A systematic method was used for the accurate calculation of defect structures in super-cells, which was illustrated via a study of the neutral vacancy in Si. This was a prototypical defect which was studied extensively by using ab initio methods and yet there was still no consensus about the energy or structure of this defect, or whether the nearest-neighbor atoms relaxed inwards or outwards. It was shown here that differences between previous calculations could be attributed to super-cell convergence errors, and it was demonstrated how to systematically reduce each such source of error. The various sources of scatter in previous theoretical studies were discussed and a different effect, that of super-cell symmetry, was identified. It was shown that a consistent treatment of this effect was crucial in understanding the systematic effects of increasing the super-cell size. This work therefore also presents the best converged ab initio study of the neutral Si vacancy to date.

Improving the Convergence of Defect Calculations in Super-Cells - an ab initio Study of the Neutral Silicon Vacancy. M.I.J.Probert, M.C.Payne: Physical Review B, 2003, 67[7], 075204 (11pp)