Using neural network potentials to study defect formation and phonon properties of nitrogen vacancies with multiple charge states in GaN

Investigation of charged defects is necessary to understand the properties of semiconductors. Whereas density functional theory calculations can accurately describe the relevant physical quantities, these calculations increase the computational loads substantially, which often limits the application of this method to large-scale systems. In this paper, we propose a different scheme of neural network potential (NNP) to analyze the point defect behavior in multiple charge states. The proposed scheme necessitates only minimal modifications to the conventional scheme. We demonstrated the prediction performance of the proposed NNP using wurzite-GaN with a nitrogen vacancy with charge states of 0, $1+$, $2+$, and $3+$. The proposed scheme accurately trained the total energies and atomic forces for all the charge states. Furthermore, it fairly reproduced the phonon band structures and thermodynamics properties of the defective structures. Based on the results of this paper, we expect that the proposed scheme can enable us to study more complicated defective systems and lead to breakthroughs in novel semiconductor applications.