Detailed atomistic calculations within the local density approximation and the generalized gradient approximation in density functional theory were used to clarify microscopic mechanisms and obtain the corresponding diffusion constant for self-diffusion in crystalline Si. The formation free energies of intrinsic defects, which mediated the self-diffusion, were calculated by accurate total-energy static calculations. Diffusivity in each mechanism was obtained from the mean-square displacements computed through Car-Parrinello molecular dynamics for a simulation time long enough to allow for these relatively slow phenomena to occur. It was found that the interstitial mechanism dominantly contributed to the self-diffusion: The self-diffusion constant via the interstitial mechanism was found to be larger than that via the vacancy mechanism by about two orders of magnitude in local density approximation. It was also found that the calculated formation free energies and migration energies in generalized gradient approximation were larger than the corresponding ones in local density approximation. Due to this, the generalized gradient approximation substantially improved the free-energy landscape, thus providing diffusion constants in quantitative agreement with the experimental values over a whole temperature range. Atomistic processes in the self-diffusion were also clarified.

Self-Diffusion in Crystalline Silicon: a Car-Parrinello Molecular Dynamics Study. K.Koizumi, M.Boero, Y.Shigeta, A.Oshiyama: Physical Review B, 2011, 84[20], 205203