The atomic configurations and formation energies of a Si vacancy in the +2, +1, 0, −1, and −2 charge states were computed using density-functional theory with norm-conserving pseudopotentials and a plane wave basis. Calculations were performed in simple cubic super-cells using two different forms of exchange and correlation: the local-density approximation (LDA) and the Perdew, Burke, Ernzerhof formulation of the generalized-gradient approximation (GGA). Convergence with respect to Brillouin zone sampling was tested for all charge states, and effects due to electrostatic interactions between the periodically repeated vacancies were removed by extrapolating the formation energies obtained in 215-, 511- and 999-atom super-cells to an infinite sized super-cell. In agreement with experimental results, the GGA yielded a configuration with C2v symmetry in the −1 charge state, whereas the LDA yielded D3d symmetry. Transition energies between the charge states were also computed. The experimentally observed negative-U behavior of the donor states was reproduced in the GGA results, but not in the LDA results. Both the LDA and GGA predict negative-U behavior for the acceptor states.

Density-Functional-Theory Calculations for the Silicon Vacancy. A.F.Wright: Physical Review B, 2006, 74[16], 165116 (8pp)