We reveal the microscopic self-diffusion process of compact tri-interstitials in silicon using a combination of molecular dynamics and nudged elastic band methods. We find that the compact tri-interstitial moves by a collective displacement, involving both translation and rotation, of five atoms in a screw-like motion along $[111]$ directions. The elucidation of this pathway demonstrates the utility of combining tight-binding molecular dynamics with textit{ab initio} density functional calculations to probe diffusion mechanisms. Using density functional theory to obtain diffusion barriers and the prefactor, we calculate a diffusion constant of $ 4 cdot 10^{-5} exp (- 0.49 {rm eV} / k_{B} T) {rm cm^2/s} $. Because of the low diffusion barrier, $I_{3}^{b}$ diffusion may be an important process under conditions such as ion implantation that creates excess interstitials, hence favoring formation of interstitial clusters.
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