4
1.4 The Long-Haul Optical Communication Link 7
1.4.1 Basic Link and Components 7
1.4.2 Materials and Integration 10
1.5 Data Network 11
1.6 Conclusions 12
1.7 Scope of the Book 12
References 18
2. Basic Properties of Silicon 21
2.1 Introduction 22
2.2 Band Structure 22
2.2.1 E-k Diagram: General Considerations 22
2.2.2 Band Properties Near Extrema 26
2.2.3 Refined Theory for Band Structures 29
2.2.4 Temperature- and Pressure-Dependent Bandgap 29
2.2.5 Band Structure in Ge 30
2.3 Density-of-States Function 32
2.4 Impurities 35
2.4.1 Donors and Acceptors 35
2.4.2 Isoelectronic Impurities 37
2.5 Alloys of Silicon and Other Group IV Elements 38
2.5.1 Different Alloy Systems 38
2.5.2 Lattice Constants 39
2.5.3 Band Structures of Unstrained Alloys 40
2.6 Heterojunctions and Band Lineup 41
2.7 Si-Based Heterostructures 43
2.7.1 Lattice-Mismatched Heteroepitaxy 43
2.7.2 Pseudomorphic Growth and Critical Thickness 43
2.7.3 Elasticity Theory: Stress and Strain 44
2.7.4 Expressions for Critical Thickness 46
2.7.5 Strain Symmetric Structures and Virtual Substrates 47
2.7.6 Band Offsets and Band Lineup 50
2.7.7 Electronic Properties of SiGe/Si Heterostructures 55
2.8 Direct Gap: Ge/SiGeSn Heterojunctions 58
2.8.1 Structures 58
2.8.2 Band Edges and Band Lineup 59
2.8.3 Direct-Gap GeSn Alloy 64
Problems 67
References 68
Suggested Readings 70
3. Quantum Structures 71
3.1 Introduction 71
3.2 Quantum Wells 71
3.2.1 Quantum Confinement 72
3.2.2 A Representative Structure 73
3.2.3 Simplified Energy Levels 74
3.2.4 Density of States in Two Dimensions 77
3.2.5 Finite Quantum Well 80
3.2.6 Refined Methods 81
3.2.7 Different Band Alignments 83
3.3 Quantum Wires and Dots 83
3.3.1 Subbands and DOS in Quantum Wires 84
3.3.2 Quantum Dots 86
3.4 Superlattices 88
3.5 Silicon-Based Quantum Structures 91
3.5.1 Electron Subband Structure 92
3.5.2 Hole Subbands 95
3.5.3 Quantum Wells and Barriers 97
3.6 Effect of Electric Field 101
3.6.1 External Electric Field in Quantum Wells 102
3.6.2 Perturbation Theory for Weak Fields 102
3.6.3 Matrix Element and Energy Shift 102
3.6.4 Physical Implications 103
3.6.5 Physical Insights of Eq. (3.44) 103
Problems 105
References 107
Suggested Readings 108
4. Optical Processes 109
4.1 Introduction 109
4.2 Optical Constants and Electromagnetic Wave Propagation 110
4.3 Basic Concepts 114
4.3.1 Absorption and Emission 114
4.3.2 Absorption and Emission Rates 115
4.4 Absorption Processes in Semiconductors 117
4.5 Fundamental Absorption in Direct Bandgap Semiconductors 119
4.5.1 Conservation Laws in Interband Absorption 119
4.5.2 Calculation of Absorption Coefficient 121
4.6 Fundamental Absorption in Indirect-Gap Semiconductors 128
4.6.1 Theory of Absorption in Indirect-Gap Semiconductors 128
4.6.2 Absorption Spectra in Silicon 131
4.6.3 Absorption Spectra in Germanium 133
4.7 Absorption and Gain in Semiconductors 134
4.7.1 From Absorption to Population Inversion 135
4.7.2 Stimulated Emission and Gain Coefficient 136
4.7.3 Gain Coefficient Derivation 137
4.8 Intervalence Band Absorption 138
4.9 Free-Carrier Absorption 139
4.10 Recombination and Luminescence 143
4.10.1 Luminescence Lifetime 143
4.10.2 Carrier Lifetime and Density Dependence 146
4.10.3 Absorption and Recombination 146
4.10.4 Microscopic Theory of Recombination 148
4.11 Nonradiative Recombination 150
4.11.1 Recombination via Traps (Shockley-Read-Hall-Theory) 150
4.11.2 Auger Recombination 154
4.11.3 Surface Recombination 156
4.11.4 Recombination of Complexes 157
4.12 Excitonic and Impurity Absorption 157
4.12.1 Excitons 158
4.12.2 Impurity Absorption 159
4.12.3 Bound Excitons 160
4.12.4 Isoelectronic Centers 161
Problems 162
References 164
5. Optical Processes in Quantum Structures 167
5.1 Introduction 167
5.2 Optical Processes in QWs 168
5.2.1 Absorption in Direct-Gap QW 168
5.2.2 Gain in QW 171
5.2.3 Recombination in QWs 173
5.2.4 Polarization-Dependent Momentum Matrix Element 174
5.2.5 Absorption in the Indirect Gap 176
5.2.6 Absorption in Type-II QWs 179
5.3 Intersubband Transitions 180
5.3.1 Conduction Subbands: Isotropic Mass 182
5.3.2 Anisotropic Mass 184
5.3.3 Intervalence Band Absorption 186
5.4 Excitonic Processes in QWs 186
5.4.1 Excitons in 2D: Preliminary Concepts 187
5.4.2 Excitons in Purely 2D Systems 187
5.4.3 Excitonic Absorption in Direct-Gap QWs 190
5.4.4 Excitonic Processes in Indirect-Gap QWs 191
5.4.5 Photoluminescence in QWs 193
5.5 Effect of Electric Fields 194
5.5.1 Qualitative Discussion of Electroabsorption 194
5.5.2 Electroabsorption and Electrorefraction in SiGe QWs 195
5.6 Optical Processes in QWRs 199
5.7 Optical Processes in QDs 202
5.8 Optical Processes in Si QWRs and QDs 205
Problems 206
References 207
6. Light Emitters in Si 211
6.1 Introduction 211
6.2 Basic Principles of Light Emission in Semiconductors 212
6.2.1 Nonradiative Recombination and Internal Quantum Efficiency 213
6.2.2 Limitations in Indirect-Gap Semiconductors: The Case of
Silicon 214
6.2.3 Outlook and Motivation for Advanced Strategies 215
6.3 Early Approaches—Zone Folding in Si-Ge Superlattices 215
6.4 Band Structure Engineering Using Alloys 217
6.5 Quantum Confinement 220
6.5.1 Quasi-Direct No-Phonon Transitions 220
6.5.2 Porous Silicon 222
6.5.3 Silicon Nanocrystals 224
6.5.4 Quantum Wells, Wires, and Dots 226
6.6 Impurities in Silicon 229
6.6.1 Isoelectronic Impurities 229
6.6.2 Rare-Earth Luminescence 229
6.7 Stimulated Emission: Prospect 237
6.7.1 Silicon Nanocrystals 237
6.7.2 Bulk Silicon 241
6.8 Intersubband Emission 242
6.8.1 Emission in the Mid-Infrared 243
6.8.2 Terahertz Emission 244
6.9 Tensile-Strained Ge Layers 248
6.10 GeSn Lasers: Toward Silicon-Compatible Light Sources 251
Problems 257
References 258
7. Si Light Modulators 263
7.1 Introduction 263
7.2 Physical Effects 265
7.2.1 Electroabsorption and Electrorefraction 266
7.2.2 Electro-Optic Effect 267
7.2.3 Franz-Keldysh Effect 270
7.2.4 Quantum-Confined Stark Effect 271
7.2.5 Carrier-Induced Effects 271
7.2.6 Thermo-Optic Effect 272
7.3 Electrorefraction in Silicon 273
7.3.1 Electro-Optic Effects 273
7.3.2 Carrier Effect 273
7.3.3 Quantum Confined Stark Effect 275
7.4 Thermo-Optic Effects in Si 276
7.5 Modulators: Some Key Characteristics 278
7.5.1 Modulation Depth 278
7.5.2 Modulation Bandwidth 278
7.5.3 Insertion Loss 279
7.5.4 Power Consumption 280
7.5.5 Isolation 280
7.6 Modulation Bandwidth Under Injection 280
7.7 Optical Structures 282
7.7.1 MZI 283
7.7.2 Fabry-Perot Resonator 284
7.7.3 MZI Versus a Resonator 286
7.8 Electrical Structures 287
7.8.1 p-i-n Structures 289
7.8.2 Three-Terminal Structures 289
7.8.3 Smaller Structures 290
7.8.4 MOS Capacitors 291
7.8.5 MQW Structures 293
7.9 High-Bandwidth Modulators 294
7.9.1 Ring Resonator 294
7.9.2 MZ Modulators at 10 Gb/s and Above 296
7.9.3 Microring Resonators 297
7.9.4 Reverse Biased p-n Diode 299
7.10 Performance of EO Modulators 299
7.11 Summarizing Comments of Performance Metrics 299
Future Trends 300
Problems 305
References 306
8. Silicon Photodetectors 309
8.1 Introduction 309
8.2 Optical Detection 311
8.3 Important Characteristics of Photodetectors 315
8.3.1 Quantum Efficiency 315
8.3.2 Responsivity 318
8.3.3 Bandwidth 320
8.3.4 Gain 321
8.3.5 Noise and Noise Equivalent Power 321
8.3.6 Wavelength Sensitivity Range 324
8.3.7 Cost and Yield 324
8.3.8 Other Characteristics 325
8.4 Examples of Types of Photodetectors 326
8.5 Examples of Photodiodes in Standard Silicon Technology 332
8.6 Phototransistors in Standard Silicon Technology 337
8.7 CMOS and BiCMOS 339
8.8 Silicon-on-Insulator 339
8.9 Photodetectors Using Heteroepitaxy 343
8.9.1 Si-SiGe Multiple Quantum Wells 344
8.9.2 Ge Detectors on Si 350
8.9.3 Related Theoretical Discussion 357
8.10 Single-Photon Avalanche Diodes (SPADs) 362
8.10.1 Introduction 362
8.10.2 Performance Parameters 366
8.10.3 State-of-the-Art Silicon-Based SPADs 373
8.10.4 Key Challenges and Future Perspectives 377
References for Tables 8.1 to 8.3 378
Problems 380
References 382
Volume 2
9. Raman Lasers 387
9.1 Introduction 387
9.2 Raman Scattering: Basic Concepts 390
9.2.1 Stokes and Anti-Stokes Lines 391
9.2.2 Stimulated Raman Scattering 395
9.3 Simplified Theory of Raman Scattering 398
9.4 Raman Effect in Silicon 402
9.5 Raman Gain Coefficient 404
9.5.1 Mathematical Model 405
9.5.2 Simulation Parameters 407
9.5.3 Threshold Power 408
9.6 Continuous-Wave Raman Laser 411
9.6.1 Device Structure and Design Considerations 412
9.7 Further Developments, Challenges, and Perspectives in Silicon Raman
Lasers 415
9.7.1 Optimization Strategies and First-Generation Enhancements 416
9.7.2 Device Design Innovations 416
9.7.3 Photonic Crystals and Nanoscale Cavity Lasers 417
9.7.4 Silicon Nanostructures and Giant Raman Enhancement 417
9.7.5 Recent Advances and Emerging Directions 417
9.7.6 Challenges and Future Perspectives 418
Problems 420
References 420
10. Guided Light Waves: Introduction 423
10.1 Introduction 423
10.2 Ray-Optic Theory for Light Guidance 424
10.3 Reflection Coefficients 426
10.4 Modes of a Planar Waveguide 428
10.4.1 Symmetrical Planar Waveguide 431
10.4.2 Asymmetric Waveguide 433
10.4.3 Single-Mode Condition 433
10.4.4 Effective Index of a Mode 434
10.5 Wave Theory of Light Guides 435
10.5.1 Wave Equation in a Dielectric 435
10.5.2 The Ideal Slab Waveguide 436
10.6 3D Optical Waveguides 445
10.6.1 Practical Waveguiding Geometries 445
10.6.2 Ray-Optic Approach for 3D Guides 448
10.6.3 Approximate Analyses of Guided Modes 448
10.7 Loss Mechanisms in Waveguides 455
10.7.1 Scattering Loss 455
10.7.2 Absorption Loss 459
10.7.3 Radiation Loss 460
10.7.4 Coupling Loss 462
10.8 Coupling to Optical Devices 463
10.8.1 Grating Couplers 463
10.8.2 Butt Coupling and End-Fire Coupling 465
10.9 Other Ways of Guiding Light Waves 473
Problems 474
References 476
Suggested Readings 477
11. Principle of Planar Waveguide Devices 479
11.1 Introduction 479
11.2 Model for Mode Coupling 480
11.2.1 Physical Interpretation 484
11.3 Directional Coupler 484
11.3.1 Phase-Matched Directional Coupler 484
11.3.2 Non-Phase-Matched Coupler 487
11.4 Distributed Bragg Reflector 489
11.4.1 Phase-Matched Grating 489
11.4.2 Non-Phase-Matched Grating 494
11.5 Some Useful Planar Devices 495
11.5.1 Splitters 495
11.5.2 Dual-Channel Directional Coupler 495
11.5.3 Mach-Zehnder Interferometer 497
11.5.4 Fabry-Perot Resonators 500
11.5.5 Bragg Gratings 503
11.5.6 Dielectric Mirrors 507
11.5.7 Ring Resonators 507
11.5.8 Multiple-Ring Resonators 511
11.5.9 Variable Optical Attenuator 512
11.5.10 Multimode Interferometer (MMI) 514
Problems 515
References 517
12. Waveguides for Dense Wavelength-Division Multiplexing Systems 519
12.1 Introduction 519
12.2 Structure and Operation of AWGs 521
12.2.1 Structure and Working Principle 521
12.2.2 Analysis 522
12.3 AWG Characteristics 526
12.3.1 Tuning and Free Spectral Range 526
12.3.2 Frequency Response 531
12.3.3 Channel Crosstalk 531
12.3.4 Polarization Dependence 532
12.4 Methods for Enhancing AWG Performance 533
12.4.1 Flat Frequency Response 533
12.4.2 Polarization Independence 535
12.4.3 Polarization Independence in Arrayed Waveguide Gratings 535
12.4.4 Temperature Insensitivity 537
12.5 Applications of AWGs 540
12.5.1 Demultiplexers and Multiplexers 540
12.5.2 Wavelength Routers 541
12.5.3 Multiwavelength Receivers and Transmitters 543
12.5.4 Add-Drop Multiplexers (ADMs) 545
12.5.5 Optical Cross-Connects: Reconfigurable Wavelength Routers 548
12.5.6 Dispersion Equalizer 550
12.6 PHASAR-Based Devices on Different Materials 552
12.6.1 Silica-on-Silicon 552
12.6.2 Silicon-On-Insulator 554
12.6.3 Silicon Oxynitride 555
12.7 Echelle Grating 557
Problems 559
References 560
13. Nonlinear Silicon Photonics 565
13.1 Introduction 565
13.2 Optical Processes and Nonlinearity 565
13.2.1 Origins of Optical Nonlinearity 565
13.2.2 First-Order Processes 570
13.2.3 Second-Order Processes 573
13.2.4 Third-Order Processes 574
13.3 Phase Matching and Quasi-Phase Matching 576
13.3.1 Phase-Matching Condition 576
13.3.2 Quasi-Phase Matching 580
13.4 Some Theoretical Aspects of Optical Pulse Propagation 583
13.4.1 Group Velocity Dispersion 583
13.4.2 Nonlinear Schrödinger Equation 589
13.5 Silicon Structures with Optical Nonlinearity 601
13.5.1 Waveguides 601
13.5.2 Microcavity Resonators 603
13.6 Optical Nonlinearity in Silicon and Applications 604
13.6.1 Second-Order Nonlinearity 604
13.6.2 Third-Order Nonlinearity 615
Problems 642
References 643
14. Fabrication Techniques and Materials Systems 647
14.1 Introduction 647
14.2 Planar Processing 651
14.3 Substrate Growth and Preparation 651
14.3.1 Deposition and Growth of Materials 652
14.3.2 Epitaxial Growth 658
14.3.3 Molecular Beam Epitaxy (MBE) 658
14.4 Material Modification 660
14.4.1 Diffusion 660
14.4.2 Ion Implantation 663
14.5 Etching 666
14.5.1 Wet Etching 666
14.5.2 Dry Etching 668
14.5.3 Maskless Etching 669
14.5.4 Reactive Etching 671
14.6 Lithography 673
14.6.1 Mask Fabrication 673
14.6.2 Pattern Transfer 674
14.7 Fabrication of Waveguides 675
14.7.1 Silica-on-Silicon 675
14.7.2 Formation of Waveguides Using Silicon-on-Insulator 676
14.8 Grating Formation Process 681
14.8.1 Photosensitivity of Glass 681
14.8.2 Grating Formation 682
14.9 Materials Systems for Waveguide Formation 685
14.9.1 General Considerations 685
14.9.2 Characteristics of Guides and Simple Planar Components 686
14.9.3 A Comparative Study of Materials Systems 702
Questions and Problems 705
References 707
Suggested Reading 710
Appendix A k p Method 713
Appendix B Bra-Ket Notation 741
Appendix C Values of Parameters 753
Index 000
