Detailed atomistic calculations within the local density and generalized gradient approximations of density functional theory were used to clarify microscopic mechanisms and to obtain corresponding diffusion constants for self-diffusion in crystalline Si (table 29). The formation free energies of intrinsic defects, which mediated self-diffusion, were calculated using accurate total-energy static calculations. The diffusivity for each mechanism was deduced from mean-square displacements calculated using Car-Parrinello molecular dynamics for a simulation time that was long enough to allow the relatively slow phenomena to occur. The interstitial mechanism predominantly contributed to self-diffusion. The self-diffusion constant for an interstitial mechanism was larger, than that for a vacancy mechanism, by about two orders of magnitude. The calculated formation free energies and migration energies in generalized gradient approximations were larger than the corresponding ones in local density approximations. The former thus substantially improved the free-energy landscape; thus providing diffusion constants which were in quantitative agreement with experimental values over the whole temperature range.

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