Band structures of all polycrystalline forms of silicon dioxide.

Abstract

The band structures and density of states of all polycrystalline forms of ${\mathrm{SiO}}_{2}$ with known crystal structures are calculated using a first-principles orthogonalized linear combination of atomic orbitals method. These include 4:2-coordinated polymorphs of \ensuremath{\alpha}-quartz, \ensuremath{\beta}-quartz, \ensuremath{\beta}-tridymite, \ensuremath{\alpha}-crystobalite, \ensuremath{\beta}-crystobalite, keatite, coesite, and two idealized forms of \ensuremath{\beta}-crystobalites, as well as the 6:3-coordinated stishovite. Linear relations between the band gaps and the average Si--O bond lengths and the minimum Si--O--Si angles are firmly established. The electronic structure of stishovite is found to be very much different from the 4:2-coordinated oxides and shows more covalency in the bonding character.