Interstitial contribution to self-diffusion in Si: Dependence of the correlation factor on the migration mechanism

Self-diffusion in Si is determined by the concentration and the mobility of both vacancies and self-interstitials. The self-diffusion coefficient is usually given by Dsd = fV CV DV + fI CI DI, where CV and CI are the relative concentrations of vacancies and self-interstitials, respectively; DV and DI denote the diffusivities. The quantities fV and fI describe the correlation between the migration of Si atoms and the migration of vacancies and self-interstitials; fV and fI are therefore called correlation factors. The statistical theory of diffusion allows the determination of these factors if certain atomic mechanisms for vacancy and self-interstitial migration are assumed. On the other hand, the self-diffusion coefficient per point defect as well as the point defect diffusivity can be calculated by molecular dynamics (MD) simulations. The ratio of both quantities yields the correlation factors fV and fI. In this manner, they can be determined without any assumption about the atomic migration mechanisms. In the present work, point defect migration and the related atomic mobility are investigated by MD simulations using the interatomic potentials of Stillinger-Weber and Tersoff. It is shown that the value for fV obtained by MD simulations is identical with that determined by the statistical diffusion theory, since the simple atomic mechanism assumed in the theory is also found by the simulations. The mechanisms of self-interstitial migration are more complex. The detailed study, including a visual analysis and investigations with the nudged elastic band method, reveals a variety of transformations between different self-interstitial configurations. MD simulations with the Stillinger-Weber potential show, that the self-interstitial migration is dominated by the dumbbell mechanism, whereas in the case of the Tersoff potential the interstitialcy mechanism prevails. The corresponding values of the correlation factor fI are different.