Atomistic analysis of the vacancy mechanism of impurity diffusion in silicon

The complete set of the four macroscopic transport coefficients describing the coupled diffusion of impurity atoms and vacancies in silicon is calculated from the atomistic mechanism by accurately taking into account the effects of the microscopic forces between dopants and vacancies. The aim of these simulations is to come to a decision concerning the validity of models like the pair diffusion model or the "non-Fickian diffusion" model that make contradicting predictions for very fundamental properties like the relative direction of the fluxes of dopants and vacancies driven by a vacancy gradient and for the relation alpha=T0 d/D0 d between two of the four transport coefficients. Simulation results are shown for a variety of assumed interaction potentials that establish a functional dependence between alpha and measurable quantities, like the factor D s/D tracer of enhancement of dopant diffusivity over tracer diffusion, that holds for an arbitrary interaction. The comparison with e x perimental values for D d/D tracer leads to the confirmation of the pair diffusion model for boron and phosphorus. For arsenic and antimony, the large scatter of the experimental data prohibits an equally definite conclusion, but at least a qualitative confirmation of pair diffusion theory (i.e., alpha > 0 which means that dopant and vacancy fluxes have the same direction if caused by a vacancy gradient) is possible