Determination of Formation and Ionization Energies of Charged Defects in Two-Dimensional Materials

TLDR

First‑principles calculations of charged defects in 2D materials suffer from divergent Coulomb energies with vacuum thickness \(L_z\), leading to widely scattered results despite many prior correction attempts. The study proposes a straightforward method to compute formation and ionization energies of charged defects in 2D materials within the supercell framework. The approach uses the supercell approximation and extrapolates the asymptotic ionization‑energy expression at large \(L_z\) back to \(L_z=0\) to obtain converged values. The method yields converged ionization energies without additional assumptions, and applied to monolayer boron nitride defects it shows that defect levels can be much deeper than in bulk materials.

Abstract

We present a simple and efficient approach to evaluate the formation energy and, in particular, the ionization energy (IE) of charged defects in two-dimensional (2D) systems using the supercell approximation. So far, first-principles results for such systems can scatter widely due to the divergence of the Coulomb energy with vacuum dimension, denoted here as L_{z}. Numerous attempts have been made in the past to fix the problem under various approximations. Here, we show that the problem can be resolved without any such assumption, and a converged IE can be obtained by an extrapolation of the asymptotic IE expression at large L_{z} (with a fixed lateral area S) back to the value at L_{z}=0. Application to defects in monolayer boron nitride reveal that defects in 2D systems can be unexpectedly deep, much deeper than the bulk.