Electronic structure of SiO2:α-quartz and the influence of local disorder

We present a comprehensive study of the electronic structure of $\alpha$-quartz employing the tight-binding method. Nearest- and second-nearest-neighbor interactions are included and treated as parameters which are adjusted to provide the closest correspondence to the recent pseudopotential-based electronic-structure calculations. A satisfactory agreement over the entire range of bands is obtained employing only eight parameters. Detailed agreement in limited ranges of energies of particular interest in various contexts can be obtained at the cost of discrepancies elsewhere. The direct or indirect nature of the fundamental band gap is found to be controlled by the second-order effects arising from the interplay between the oxygen-oxygen and oxygen-silicon-oxygen interactions. Results for the density of states are obtained and, after proper weighting by the appropriate photoelectric cross sections, compared with the observed x-ray photoelectron spectra (XPS). The computed charge density indicates a charge transfer to oxygen of order unity. The flexibility of the tight-binding method and the insulating nature of Si${\mathrm{O}}_2$ are exploited to study the influence of local geometrical distortions from the $\alpha$-quartz configuration. We find the behavior of the bands near the fundamental band gap to be more sensitive to the precise local geometry than is the overall behavior of the bands. Results for the changes in the bands, density of states, and charge transfer to oxygen as a function of variations in the Si-O-Si bridging-bond angle, as well as the O-O bond length, are presented. It is suggested that such information may be of considerable use in elucidating the nature of amorphous Si${\mathrm{O}}_2$. To this end, a framework capable of providing much needed chemical and structural information regarding glassy materials is presented and discussed in the context of recent XPS studies of the core level chemical shifts and of the valence-band structure of amorphous Si${\mathrm{O}}_2$.