Atomic structures of grain boundaries for Si and Ge: A simulated annealing method with artificial-neural-network interatomic potentials

Abstract

To accurately predict low-energy structures for symmetric tilt grain boundaries (GBs) in Si and Ge, artificial-neural-network (ANN) interatomic potentials are constructed and are combined with a simulated annealing (SA) method based on molecular dynamics simulations. The ANN-driven SA method is demonstrated to predict GB structures that are in good agreement with previous electron microscopy observations, without prior knowledge about their atomic configurations. Their GB energies also reasonably agree with density-functional-theory (DFT) calculations. By contrast, a conventional empirical potential fails to predict those GB structures. For misorientation angles 2θ≥93.37°, the lowest-energy structures are found to contain atomic configurations that cannot be reproduced by one repeat unit of the perfect crystal along the tilt axis. Such GB structures cannot be obtained using the γ-surface method, although it is most commonly used for exploring low-energy GB structures. These results highlight the importance of using simulation cells with multiple repeat units along the tilt axis and of performing the SA method with high-accuracy interatomic potentials transferable to GBs.