Model semiconductor dielectric function

Abstract

The θ and q-dependent dielectric function is calculated in the RPA for a model semiconductor orginally proposed by Callaway. The basic inconsistency of the original model is overcome by requiring the f-sum rule to be obeyed. The long wavelength behaviour is shown to coincide with the classical Lorentz oscillator result. The static limit compares reasonably with that of Penn, which is extensively used in the literature. In spite of the extreme simplicity of the model the present result, which is expressed in closed analytical form, is believed to be of some value whenever an explicit expression for the dielectric screening in a semiconductor is needed.