Optical Properties of Narrow-Gap Low-Dimensional Structures PDF
Preview Optical Properties of Narrow-Gap Low-Dimensional Structures
Optical Properties of Narrow-Gap Low-Dimensional Structures NA TO ASI Series Advanced Science Institutes Series A series presenting the results of activities sponsored by the NA TO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities. The series is published by an international board of publishers in conjunction with the NATO Scientific Affairs Division A Llf. Sciences Plenum Publishing Corporation B Physics New York and London C Mathematical D. Reidel Publishing Company and Physical Sciences Dordrecht, Boston, and Lancaster D Behavioral and Social Sciences Martinus Nijhoff Publishers E Engineering and The Hague, Boston, Dordrecht, and Lancaster Materials Sciences F Computer and Systems Sciences Springer-Verlag G Ecological Sciences Berlin, Heidelberg, New York, London, H Cen Biology Paris, and Tokyo Recent Volumes In this Series Volume 150-Particle Physics: Cargese 1985 edited by Maurice L~vy, Jean-Louis Basdevant, Maurice Jacob, David Speiser, Jacques Weyers, and Raymond Gastmans Volume 151-Glant Resonances in Atoms, Molecules, and Solids edited by J. P. Connerade, J. M. Esteva, and R. C. Karnatak Volume 152-0ptical Properties of Narrow-Gap Low-Dimensional Structures edited by C. M. Sotomayor Torres, J. C. Portal, J. C. Maan, and R. A. Stradling Volume 153-Physics of Strong Fields edited by W. Greiner Volume 154-Strongly Coupled Plasma Physics edited by Forrest J. Rogers and Hugh E. Dewitt Volume 155-Low-Dlmensional Conductors and Superconductors edited by D. Jerome and L. G. Caron Volume 156-Gravitation in Astrophysics: Cargese 1986 edited by B. Carter and J. B. Hartle Series 8: PhysiCS Optical Properties of Narrow-Gap Low-Dimensional Structures Edited by C. M. Sotomayor Torres University of St. Andrews St. Andrews, Scotland J. C. Portal CNRS-INSA Toulouse, France and CNRS-SNCI Grenoble, France J. C. Maan Max·Planck·lnstitut fOr FestkOrperforschung Grenoble, France and R. A. Stradling Imperial College of Science and Technology London, England Plenum Press New York and London Published in cooperation with NATO Scientific Affairs Division Proceedings of a NATO Advanced Research Workshop on Optical Properties of Narrow-Gap Low-Dimensional Structures, held July 29-August 1, 1986, at St. Andrews, Scotland L(brary of Congress Cataloging in Publication Data NATO Advanced Research Workshop on Optical Properties of Narrow-Gap Low-Dimensional Structures (1986 Saint Andrews, Fife) Optical properties of narrow-gap low-dimensional structures. e, (NATO ASI series. Series Physics; v. 152) "Proceedings of a NATO Advanced Research Workshop on Optical Proper ties of Narrow-Gap Low-Dimensional Structures, held July 29-August 1, 1986, at St. Andrews, Scotland" - T.p. verso. "Published in cooperation with NATO Scientific Affairs Division." Includes bibliographies and indexes. 1. Narrow gap semiconductors-Optical properties-Congresses. 2. One dimensional conductors-Optical properties-Congresses. I. Sotomayor To rres, C.M. II. North Atlantic Treaty Organization. Scientific Division. III. Title. IV. Series. QC611.8.N35N38 1986 537.6'22 87-12355 ISBN-13: 978-1-4612-9047-6 e-ISBN-13: 978-1-4613-1879-8 001: 10.1007/978-1-4613-1879-8 © 1987 Plenum Press, New York Softcover reprint of the hardcover 1s t edition 1987 A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013 All rights reserved No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher PREFACE This volume contains the Proceedings of the NATO Advanced Research Workshop on "Optical Properties of Narrow-Gap Low-Dimensional Structures", held from July 29th to August 1st, 1986, in St. Andrews, Scotland, under the auspices of the NATO International Scientific Exchange Program. The workshop was not limited to optical properties of narrow-gap semiconductor structures (Part III). Sessions on, for example, the growth methods and characterization of III-V, II-VI, and IV-VI materials, discussed in Part II, were an integral part of the workshop. Considering the small masses of the carriers in narrow-gap low dimensional structures (LOS), in Part I the enhanced band mixing and magnetic field effects are explored in the context of the envelope function approximation. Optical nonlinearities and energy relaxation phenomena applied to the well-known systems of HgCdTe and GaAs/GaAIAs, respectively, are reviewed with comments on their extension to narrow gap LOS. The relevance of optical observations in quantum transport studies is illustrated in Part IV. A review of devices based on epitaxial narrow-gap materials defines a frame of reference for future ones based on two-dimensional narrow-gap semiconductors; in addition, an analysis of the physics of quantum well lasers provides a guide to relevant parameters for narrow-gap laser devices for the infrared (Part V). The roles and potentials of special techniques are explored in Part VI, with emphasis on hydrostatic pressure techniques, since this has a pronounced effect in small-mass, narrow-gap, non-parabolic structures. Poster contributions were displayed throughout this NATO workshop, and their results were incorporated in the relevant sessions. An informal session on band offsets was held one evening, with many short contributions on recent results, followed by a lively discussion. The Organizing Committee would like to express its sincere thanks to Eric Thirkell, John Speed, Ian Ferguson, and Morag Watt for their assistance with the smooth running of the workshop. It would also like to thank the following companies for financial assistance for entertainment: Hughes Microelectronics (Glenrothes), Barr and Stroud (Glasgow), and Ferranti Defense Systems Ltd (Edinburgh). Their contribution in stationery is also acknowledged. The hospitality of the Department of Physics of St. Andrews University is cordially acknowledged. Finally, we would like to express our appreciation of the assistance provided by Madeleine Carter (Plenum Publishing Corporation), Karen Lumsden, and Morag Watt in the preparation of this volume. Autumn 1986 C.M. Sotomayor Torres J.C. Portal J.C. Mann R.A. Stradling v CONTENTS PART I. THEORY Electronic Energy Levels in Narrow-Gap Low-Dimensional Structures G. Bastard, J.A. Brum and J.M. Berroir Magnetic Field Effects on the Electronic States of Narrow-Gap Low- Dimensional Structures 15 M. Altarelli PART II. GROWTH AND CHARACTERIZATION Growth and Properties of Hg-Based Superlattices 25 J-P. Faurie MOCVD-Growth, Characterization and Application of III-V Semi- conductor Strained Heterostructures 39 M. Razeghi, P. Maurel, F. Omnes and E. Thorngren Crystal Qualities and Optical Properties of MBE Grown GaSb/AIGaSb Superlattices and Multi-Quantum-Wells 55 S. Tarucha The MBE Growth of InSb-Based Heterojunctions and LDS (Abs.) 71 C.R. Whitehouse PART III. OPTICAL PROPERTIES AND ENERGY RELAXATION Optical Properties of HgTe-CdTe Superlattices 73 T.C. McGill and G.Y. Wu Optical Properties of InAs-GaSb and GaSb-AISb Superlattices 85 P. Voisin Strained Layer Superlattices of GalnAs-GaAs 99 J-Y. Marzin Properties of PbTe/Pb1- x Sn xT e Superlattices 117 G. Bauer and M. Kriechbaum Quantum Wells and Superlattices of Diluted Magnetic Semiconductors 135 J.K. Furdyna, J. Kossut and A.K. Ramdas Optical Nonlinearities in Narrow-Gap Semiconductors 149 A. Miller and D. Craig Optical Nonlinearities in Low-Dimensional Structures (Abs.) 165 D.A.B. Miller Energy Relaxation Phenomena in GaAs/GaAIAs Structures 167 E. Gornik The Rate of Capture of Electrons into the Wells of a Superlattice 177 B.K. Ridley PART IV. OPTICAL EFFECTS IN QUANTUM TRANSPORT Subband Physics for H90•8CdO•2Te in the Electric Quantum Limit 187 F. Koch The Far Infra-Red Magnetotransmission of Accumulation Layers on n-(Hg,Cd)Te 195 J. Singleton, F. Nasir and R. Nicholas Cyclotron Resonance of Inversion Electrons on InSb 205 U. Merkt Optical, Magneto-Optical and Transport Investigations of the Narrow Gap System InAs xS b1- x 219 F. Kuchar, Z. Wasilewski, R.A. Stradling and R.J. Wagner PART V. PHYSICS OF DEVICES Narrow Bandgap Semiconductor Devices 231 H.H. Wieder The Physics of the Quantum Well Laser 251 J. Nagle and C. Weisbuch PART VI. SPECIAL TECHNIQUES Raman Scattering at Interfaces 269 G. Abstreiter Sources and Detectors for Picosecond/Femtosecond Spectroscopy (Abs.) 279 W. Sibbett High Pressure Techniques for Research in Semiconductors: A Review 281 I.L. Spain High Pressure Transport Experiments in 3 Dimensional Systems 299 R-L. Aulombard, A. Kadri and K. Zitouni High Pressure Transport Experiments in 2D Systems 313 J.L. Robert, A. Raymond and C. Bousquet Optical Properties of InAs-GaSb Superlattices under Hydrostatic Pressure 325 J.C. Maan Magnetotransport Measurements under Hydrostatic Pressure in Two Dimensional Electron and Electron-Hole Systems 337 G. Gregoris, J. Beerens, L. Dmowski, S. Ben Amor and J.C. Portal vm Participants 349 Author Index 353 Subject Index 355 ix ELECTRONIC ENERGY LEVELS IN NARROW-GAP LOW-DIMENSIONAL STRUCTURES G. Bastard, J.A. Brum and J.M. Berroir Groupe de Physique des Solides de l'Ecole Normale Superieure 24 rue Lhomond, F-75005 Paris (France) I INTRODUCTION The last few years have witnessed an increasing effort to better describe the electronic structure of semiconductor heterostructures (quantum wells, superlattices .•. ). Here, we restrict our considerations to the envelope description of the subband structure in heterolayers1-5. Such a description has proved to be versatile and reliable for the electronic states which are energetically close to the hosts' band extrema. Meanwhile, efforts in growth techniques have considerably increased the number of heterolayers, In particular, the quality of heterostructures involving narrow bandgap materials (eg. Ga(In)As, Hg(Cd)Te) has been significantly improved. These materials are important for the infra-red detection. The band structure of bulk narrow gap materials is in the vicinity of the r point well described by the Kane model6• In this model the k.p r r ra interaction between the closely spaced 6, 7, bands is exactly diagonalised while the effect of remote bands is taken into account only up to the second order in k. Let us denote by z the quantization axis of the total angular momentum J of the carrier. Then, mJ = ±3/2 ra correspond to the heavy hole band while mJ= ±1/2 correspond to the r r7 ra light particle bands, ie. the 6, and the light bands. This classification holds only if the carrIer wavevector k is parallel to J. It is always possible in bulk materials to find a basis where k andJ are lined up. In A-B heterostructures the existence of a preferential axis, the growth (z) axis, and of a band edge profile, which is z dependent, implies that the splitting of electronic states into decoupled heavy hole and light particle states is possible only if the carrier wavevectors kA and kB are parallel to z; in other words if the in-plane wavevector kJl which is conserved at the interfaces, is equal * to zero. If k~ 0 the light and heavy particle states become hybridized and the in-plane subband structure becomes complicated. We shall return to this point in section III. II HETEROLAYER ELECTRONIC STATES AT k~ = 0 If k~= 0, one may describe the heavy hole and light particle states independently. The heavy hole states are without surprise. If we , I\ p,' \p,2 \\ p:3 '",4 >.. 200 I\\ \ \ \ \\ \ \ \ \\ \ \ \ \ \ \ \ \ \ \ ~ .a(~.!5:) IVpl I\\ \ \\ \\ \ \ \ \ \ \ ~a(E!:) IVpl :UzJ :UzJ UJ UJ UJ UJ -' -' 0 0 :::I: :::I: X=Q3 OoL -________~ ---------1'00 Oo~ ______~ 1~00 ________2~ 00 d (A) Fig. 1. The heavy hole confinement Fig. 2. The heavy hole superlattice energies in GaAs-Ga(AI)As, bands in GaAs-Ga(AI)As, x=O.3 single quantum wells x=O.3 super lattices are are plotted versus the GaAs plotted versus the super slab thickness L. The lattice period d. The solid lines correspond to hatched areas correspond to bound states and the allowed superlattice states dashed lines to virtual LA=LS' bound states. ra denote by Vp the algebraic energy shift of the edge when going from the A to the S materials and if Vp.<O the A material is a potential well for holes whose motion becomes size-quantized for hole ener~ies such that o<€h<lvpl (see fig.n. Th~re are 1+Int(2mhhIVpILA2Ih n2)1/2such bound levels, where mhh is the heavy hole mass along tne growth axis in the A material, LA is the A slab thickness and Int(x) denotes the integer part of x. If the heterostructure consists of a super lattice instead of a single quantum well, the bound states of isolated wells hybridize and give rise to the superlattice minibands (fig.2) whose widths decrease almost exponentially with the barrier thickness LB, The allowed light particle states of a A-S super lattice are the solutions of: (1) with: 222 €(€+€A)(€+€A+6A)=h kA p (€+€A+26A/3) (2) 222 (€-VS)(€-VS+€S)(€-VS+€S+6S)=h kS p (€-VS+26S/3) (3) ~=kAVS/kSVA (4) ~=kA/kS[2/(€+€A)+1/(€+€A+6A)]/[2/(€-VS+€S)+1/(€-VS+€S+6S)] (5) d=LA+LS (6) 2
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