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 ( E f ). By varying the number of interstitials n to around 1,000, E f is calculated for the compact cluster, I 12 -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 E f and defect structures . Furthermore, ANN values of E f are fitted to analytic functions with the aim of refining macroscopic simulations for device manufacturing processes.