Statistics on Oxygen Vacancy Defects in Amorphous HfO ₂ : A Neural‐Network Interatomic Potential Assisted High‐Throughput Prediction

Accurate statistical prediction of defect properties in amorphous materials is a long-term challenge, hindering their applications in functional devices. In this work, the oxygen vacancy (Vo) in amorphous hafnium oxide (a-HfO₂) is taken as an example, and we develop a graph-neural-network inter-atomic potential based on the density functional theory (DFT) calculations of 6894 stoichiometric a-HfO₂ structures and 14219 structures with V_O defects, achieving an energy precision of ≈1 meV atom^-1. Combining this potential with the supercell model, the structures and energies of neutral Vo defects can be calculated with DFT-level accuracy and low computational cost, which enables high-throughput calculations using supercells with a wide size range, from 96 to 32928 atoms. The results show: i) small supercells with 1000 or fewer atoms cause serious errors in the statistic distribution of Vo formation energies, ii) a converged calculation is possible only when the supercell is up to 1500 atoms, iii) the converged results can also be achieved using the average of various small supercells, e.g., 30 a-HfO₂ supercells with only 96 atoms. These findings unveil a clear statistics of V_O defects in a-HfO₂ and demonstrate a quantitative accuracy-estimation criterion for predicting the point defect properties in amorphous materials using supercell models.