Application of neural-network potential based on trainable descriptor to crystallographically complex lattice defects in silicon

A trainable descriptor based on artificial neural networks (ANN), developed in our recent study [M. Uchida et al., Phys. Rev. Mater. 8, 103805 (2024)], is integrated into a neural-network potential (NNP) and applied to various lattice defects in molecular simulations of silicon. The ANN descriptor achieves higher predictive accuracy for point defects, surfaces, and symmetric tilt grain boundaries (STGBs) than analytic-function-based descriptors. As a case study of crystallographically complex defects, the ANN descriptor is applied to asymmetric tilt grain boundaries (ATGBs), where favorable atomic structures are governed by the competition between multiple structural units. For the \ensuremath{\Sigma}9(111)||(115) ATGB, the predicted atomic structure shows a grain boundary energy close to the DFT value and agrees with previous electron microscopy observations. Similarly, \ensuremath{\Sigma}3, \ensuremath{\Sigma}5, and \ensuremath{\Sigma}9 ATGBs are also systematically examined with the combination of the ANN descriptor and DFT calculations. ATGBs in the \ensuremath{\Sigma}5 system can be described by structural units of two STGBs with the same \ensuremath{\Sigma} value, indicating that \ensuremath{\Sigma}5 ATGBs ideally facet into \ensuremath{\Sigma}5 STGB structures. In contrast, this trend does not hold for the \ensuremath{\Sigma}3 and \ensuremath{\Sigma}9 ATGBs due to the crystallographic incompatibility of the constituent STGBs. As a result, \ensuremath{\Sigma}3 and \ensuremath{\Sigma}9 ATGBs involve structural units that cannot be predicted by the crystallographic misorientation of the two gains. Electronic-structure analysis reveals that specific atoms at ATGBs create defect levels within the band gap, depending on the inclination angle of ATGBs. These results highlight that the high-accuracy ANN descriptor provides a deeper understanding of atomic and electronic structures and energetics of complex lattice defects.