Theoretical study of the insulating oxides and nitrides: SiO2, GeO2, Al2O3, Si3N4, and Ge3N4

An extensive theoretical study is performed for wide bandgap crystalline oxides and nitrides, namely, SiO₂, GeO₂, Al₂O₃, Si₃N₄, and Ge₃N₄. Their important polymorphs are considered which are for SiO₂: $α$-quartz, $α$- and $β$-cristobalite and stishovite, for GeO₂: $α$-quartz, and rutile, for Al₂O₃: $α$-phase, for Si₃N₄ and Ge₃N₄: $α$- and $β$-phases. This work constitutes a comprehensive account of both electronic structure and the elastic properties of these important insulating oxides and nitrides obtained with high accuracy based on density functional theory within the local density approximation. Two different norm-conserving \textit{ab initio} pseudopotentials have been tested which agree in all respects with the only exception arising for the elastic properties of rutile GeO₂. The agreement with experimental values, when available, are seen to be highly satisfactory. The uniformity and the well convergence of this approach enables an unbiased assessment of important physical parameters within each material and among different insulating oxide and nitrides. The computed static electric susceptibilities are observed to display a strong correlation with their mass densities. There is a marked discrepancy between the considered oxides and nitrides with the latter having sudden increase of density of states away from the respective band edges. This is expected to give rise to excessive carrier scattering which can practically preclude bulk impact ionization process in Si₃N₄ and Ge₃N₄.