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Frequency‐ and wave‐vector‐dependent dielectric function of a model semiconductor
Author(s) -
Milchev A.
Publication year - 1978
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220900229
Subject(s) - dielectric function , lorentz transformation , wave vector , semiconductor , plasmon , function (biology) , computation , long wavelength limit , wave function , physics , dispersion relation , quantum mechanics , limit (mathematics) , hyperboloid model , wavelength , electron , sum rule in quantum mechanics , free electron model , dielectric , condensed matter physics , mathematical analysis , mathematics , algorithm , evolutionary biology , minkowski space , biology , quantum chromodynamics
Closed analytical expressions for the real part ϵ 1 ( q , ω) and the imaginary part ϵ 2 ( q , ω) of the frequency‐ and wave‐vector‐dependent dielectric function are obtained including a gap E g in an appropriate manner in the spirit of the nearly‐free electron approximation, and requiring that these functions will exactly satisfy the Kramers‐Kronig relations and the f ‐sum rule. In the long wavelength limit the classical Lorentz oscillator result comes out, whereas for ω = 0 the static screening function is decisively improved with regard to earlier model calculations. The results also yield the plasmon dispersion relations ω L ( q ) and ω T ( q ) for Si, Ge, GaAs, and ZnSe in good agreement with previous detailed computations. With the average gap width E g going to zero the expressions obtained transform into the well‐known RPA (Lindhard) formulae for a free electron gas.