No abstract

An artificial-neural-network (ANN) interatomic potential trained with data from density-functional-theory (DFT) calculations is developed to reveal favorable modes of large-sized vacancy clusters in silicon. By varying the number of vacancies (n) up to around 103, formation energies (E f) and relaxed structures for four typical modes of vacancy clusters are examined: the 4-fold coordinated configuration (FC), hexagonal ring cluster (HRC), spherically shaped cluster (SPC), and (111)-oriented stacking fault (SF). The present ANN potential reasonably predicts E f values and relaxed structures obtained from DFT calculations for all modes examined. It also predicts that the order of E f is HRC < SPC ≤ SF for 6 < n ≲ 30, HRC ≈ SPC < SF for 30 ≲ n ≲ 300, and SPC ≤ HRC < SF for 300 ≲ n, with the prediction of reasonable relaxed structures in all the ranges of n. This indicates that the favorable agglomeration mechanism becomes the SPC mode as vacancy clusters involve large numbers of vacancies. By contrast, commonly used empirical potentials significantly overestimate E f for FC and SPC. This supports much better transferability of the present ANN potential for studies of vacancy clusters in Si.