Self-consistent pseudopotential calculation of electronic states associated with a reconstructed silicon vacancy

We have extended our pseudopotential method and carried out a self-consistent calculation of electronic states associated with a single vacancy in silicon, with a particular emphasis on the problem of lattice reconstruction in the vicinity of the defect. We find that the vacancy with three dangling electrons, i.e., $V_{\mathrm{Si}}^{+}$, has a localized state close to the valence-band edge. We show that the nonspherical part of the vacancy potential, which is related to the rearrangement of the electron charge density along the bonding directions, plays an important part in the quantitative assessment of the position of the bound state in the gap. The lattice reconstruction consists of a symmetric, outward displacement of the nearest-neighbor silicon atoms by about 0.1 Å, and a similar tetragonal displacement that gives rise to a characteristic splitting of the degenerate $t_2$ state in the gap. The final lattice configuration is deduced from minimum-energy considerations. The net reduction in the total energy associated with the lattice reconstruction is about 1 eV. A critical discussion of the results is given in the light of existing theoretical and experimental evidence.