Self-diffusion in crystalline silicon: A Car-Parrinello molecular dynamics study

We report detailed atomistic calculations within the local density approximation (LDA) and the generalized gradient approximation (GGA) in density functional theory to clarify microscopic mechanisms and obtain the corresponding diffusion constant for self-diffusion in crystalline Si. The formation free energies of intrinsic defects, which mediate the self-diffusion, are calculated by accurate total-energy static calculations. Diffusivity in each mechanism is 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. We find that the interstitial mechanism dominantly contributes to the self-diffusion: The self-diffusion constant via the interstitial mechanism is found to be larger than that via the vacancy mechanism by about two orders of magnitude in LDA. We also find that the calculated formation free energies and migration energies in GGA are larger than the corresponding ones in LDA. Due to this, GGA substantially improves 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 are also clarified.