Density-functional-theory calculations for silicon vacancy migration

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 supercells, 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 (0.27 eV in the +2 charge state, 0.19 eV in the +1 charge state, 0.36 eV in the 0 charge state, 0.04 eV in the -1 charge state, and 0.15 eV in the -2 charge state) are in good overall agreement with experimental results obtained at low temperatures. © 2008 American Institute of Physics.