First-principles calculations of the band gap ofHfxSi1−xO2andZrxSi1−xO2alloys

Abstract

A generalized quasichemical method and the cluster expansion approach are applied to calculate the band gap of amorphous ${\mathrm{Hf}}_{x}{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ and ${\mathrm{Zr}}_{x}{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ alloys within the pseudopotential based density-functional theory. The dependence of the band gap of ${\mathrm{Hf}}_{x}{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ and ${\mathrm{Zr}}_{x}{\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{O}}_{2}$ compounds on the molar concentration $x$ is computed to be nearly linear with small bowing parameter $b$. The mean-square deviation of the band gap, which defines the leakage current fluctuations, is explicitly calculated. The calculation of the internal stress in these compounds due to alloying yields a small value, which may be a reason for the small bowing in the band gap.