Existence of a Gap in the Electronic Density of States of a Tetrahedrally Bonded Solid of Arbitrary Structure

Abstract

Rigorous bounds for the density of electronic states are given for an idealized model of a group-IV semiconductor based on the tight-binding method. These include inner bounds which define a minimum gap in the density of states. The importance of this development lies in its independence of periodicity. It applies not only to crystalline structures made up of tetrahedral bonds but also the random tetrahedral network which recent studies have suggested for amorphous Si and Ge.