The saddle-point configurations and associated formation energies of a migrating silicon vacancy in the +2, +1, 0, −1 and −2 charge states were computed using density-functional theory with a plane wave basis set, norm-conserving pseudopotentials, and the generalized-gradient approximation for exchange and correlation. Spurious electrostatic and strain contributions arising from use of periodic boundary conditions were removed by performing maximum likelihood fits on results from 215-, 511- and 999-atom super-cells, and thereby obtaining formation energies corresponding to isolated vacancies. Migration enthalpies were computed by subtracting similarly obtained formation energies for vacancies in local-energy minimum configurations. The results (0.27eV in the +2 charge state, 0.19eV in the +1 charge state, 0.36eV in the 0 charge state, 0.04eV in the −1 charge state, and 0.15eV in the −2 charge state) were in good overall agreement with experimental results obtained at low temperatures.

Density-Functional-Theory Calculations for Silicon Vacancy Migration. A.F.Wright, R.R.Wixom: Journal of Applied Physics, 2008, 103[8], 083517