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A First Order Generalized Thomas‐Fermi Approximation for the Electron Density in Inversion Layers
Author(s) -
Übensee H.,
Paasch G.
Publication year - 1989
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19895010705
Subject(s) - physics , density matrix , degenerate energy levels , operator (biology) , electron density , density of states , inversion (geology) , electron , fermi's golden rule , quantum mechanics , quantum tunnelling , local density of states , fermi gamma ray space telescope , fermi gas , airy function , order (exchange) , quantum electrodynamics , quantum , biochemistry , chemistry , finance , repressor , transcription factor , economics , gene , paleontology , structural basin , biology
An operator evaluation of the one‐particle density matrix of a degenerate system of independent particles in first order with respect to the gradient of the potential developed by Macke and Rennert yields an analytic expression for the particle density. This method is extended here to potentials with an infinite step and to finite temperatures – a situation which is characteristic for inversion electrons in MIS‐systems. The resulting density can be expressed as the Airy transform of the zeroth order (local density approximation). The first order yields both the tunneling into the classically forbidden region and oscillations of the density near the step of the potential. The operator evaluation of the density matrix is shown to be equivalent to solving a Schrödinger like equation. The first order density yields results for the subband structure of (100)Si inversion and accumulation layers at OK in remarkable agreement to density functional calculations of Ando.