Semiconductor Optoelectronic Devices Introduction to Physics and Simulation www.com Semiconductor Optoelectronic Devices Introduction to Physics and Simulation JOACHIM PIPREK University of California at Santa Barbara Amsterdam Boston London New York Oxford Paris San Diego San Francisco Singapore Sydney Tokyo www.com This book is printed on acid-free paper. Copyright 2003, Elsevier Science (USA) All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording or any information storage and retrieval system, without permission in writing from the publisher. Permissions may be sought directly from Elsevier’s Science & Technology Rights Department in Oxford, UK: phone: (+44) 1865 843830, fax: (+44) 1865 853333, e-mail: permissions@elsevier.
You may also complete your request on-line via the Elsevier Science homepage (http://elsevier.com), by selecting “Customer Support” and then “Obtaining Permissions.” Academic Press An imprint of Elsevier Science 525 B Street, Suite 1900, San Diego, California 92101-4495, USA http://www.com Academic Press 84 Theobald’s Road, London WC1X 8RR, UK http://www.com Library of Congress Control Number: 2002111026 International Standard Book Number: 0-12-557190-9 PRINTED IN THE UNITED STATES OF AMERICA 02 03 04 05 06 9 8 7 6 5 4 3 2 1 www.com To Lisa www.com Contents Preface xi List of Tables xiii I Fundamentals 1 1 Introduction to Semiconductors 3 1.1 Electrons, Holes, Photons, and Phonons .2 Fermi distribution and density of states. 7 2 Electron energy bands 13 2.2 Effective Mass of Electrons and Holes .3 Energy Band Gap .2 Electronic Band Structure: The k · p Method .1 Two-Band Model (Zinc Blende) .3 Three- and Four-Band Models (Zinc Blende) .4 Three-Band Model for Wurtzite Crystals .5 Band Offset at Heterointerfaces .1 Drift and Diffusion .1 Insulator–Semiconductor Interface .2 Metal–Semiconductor Contact .com viii CONTENTS 3.7 Electron–Hole Recombination .8 Electron–Hole Generation .3 Band-to-Band Tunneling .9 Advanced Transport Models .1 Energy Balance Model .2 Boltzmann Transport Equation .2 Index of Refraction .5 Plane Waves at Interfaces .8 Symmetric Planar Waveguides .10 Facet Reflection of Waveguide Modes .1 Transition Matrix Element .2 Transition Energy Broadening .4 Many-Body Effects. 136 6 Heat Generation and Dissipation 141 6.1 Heat Flux Equation .com CONTENTS ix 6.4 Optical Absorption Heat. 147 II Devices 149 7 Edge-Emitting Laser 151 7.2 Models and Material Parameters .1 Drift–Diffusion Model .3 Cavity Length Effects on Loss Parameters .4 Slope Efficiency Limitations .5 Temperature Effects on Laser Performance.
164 8 Vertical-Cavity Laser 171 8.2 Long-Wavelength Vertical-Cavity Lasers .3 Model and Parameters .4 Carrier Transport Effects .7 Temperature Effects on the Optical Gain. 184 9 Nitride Light Emitters 187 9.2 Nitride Material Properties .3 InGaN/GaN Light-Emitting Diode .4 InGaN/GaN Laser Diode .3 Comparison to Measurements .2 Multiquantum Well Active Region .2 Device Structure and Material Properties .3 Waveguide Mode Analysis. 234 A Constants and Units 237 A. 237 B Basic Mathematical Relations 239 B.2 Vector and Matrix Analysis.
243 C Symbols and Abbreviations 245 Bibliography 251 Index 273 www.com Preface Optoelectronics has become an important part of our lives. Wherever light is used to transmit information, tiny semiconductor devices are needed to transfer elec- trical current into optical signals and vice versa. Examples include light-emitting diodes in radios and other appliances, photodetectors in elevator doors and digi- tal cameras, and laser diodes that transmit phone calls through glass fibers. Such optoelectronic devices take advantage of sophisticated interactions between elec- trons and light.
Nanometer scale semiconductor structures are often at the heart of modern optoelectronic devices. Their shrinking size and increasing complexity make computer simulation an important tool for designing better devices that meet ever-rising performance requirements. The current need to apply advanced design software in optoelectronics follows the trend observed in the 1980s with simula- tion software for silicon devices. Today, software for technology computer-aided design (TCAD) and electronic design automation (EDA) represents a fundamen- tal part of the silicon industry.
In optoelectronics, advanced commercial device software has emerged, and it is expected to play an increasingly important role in the near future. The target audience of this book is students, engineers, and researchers who are interested in using high-end software tools to design and analyze semicon- ductor optoelectronic devices. The first part of the book provides fundamental knowledge in semiconductor physics and in waveguide optics. Optoelectronics combines electronics and photonics and the book addresses readers approaching the field from either side.
The text is written at an introductory level, requiring only a basic background in solid state physics and optics. Material properties and corresponding mathematical models are covered for a wide selection of semi- conductors used in optoelectronics. The second part of the book investigates modern optoelectronic devices, including light-emitting diodes, edge-emitting lasers, vertical-cavity lasers, electroabsorption modulators, and a novel combi- nation of amplifier and photodetector. InP-, GaAs-, and GaN-based devices are analyzed.
The calibration of model parameters using available measurements is emphasized in order to obtain realistic results. These real-world simulation exam- ples give new insight into device physics that is hard to gain without numerical modeling. Most simulations in this book employ the commercial software suite developed by Crosslight Software, Inc. Interested readers can obtain a free trial version of this software including example input files on the Internet at http://www.com xii PREFACE I would like to thank all my students in Germany, Sweden, Great Britain, Taiwan, Canada, and the United States, for their interest in this field and for all their questions, which eventually motivated me to write this book.
I am grateful to Dr. Simon Li for creating the Crosslight software suite and for supporting my work. John Bowers gave me the opportunity to participate in several leading edge research projects, which provided some of the device examples in this book. I am also thankful to Prof.
Shuji Nakamura for valuable discussions on the nitride devices. Parts of the manuscript have been reviewed by colleagues and friends, and I would like to acknowledge helpful comments from Dr. Justin Hodiak, Dr. Monica Hansen, Dr.
Hans-Jürgen Wünsche, Daniel Lasaosa, Dr. Donato Pasquariello, and Dr. I appreciate especially the extensive suggestions I received from Dr. Hans Wenzel who carefully reviewed part I of the book.
Writing this book was part of my ongoing commitment to build bridges between theoretical and experimental research. I encourage readers to send comments by e-mail to piprek@ieee.org and I will continue to provide additional help and information at my web site http://www. Joachim Piprek Santa Barbara, California www.com List of Tables 1.1 Energy Band Gap Eg , Density-of-States Effective Masses mc and mv , Effective Densities of States Nc and Nv , and Intrinsic Carrier Concentration ni at Room Temperature [1, 2, 3, 4, 5, 6, 7] .1 Electron Effective Masses mc in Units of m0 for Conduction Band Minima in Cubic Semiconductors at Low Temperatures [2, 13] .2 Hole Effective Masses in Units of m0 for the Heavy-Hole Band (mhh ), the Light-Hole Band (mlh ), and the Split-Off Band (mso ) at Room Temperature [1, 2, 4, 5, 6] .3 Energy Band Gaps at T = 0 K and Varshni Parameters of Eq.4 Fundamental Energy Band Gap at T = 0 K (Type Given in Parentheses) and Pässler Parameters of Eq.11) for Cubic Semiconductors [16] .5 Luttinger Parameters γ for Cubic Semiconductors at Low Tem- peratures [2, 13] .6 Lattice Constant a0 , Thermal Expansion Coefficient da0 /dT , Elastic Stiffness Constants C11 and C12 , and Deformation Poten- tials b, av , ac for Cubic Semiconductors at Room Temperature [1, 2, 13, 23] .7 Electron Band-Structure Parameters for Nitride Wurtzite Semi- conductors at Room Temperature [13, 16, 29, 31, 32, 33, 34, 35, 36, 37, 38] .8 Bowing Parameter in Eq.108) for Energy Gaps Eg , EgX , EgL , Valence Band Edge Ev0 , and Spin–Orbit Splitting 0 at Room Temperature [13, 42, 43] .9 Valence Band Edge Reference Level Ev0 [13], Split-Off Energy 0 [13, 23], Average Valence Band Energy Ev,av 0 [23], and Electron Affinity χ0 [46] for Unstrained Cubic Semiconductors .1 Work functions M of Selected Metals in Electron Volts (eV) [55] 59 3.2 Mobility Model Parameters of Eqs.28) at Room Temperature .com xiv LIST OF TABLES 3.3 Parameters for High-Field Mobility Models (Eqs.4 Impact Ionization Parameters of Eq.52) at Room Temperature .5 Impact Ionization Parameters of Eq.53) at Room Temperature [81] .6 Impact Ionization Parameters for Electrons: High-Field Room- Temperature Mean Free Path λn , Low-Temperature Optical Phonon Energy EOP 0 , and Ionization Threshold Energy E I [9] .1 Parameters si and λi of the Sellmeier Refractive Index Model for Undoped Semiconductors at Room Temperature (Eq.2 Parameters for the Simplified Adachi Model for the Refractive Index below the Band Gap (h̄ω < Eg ) as Given in Eqs.3 Static (εst ) and Optical (εopt ) Dielectric Constants, Reststrahlen Wavelength λr [99], Band Gap Wavelength λg , Refractive Index nr at Band Gap Wavelength, and Refractive Index Change with Temperature .1 Energy Parameter Ep of the Bulk Momentum Matrix Element Mb , Correction Factor Fb in Eqs.61) [13], and Longitu- dinal Optical Phonon Energy h̄ωLO [2, 89] as Used in the Asada Scattering Model (Section 5.1 Crystal Lattice Thermal Conductivity κL , Specific Heat CL , Den- sity ρL , Debye Temperature D , and Temperature Coefficient δκ at Room Temperature [1, 3, 6, 38, 46, 69] .2 Thermal Conductivity Bowing Parameter CABC (Km/W) in Eqs.9) for Ternary Alloys A(B,C) [43, 160] .1 Layer Materials and Room-Temperature Parameters of the MQW Fabry–Perot Laser .1 Layer Materials and Parameters of the Double-Bonded VCSEL .1 Parameters for the High-Field Electron Mobility Function Given in Eq.2 Polarization Parameters for Nitride Materials [232] .3 Layer Structure and Room-Temperature Parameters of the InGaN/ GaN LED .4 Epitaxial Layer Structure and Room-Temperature Parameters of the Nitride Laser .com LIST OF TABLES xv 10.1 Layer Structure and Parameters of the Electroabsorption Modula- tor with a Total of 10 Quantum Wells and 11 Barriers .1 Epitaxial Layer Structure and Parameters of the Amplification Photodetector .2 Optical Confinement Factors amp and det of the Vertical Modes in Fig.2 for the Amplification and Detection Layers, Respectively .com Part I Fundamentals www.com Chapter 1 Introduction to Semiconductors This chapter gives a brief introduction to semiconductors. Electrons and holes are carriers of electrical current in semiconductors and they are separated by an energy gap.
Photons are the smallest energy packets of light waves and their interaction with electrons is the key physical mechanism in optoelec- tronic devices. The internal temperature of the semiconductor depends on the energy of lattice vibrations, which can be divided into phonons. The Fermi distribution function for the electron energy and the density of electron states are introduced.1 Electrons, Holes, Photons, and Phonons Optoelectronics brings together optics and electronics within a single device, a sin- gle material. The material of choice needs to allow for the manipulation of light, the manipulation of electrical current, and their interaction.
Metals are excellent elec- trical conductors, but do not allow light to travel inside. Glass and related dielectric materials can accommodate and guide light waves, like in optical fibers, but they are electrical insulators. Semiconductors are in between these two material types, as they can carry electrical current as well as light waves. Even better, semiconductors can be designed to allow for the transformation of light into current and vice versa.
The conduction of electrical current is based on the flow of electrons. Most electrons are attached to single atoms and are not able to move freely. Only some loosely bound electrons are released and become conduction electrons. The same number of positively charged atoms (ions) is left behind; the net charge is zero.
The positive charges can also move, as valence electrons jump from atom to atom. Thus, both valence electrons (holes) and conduction electrons are able to carry electrical current. Both the carriers are separated by an energy gap; i., valence electrons need to receive at least the gap energy Eg to become conduction electrons. In semiconductors, the gap energy is on the order of 1 eV.