Comparison of charged-defect finite-size supercell correction methods in a general framework

Starting from the total energy expressions within density functional theory, we are able to perform a comparison of several currently used charged-defect finite-size supercell correction schemes in a unified manner. This approach also provides a framework for a further development of corrections not only for DFT supercell calculations, but also for more advanced methods and for complex geometries. The comparison is performed for three separate defect cases: a gallium vacancy in GaAs, a beryllium interstitial in GaAs and a vacancy in diamond. We found two methods working sufficiently well for all three cases: a method which is very similar to one presented by Freysoldt, and a slightly altered potential alignment method.