Electronic and optical properties of all polymorphic forms of silicon dioxide.

Abstract

With use of the self-consistent orthogonalized linear combination of atomic orbitals method in the local-density approximation, the electronic structures and the optical properties of eight different polycrystalline phases of ${\mathrm{SiO}}_{2}$ have been studied: They are \ensuremath{\alpha}-quartz, \ensuremath{\beta}-quartz, \ensuremath{\beta}-tridymite, \ensuremath{\alpha}-cristobalite, \ensuremath{\beta}-cristobalite, keatite, coesite, and stishovite. The band structure, density of states, and valence-charge distribution for each phase are studied in relation to their local-bonding structure. The octahedrally coordinated stishovite phase has a higher covalent binding character than the 4:2-coordinated polycrystals. The interband optical absorption for each crystal is also calculated, thus allowing the dielectric function and the electron-energy-loss function to be derived. For \ensuremath{\alpha}-quartz, for which much experimental data are available, the calculated optical absorption and the electron-energy-loss function are in good agreement with the measurements. Apart from the main strong excitonic peak at 10.3 eV, the other three structures at 11.4, 14.2, and 17.0 eV in the absorption curve are reproduced by the calculation without the need to invoke excitonic resonances.It is pointed out that the calculated band gap in \ensuremath{\alpha}-quartz does not reflect directly the measured optical gap because transitions near the zone center are symmetry forbidden. It is also argued that the sharp peak at 10.4 eV in the electron-energy-loss spectrum of \ensuremath{\alpha}-quartz is mainly due to the fact that ${\mathrm{\ensuremath{\epsilon}}}_{1}$(\ensuremath{\omega}) vanishes at this frequency. Correlations between structural properties such as mass density, average bond length, and average bond angle with the calculated band gap ${\mathit{E}}_{\mathit{g}}$ and the static dielectric constant ${\mathrm{\ensuremath{\epsilon}}}_{1}$(0) in the polycrystals are explored. It is found that there is no apparent correlation between ${\mathit{E}}_{\mathit{g}}$ or ${\mathrm{\ensuremath{\epsilon}}}_{1}$(0) with the average Si-O-Si angle. There are strong correlations with the mass density (or the crystal volume). The high-mass-density phase has a smaller band gap and a larger ${\mathrm{\ensuremath{\epsilon}}}_{1}$(0) value. There is a weak correlation between the average bond length and ${\mathit{E}}_{\mathit{g}}$, but not with ${\mathrm{\ensuremath{\epsilon}}}_{1}$(0).