Dependence of the correlation factor for self-diffusion by vacancies and self-interstitials on the migration mechanism: an atomistic study

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 [1,2] 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 of fV = 0.5 obtained by MD simulations is identical with that determined by the statistical diffusion theory, since the simple atomic mechanism assumed in this 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, namely 0.56 and 0.73 for the dumbbell and the interstitialcy mechanism, respectively. The latter value corresponds to that obtained by the statistical theory [2] which assumes an interstitialcy mechanism. However, results of recent investigations on intrinsic point defects in silicon using a unified view from crystal growth, wafer processing and metal diffusion [3], and on dopant and defect diffusion [4] demonstrate, that in the framework of state-of-the-art modeling a reasonable interpretation of experimental data can be only given by assuming fI = 0.5…0.6. The comparison with results of the present atomistic study leads to the conclusion that self-interstitial migration in Si should mainly occur via the dumbbell mechanism.
References:
[1] K. Compaan, Y. Haven, Trans. Faraday Soc. 52 (1956) 786
[2] K. Compaan, Y. Haven, Trans. Faraday Soc. 54 (1958) 1498
[4] V.V. Voronkov, R. J. Falster, Solid State Phenomena 108-109 (2005) 1
[3] H.Bracht, Physica B 376-377 (2006) 11