Density functional theory calculations of helium clustering in mono‐, di‐, and hexa‐vacancy in silicon

Abstract

Combining classical molecular dynamics and first-principles DFT calculations, we perfom an extensive investigation of low energy configurations for He n V m complexes in silicon. The optimal helium fillings are hence determined for V 1 , V 2 , and V 6 (figure on the right), and the structures formed by helium atoms arrangements in the vacancy defect are analyzed. For V 1 and V 2 , the He atoms structure is mainly controled by the host silicon matrix, whereas a high density helium packing is obtained for V 6 . For the latter, we estimate a helium density of about 170 He nm −3 in the center of the hexa-vacancy at the optimal helium filling.Relaxed structures obtained from DFT calculations for configurations with the lowest formation energies: (a) He 14 V 1 , (b) He 20 V 2 , and (c) He 40 V 6 .

Influence of helium on the nucleation and growth of bubbles in silicon: a multiscale modelling study

“…2) E f (n, p) is the energy needed to insert p interstitial He atoms into a cavity of n vacancies. Recent investigations revealed that the variation of this term as a function of p is quadratic [59], for a given n. We can then writẽ E f (n, p) = a(n) p 2 + b(n) p (A.3) a(n) and b(n) are calculated for all simulated bubbles with n > 10. We find that both coefficients can then be fitted by the respective expressions This expression is used for bubbles of at least 11 vacancies, or containing at least 21 helium atoms.…”

“…Ẽ f (n, p) is the energy needed to insert p interstitial He atoms into a cavity of n vacancies. Recent investigations revealed that the variation of this term as a function of p is quadratic [59], for a given n. We can then write The formation energy (in eV) of a bubble formed of n vacancies and encompassing p helium atoms is then obtained as This expression is used for bubbles of at least 11 vacancies, or containing at least 21 helium atoms. Otherwise, the binding energies are directly calculated from atomistic data.…”