Improving the convergence of defect calculations in supercells: An ab initio study of the neutral silicon vacancy

We present a systematic methodology for the accurate calculation of defect structures in supercells, which we illustrate with a study of the neutral vacancy in silicon. This is a prototypical defect which has been studied extensively using ab initio methods, yet remarkably there is still no consensus about the energy or structure of this defect, or even whether the nearest-neighbor atoms relax inwards or outwards. In this paper, we show that the differences between previous calculations can be attributed to supercell convergence errors, and we demonstrate how to systematically reduce each such source of error. The various sources of scatter in previous theoretical studies are discussed and a different effect, that of supercell symmetry, is identified. It is shown that a consistent treatment of this effect is crucial in understanding the systematic effects of increasing the supercell size. This work therefore also presents the best converged ab initio study of the neutral silicon vacancy to date.