Comparative study of electronic structures and dielectric properties of alumina polymorphs by first-principles methods

Abstract

Based on density functional methods, we investigate the origin of variations in electronic structures and dielectric constants of representative alumina polymorphs. We consider the most stable $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ and three metastable phases of alumina, $\ensuremath{\kappa}$, $\ensuremath{\theta}$, and $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}$. Computed energy gaps are found to be in the order of $\ensuremath{\alpha}>\ensuremath{\kappa}>\ensuremath{\theta}>\ensuremath{\gamma}$, which can be understood based on electrostatic potentials at specific lattice sites; while cations occupying tetrahedral sites explain downshifts of conduction bottoms in the metastable alumina, vacant sites in $\ensuremath{\gamma}\text{\ensuremath{-}}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ account for the gap reduction originated in the valence band. On the other hand, dielectric properties are also calculated based on density functional perturbation methods. On average, the static dielectric constants follow the order of $\ensuremath{\kappa}>\ensuremath{\alpha}>\ensuremath{\theta}>\ensuremath{\gamma}$. The substantial enhancement of the dielectric constant for $\ensuremath{\kappa}\text{\ensuremath{-}}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ is attributed to elongated Al-O bonds due to a simultaneous occupation of tetrahedral and octahedral sites by cations within a single layer.