One-electron energy bands of silicon dioxide in the idealβ-cristobalite structure

The generalized mixed-basis method developed in another paper has been applied to compute the valence and conduction bands of silicon dioxide in the ideal β-cristobalite structure. Calculations were made for the symmetry points Γ, X, and L in the first Brillouin zone. A tight-binding interpolation scheme was developed in order to treat the valence bands at general points of the Brillouin zone. The light- and heavy-hole effective masses at the top of the valence band were calculated to be approximately three and six electron masses, respectively. The computed optical absorption edge, from Γ₂₅ to Γ₁, was found to be direct but forbidden by the dipole selection rules. As a consequence, transitions to the $n=1$ exciton level are unobservable. Experimental data on x-ray emission, optical reflectivity, and photoemission were analyzed in detail and were found to be consistent with these theoretical results.