Density matrix theory of coherent ultrafast dynamics

Abstract

First edition. The theoretical understanding of transport properties of semiconductor structures on short length and short time scales, and in the nonlinear high-field regime is of particular relevance for future electronic and optoelectronic materials. In recent years great progress has been made in a variety of aspects. Theory of Transport Properties of Semiconductor Nanostructures presents a state-of-the-art overview of theoretical methods, results, and applications in the field. It contains eleven chapters which are written by leading researchers. This book starts with a tutorial introduction to the subject, then in the following five chapters a hierarchy of different approaches to transport theory is presented, descending from a macroscopic level (quasihydrodynamic simulation) via semiclassical Monte Carlo techniques and cellular automata to a full quantum transport theory covering both Green's functions and density matrix theory. In the last five chapters the formalism is applied to more specific topics which are of great current interest such as transport in mesoscopic structures, chaotic dynamics in lateral superlattices, Bloch oscillations and Wannier-Stark localization, field domain formation in superlattices, and scattering processes in low-dimensional structures. Theory of Transport Properties of Semiconductor Nanostructures is aimed at physicists, electronic engineers, materials scientists and applied mathematicians. It may be used in research, as a professional reference in microelectronics, optoelectronics, and graduate teaching. This book should be useful not only to graduate students but also to professional scientists working in the field. It attempts to present comprehensive reviews of the most important advances, and often takes a tutorial approach. 1 Introduction -- 1.1 Introduction -- 1.2 What are Nanostructures? -- 1.3 Physical Length Scales in Transport -- 1.4 Hierarchy of Modelling Approaches -- 1.5 Scope of This Book -- 2 Hydrodynamic simulation of semiconductor devices -- 2.1 Introduction -- 2.2 Statistical Averages and Moments of the Bte -- 2.3 The Hydrodynamic Model -- 2.4 Model Coefficients -- 2.5 Examples of Application to Hot-Carrier Effects -- 3 Monte Carlo simulation of semiconductor transport -- 3.1 Introduction -- 3.2 Semiclassical Transport in Semiconductors -- 3.3 The Monte Carlo Method for Bulk Transport -- 3.4 Results -- 3.5 From Semiclassical to Quantum Transport -- 3.6 Conclusions -- 4 Cellular automaton approach for semiconductor transport -- 4.1 Introduction -- 4.2 Examples of Cellular Automata in Fluid Dynamics -- 4.3 Full Boltzmann Transport Equation as Cellular Automaton -- 4.4 Validation and Comparison with Monte Carlo Results -- 4.5 Comparison with Experiment -- 4.6 Summary -- 5 Quantum transport theory -- 5.1 Introduction -- 5.2 Coulomb Drag -- 5.3 Kubo Formula for Transconductivity -- 5.4 Impurity Scattering -- 5.5 Coulomb Drag in a Magnetic Field -- 5.6 Summary of Coulomb Drag -- 5.7 Nonequilibrium Greens Function Techniques -- 5.8 Model Hamiltonian -- 5.9 Calculation of the Tunnelling Current -- 5.10 Noninteracting Resonant-Level Model -- 5.11 Resonant Tunnelling with Electron-Phonon Interactions -- 6 Density matrix theory of coherent ultrafast dynamics -- 6.1 Introduction -- 6.2 Density Matrix Formalism -- 6.3 Interaction with an External Field -- 6.4 Carrier-Phonon Interaction -- 6.5 Carrier-Carrier Interaction -- 6.6 Multiple Interactions -- 6.7 Results -- 6.8 Conclusions -- 7 Dynamic and nonlinear transport in mesoscopic structures -- 7.1 Introduction -- 7.2 Theory -- 7.3 Examples -- 7.4 Conclusion -- 8 Transport in systems with chaotic dynamics: Lateral superlattices -- 8.1 Introduction -- 8.2 Experiments -- 8.3 Classical Chaos and Transport -- 8.4 Quantum-Mechanical Band Structure -- 8.5 Quantum Signatures of Chaos -- 8.6 Quantum Transport -- 8.7 Summary and Outlook -- 9 Bloch oscillations and Wannier-Stark localization in semiconductor superlattices -- 9.1 Introduction -- 9.2 Historical Background -- 9.3 Theoretical Analysis -- 9.4 Two Equivalent Pictures -- 9.5 Some Simulated Experiments -- 10 Vertical transport and domain formation in multiple quantum wells -- 10.0 Introduction -- 10.1 The Different Transport Regimes -- 10.2 Transport between Weakly Coupled Quantum Wells -- 10.3 Formation of Field Domains -- 10.4 Imperfect Superlattices -- 10.5 Oscillatory Behaviour -- 10.6 Details of the Calculations -- 10.7 Conclusions -- 11 Scattering processes in low-dimensional structures -- 11.1 Introduction -- 11.2 The Scattering Rate -- 11.3 Optical Phonons in a Quantum Well -- 11.4 Acoustic Phonons -- 11.5 Charged Impurities -- 11.6 Interface Roughness Scattering -- 11.7 Alloy Scattering -- 11.8 Other Scattering.