Semiconductor properties based upon universal tight-binding parameters

Abstract

The bond-orbital model for calculating properties of semiconductors utilizes nearest-neighbor universal matrix elements in a minimal-basis tight-binding formulation. It also neglects the coupling between bond orbitals and neighboring antibonding orbitals. The accuracy of these two approximations is tested by making only the first and calculating the bands, densities of states, and dielectric susceptibilities without further approximation. ${\ensuremath{\chi}}_{1}(0)$ is calculated for 30 semiconductors and ${\ensuremath{\chi}}_{2}(\ensuremath{\omega})$ is calculated for silicon. Errors in the conduction bands shift the ${E}_{1}$ and ${E}_{2}$ peaks (seen to be associated with $\mathrm{sp}$ and $\mathrm{pp}$ coupling, respectively) to higher energy and cause an underestimate in ${\ensuremath{\chi}}_{1}(0)$ by a factor of about 2 for all semiconductors. The calculations described were based upon the Gilat-Raubenheimer scheme with tetrahedral decomposition for both zinc-blende and wurtzite structures. The calculation for zinc blende was greatly simplified, at some cost in efficiency, by use of hexagonal or quadrangular Brillouin zones. This also allowed a direct calculation of the photoelastic tensors, carried out for 30 cubic semiconductors and apparently the first values, theoretical or experimental, for most of these.