Theoretical Investigation of Oxygen-Vacancy Diffusion in SrTiO$_3$ using Neural Network Potentials

Abstract

Oxygen-vacancy formation and diffusion play important roles in determining the electronic and atomic transport properties of SrTiO$_3$ (STO). Accurate analysis of such point defects requires sufficiently large-scale and long-time molecular dynamics (MD) simulations; however, direct investigations of oxygen-vacancy dynamics using {\it ab initio} MD (AIMD) based on density functional theory (DFT) are limited to relatively small systems and short time scales because of their high computational cost. In this study, we develop a neural network potential (NNP) for pristine and oxygen-deficient STO using a reference dataset generated from AIMD simulations. The trained NNP model accurately reproduces the DFT reference energies, atomic forces, and virials for both pristine STO and STO containing an oxygen vacancy. The NNP also reproduces the supercell-size dependence of the total energies and oxygen-vacancy formation energies, including the formation energy extrapolated to the dilute limit. Large-scale and long-time MD simulations using the NNP (NNP-MD) are then performed to investigate oxygen-vacancy diffusion. The resulting oxygen-vacancy diffusion coefficients show substantially better agreement with experimental data than those obtained from conventional classical MD simulations. An Arrhenius analysis yields an oxygen-vacancy migration enthalpy of 0.64 eV, in close agreement with the experimental value of 0.67 eV. These results demonstrate that NNPs trained on first-principles data provide an accurate and computationally efficient framework for investigating defect formation and long-time vacancy transport in perovskite oxides.