Finite-size corrections for charged defect supercell calculations typically consist of image-charge and potential alignment corrections. Regarding the image-charge correction, Freysoldt, Neugebauer, and Van de Walle (FNV) recently proposed a scheme that constructs the correction energy a posteriori through alignment of the defect-induced potential to a model charge potential [C. Freysoldt et al., Phys. Rev. Lett. 102, 016402 (2009)]. This, however, still has two shortcomings in practice. First, it uses a planar-averaged electrostatic potential for determining the potential offset, which can not be readily applied to defects with large atomic relaxation. Second, Coulomb interaction is screened by a macroscopic scalar dielectric constant, which can bring forth large errors for defects in layered and low-dimensional structures. In this study, we use the atomic site potential as a potential marker, and extend the FNV scheme by estimating long-range Coulomb interactions with a point charge model in an anisotropic medium. We also revisit the conventional potential alignment and show that it is unnecessary for correcting defect formation energies after the image-charge correction is properly applied. A systematic assessment of the accuracy of the extended FNV scheme is performed for defects and impurities in diverse materials: $\beta$-Li${}_2$TiO${}_3$, ZnO, MgO, Al${}_2$O${}_3$, HfO${}_2$, cubic and hexagonal BN, Si, GaAs, and diamond. Defect formation energies with $-6$ to $+3$ charges calculated using supercells containing around 100 atoms are successfully corrected even after atomic relaxation within 0.2 eV compared to those in the dilute limit.

• Received 9 February 2014
• Revised 22 April 2014

DOI:https://doi.org/10.1103/PhysRevB.89.195205