Density-functional-theory calculations were performed for the unrelaxed +2 Si vacancy and +2 self-interstitial utilizing periodic boundary conditions and two different methods—the uniform background charge method and the local moment counter charge method—for circumventing the divergence of the Coulomb potential. Formation energies in nominal 64-, 216-, 512-, 1000- and 1728-atom super-cells were converged with respect to Brillouin zone sampling and then extrapolated to an infinite sized super-cell by fitting to a polynomial in odd powers of 1/L where L was the cubed root of the super-cell volume. The extrapolated values from the two methods agreed very well (2meV difference for the vacancy and 13meV difference for the interstitial) as expected from inspection of their respective energy expressions. The extrapolated values and fitting parameters were then employed to evaluate analytic correction formulas that were proposed to remove spurious electrostatic contributions from defect formation energies. The results indicated that existing formulas were not capable of removing these contributions and that further development was needed in this area.

Comparison of Two Methods for Circumventing the Coulomb Divergence in Super-Cell Calculations for Charged Point Defects. A.F.Wright, N.A.Modine: Physical Review B, 2006, 74[23], 235209 (8pp)