Density-functional theory combined with periodic boundary conditions was used to systematically study the dependence of defect formation energy on super-cell size for material containing vacancy and self-interstitial defects. An investigation was made of the effect of the electrostatic energy due to the neutralization of charged super-cells and the effect of the alignment of the valence band maximum on the formation energy. For negatively charged vacancies and positively charged interstitials, the formation energies exhibited a clear dependence upon super-cell size, and the electrostatic corrections agreed with the trend given by the Makov-Payne scheme. For positively charged vacancies and negatively charged interstitials, the size dependence and the electrostatic corrections were quite weak. An analysis of the spatial charge density distributions revealed that these large variations in electrostatic terms with defect-type originated from differences in the screening of the defect-localized charge; as explained by using a simple electron-gas model. Several valence band maximum alignment schemes were tested. The best agreement between calculated and asymptotically exact ionization levels was obtained when the levels were based upon formation energies referenced to the valence band maximum of the defect-containing super-cell.

Density-Functional Calculations of Defect Formation Energies using Supercell Methods - Defects in Diamond. J.Shim, E.K.Lee, Y.J.Lee, R.M.Nieminen: Physical Review B, 2005, 71[3], 035206 (12pp)