Physics of Low-Dimensional Semiconductor Structures

Transcription

1 Physics of Low-Dimensional Semiconductor Structures

2 PHVSICS OF SOllOS ANO llquios Editorial Board: Jozef T. Devreese University 0/ Antwerp, Belgium Roger P. Evrard University 0/ L i ~ Belgium g e, Stig Lundqvist Chalmers University 0/ Technology, Sweden Gerald D. Mahan University 0/ Tennessee, USA Norman H. March. University o/ox/ord, England Cu"ent Volumes in the Series AMORPHOUS SOLIDS AND THE LIQUID STATE Edited by Norman H. March, Robert A. Street, and Mario P. Tosi CHEMICAL BONDS OUTSIDE METAL SURFACES Norman H. March CRYSTALLINE SEMICONDUCTING MATERIALS AND DEVICES Edited by Paul N. Butcher, Norman H. March, and Mario P. Tosi FRACTALS Jens Feder INTERACTION OF ATOMS AND MOLECULES WITH SOLID SURFACES Edited by V. Bortolani, N. H. March, and M. P. Tosi LOCAL DENSITY THEORY OF POLARIZABILITY Gerald D. Mahan and K. R. Subbaswamy ORDER AND CHAOS IN NONLINEAR PHYSICAL SYSTEMS Edited by Stig Lundqvist, Norman H. March, and Mario P. Tosi PHYSICS OF LOW-DIMENSIONAL SEMICONDUCTOR STRUCTURES Edited by Paul Butcher, Norman H. March, and Mario P. Tosi QUANTUM TRANSPORT IN SEMICONDUCTORS Edited by David K. Ferry and Carlo Jacoboni A Continuation Order Plan is available for this series. A continuation order will bring delivery of each new volume immediately upon publication. Volumes are billed only upon actual shipment. For further information please contact the publisher.

3 Physics of Low-Dimensional Semiconductor Structures Edited by Pani Bntcher University o[ Warwick Coventry, England Norman H. March University o[ Ox[ord Ox[ord, England and Mario P. Tosi Scuola Normale Superiore Pisa, Italy Springer Science+Business Media, LLC

4 Llbrary of Congress Catalogtng-In-Publtcatlon Data Physlcs of low-dlnensional senlconductor structures / edlted by Paul Butcher. NorNan H. March. and Marlo P. Tosi. p. CN. -- (Physics of solids and 11quids) Includes bibliographical references and index. ISBN SeNiconductors. 2. OuantuN wells. 3. Phonons. 4. Superlatttces as.aterials. I. Butcher. Paul N. II. March. Norllan H. <Norun Henry) III. Tost. M. P. IV. Sertes. OCS11.P S'221--dc CIP ISBN ISBN (ebook) DOI / Springer Science+Business Media New York 1993 Originally published by Plenum Press, New York in 1993 Softcover reprint of the hardcover 1 st edition 1993 AU 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, microfilm ing, record ing, or otherwise. without written permission from the Publisher

5 Contributors E. Y. Andrei, Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08855, USA N. d'ambrumenil, Department of Physics, University of Warwick, Coventry CV47AL, UK F. Be/tram, AT&T Bell Laboratories, Murray Hill, NJ 07974, USA G. Bergman, Department of Physics, University of Southem California, University Park, Los Angeles, CA , USA P. N. Butcher, Department of Physics, University of Warwick, Coventry CV47AL, UK F. Capasso, AT &T Bell Laboratories, Murray Hill, NJ 07974, USA L. J. Challis, Department of Physics, University of Nottingham, University Park, Nottingham NG72RD, UK s. Datta, School of Electrical Engineering, Purdue University, W. Lafayette, IN 47907, USA G. Deville, D.Ph. S.R.M., Centre d'etudes Nuc1eares-Sac1ay, Gif-sur-Yvette 91191, France G. H. Döhler, University of Erlangen-Nürnberg, Institut für Technische Physik, 8520 Erlangen, Germany G. Fasol, RCast-University oftokyo, Komaba, Meguro-Ku, Tokyo 153,Japan v

6 vi Contributors G. Garcia-Calderon, Instituto de Fisica, Universidad Nacional Autonoma de Mexico, Mexico D.F., Mexico D. C. Glattli, D.Ph. S.R.M., Centre d'etudes Nudeares-Saday, Gif-sur Yvette 91191, France D. Kerkmann, Institut für Physik 2 der RWTH Aachen, D-5100 Aachen, Germany L. P. Kouwenhoven, Faculty of Applied Physics, DeIft University of Technology, 2600 GA Delft, The Netherlands J. C. Maan, Max Planck Institut für Festkörperforschung, F-38042, Grenoble Cedex, France D. Pescia, Institut für Physik 2 der RWTH Aachen, D-5100 Aachen, Germany L. J. Sham, Department of Physics, University of California, San Diego, La Jolla, California , USA F. Stern, IBM Research Division, Thomas J. Watson Research Center, Y orktown Heights, New Y ork 10598, USA J. D. White, Hitachi Cambridge Laboratory, Cavendish Laboratory, Madingley Road, Cambridge CB3 OHE, UK F. I. B. Williams, D.Ph. S.R.M., Centre d'etudes Nudeares-Saday, Gif-sur-Yvette 91191, France

7 Preface Over the last two decades artificial structures have become the cutting edge of semiconductor research. This book gives a comprehensive account of their behavior. The characteristic features of these structures are interfaces between different materials which restrict the motion of the electrons to two, one, or zero dimensions and modify the behavior of phonons. The first four chapters deal with the e1ectronic and phonon structure of quantum wells, superlattices, quantum wires, and quantum dots and introduce the ideas involved in diffusive, mesoscopic, and ballistic electron transport. These transport regimes are discussed in more detail in subsequent chapters on quantum interference, the quantum Hall effect, tunneling structures, quantum point contacts, and the very successful Landauer-Buttiker formalism. Other chapters treat the solidification of a 2D electron gas at high magnetic fie1ds, magneto-optical spectroscopy, and phonon scattering experiments. A chapter on metallic superlattices is inc1uded to illustrate the interesting physics which can arise when semiconductor fabrication methods are used to make artificial structures in other material systems. Finally, the last chapter describes some applications of low-dimensional semiconductor structures to the fabrication of electronic devices. The book took shape in a College organized at the International Centre for Theoretical Physics, Trieste, in The level of presentation is appropriate to postgraduate students and research workers in solid state physics, materials science, and electrical and electronic engineering. A comparison of this volume with another one in the same series, Crystalline Semiconducting Materials and Devices, which was based on an ICTP College held in 1984 is interesting. It illustrates the dramatic transformation of research on semiconducting materials which has been brought about by the development of artificial structures. P. N. Butcher N. H. March M. P. Tosi vii

8 Contents 1. Electronic Properties in Semiconductor Heterostructures L. J. Sham 1.1. Introduction Basic Electronic Properties in Quantum WeHs Typical Band Structure of Bulk Semiconductors Electron Confinement Hole Subbands Interface Effects on Electrons Effective Mass Theory for Heterostructures Band Off sets Types of Superlattices Classification According to Band Edge Alignment Two-Band Model Metal-Insulator Transition in Type 11 GaSbjInAs Type III HgTejCdTe Electrons in Short-Period Superlattices The Kronig-Penney Model Symmetry Properties of Superlattices Computation Methods for Superlattice Electronic Structure Valley Mixing between rand X... '" Valley Mixing between Xx and X y Fractional Layer Numbers Effects of Magnetic Fields Conduction Electron in a Magnetic Field Normal to the Interface Valence Holes in a Magnetic Field Normal to the Interface Conduction Electron in a Magnetic Field Parallel to the Interface Electron Self-Energy Effects in a Doped Quantum WeIl.. ~ The Interaction Hamiltonian Screening Electron and Hole Self-Energies Comparison with Experiment ix

9 x Contents 1.8. Photoluminescence in Undoped and Doped Quantum WeHs Selection Rules Polarization Spectrum in the Backscatter Configuration Luminescence Polarization in the Waveguide Configuration.. " 47 References Phonons in Low-Dimensional Systems J. D. White and G. Fasol 2.1. Introduction Phonons in Bulk Semiconductors Real and Reciprocal Space Unit Cells Phonons in Crystals Raman Scattering Phonons in Layered Media Raman Investigations of Superlattices Phonon Dispersion in Superlattices Acoustic Phonons Confined Optical Phonons Phonon Dispersion in Superlattices with Various Space Group Symmetries Interface Phonons Experimental Procedure Introduction Configuration of Raman Apparatus Conclusions References Theory of Electron Transport in Low-Dimensional Semiconductor Structures P. N. B utcher 3.1. Introduction The Energy Band Structure of 2D and ID Electron Gases Two-Dimensional Electron Gas... " One-Dimensional Electron Gas Boltzmann Transport Theory The Transport Coefficient Boltzmann's Equation in the Quantum Limit The Relaxation Time Ansatz in the Quantum Limit Boltzmann Transport Theory for More Than One Subband Quantum Size Effects in the Transport Coefficients The Boltzmann Transport Approximation to the Electrical Conductivity of a 2DEG

10 Contents xi The Etfect of Level Broadening on the E1ectrica1 Conductivity of a 2DEG Quantum Size Etfect in the Thermopower of a 2DEG Quantum Size Etfect in a IDEG Discussion Phonon Drag Thermopower of a 2DEG Introduction An E1ementary Treatment of Phonon Drag Thermopower Calcu1ation of the Phonon Drag Thermopower from Coupled E1ectron and Phonon Boltzmann Equations Recovering the E1ementary Formu1a for Phonon Drag Comparison of Theory and Experiment Quantum Corrections to the Boltzmann Transport Formalism Introduction Kubo-Greenwood Formu1as When B = O Kubo Formulas When B =f: Onsager Symmetry Weak Localization Corrections to the Conductivity Universal Fluctuations Thermal and Electrica1 Transport Formalism for Electronic Microstructures with Many Terminals Introduction The Electron States in the Terminals The Scattering Matrix General Terminal Transport Relations for Microstructures Simplification of the Terminal Transport Relations for a Microstructure Onsager Symmetry and Reciprocity Conc1usion The Aharonov-Bohm Effect, Quantum Point Contacts, and the Integer Quantum Hall Etfect Introduction The Aharonov-Bohm Effect Quantum Point Contacts The Integer Quantum Hall Etfect Conclusion References Quantum Wires and Quantum Dots F. Stern 4.1. Dimensionality Structures and Fabrication Electronic States Phonons

11 xii Contents 4.5. Charges in Quantum Wires and Quantum Dots Dielectric Response, Screening, and Plasmons Transport Properties Bound States Optical Properties Magnetic Field Effects Prospects for Device Applications References Quantum Interference In Disordered Electron Systems G. Bergmann 5.1. The Echo of the Scattered Conduction Electron Time-of-Flight Experiment by a Magnetic Field Spin-Orbit Coupling Magnetic Scattering in Kondo Systems Kondo Maximum Low-Temperature Behavior of the Magnetic Scattering Rate Quenching of Interacting Moments Far Below the Kondo Temperature Electrons Confined in Tunneling Junctions The Range of the Dynamical Coulomb Interaction References Theory of the Quantum Hall Effect N. ä Ambrumenil 6.1. Introduction The Quantum Hall Effect The Measurement Interpretation of the Measurement Laughlin's Gedanken Experiment Aspects of a Microseopie Theory of the Quantum Hall Effect Edge States..., The Fractional Quantum Hall Effect Interpretation of the Measurement: Many-Body Gap and Fractional Charge Zeros and Flux Quanta Laughlin's Wave' Function Haldane's Argument Other Filling Fractions: The Hierarchy Microscopic Trial Wave Functions for the Hierarchy Spin Polarization

12 Contents xiii Higher Landau Levels Ring Exchange Summary Appendix: (More or Less) Standard Results A.l. Hamiltonian and Energy Spectrum A.2. Gauge Choice A.3. Conserved Momenta, Magnetic Translations, and Rotations A.4. The Single-Particle Green's Function A.5. Exactness of Laughlin's Wave Function A.6. The Hierarchy References Tunneling in Semiconductor Resonant Structures G. Garcla-Calder6n 7.1. Introduction Concept of Tunneling Brief History of Tunneling Resonant Structures Physics of Resonant Tunneling Resonant States Coherent Tunneling Current Inelastic Effects Conclusion References Keldysh Formalism and the Landauer Approach S. Datta 8.1. Introduction A Few Concepts Equilibrium Solution Transport Equation Terminal Current Linear Response Reclproclty Heat Exchange Concluding Remarks Appendix: Mathematical Details References

13 xiv Contents 9. Magneto-Optical Properties of Semiconductor Heterostructu res J. C. Maan 9.1. Introduction Energy Levels of Heterostructures in a Magnetic Field and a Confining Potential l. Perpendicular Field Tilted Field Parallel Field Superlattices in a Parallel Field Selection Rules and Transition Matrix Elements Cyclotron Resonance Parabolic Bands Nonparabolicity Tilted Field Intraband Experiments Interband Transitions l. Simple Bands Excitons in a Magnetic Field Valence Band Structure Doped SampIes Applications of Magneto-Optics High-Excitation Luminescence in Quantum WeHs Spin Relaxation in Quantum WeHs Summary References Electrons In Superlattices G. H. Döhler Introduction Electronic Band Structure of Superlattices Compositional Superlattices Doping Superlattices (n-i-p-i Structures) Dynamics of Electrons in Superlattices..., Bloch OsciHations and the Wannier-Stark Ladder Transitions on the Wannier-Stark Ladder and Transport Properties Intersubband Transitions Interband Transitions in Superlattices Dipole Matrix Elements in Type-I and Type-lI Compositional and n-i-p-i Doping Superlattices The Internal Franz-Keldysh Effect in n-i-p-i Superlattices The Quantum Confined StarkEffect: "MQW-Hetero-n-i-p-i's"

14 Contents xv Magnetic Wave Function Tuning in Doping Superlattices Impurity States and Impurity Bands in 8-Doped n-i-p-i Superlattices References Metallic Superlattices D. Kerkmann and D. Pescia Growth Modes and Structural Analysis of Metallic Superlattices Growth of Metallic Epitaxial Layers Growth Detection Magnetic Ground State of Epitaxial Layer "Enhanced" Magnetic Moments The Many-Spin Ground State and Low-Lying Excited States Magnetism of Epitaxial Films at Finite Temperatures Long-Range Order at Finite Temperatures Magnetic Anisotropy and Long-Range Order Existence of a Phase Transition at Temperatures T", r References Phonon Emission, Absorption, and Reflection from a Two-Dimensional Electron Gas L. J. Challis Introduction Phonon Emission Zero Magnetic Fields Quantizing Magnetic Fields Phonon Scattering Conclusion References Quantum Adiabatic Electron Transport in Ballistic Conductors L. P. K ouwenhoven Introduction Fabrication and Working Principles of a Split-Gate Device Quantized Conductance of a Point Contact Depopulation of ID Magnetoelectric Subbands Electron Motion in a Magnetic Field Electron Focusing... ". " Edge Channels Quantized Longitudinal Conductance

15 xvi Contents Anomalous Integer Quantum Hall Effect Transition from Ohmic to Adiabatic Transport Transport Through Two QPCs in Series Electron-Beam Collimation and Electron Focusing in a Dot Summary and Conc1usions References Experiments on Two-Dimensional Wigner Crystals E. Y. Andrei, F. J. B. Williams, D. C. Glattli, and G. Deville Introduction The Phase Diagram Coulomb System of Classical Partic1es Coulomb System of Quantum Partic1es T = 0, B = Coulomb System of Quantum Partic1es T = 0, B # Coulomb System of Quantum Partic1es T #- 0, B # How to Recognize the Solid? Experimental Realizations of a 2D Plasma Experiments on the Quantum Wigner Crystal Shear Modulus Measurements Conductivity Measurements Discussion Experiments on the Classical Wigner Crystal Shear Modulus Experiments Specific Heat Experiments Summary References Artificial Semiconductor Structures: Electronic Properties and Device Applications F. Be/tram and F. Capasso Introduction Quantum Electron Devices Resonant Tunneling Bipolar Transistors with Double Barrier in the Base Devices with Multiple Peak 1-V Characteristics and Multiple-State RTBTs Gated Quantum-WeH and ~ u p e r l Base a t t Transistor i c e Transport in Superlattices Transport and Negative Differential Conductance in Superlattices with Wide Minibands Localization and Transport in Superlattices

16 Contents xvii Bloch Oscillations Observation of Negative Differential Conductance in a Superlattice Scattering-Controlled Resonances References Index