Electron states in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>α</mml:mi></mml:math>-quartz: A self-consistent pseudopotential calculation

Abstract

Self-consistent pseudopotentials are used to investigate the electronic structure of $\ensuremath{\alpha}$-quartz. We present calculations for the band structure, electronic density of states, optical response functions, pseudocharge densities, and x-ray emission spectra. We find excellent agreement between theory and experiment with respect to photoemission and uv absorption data. The chemical bonding present in $\ensuremath{\alpha}$-quartz as determined from pseudocharge density contour maps is consistent with other theoretical calculations. The theoretical x-ray emission spectra, as obtained from an orthogonalized-plane-wave scheme, are compared with experimental data. The calculated silicon and oxygen $K$ spectra agree very well with experiment; however, the $\mathrm{Si} {L}_{2,3}$ spectrum exhibits substantial disagreement with the data. An explanation is proposed based upon the formation of amorphous elemental Si in Si${\mathrm{O}}_{2}$ during electron irradiation.