Bulk electronic structure of SiO2

The electronic structures of crystalline and amorphous Si${\mathrm{O}}_2$ are examined via the tight-binding method. A new tight-binding Hamiltonian, fit to experiment and to the pseudopotential band structure of $\alpha$ quartz, is used to calculate densities of states for both $\alpha$ quartz and an Si${\mathrm{O}}_2$ Bethe lattice. These are shown to compare favorably with x-ray photoemission spectra of $\alpha$ quartz and amorphous Si${\mathrm{O}}_2$. The computational results are analyzed qualitatively using the bond-orbital approach. For both crystalline and amorphous Si${\mathrm{O}}_2$ it is suggested that oxygen $2s$ character in the lower conduction bands may be necessary to account for the large gap. Local symmetries of the lone-pair-like bands of possible relevance to the optical properties are discussed.