It was noted that most theoretical calculations for point defects employed the super-cell approach. The super-cell consisted of a few dozen or up to 100 atoms of the bulk material with a single defect, and was extended by using periodic boundary conditions. However, the large density and periodic arrangement of the defects introduced artefacts. These needed to be corrected for in order to extrapolate to the isolated-defect limit. This was particularly important for electrostatic interactions between charged defects, which decayed only very slowly (asymptotically like L−1) with increasing super-cell lattice constant, L. The underlying electrostatics in condensed matter were summarized here. A novel defect scheme was derived from this analysis which overcame the limitations of previous schemes with respect to applicability, systematic improvement and formal justification. A good performance was demonstrated for vacancies in diamond and GaAs.

Electrostatic Interactions Between Charged Defects in Supercells. C.Freysoldt, J.Neugebauer, C.G.Van de Walle: Physica Status Solidi B, 2011, 248[5], 1067–76