Generalized Algorithm for Recognition of Complex Point Defects in Large-Scale β-$\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$

The electrical and optical properties of semiconductor materials are profoundly influenced by the atomic configurations and concentrations of intrinsic defects. This influence is particularly significant in the case of $\beta$-$\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$, a vital ultrawide bandgap semiconductor characterized by highly complex intrinsic defect configurations. Despite its importance, there is a notable absence of an accurate method to recognize these defects in large-scale atomistic computational modeling. In this work, we present an effective algorithm designed explicitly for identifying various intrinsic point defects in the $\beta$-$\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$ lattice. By integrating particle swarm optimization and hierarchical clustering methods, our algorithm attains a recognition accuracy exceeding 95% for discrete point defect configurations. Furthermore, we have developed an efficient technique for randomly generating diverse intrinsic defects in large-scale $\beta$-$\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$ systems. This approach facilitates the construction of an extensive atomic database, crucially instrumental in validating the recognition algorithm through a substantial number of statistical analyses. Finally, the recognition algorithm is applied to a molecular dynamics simulation, accurately describing the evolution of the point defects during high-temperature annealing. Our work provides a useful tool for investigating the complex dynamical evolution of intrinsic point defects in $\beta$-$\mathrm{G}{\mathrm{a}}_2{\mathrm{O}}_3$, and moreover, holds promise for understanding similar material systems, such as $\mathrm{A}{\mathrm{l}}_2{\mathrm{O}}_3$, $\mathrm{I}{\mathrm{n}}_2{\mathrm{O}}_3$, and $\mathrm{S}{\mathrm{b}}_2{\mathrm{O}}_3$.