Physics of Optoelectronic Devices - Gbv.de

Physics of Optoelectronic Devices

SHUN LIEN CHUANG Professor of Electrica! and Computer Engineering University of Illinois at Urbana-Champaign

A Wiley-Interscience Publication

John Wiley & Sons, Inc.

New York / Chichester / Brisbane / Toronto / Singapore

Contents

Chapter 1. Introduction 1

1.1 Basic Concepts 1 1.2 Overview 8 Problems 13 References 14 Bibliography 14

PARTI FUNDAMENTALS

Chapter 2. Basic Semiconductor Electronics 21

2.1 Maxwell's Equations and Boundary Conditions 21 2.2 Semiconductor Electronics Equations 25 2.3 Generation and Recombination in Semiconductors 35 2.4 Examples and Applications to Optoelectronic Devices 43 2.5 Semiconductor p-N and w-P Heterojunctions 49 2.6 Semiconductor n-N Heterojunctions and

Metal-Semiconductor Junctions 70 Problems 79 References 80

Chapter 3. Basic Quantum Mechanics 82

3.1 Schrödinger Equation 83 3.2 The Square Well 85 3.3 The Harmonie Oscillator 97 3.4 The Hydrogen Atom (3D and 2D Exciton Bound and

Continuum States) 102 3.5 Time-Independent Perturbation Theory 106 3.6 Löwdin's Renormalization Method 114 3.7 Time-Dependent Perturbation Theory 116 Problems 120 References 122

Chapter 4. Theory of Electronic Band Structures in Semiconductors 124

4.1 The Bloch Theorem and the k • p Method for Simple Bands 124

4.2 Kane's Model for Band Structure: The k • p Method With the Spin-Orbit Interaction 129

Xll CONTENTS

4.3 Luttinger-Kohn's Model: The k • p Method for Degenerate Bands 137

4.4 The Effective Mass Theory for a Single Band and Degenerate Bands 141

4.5 Strain Effects on Band Structures 144 4.6 Electronic States in an Arbitrary One-Dimensional

Potential 157 4.7 Kronig-Penney Model for a Superlattice 166 4.8 Band Structures of Semiconductor Quantum Wells 175 4.9 Band Structures of Strained Semiconductor

Quantum Wells 185 Problems 190 References 195

Chapter 5. Electromagnetics 200

5.1 General Solutions to Maxwell's Equations and Gauge Transformations 200

5.2 Time-Harmonic Fields and Duality Principle 203 5.3 Plane Wave Reflection From a Layered Medium 205 5.4 Radiation and Far-Field Pattern 214 Problems 219 References 220

PART II PROPAGATION OF LIGHT

Chapter 6. Light Propagation in Various Media 223

6.1 Plane Wave Solutions for Maxwell's Equations in Homogeneous Media 223

6.2 Light Propagation in Isotropie Media 224 6.3 Light Propagation in Uniaxial Media 228 Problems 240 References 241

Chapter 7. Optical Waveguide Theory 242

7.1 Symmetrie Dielectric Slab Waveguides 242 7.2 Asymmetrie Dielectric Slab Waveguides 257 7.3 Ray Optics Approach to the Waveguide Problems 261 7.4 Rectangular Dielectric Waveguides 263 7.5 The Effective Index Method 270 7.6 Wave Guidance in a Lossy or Gain Medium 273 Problems 278 References 281

CONTENTS xiu

Chapter 8. Waveguide Couplers and Coupled-Mode Theory 283

8.1 Waveguide Couplers 283 8.2 Coupling of Modes in the Time Domain 288 8.3 Coupled Optical Waveguides 294 8.4 Improved Coupled-Mode Theory and Its Applications 302 8.5 Applications of Optical Waveguide Couplers 309 8.6 Distributed Feedback Structures 315 Problems 323 References 331

PART III GENERATION OF LIGHT

Chapter 9. Optical Processes in Semiconductors 337

9.1 Optical Transitions Using Fermi's Golden Rule 337 9.2 Spontaneous and Stimulated Emissions 345 9.3 Interband Absorption and Gain 352 9.4 Interband Absorption and Gain in a Quantum-Well

Structure 358 9.5 Momentum Matrix Elements of Bulk and

Quantum-Well Semiconductors 366 9.6 Intersubband Absorption 373 9.7 Gain Spectrum in a Quantum-Well Laser with

Valence-Band-Mixing Effects 381 Problems 388 References 392

Chapter 10. Semiconductor Lasers 394

10.1 Double Heterojunction Semiconductor Lasers 395 10.2 Gain-Guided and Index-Guided Semiconductor Lasers 412 10.3 Quantum-Well Lasers 421 10.4 Strained Quantum-Well Lasers 437 10.5 Coupled Laser Arrays 449 10.6 Distributed Feedback Lasers 457 10.7 Surface-Emitting Lasers 464 Problems 471 References 473

PART IV MODULATION OF LIGHT

Chapter 11. Direct Modulation of Semiconductor Lasers 487

11.1 Rate Equations and Linear Gain Analysis 487

XIV CONTENTS

11.2 High-Speed Modulation Response With Nonlinear Gain Saturation 493

11.3 Semiconductor Laser Spectral Linewidth and the Linewidth Enhancement Factor 497

Problems 504 References 505

Chapter 12. Electrooptic and Acoustooptic Modulators 508

12.1 Electrooptic Effects and Amplitude Modulators 508 12.2 Phase Modulators 517 12.3 Electrooptic Effects in Waveguide Devices 522 12.4 Scattering of Light by Sound: Raman-Nath and

Bragg Diffractions 527 12.5 Coupled-Mode Analysis for Bragg Acoustooptic Wave

Coupler 530 Problems 534 References 536

Chapter 13. Electroabsorption Modulators 538

13.1 General Formulation for Optical Absorption due to an Electron-Hole Pair 539

13.2 Franz-Keldysh Effect 546 13.3 Exciton Effect 550 13.4 Quantum Confined Stark Effect (QCSE) 557 13.5 Interband Electroabsorption Modulator 570 13.6 Self-Electrooptic Effect Devices (SEEDs) 572 Problems 575 References 577

PARTV DETECTION OF LIGHT

Chapter 14. Photodetectors 583

14.1 Photoconductors 14.2 p-n Junction Photodiodes 14.3 p-i-n Photodiodes 14.4 Avalanche Photodiodes 14.5 Intersubband Quantum-Well Photodetectors Problems References

583 595 601 604 616 622 624

CONTENTS xv

APPENDICES

A. The Hydrogen Atom (3D and 2D Exciton Bound and Continuum States) 631

B. Proof of the Effective Mass Theory 651

C. Derivations of the Pikus-Bir Hamiltonian for a Strained Semiconductor 655

D. Semiconductor Heterojunction Band Lineups in the

Model-Solid Theory 662

E. Kramers-Kronig Relations 671

F. Poynting's Theorem and Reciprocity Theorem 675

G. Light Propagation in Gyrotropic Media—Magnetooptic

Effects 679

H. Formulation of the Improved Coupled-Mode Theory 686

I. Density-Matrix Formulation of Optical Susceptibility 693

J. Optical Constants of GaAs and InP 702

K. Electronic Properties of Si, Ge, and a Few Binary, Ternary, and Quarternary Compounds 707

Index 715