Physics of Low-Dimensional Semiconductor Structures
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1 Physics of Low-Dimensional Semiconductor Structures Edited by Paul Butcher University of Warwick Coventry, England Norman H. March University of Oxford Oxford, England and Mario P. Tosi Scuola Normale Superiore Pisa, Italy Plenum Press New York and London
2 1. Electronic Properties in Semiconductor Heterostructures L. J. Sham 1.1. Introduction Basic Electronic Properties in Quantum Wells Typical Band Structure of Bulk Semiconductors Electron Confinement Hole Subbands Interface Effects on Electrons Effective Mass Theory for Heterostructures Band Offsets Types of Superlattices Classification According to Band Edge Alignment Two-Band Model Metal-Insulator Transition in Type II GaSb/InAs Type III HgTe/CdTe Electrons in Short-Period Superlattices The Kronig-Penney Model Symmetry Properties of Superlattices Computation Methods for Superlattice Electronic Structure Valley Mixing between Г and X Valley Mixing between X x 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 Well The Interaction Hamiltonian Screening Electron and Hole Self-Energies Comparison with Experiment 41 ix
3 x 1.8. Photoluminescence in Undoped and Doped Quantum Wells Selection Rules Polarization Spectrum in the Backscatter Configuration Luminescence Polarization in the Waveguide Configuration References Phonons in Low-Dimensional Systems J. D. White and G. Faso/ 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 90 References Theory of Electron Transport in Low-Dimensional Semiconductor Structures P. N. Butcher 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 107
4 x ' The Effect of Level Broadening on the Electrical Conductivity of a 2DEG Quantum Size Effect in the Thermopower of a 2DEG Quantum Size Effect in a 1DEG Discussion Phonon Drag Thermopower of a 2DEG Introduction An Elementary Treatment of Phonon Drag Thermopower Calculation of the Phonon Drag Thermopower from Coupled Electron and Phonon Boltzmann Equations Recovering the Elementary Formula for Phonon Drag Comparison of Theory and Experiment Quantum Corrections to the Boltzmann Transport Formalism Introduction Kubo-Greenwood Formulas When В = Kubo Formulas When В Ф Onsager Symmetry Weak Localization Corrections to the Conductivity Universal Fluctuations Thermal and Electrical 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 Conclusion The Aharonov-Bohm Effect, Quantum Point Contacts, and the Integer Quantum Hall Effect Introduction The Aharonov-Bohm Effect Quantum Point Contacts The Integer Quantum Hall Effect Conclusion 170 References Quantum Wires and Quantum Dots F. Stern 4.1. Dimensionality Structures and Fabrication Electronic States Phonons 187
5 xii 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 197 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 222 References Theory of the Quantum Hall Effect N. d'ambrumenil 6.1. Introduction The Quantum Hall Effect The Measurement Interpretation of the Measurement Laughlin's Gedanken Experiment Aspects of a Microscopic 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 250
6 xiii Higher Landau Levels Ring Exchange Summary 252 Appendix: (More or Less) Standard Results А.1. 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 262 References Tunneling in Semiconductor Resonant Structures G. Garcia-Calderön 7.1. Introduction Concept of Tunneling Brief History of Tunneling Resonant Structures Physics of Resonant Tunneling Resonant States Coherent Tunneling Current Inelastic Effects Conclusion 294 References Keldysh Formalism and the Landauer Approach S. Datta 8.1. Introduction A Few Concepts Equilibrium Solution Transport Equation Terminal Current Linear Response Reciprocity Heat Exchange Concluding Remarks 320 Appendix: Mathematical Details 321 References 329
7 xiv 9. Magneto-Optical Properties of Semiconductor Heterostructures J. С. Maan 9.1. Introduction Energy Levels of Heterostructures in a Magnetic Field and a Confining Potential 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 Simple Bands Excitons in a Magnetic Field Valence Band Structure Doped Samples Applications of Magneto-Optics High-Excitation Luminescence in Quantum Wells Spin Relaxation in Quantum Wells Summary 370 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 Oscillations 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-II Compositional and n-i-p-i Doping Superlattices The Internal Franz-Keldysh Effect in n-i-p-i Superlattices The Quantum Confined Stark Effect: "MQW-Hetero-n-i-p-fs" 395
8 xv Magnetic Wave Function Tuning in Doping Superlattices Impurity States and Impurity Bands in 5-Doped n-i-p-i Superlattices References Metallic Superlattices D. Kerkmann and D. Peseta 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 ~ Г 432 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 459 References Quantum Adiabatic Electron Transport in Ballistic Conductors L. P. Kouwenhoven 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 480
9 xvi 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 Conclusions 494 References Experiments on Two-Dimensional Wigner Crystals E. Y. Andrei, F. J. B. Williams, D. С Glattli, and G. Devil/e Introduction The Phase Diagram Coulomb System of Classical Particles Coulomb System of Quantum Particles T = 0, В = Coulomb System of Quantum Particles T = 0, В Ф Coulomb System of Quantum Particles T Ф 0, В Ф 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 535 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 /- V Characteristics and Multiple-State RTBTs Gated Quantum-Well and Superlattice Base Transistor Transport in Superlattices Transport and Negative Differential Conductance in Superlattices with Wide Minibands Localization and Transport in Superlattices 565
10 xvii Bloch Oscillations Observation of Negative Differential Conductance in a Superlattice Scattering-Controlled Resonances 571 References 573 Index 577
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