Electron and chemical reservoir corrections for point-defect formation energies

The formation energies of semiconductor point defects are nowadays predicted much more accurately by density functional theory than a decade ago, thanks to the use of modern hybrid functionals. The drawback is the high computational effort compared to the traditional local density approximation (LDA) or generalized gradient approximation (GGA). In this work, the authors trace back the main variations between the functionals to differences in the position of the bulk valence-band maximum, as well as in the reference energies for the chemical potential obtained with each functional. For point defects relevant for $p$-type GaN, these differences are accounted for by corrections, reducing the maximum disagreement between the different functionals from more than 2 eV to below 0.2 eV. The correction scheme should be useful for performing high-throughput calculations in cases where full hybrid functional calculations are prohibitively expensive.