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Comprehensive treatment of electronic structure of and transport in solids including nanostructures
Includes a historical perspective on the evolution of quantum theory and how it has shaped our knowledge of electrons in crystals
Rigorous mathematical development is supplemented by numerical and computational methodologies which convey a practical understanding of the challenges and successes of using quantum mechanics for real world applications
Exercises for students, based on homework problems assigned by the authors, and suggested reading will be included
This textbook is aimed at second-year graduate students in Physics, Electrical Engineering or Materials Science. It presents a rigorous introduction to electronic transport in solids, especially at the nanometer scale. Understanding electronic transport in solids requires some basic knowledge of Hamiltonian Classical Mechanics, Quantum Mechanics, Condensed Matter Theory, and Statistical Mechanics. Hence this book discusses those sub-topics of these four disciplines which are required to deal with electronic transport in a single, self-contained course. This will be useful for students who intend to work in academia or the nano/micro-electronics industry. Further topics covered include: the theory of energy bands in crystals, of second quantization and elementary excitations in solids, of the dielectric properties of semiconductors with an emphasis on dielectric screening and coupled interfacial modes, on electron scattering with phonons, plasmons, electrons and photons, on the derivation of transport equations in semiconductors and semiconductor nanostructures also at the quantum level. but mainly at the semi-classical level. The text presents examples relevant to current research, thus not only about Si, but also III-V compound semiconductors, nanowires, graphene and graphene nanoribbons. In particular, the text gives major emphasis to plane-wave methods regarding the electronic structure of solids, both DFT and empirical pseudopotentials, always paying attention to their effects on electronic transport and its numerical treatment. The core of the text is electronic transport, with ample discussions on the transport equations derived both in the quantum picture (the Liouville-von Neumann equation) and semi-classically (the Boltzmann transport equation, BTE). Several methods for solving the BTE are also reviewed, including the method of moments, iterative methods, direct matrix inversion, Cellular Automata and Monte Carlo. The first appendix, on the principles of special relativity, is required to understand the ‘minimal’ electromagnetic coupling between electrons and photons and also to introduce the relativistic wave equation for massless spin-1/2 particles. This is of current interest since it is used to describe approximately the electron dispersion in graphene. The second appendix, on alternative interpretations of quantum mechanics, is strictly related to the ‘tricky’ transition from the time-reversible Liouville-von Neumann equation to the time-irreversible Green’s functions, to the density-matrix formalism and, classically, to the Boltzmann transport equation.
Content Level »Graduate
Keywords »Alternative Interpretations of Quantum - Carbon-based Nanostructures - Electronic Transport in Solids - Mechanics - Nano-electronics - Semiconductor Nanostructures - Semiconductor Physics - Solid-state Electronics - Special Relativity for Electromagnetic Coupling
Part I A Brief Review of Classical and Quantum Mechanics.- Lagrangian and Hamiltonian formulation of Classical Mechanics.- Superposition principle and Hilbert spaces.- Canonical Quantization.- Review of time-independent and time-dependent perturbation theory.- The Periodic Table, molecules and bonds in a nutshell.- Part II Crystals and Electronic Properties of Solids.- Crystals: Lattices, structure, symmetry, reciprocal lattice.- The electronic structure of crystals.- Single-electron dynamics: Acceleration theorems, Landau levels, Stark-ladder quantization.- Part III Second Quantization and Elementary Excitations in Solids.- Lagrangian and Hamiltonian formulation of classical fields.- Canonical Quantization of fields (‘Second Quantization’).- An example: Quantization of the Schrödinger Field.- Elements of Quantum Statistical Mechanics and the Spin-Statistics Theorem.- Quantization of the charge density: Plasmons.- Quantization of the vibrational properties of solids: Phonons.- Quantization of the Electromagnetic Fields: Photons.- Dielectric properties of semiconductors.- Part IV Electron Scattering in Solids.- Generalities about scattering in semiconductors.- Electron-phonon Interactions.- Scattering with Ionized Impurities: Brooks-Herring and Conwell-Weisskopf models, Ridley’s statistical screening, Friedel sum rule and partial-waves.- Coulomb interactions among free carriers, impact-ionization, Auger recombination.- Interfacial and line-edge roughness with examples: Si/SiO2, heterostructures, graphene nanoribbons.- Interfacial excitations with examples: III-Vs plasmon/phonon coupled modes, suspended grapheme.- Radiative Processes: The dipole approximation, absorption spectrum for III-Vs.- Part V Electronic Transport.- The Density Matrix and the Liouville-von Neumann equation.- Overview of quantum-transport formalisms.- From Liouville-von Neumann to Boltzmann: The semiclassical limit.- From Liouville-von Neumann to Boltzmann: The semiclassical limit.
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