Fast diffusion mechanism of silicon tri-interstitial defects

Molecular dynamics combined with the nudged elastic band method reveals the microscopic self-diffusion process of compact silicon tri-interstitials. Tight-binding molecular dynamics paired with ab initio density functional calculations speed the identification of diffusion mechanisms. The diffusion pathway can be visualized as a five defect-atom object both translating and rotating in a screwlike motion along ⟨111⟩ directions. The density functional theory yields a diffusion constant of $4\times {10}^{-5}\exp (-0.49\mathrm{eV}∕k_{B}T){\mathrm{cm}}^2∕\mathrm{s}$. The low diffusion barrier of the compact tri-interstitial may be important in the growth of ion-implantation-induced extended interstitial defects.

Figure 1

(Color online) Diffusion of $I_3^b$ to the neighboring site along the ⟨111⟩ direction. The initial, saddle, and final configurations are shown in (a), (b), and (c), respectively. Defect atoms are solid colored. The figures with more atoms can be found in Ref. 31.

Figure 2

(Color online) Transition paths of $I_3^b$ in DFT-GGA and the approximation of collective motion of five atoms within DFT-GGA.

Figure 3

(Color online) The five most displaced atoms during the diffusion. These five atoms move collectively. Atoms $D$ and $E$ define an axis of rotation ([111]), around which atoms $A$, $B$, and $C$ rotate clockwise or counterclockwise.

Figure 4

(Color online) Transition path with seven images projected onto two-dimensional reduced coordinates. The inset shows images 3, 5 (saddle point), and 7 along the transition path.