Semiconductor-Laser Fundamentals

Transcription

1 Semiconductor-Laser Fundamentals

2 Springer-Verlag Berlin Heidelberg GmbH

3 Weng W. Chow Stephan W. Koch Semiconductor-laser Fundamentals Physics of the Gain Materials With 132 Figures and 3 Tables Springer

4 Dr. Weng W. Chow Sandia National Laboratories, Albuquerque, NM USA Professor Dr. Stephan W. Koch Philipps-Universitiit Marburg, Fachbereich Physik und Wissenschaftliches Zentrum fur Materialwissenschaften Mainzergasse 33 D Marburg, Germany ISBN ISBN (ebook) DOl / Library of Congress Cataloging-in-Publication Data. Chow, W.W. (Weng W.), Semiconductor-laser fundamentals: physics of the gain materials / W. W. Chow, S. W. Koch. p. cm. Includes bibliographical references and index. 1. Semiconductor lasers. I. Koch, S. W. (Stephan W.) QC S45C '6-dc This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg 1999 Urspriinglich erschienen bei Springer-Verlag Berlin Heidelberg Softcover reprint of the hardcover I st edition 1999 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Data conversion by LE-TJYC Jelonek, Schmidt & Vockler GbR, Leipzig Cover design: design & production GmbH, Heidelberg Computer to film: Saladruck, Berlin Binding: Buchbinderei Liideritz & Bauer, Berlin SPIN: / Printed on acid-free paper

5 To our parents, Ho Yin Hong, Hildegard and Friedrich Koch and to Ruth and Rita

6 Preface Since Fall of 1993, when we completed the manuscript of our book "Semiconductor-Laser Physics" [W.W. Chow, S.W. Koch, and M. Sargent III (Springer, Berlin, Heidelberg, 1994)] many new and exciting developments have taken place in the world of semiconductor lasers. Novel laser and amplifier structures were developed, and others, for example, the VCSEL (vertical cavity surface emitting laser) and monolithic MOPA (master oscillator power amplifier), made the transition from research and development to production. When investigating some of these systems, we discovered instances when device performance, and thus design depend critically on details of the gain medium properties, e.g., spectral shape and carrier density dependence of the gain and refractive index. New material systems were also introduced, with optical emission wavelengths spanning from the mid-infrared to the ultraviolet. Particularly noteworthy are laser and light-emitting diodes based on the wide-bandgap group-iii nitride and II~VI compounds. These devices emit in the visible to ultra-violet wavelength range, which is important for the wide variety of optoelectronic applications. While these novel semiconductor-laser materials show many similarities with the more conventional near-infrared systems, they also possess rather different material parameter combinations. These differences appear as band structure modifications and as increased importance of Coulomb effects, such that, e.g., excitonic signatures resulting from the attractive electron-hole interaction are generally significantly more prominent in the wide bandgap systems. On the theoretical side, important progress was made concerning the longstanding problem of the semiconductor laser lineshape. The solution of this problem may be obtained on the basis of a systematic analysis of carrier damping and de phasing processes. This improved level of theoretical analysis led to quantitative agreement between experimentally measured and theoretically predicted gain/absorption and refractive index spectra for a wide variety of semiconductor-laser materials. Since it can be used directly in the engineering of laser and amplifier structures, the improved gain medium theory is of more than academic interest. The success and usefulness of the new gain medium theory in explaining experiments and designing devices, combined with the complexity in implementing the calculations provided motivation for the present book,

7 VIII Preface "Semiconductor-Laser Fundamentals: Physics of the Gain Materials". To provide the background of introducing the new developments, we integrated into this book the material related part of our original "Semiconductor-Laser Physics" book. Besides some of the basic chapters, that have been updated and reorganized, we extensively cover band structure engineering aspects and the microscopic theory of the semiconductor gain materials in order to adequately account for the recent progress in materials and theoretical understanding. We included a wealth of examples, involving many different material combinations that are used in quantum-well laser systems. All of these results are obtained consistently at the level of the full microscopic many-body theory, and we expect a good degree of quantitative and predictive value from these numerical examples. As a guide for people interested in reproducing our numerical results, we included a variety of technical details involved with the coding of the set of many-body equations. As always, this book could not have been written without the interaction and collaboration with numerous colleagues, including (in alphabetical order) K. Choquette, M. Crawford, A. Girndt, F. Jahnke, E. Jones, A. Knorr, J. Moloney and A. Wright. It is our pleasure to thank Murray Sargent III for his collaboration on the first book, and we are very sorry that his new job does not allow him the time to continue working in this area. Special thanks are due to Renate Schmid for her expert technical help in preparing the manuscript and handling the extensive exchanges between Marburg and Albuquerque. SWK thanks Sandia National Laboratories for the hospitality during the three months when this book was finished. The research has been funded by the Deutsche Forschungsgemeinschaft, partly through the Leibniz prize, and by the U. S. Department of Energy under Contract DE-AC04-94AL Albuquerque, NM Marburg October 1998 W.W. Chow S.W. Koch

8 Contents 1. Basic Concepts Historical Background Laser Device Heterostructures Elementary Aspects of Band Structures Units Fermi-Dirac Distributions Quantum Confinement Slowly-Varying Maxwell Equations Quantum Mechanics of the Semiconductor Medium Free-Carrier Theory Free-Carrier Equations of Motion Quasi-Equilibrium Approximation Semiconductor Gain Temperature Dependence of Gain Gain Saturation Carrier Induced Refractive Index Linewidth Enhancement or Antiguiding Factor Coulomb Effects Semiconductor Bloch Equations Interband Coulomb Effects Screened Hartree-Fock Approximation Bandgap Renormalization in the Screened Hartree-Fock Approximation Pade Approximation Bulk Semiconductors Quantum-Wells Correlation Effects Coulomb Correlation Effects Carrier Quantum Boltzmann Equation Dephasing and Screening

9 X Contents 4.4 Formulation of Numerical Problem Quantum-Wells Bulk-Material Carrier-Phonon Scattering Characteristic Relaxation Times Bulk Band Structures Bloch Theorem Electronic States at k = k p Theory Conduction Bands Valence Bands Luttinger Hamiltonian Quantum Wells Envelope Approximation Method Band Mixing Strained Quantum Wells Dipole Matrix Elements x 6 Luttinger Hamiltonian Wurtzite Crystal Applications GaAs-AlGaAs Quantum Wells InGaAs-AlGaAs Strained Quantum Wells InGaAs-InP InGaP-InAlGaP Red-Wavelength Lasers II-VI Wide-Bandgap Systems Group-III Nitrides References Index