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The errors arising in ab initio density functional theory studies ofsemiconductor point defects using the supercell approximation are analyzed. Itis demonstrated that a) the leading finite size errors are inverse linear andinverse cubic in the supercell size, and b) finite size scaling over a seriesof supercells gives reliable isolated charged defect formation energies toaround +-0.05 eV. The scaled results are used to test three correction methods.The Makov-Payne method is insufficient, but combined with the scalingparameters yields an ab initio dielectric constant of 11.6+-4.1 for InP. Gammapoint corrections for defect level dispersion are completely incorrect, evenfor shallow levels, but re-aligning the total potential in real-space betweendefect and bulk cells actually corrects the electrostatic defect-defectinteraction errors as well. Isolated defect energies to +-0.1 eV are thenobtained using a 64 atom supercell, though this does not improve for largercells. Finally, finite size scaling of known dopant levels shows how to treatthe band gap problem: in less than about 200 atom supercells with nocorrections, continuing to consider levels into the theoretical conduction band(extended gap) comes closest to experiment. However, for larger cells or whensupercell approximation errors are removed, a scissors scheme stretching thetheoretical band gap onto the experimental one is in fact correct.Comment: 11 pages, 3 figures (6 figure files). Accepted for Phys Rev

physical review. b, condensed matter and materials physics

Managing the supercell approximation for charged defects in semiconductors: Finite-size scaling, charge correction factors, the band-gap problem, and the<i>ab initio</i>dielectric constant

Managing the supercell approximation for charged defects in semiconductors: Finite-size scaling, charge correction factors, the band-gap problem, and theab initiodielectric constant