The Linear Dielectric Response of a Semiconductor: A New Analytic Form for the Dielectric Function

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.