Atomic structures and stability of finite-size extended interstitial defects in silicon: Large-scale molecular simulations with a neural-network potential

Abstract

The energetics of various extended interstitial (I) defects in crystalline Si is examined by constructing an artificial-neural-network (ANN) potential trained with density-functional-theory (DFT) data, enabling us to perform accurate large-scale simulations and to obtain well-converged formation energies (Ef). By varying the number of interstitials n to around 1,000, Ef is calculated for the compact cluster, I12-like, (001)-plane, (311)-rod-like and Frank-loop defects. For n ≤ 36, the compact cluster or (311)-rod-like defect is found to be most stable, depending on n. This trend strongly depends on simulation cell sizes, suggesting the importance of sufficiently large cells. For 36 < n ≲ 860, the (311)-rod-like defect is most stable whereas the Frank-loop defect becomes most stable for larger n. The ANN potential is demonstrated to outperform empirical potentials in prediction of Ef and defect structures. Furthermore, ANN values of Ef are fitted to analytic functions with the aim of refining macroscopic simulations for device manufacturing processes.