Silicon Photonics, 2 Volume Set

M. Jamal Deen, PhD, is Director of the Micro- & Nano Systems Lab and Research Chair in Information Technology at McMaster University, Canada. Prasanta Kumar Basu, PhD, worked in the Institute of Radio Physics and Electronics at the University of Calcutta, India, as a Lecturer, then as a Reader and a Professor, until his retirement. Nikhil R. Das, PhD, Professor at the University of Calcutta, India, specializes in semiconductor nanoelectronics and photonics.

• Preface xiVolume 11. Introduction to Silicon Photonics 11.1 Introduction 11.2 VLSI: Past, Present, and Future Roadmap 31.3 The Interconnect Problem in VLSI 41.4 The Long-Haul Optical Communication Link 71.4.1 Basic Link and Components 71.4.2 Materials and Integration 101.5 Data Network 111.6 Conclusions 121.7 Scope of the Book 12References 182. Basic Properties of Silicon 212.1 Introduction 222.2 Band Structure 222.2.1 E–k Diagram: General Considerations 222.2.2 Band Properties Near Extrema 262.2.3 Refined Theory for Band Structures 292.2.4 Temperature- and Pressure-Dependent Bandgap 292.2.5 Band Structure in Ge 302.3 Density-of-States Function 322.4 Impurities 352.4.1 Donors and Acceptors 352.4.2 Isoelectronic Impurities 372.5 Alloys of Silicon and Other Group IV Elements 382.5.1 Different Alloy Systems 382.5.2 Lattice Constants 392.5.3 Band Structures of Unstrained Alloys 402.6 Heterojunctions and Band Lineup 412.7 Si-Based Heterostructures 432.7.1 Lattice-Mismatched Heteroepitaxy 432.7.2 Pseudomorphic Growth and Critical Thickness 432.7.3 Elasticity Theory: Stress and Strain 442.7.4 Expressions for Critical Thickness 462.7.5 Strain Symmetric Structures and Virtual Substrates 472.7.6 Band Offsets and Band Lineup 502.7.7 Electronic Properties of SiGe/Si Heterostructures 552.8 Direct Gap: Ge/SiGeSn Heterojunctions 582.8.1 Structures 582.8.2 Band Edges and Band Lineup 592.8.3 Direct-Gap GeSn Alloy 64Problems 67References 68Suggested Readings 703. Quantum Structures 713.1 Introduction 713.2 Quantum Wells 713.2.1 Quantum Confinement 723.2.2 A Representative Structure 733.2.3 Simplified Energy Levels 743.2.4 Density of States in Two Dimensions 773.2.5 Finite Quantum Well 803.2.6 Refined Methods 813.2.7 Different Band Alignments 833.3 Quantum Wires and Dots 833.3.1 Subbands and DOS in Quantum Wires 843.3.2 Quantum Dots 863.4 Superlattices 883.5 Silicon-Based Quantum Structures 913.5.1 Electron Subband Structure 923.5.2 Hole Subbands 953.5.3 Quantum Wells and Barriers 973.6 Effect of Electric Field 1013.6.1 External Electric Field in Quantum Wells 1023.6.2 Perturbation Theory for Weak Fields 1023.6.3 Matrix Element and Energy Shift 1023.6.4 Physical Implications 1033.6.5 Physical Insights of Eq. (3.44) 103Problems 105References 107Suggested Readings 1084. Optical Processes 1094.1 Introduction 1094.2 Optical Constants and Electromagnetic Wave Propagation 1104.3 Basic Concepts 1144.3.1 Absorption and Emission 1144.3.2 Absorption and Emission Rates 1154.4 Absorption Processes in Semiconductors 1174.5 Fundamental Absorption in Direct Bandgap Semiconductors 1194.5.1 Conservation Laws in Interband Absorption 1194.5.2 Calculation of Absorption Coefficient 1214.6 Fundamental Absorption in Indirect-Gap Semiconductors 1284.6.1 Theory of Absorption in Indirect-Gap Semiconductors 1284.6.2 Absorption Spectra in Silicon 1314.6.3 Absorption Spectra in Germanium 1334.7 Absorption and Gain in Semiconductors 1344.7.1 From Absorption to Population Inversion 1354.7.2 Stimulated Emission and Gain Coefficient 1364.7.3 Gain Coefficient Derivation 1374.8 Intervalence Band Absorption 1384.9 Free-Carrier Absorption 1394.10 Recombination and Luminescence 1434.10.1 Luminescence Lifetime 1434.10.2 Carrier Lifetime and Density Dependence 1464.10.3 Absorption and Recombination 1464.10.4 Microscopic Theory of Recombination 1484.11 Nonradiative Recombination 1504.11.1 Recombination via Traps (Shockley–Read–Hall–Theory) 1504.11.2 Auger Recombination 1544.11.3 Surface Recombination 1564.11.4 Recombination of Complexes 1574.12 Excitonic and Impurity Absorption 1574.12.1 Excitons 1584.12.2 Impurity Absorption 1594.12.3 Bound Excitons 1604.12.4 Isoelectronic Centers 161Problems 162References 1645. Optical Processes in Quantum Structures 1675.1 Introduction 1675.2 Optical Processes in QWs 1685.2.1 Absorption in Direct-Gap QW 1685.2.2 Gain in QW 1715.2.3 Recombination in QWs 1735.2.4 Polarization-Dependent Momentum Matrix Element 1745.2.5 Absorption in the Indirect Gap 1765.2.6 Absorption in Type-II QWs 1795.3 Intersubband Transitions 1805.3.1 Conduction Subbands: Isotropic Mass 1825.3.2 Anisotropic Mass 1845.3.3 Intervalence Band Absorption 1865.4 Excitonic Processes in QWs 1865.4.1 Excitons in 2D: Preliminary Concepts 1875.4.2 Excitons in Purely 2D Systems 1875.4.3 Excitonic Absorption in Direct-Gap QWs 1905.4.4 Excitonic Processes in Indirect-Gap QWs 1915.4.5 Photoluminescence in QWs 1935.5 Effect of Electric Fields 1945.5.1 Qualitative Discussion of Electroabsorption 1945.5.2 Electroabsorption and Electrorefraction in SiGe QWs 1955.6 Optical Processes in QWRs 1995.7 Optical Processes in QDs 2025.8 Optical Processes in Si QWRs and QDs 205Problems 206References 2076. Light Emitters in Si 2116.1 Introduction 2116.2 Basic Principles of Light Emission in Semiconductors 2126.2.1 Nonradiative Recombination and Internal Quantum Efficiency 2136.2.2 Limitations in Indirect-Gap Semiconductors: The Case ofSilicon 2146.2.3 Outlook and Motivation for Advanced Strategies 2156.3 Early Approaches—Zone Folding in Si–Ge Superlattices 2156.4 Band Structure Engineering Using Alloys 2176.5 Quantum Confinement 2206.5.1 Quasi-Direct No-Phonon Transitions 2206.5.2 Porous Silicon 2226.5.3 Silicon Nanocrystals 2246.5.4 Quantum Wells, Wires, and Dots 2266.6 Impurities in Silicon 2296.6.1 Isoelectronic Impurities 2296.6.2 Rare-Earth Luminescence 2296.7 Stimulated Emission: Prospect 2376.7.1 Silicon Nanocrystals 2376.7.2 Bulk Silicon 2416.8 Intersubband Emission 2426.8.1 Emission in the Mid-Infrared 2436.8.2 Terahertz Emission 2446.9 Tensile-Strained Ge Layers 2486.10 GeSn Lasers: Toward Silicon-Compatible Light Sources 251Problems 257References 2587. Si Light Modulators 2637.1 Introduction 2637.2 Physical Effects 2657.2.1 Electroabsorption and Electrorefraction 2667.2.2 Electro-Optic Effect 2677.2.3 Franz–Keldysh Effect 2707.2.4 Quantum-Confined Stark Effect 2717.2.5 Carrier-Induced Effects 2717.2.6 Thermo-Optic Effect 2727.3 Electrorefraction in Silicon 2737.3.1 Electro-Optic Effects 2737.3.2 Carrier Effect 2737.3.3 Quantum Confined Stark Effect 2757.4 Thermo-Optic Effects in Si 2767.5 Modulators: Some Key Characteristics 2787.5.1 Modulation Depth 2787.5.2 Modulation Bandwidth 2787.5.3 Insertion Loss 2797.5.4 Power Consumption 2807.5.5 Isolation 2807.6 Modulation Bandwidth Under Injection 2807.7 Optical Structures 2827.7.1 MZI 2837.7.2 Fabry–Perot Resonator 2847.7.3 MZI Versus a Resonator 2867.8 Electrical Structures 2877.8.1 p–i–n Structures 2897.8.2 Three-Terminal Structures 2897.8.3 Smaller Structures 2907.8.4 MOS Capacitors 2917.8.5 MQW Structures 2937.9 High-Bandwidth Modulators 2947.9.1 Ring Resonator 2947.9.2 MZ Modulators at 10 Gb/s and Above 2967.9.3 Microring Resonators 2977.9.4 Reverse Biased p–n Diode 2997.10 Performance of EO Modulators 2997.11 Summarizing Comments of Performance Metrics 299Future Trends 300Problems 305References 3068. Silicon Photodetectors 3098.1 Introduction 3098.2 Optical Detection 3118.3 Important Characteristics of Photodetectors 3158.3.1 Quantum Efficiency 3158.3.2 Responsivity 3188.3.3 Bandwidth 3208.3.4 Gain 3218.3.5 Noise and Noise Equivalent Power 3218.3.6 Wavelength Sensitivity Range 3248.3.7 Cost and Yield 3248.3.8 Other Characteristics 3258.4 Examples of Types of Photodetectors 3268.5 Examples of Photodiodes in Standard Silicon Technology 3328.6 Phototransistors in Standard Silicon Technology 3378.7 CMOS and BiCMOS 3398.8 Silicon-on-Insulator 3398.9 Photodetectors Using Heteroepitaxy 3438.9.1 Si-SiGe Multiple Quantum Wells 3448.9.2 Ge Detectors on Si 3508.9.3 Related Theoretical Discussion 3578.10 Single-Photon Avalanche Diodes (SPADs) 3628.10.1 Introduction 3628.10.2 Performance Parameters 3668.10.3 State-of-the-Art Silicon-Based SPADs 3738.10.4 Key Challenges and Future Perspectives 377References for Tables 8.1 to 8.3 378Problems 380References 382  Volume 29. Raman Lasers 3879.1 Introduction 3879.2 Raman Scattering: Basic Concepts 3909.2.1 Stokes and Anti-Stokes Lines 3919.2.2 Stimulated Raman Scattering 3959.3 Simplified Theory of Raman Scattering 3989.4 Raman Effect in Silicon 4029.5 Raman Gain Coefficient 4049.5.1 Mathematical Model 4059.5.2 Simulation Parameters 4079.5.3 Threshold Power 4089.6 Continuous-Wave Raman Laser 4119.6.1 Device Structure and Design Considerations 4129.7 Further Developments, Challenges, and Perspectives in Silicon RamanLasers 4159.7.1 Optimization Strategies and First-Generation Enhancements 4169.7.2 Device Design Innovations 4169.7.3 Photonic Crystals and Nanoscale Cavity Lasers 4179.7.4 Silicon Nanostructures and Giant Raman Enhancement 4179.7.5 Recent Advances and Emerging Directions 4179.7.6 Challenges and Future Perspectives 418Problems 420References 42010. Guided Light Waves: Introduction 42310.1 Introduction 42310.2 Ray-Optic Theory for Light Guidance 42410.3 Reflection Coefficients 42610.4 Modes of a Planar Waveguide 42810.4.1 Symmetrical Planar Waveguide 43110.4.2 Asymmetric Waveguide 43310.4.3 Single-Mode Condition 43310.4.4 Effective Index of a Mode 43410.5 Wave Theory of Light Guides 43510.5.1 Wave Equation in a Dielectric 43510.5.2 The Ideal Slab Waveguide 43610.6 3D Optical Waveguides 44510.6.1 Practical Waveguiding Geometries 44510.6.2 Ray-Optic Approach for 3D Guides 44810.6.3 Approximate Analyses of Guided Modes 44810.7 Loss Mechanisms in Waveguides 45510.7.1 Scattering Loss 45510.7.2 Absorption Loss 45910.7.3 Radiation Loss 46010.7.4 Coupling Loss 46210.8 Coupling to Optical Devices 46310.8.1 Grating Couplers 46310.8.2 Butt Coupling and End-Fire Coupling 46510.9 Other Ways of Guiding Light Waves 473Problems 474References 476Suggested Readings 47711. Principle of Planar Waveguide Devices 47911.1 Introduction 47911.2 Model for Mode Coupling 48011.2.1 Physical Interpretation 48411.3 Directional Coupler 48411.3.1 Phase-Matched Directional Coupler 48411.3.2 Non-Phase-Matched Coupler 48711.4 Distributed Bragg Reflector 48911.4.1 Phase-Matched Grating 48911.4.2 Non-Phase-Matched Grating 49411.5 Some Useful Planar Devices 49511.5.1 Splitters 49511.5.2 Dual-Channel Directional Coupler 49511.5.3 Mach–Zehnder Interferometer 49711.5.4 Fabry–Perot Resonators 50011.5.5 Bragg Gratings 50311.5.6 Dielectric Mirrors 50711.5.7 Ring Resonators 50711.5.8 Multiple-Ring Resonators 51111.5.9 Variable Optical Attenuator 51211.5.10 Multimode Interferometer (MMI) 514Problems 515References 51712. Waveguides for Dense Wavelength-Division Multiplexing Systems 51912.1 Introduction 51912.2 Structure and Operation of AWGs 52112.2.1 Structure and Working Principle 52112.2.2 Analysis 52212.3 AWG Characteristics 52612.3.1 Tuning and Free Spectral Range 52612.3.2 Frequency Response 53112.3.3 Channel Crosstalk 53112.3.4 Polarization Dependence 53212.4 Methods for Enhancing AWG Performance 53312.4.1 Flat Frequency Response 53312.4.2 Polarization Independence 53512.4.3 Polarization Independence in Arrayed Waveguide Gratings 53512.4.4 Temperature Insensitivity 53712.5 Applications of AWGs 54012.5.1 Demultiplexers and Multiplexers 54012.5.2 Wavelength Routers 54112.5.3 Multiwavelength Receivers and Transmitters 54312.5.4 Add-Drop Multiplexers (ADMs) 54512.5.5 Optical Cross-Connects: Reconfigurable Wavelength Routers 54812.5.6 Dispersion Equalizer 55012.6 PHASAR-Based Devices on Different Materials 55212.6.1 Silica-on-Silicon 55212.6.2 Silicon-On-Insulator 55412.6.3 Silicon Oxynitride 55512.7 Echelle Grating 557Problems 559References 56013. Nonlinear Silicon Photonics 56513.1 Introduction 56513.2 Optical Processes and Nonlinearity 56513.2.1 Origins of Optical Nonlinearity 56513.2.2 First-Order Processes 57013.2.3 Second-Order Processes 57313.2.4 Third-Order Processes 57413.3 Phase Matching and Quasi-Phase Matching 57613.3.1 Phase-Matching Condition 57613.3.2 Quasi-Phase Matching 58013.4 Some Theoretical Aspects of Optical Pulse Propagation 58313.4.1 Group Velocity Dispersion 58313.4.2 Nonlinear Schrödinger Equation 58913.5 Silicon Structures with Optical Nonlinearity 60113.5.1 Waveguides 60113.5.2 Microcavity Resonators 60313.6 Optical Nonlinearity in Silicon and Applications 60413.6.1 Second-Order Nonlinearity 60413.6.2 Third-Order Nonlinearity 615Problems 642References 64314. Fabrication Techniques and Materials Systems 64714.1 Introduction 64714.2 Planar Processing 65114.3 Substrate Growth and Preparation 65114.3.1 Deposition and Growth of Materials 65214.3.2 Epitaxial Growth 65814.3.3 Molecular Beam Epitaxy (MBE) 65814.4 Material Modification 66014.4.1 Diffusion 66014.4.2 Ion Implantation 66314.5 Etching 66614.5.1 Wet Etching 66614.5.2 Dry Etching 66814.5.3 Maskless Etching 66914.5.4 Reactive Etching 67114.6 Lithography 67314.6.1 Mask Fabrication 67314.6.2 Pattern Transfer 67414.7 Fabrication of Waveguides 67514.7.1 Silica-on-Silicon 67514.7.2 Formation of Waveguides Using Silicon-on-Insulator 67614.8 Grating Formation Process 68114.8.1 Photosensitivity of Glass 68114.8.2 Grating Formation 68214.9 Materials Systems for Waveguide Formation 68514.9.1 General Considerations 68514.9.2 Characteristics of Guides and Simple Planar Components 68614.9.3 A Comparative Study of Materials Systems 702Questions and Problems 705References 707Suggested Reading 710Appendix A k p Method 713Appendix B Bra-Ket Notation 741Appendix C Values of Parameters 753Index 000