Quantum Transport: Atom to TransistorThis book presents the conceptual framework underlying the atomistic theory of matter, emphasizing those aspects that relate to current flow. This includes some of the most advanced concepts of non-equilibrium quantum statistical mechanics. No prior acquaintance with quantum mechanics is assumed. Chapter 1 provides a description of quantum transport in elementary terms accessible to a beginner. The book then works its way from hydrogen to nanostructures, with extensive coverage of current flow. The final chapter summarizes the equations for quantum transport with illustrative examples showing how conductors evolve from the atomic to the ohmic regime as they get larger. Many numerical examples are used to provide concrete illustrations and the corresponding Matlab codes can be downloaded from the web. Videostreamed lectures, keyed to specific sections of the book, are also available through the web. This book is primarily aimed at senior and graduate students. |
Contents
an atomistic view of electrical resistance | 1 |
2 Schrödinger equation | 33 |
3 Selfconsistent field | 51 |
Basis functions | 81 |
Bandstructure | 104 |
Subbands | 129 |
Capacitance | 155 |
8 Level broadening | 183 |
advanced formalism | 319 |
Correlation functions | 321 |
Nonequilibrium density matrix | 324 |
Inflow and outflow | 329 |
Inelastic flow | 332 |
Coulomb blockadeKondo resonance | 337 |
MATLAB Codes used to generate text figures | 343 |
| 394 | |
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Common terms and phrases
assuming bandstructure basis functions broadening Büttiker calculate capacitance channel Chapter clear all Constants coherent conduction band conductor Constants all MKS correlation function coupling current flow density matrix described device diagonal elements discrete lattice discussed dispersion relation drain voltage effective mass eigenstates eigenvalues electrochemical potential electron density emission energy levels equal equilibrium evaluate example Fermi function gate voltage given Green's function grid ħ² Hamiltonian matrix hydrogen atom inflow inscattering interaction modes molecule multi-electron nanotube Note number of electrons obtain one-dimensional one-electron one-level orbitals outflow parameters periodic boundary conditions phase-breaking phonons problem quantum transport quantum wire representation represents reservoir result scattering Schrödinger equation Section self-energy semiconductors shown in Fig solid source and drain spectral function subbands t₁ transmission unit cell valence band vector velocity wavefunction wire write ylabel zero