Atomistic study of the migration of di- and tri-interstitials in silicon

A comprehensive study on the migration of di- and tri-interstitials in silicon is performed using classical molecular dynamics simulations with the Stillinger-Weber potential. At first the structure and energetics of the di- and the tri-interstitial are investigated, and the accuracy of the interatomic potential is tested by comparing the results with literature data obtained by tight-binding and density-functional-theory calculations. Then the migration is investigated for temperatures between 800 and 1600 K. Very long simulation times, large computational cells and different initial conditions are considered. The defect diffusivity, the self-diffusion coefficient per defect and the corresponding effective migration barriers are calculated. Compared to the mono-interstitial, the di-interstitial migrates faster, whereas the tri-interstitial diffuses slower. The mobility of the di- and the mono-interstitial is higher than the mobility of the lattice atoms during the diffusion of these defects. On the other hand, the tri-interstitial mobility is lower than the corresponding atomic mobility. The migration mechanism of the di-interstitial shows a pronounced dependence on the temperature. At low temperature a high mobility on zig-zag-like lines along a $⟨110⟩$ axis within a {110} plane is found, whereas the change between equivalent $⟨110⟩$ directions or equivalent {110} planes occurs seldom and requires a long time. At high temperature a frequent change between equivalent $⟨110⟩$ directions or {110} planes is observed. During the diffusion within {110} planes the di-interstitial moves like a wave packet so that the atomic mobility is lower than that of the defect. On the other hand, the change between equivalent {110} migration planes is characterized by frequent atomic rearrangements. The visual analysis of the tri-interstitial diffusion reveals complex migration mechanisms and a high atomic mobility. The diffusivities and effective migration barriers obtained are compared with the few data from the literature. The implications of the present results for the explanation of experimental data on defect evolution and migration are discussed.