Microscopic Dielectric Function of a Model Semiconductor

Abstract

Penn's model of an isotropic semiconductor is used to calculate $\epsilon \mathrm{}\left(q\right)\mathrm{}$, the diagonal part of the static micro-scopic dielectric function. Penn's results have been extended beyond $q=K_F$. This region is important in developing a quantum theory of lattice vibrations of diamond and zinc-blende crystals. Explicit results are given for the range $0<q<\mathrm{}4\mathrm{}{K}_F$.