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.