Local field effects and a model dielectric response matrix ϵG,G′(q) for a covalent semiconductor

A model for the microscopic dielectric response ϵ G,G ′( q ) of a covalent semiconductor is proposed in which the effects of the localized and plane wave features of the band structure on the polarizability are separated. Within this model for diamond a calculation is performed of the static longitudinal wave vector dependent macroscopic dielectric function ϵ M ( q ), including local field corrections, together with an analysis in real space of the microscopic local field E ( r ) and polarization charge density ϱ ind r ) induced by a uniform externally applied electric field. The results indicate that although the macroscopic dielectric function is essentially insensitive with respect to small changes in the effective charge model parameter Z , microscopic quantities such as the induced charge density and microscopic local field can be fairly sensitive to variations in Z . This suggests that careful tests on model based dielectric responses ϵ G,G ′ ( q ) are probably necessary before one calculates, for instance, phonon frequencies.