Electronic Quantum Transport in Mesoscopic Semiconductor Structures

Transcription

1 Thomas Ihn Electronic Quantum Transport in Mesoscopic Semiconductor Structures With 90 Illustrations, S in Full Color Springer

2 Contents Part I Introduction to Electron Transport l Electrical conductance : Historical account from Ohm to the semiclassical Drade--Boltzmann theory 3 2 Toward the microscopic understanding of conductance on a quantum mechanical basis,, 7 21 Quantum transport in metals 7 22 Transistors and two-dimensional electron gases in semiconductors tvo-dimensional electron gases in field-effect transistors 10 2,12 Resonant tunneling in semiconductors Integer and fractional quantum Hall effect Weak localization Basic phenomena in semiconductor structures of reduced size and dimensionality The Aharonov-Rohm effect and conductance fluctuations Conductance quantization in semiconductor quantum point contacts Semiconductor quantum dots and artificial atoms 19 Part II Conductance in Strongly Interacting and Disordered Two-Dimensional Systems 3 The concept ofmetals and insulators 25 4 Scaling theory of localization 27 5 Electron-electron interactions within the Fermi-liquid concept Dephasing in diffusive two-dimensional systems Interaction corrections to the conductivity 30

3 V ill Contents Temperature-dependent screening Interaction corrections due to interference of multiply scattered paths A comprehensive theory of interaction corrections based on the Fermiliquid concept 34 6 Beyond Fermi-liquid theory 7 Summary of disorder and interaction effects 8 Experiments on strongly interacting two-dimensional systems and the metal-insulator transition Theoretical work related to the metal--insulator transition Metallic behavior in p-sige quantum wells 10 1 Samples and structures 10 2 Scaling analysis, quantum phase transition, and heating effects 10 3 Magnetoresistance measurements 10 4 Weak-localization correction 10 5 Interaction corrections to the conductivity : multiple impurity scattering 106 Interaction corrections of the Drude conductivity due to T-dependent screening 107 Reentrant insulating behavior 108 Parallel magnetic field 109 Discussion of the results and conclusions Part III Electron Transport through Quantum Dots and Quantum Rings 11 Introduction to electron transport through quantum dots Resonant tunneling and the quantization of the particle number on weakly coupled islands Quantum dot states : from a general hamiltonian to the constant-interaction model Transport through quantum dots Coulomb-blockade oscillations Coulomb-blockade diamonds Conductance peak line shape at finite temperatures Beyond the constant-interaction model Energy spectra of quantum rings Introduction to quantum rings Samples and structures Magnetotransport measurements on a quantum ring 89

4 Contents IX 12 4 Interpretation within the constant-interaction model One-dimensional ring model Ring with finite width,,,,, Experimental single-particle level spectrum Effects of broken symmetry Interaction effects and spin-pairing OCoulomb-blockade in a Sinai billiard Relation of the ring spectra to persistent currents Summary Spin filling in quantum dots Introduction to spins in quantum dots Samples and structures Experiments Weak-coupling regime Intermediate-coupling regime Strong coupling Diamagnetic shift, Discussion of the results Conclusions, 127 Part IV Local Spectroscopy ofsemiconductor Nanostructures 14 Instrumentation : Scanning force microscopes for cryogenic temperatures and magnetic fields Introduction : low-temperature scanning force microscopes Design criteria for a low-temperature scanning force microscope for the investigation of semiconductor nanostructures A scanning force microscope operated in a 3He system Scanning Sensors Introduction, Types of sensors : an overview Piezoelectric tuning fork sensors Electronics for a high-q tuning fork sensor Tuning fork admittance and frequency demodulation ,5 2 Frequency detection with a phase-locked loop ,5 3 Frequency shift and tip-sample interaction The z-feedback ,5 5 About feedback parameters Force-distance studies on HOPO with piezoelectric tuning forks at 1 7 K,, 164

5 X Contents 15 Local investigation of a two-dimensional electron gas with an SI+'M at cryogenic temperatures Samples and structures Kelvin-probe measurements General electrostatic consideration Plate capacitor model Local investigation ofedge channels Brief introduction to edge channels Scanning probe experiments Scanning SET measurements Scanned potential microscopy Subsurface charge accumulation imaging Local modification of inter-edge-channel tunneling with a scanning force microscope Scanning gate measurements on a quantum wire Introduction to scanning gate measurements on mesoscopic systems Samples and structures Results of low-temperature scanning gate measurements on a quantum wire Modeling scanning gate measurements : Classical and quantum effects Classical billiard model Quantum description of scattering in wires 200 A Formal solution of the electrostatic problem with Green's functions 207 A 1 The electrostatic problem 207 A2 Formal solution with Green's functions 208 A 3 induced charges on the electrodes 209 A 4 Total electrostatic energy of the system 210 A 5 Force gradient acting on an electrode Screened addition energy of an electron to a quantum ring 211 C Scattering in quantum wires 217 C i Single 9 scatterer 217 C2 Multiple ä seatterers 219 C3 Delta scatterer with finite extent in V-direction 220 C 4 Scatterer with finite extent in y-direction and rectangular shape in -direction 220 D Response ofa harmonic oscillator to a resonance frequency step 223 E Acknowledgements 225

6 Contents X1 F List of symbols 227 F1 Physics constants 227 F2 Variables 228 F3 Special functions 238 References 239 Index 267