The electronic energy bands of silicon dioxide in the $\alpha$-quartz structure have been calculated at several pôints of high symmetry in the Brillouin zone by the mixed-basis method. A tight-binding interpolation scheme has been used to determine complete valence bands and their state densities. The results are compared with experiment and with calculations on the higher-symmetry $\beta$-cristobalite. The quartz and cristobalite bands share many properties; for example, in both cases the optical-absorption edge is predicted to be direct but forbidden. These results are in partial agreement with pseudopotential calculations by Chelikowsky and Schluter (CS). The major disagreements are that CS predict an indirect absorption edge, and their conduction bands are much wider than ours. Possible reasons for these disagreements are suggested.

• Received 29 June 1977

DOI:https://doi.org/10.1103/PhysRevB.18.2888