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The Linear Dielectric Response of a Semiconductor: A New Analytic Form for the Dielectric Function
Author(s) -
Schulze K. R.,
Unger K.
Publication year - 1974
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.2220660211
Subject(s) - dielectric , function (biology) , convolution (computer science) , mathematics , semiconductor , analytic function , simple (philosophy) , limiting , mathematical analysis , dielectric function , filter (signal processing) , physics , quantum mechanics , computer science , engineering , evolutionary biology , biology , mechanical engineering , philosophy , epistemology , machine learning , artificial neural network , computer vision
A simple analytic form for the linear dielectric function ϵ( q ) of a semiconductor is constructed, which accounts correctly for the limiting cases q = 0 and asymptotic large q values. For ϵ(0) → ∞ a Weizsäcker type of screening is obtained. Numerical comparison with dielectric functions calculated on the basis of exact band structures shows very good agreement. Analytical expressions for the r‐dependent dielectric function, for the filter function, and for the convolution function are also given and their implications are discussed.