First-principles study of neutral oxygen vacancies in amorphous silica and germania

Abstract

Neutral oxygen vacancies in amorphous $(a\ensuremath{-})$ ${\mathrm{SiO}}_{2}$ and ${\mathrm{GeO}}_{2}$ as well as bulk $a\ensuremath{-}{\mathrm{SiO}}_{2}$ and $a\ensuremath{-}{\mathrm{GeO}}_{2}$ configurations have been investigated by using the first-principles pseudopotential method in order to elucidate the mechanism of the photorefractive effect of Ge-doped ${\mathrm{SiO}}_{2}.$ Amorphous configurations of ${\mathrm{SiO}}_{2}$ and ${\mathrm{GeO}}_{2}$ have been constructed by quenching using classical molecular-dynamics method and subsequent relaxation using the first-principles method. Obtained configurations and electronic properties are in good agreement with experiments of $a\ensuremath{-}{\mathrm{SiO}}_{2}$ and $a\ensuremath{-}{\mathrm{GeO}}_{2},$ and the gross features of the densities of states (DOS's) of these glasses are similar to each other. The highest valence band is the $\mathrm{O}\ensuremath{-}2p$ nonbonding band and the lowest conduction band consists of Si or Ge orbitals. However, the structural differences between the $a\ensuremath{-}{\mathrm{SiO}}_{2}$ and $a\ensuremath{-}{\mathrm{GeO}}_{2}$ configurations such as the larger O-O distance in $a\ensuremath{-}{\mathrm{GeO}}_{2}$ and the relatively shorter Ge-Ge distance in $a\ensuremath{-}{\mathrm{GeO}}_{2}$ induce the peculiar differences in the DOS's. And the band gap of $a\ensuremath{-}{\mathrm{GeO}}_{2}$ is much smaller than that of $a\ensuremath{-}{\mathrm{SiO}}_{2}.$ The oxygen deficient centers (ODC's) are formed by removing identical oxygen atoms from the Si-O-Si and Ge-O-Ge networks. One occupied defect state is generated in the band gap. The Ge-Ge bond at the Ge-ODC is shorter than the Si-Si bond at the Si-ODC in the present configurations. The larger network flexibility and the less electrostatic repulsion in $a\ensuremath{-}{\mathrm{GeO}}_{2}$ than in $a\ensuremath{-}{\mathrm{SiO}}_{2}$ should cause the shorter Ge-Ge bond length at the Ge-ODC, which results in the lower occupied defect level in the gap in $a\ensuremath{-}{\mathrm{GeO}}_{2}$ and the much lower ODC formation energy in $a\ensuremath{-}{\mathrm{GeO}}_{2}.$ This smaller formation energy indicates much more ODC's in $a\ensuremath{-}{\mathrm{GeO}}_{2}$ than in $a\ensuremath{-}{\mathrm{SiO}}_{2}.$ Therefore more ${E}^{\ensuremath{'}}$ centers may be generated in Ge-doped $a\ensuremath{-}{\mathrm{SiO}}_{2}$ than in pure $a\ensuremath{-}{\mathrm{SiO}}_{2}$ if $a\ensuremath{-}{\mathrm{GeO}}_{2}$ clusters exist in Ge-doped $a\ensuremath{-}{\mathrm{SiO}}_{2}.$ Furthermore, we have discussed the electron trapping defects.