Electronic structure of vacancy defects in MgO crystals

The electronic structure of oxygen-vacancy defects (F, $F^{+}$ and $F^{2+}$ centers) in MgO crystals has been studied within local-density theory, using the self-consistent mixed-basis pseudopotential techniques. The defects were modeled within a supercell having a volume 8 times that of the perfect MgO crystal. The band structure, density of states, charge-density contours, and total energy were calculated as a function of lattice relaxation. The partial density of states shows that each of the F-type centers introduces impurity states into the band gap as well as near the conduction-band edge of MgO. The total energy was calculated as a function of relaxation of the nearest-neighbor shell of ${\mathrm{Mg}}^{2+}$ ions. For F centers, the lowest-energy configuration was found to be a small inward relaxation of the nearest ${\mathrm{Mg}}^{2+}$ ions toward the vacancy site. For $F^{+}$ and $F^{2+}$ centers, the lowest total energies correspond to a small outward relaxation of the ${\mathrm{Mg}}^{2+}$ ions away from the vacancy site. The electronic structure of hydrogen impurities (${\mathrm{H}}^{\mathrm{-}}$ and ${\mathrm{H}}^{2\mathrm{-}}$ substitutional defects) in MgO was also investigated using the same approach. These impurities contribute defect states within and below the oxygen p bands as well as near the conduction-band edge of MgO. The lowest-total-energy configurations of both ${\mathrm{H}}^{\mathrm{-}}$ and $H^{2\mathrm{-}}$ substitutional defects correspond to a slight outward relaxation of the nearest ${\mathrm{Mg}}^{2+}$-ion shell.