Band structures of all polycrystalline forms of silicon dioxide

The band structures and density of states of all polycrystalline forms of SiO₂ with known crystal structures are calculated using a first-principles orthogonalized linear combination of atomic orbitals method. These include 4:2-coordinated polymorphs of {α}-quartz, {β}-quartz, {β}-tridymite, {α}-crystobalite, {β}-crystobalite, keatite, coesite, and two idealized forms of {β}-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.