Generalized first-principles finite-size correction schemes for strongly and weakly localized point defects

Point defects are responsible for key properties of semiconductors, such as electrical conductivity and photoluminescence spectra, and may lead to functional properties on photovoltaics, photocatalysis, and batteries. Accurate simulation of point defects using first principles and the supercell approach requires size-correction methods due to the long-range Coulomb interaction between the defect charge and its periodic images. Previous methods such as Makov-Payne, Lany-Zunger, in combination with potential alignment, are able to accurately describe monopole-monopole (1/L) and monopole-quadrupole (1/L³) interactions (with L the size of the supercell). However, despite considerable success, several cases of defects deviate from these scaling models due to additional long-range interactions, e.g. dipole-dipole (1/L²), dipole-quadrupole (1/L³), and quadrupole-quadrupole (1/L⁴). In addition, small supercell sizes may introduce sizable short-range interactions due to elastic effects (1/L³). Here, we introduce generalized polynomial and exponentially decaying scaling correction methods to describe strongly and weakly localized defects in semiconductors. We compare the performance of our generalized scaling methods to previous ones, and provide microscopic origin for the additional (1/L) terms in the scaling method. As a prototypical example, we study low-energy defects of Cu₃N, a material with important technological applications in solar energy conversion and electronic semiconducting devices. We employ density functional theory calculations, hybrid functionals, and large supercells up to 2048 atoms to investigate the formation energy and band gap defect levels of intrinsic point defects of Cu₃N using various size correction models. Our work introduces an approach that facilitates the description of strongly and weakly localized defects at a reduced computational cost. For the particular case of Cu₃N, our results confirm the p-type character of Cu₃N. This work is supported by ANID Fondecyt grant number 1220986.