Abstract
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: -LiTiO, ZnO, MgO, AlO, HfO, cubic and hexagonal BN, Si, GaAs, and diamond. Defect formation energies with to 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.
2 More- Received 9 February 2014
- Revised 22 April 2014
DOI:https://doi.org/10.1103/PhysRevB.89.195205
©2014 American Physical Society