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Quantum Mechanics of Electrons in Crystals

  • Karl W. Böer
  • Udo W. PohlEmail author
Living reference work entry

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Abstract

The electronic band structure of semiconductors reveals most of their intrinsic properties. It consists of the dispersion relation En(k) for the various bands and is obtained from solving the Schrödinger equation for all electrons and nuclei in the solid. A manageable solution of this many-body problem requires substantial approximations for the interaction potential of all involved particles. Both empirical and ab initio approaches were developed for a one-electron scheme with different ways to approximate the actual interaction potential. Most approaches expand the wavefunction in terms of a set of orthogonal trial functions, followed by variation of the expansion coefficients for finding a self-consistent solution. The more recent density-functional method calculates self-consistently the ground-state energy of the many-electron system from the charge-density distribution.

Keywords

Ab initio approaches APW method Born-Oppenheimer approximation Density-functional method Density of states Dispersion relation Electronic band structure Empty lattice GW approximation Hartree-Fock approximation Hartree approximation Interaction potential KKR method K.p method LCAO method LMTO method Many-body problem Many-electron system One-electron scheme Pseudopotentials Schrödinger equation Tight-binding approach Wavefunction 

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Authors and Affiliations

  1. 1.NaplesUSA
  2. 2.Institut für Festkörperphysik, EW5-1Technische Universität BerlinBerlinGermany

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