Electronic structure of the silicon divacancy

We have calculated the electronic structure of the silicon divacancy using the self-consistent Green’s-function method. We find that, for the ideal divacancy, there are two deep levels (${\mathit{e}}_{\mathit{g}}$ and ${\mathit{e}}_{\mathit{u}}$) in the band gap and that the charge state changes from ${\mathit{V}}_2^{2\mathrm{-}}$ to ${\mathit{V}}_2^{+}$ as the Fermi level varies from the bottom of the conduction band to the top of the valence band. The Fermi-level dependence of the most stable charge state, i.e., the occupancy level structure, is in agreement with the experiment. We investigate the lattice relaxation of the surrounding silicon atoms by combining the electronic-structure results from the Green’s-function calculation with the valence-force model, and evaluate the amount of the Jahn-Teller relaxation. We find that the relaxation is small; the Jahn-Teller energy is ≃20 meV for ${\mathit{V}}_2^{+}$, in reasonable agreement with the electron paramagnetic resonance experiment. Examination of the calculated results and the experimental data available leads us to conclude that the electronic level structures of the distorted divacancy are (${\mathit{b}}_{\mathit{u}}$ ${)}^1$ for ${\mathit{V}}_2^{+}$, (${\mathit{b}}_{\mathit{u}}$ ${)}^2$ for ${\mathit{V}}_2^0$, (${\mathit{b}}_{\mathit{u}}$ ${)}^2$(${\mathit{a}}_{\mathit{g}}$ ${)}^1$ for ${\mathit{V}}_2^{\mathrm{-}}$, and (${\mathit{b}}_{\mathit{u}}$ ${)}^2$(${\mathit{a}}_{\mathit{g}}$ ${)}^2$ for ${\mathit{V}}_2^{2\mathrm{-}}$, respectively. On the basis of the obtained electronic structure, we propose a new reorientation process of ${\mathit{V}}_2^{\mathrm{-}}$ via a metastable configuration.