A Simple Tight‐Binding Model Applicable to Calculations of the Band Structure of Amorphous Germanium

Abstract

A simple semi‐empirical tight‐binding model applicable to germanium is presented which takes into account the effects of rotation of the dihedral angle and of bond distortions. The effects of rotation of the dihedral angle are taken into account by including all interactions between nearest‐neighbors, the effects of distortions in bond angles by means of a two‐center approximation together with the properties of spherical harmonics, and the effects of distortions in bond‐length by fitting the matrix elements to the sophisticated band calculations of Herman et al. not only for crystalline Ge at the observed density but also for uniformly compressed and dilated crystalline Ge. Comparison of the results of this model with sophisticated calculations for various polymorphs of Ge shows that this model is, at very least, qualitatively satisfactory and should be useful in band structure calculations for amorphous Ge. Copyright © 1974 WILEY‐VCH Verlag GmbH & Co. KGaA