Revisiting the Formulation of Charged Defect in Solids

TL;DR

This paper revisits charged defect calculations in solids, demonstrating that potential alignment corrections are unnecessary when reference energies are properly tracked, and introduces improved correction formulas for defect formation energies.

Contribution

It provides a refined formulation for defect charge corrections, eliminating the need for potential alignment and improving accuracy in defect energy calculations.

Findings

Potential alignment correction vanishes with proper reference energy tracking.

Classic Markov-Payne correction yields accurate results.

Slow convergence in 2+ diamond vacancy is due to defect gap level variations.

Abstract

Defect physics is at the heart of microelectronics. By keeping track of the reference energy in total energy calculations, we explicitly show that the "potential alignment" correction vanishes, and the classic Markov-Payne correction yields accurate results. From linear response theory, we further formulate an accurate expression for the quadrupole correction. Application to numerous defects including anisotropic material yields accurate formation energies in small supercells and the historically slow convergence of the 2+ diamond vacancy is shown to be a result of slow varying gap levels of the defect leading to a size dependent dielectric constant.