DIPOLE WAVES IN SEMICONDUCTORS: THE DIELECTRIC FUNCTION AND PLASMA OSCILLATIONS OF SILICON

Abstract

The relationship between bond polarisability, local fields and the dielectric function of bulk silicon is investigated using the discrete dipole model. In this model a valence electron pair (a bond) is treated as a point-like polarisable unit which responds to the local field at the bond by creating a dipole moment there. We assume an unretarded form for bond-bond interactions (local fields) and find the normal modes of an infinite lattice of bonds with the diamond structure. We call these normal modes dipole waves and express the dielectric function for bulk silicon in terms of them. Dipole waves corresponding to optical transitions and bulk plasma oscillations are identified and it is shown that the experimental peak positions and intensities in both the dielectric function and the dielectric loss function of silicon are reproduced by this model. The form of bond-bond interaction chosen is the electrostatic interaction between point-like dipoles but this approximation breaks down at short range. Bond-bond interactions at short range and bond polarisabilities are therefore calculated from ab initio cluster calculations. The static dielectric function is obtained as a function of bond polarisability using point dipolar local fields and local fields corrected at short range for the finite size of a bond. Comparison is made with the Clausius-Mossotti relationship between dielectric function and polarisability. © 1997 Elsevier Science Limited. All rights reserved.