Effective scheme to determine accurate defect formation energies and charge transition levels of point defects in semiconductors

We propose an effective method to accurately determine the defect formation energy Ef and charge transition
level ε of the point defects using exclusively cohesive energy Ecoh and the fundamental band gap Eg of pristine
host materials. We find that Ef of the point defects can be effectively separated into geometric and electronic
contributions with a functional form: Ef = χEcoh + λEg, where χ and λ are dictated by the geometric and
electronic factors of the point defects (χ and λ are defect dependent). Such a linear combination of Ecoh and Eg
reproduces Ef with an accuracy better than 5% for electronic structure methods ranging from hybrid densityfunctional
theory (DFT) to many-body random-phase approximation (RPA) and experiments. Accordingly, ε
is also determined by Ecoh/Eg and the defect geometric/electronic factors. The identified correlation is rather
general for monovacancies and interstitials, which holds in a wide variety of semiconductors covering Si, Ge,
phosphorenes, ZnO, GaAs, and InP, and enables one to obtain reliable values of Ef and ε of the point defects for
RPA and experiments based on semilocal DFT calculations.