# Accurate formation energies of charged defects in solids: a systematic approach

## TL;DR

This paper introduces a systematic, internally consistent method for accurately calculating defect formation energies in inhomogeneous and anisotropic dielectric environments, improving the reliability of first-principles defect studies in surfaces and 2D materials.

## Contribution

The authors develop a new approach that reduces electrostatic energy errors in defect calculations for complex dielectric environments, enhancing the accuracy of first-principles methods.

## Key findings

- Effective correction for electrostatic errors in defect calculations.
- Application to Cl vacancy on NaCl surface and S vacancy in MoS2.
- Improved accuracy in defect formation energy predictions.

## Abstract

Defects on surfaces of semiconductors have a strong effect on their reactivity and catalytic properties. The concentration of different charge states of defects is determined by their formation energies. First-principles calculations are an important tool for computing defect formation energies and for studying the microscopic environment of the defect. The main problem associated with the widely used supercell method in these calculations is the error in the electrostatic energy, which is especially pronounced in calculations that involve surface slabs and 2D materials. We present an internally consistent approach for calculating defect formation energies in inhomogeneous and anisotropic dielectric environments, and demonstrate its applicability to the cases of the positively charged Cl vacancy on the NaCl (100) surface and the negatively charged S vacancy in monolayer MoS2.