Band structures of all polycrystalline forms of silicon dioxide

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 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.