General model for intrinsic dopant diffusion in silicon under nonequilibrium point-defect conditions

Abstract

A general expression for the intrinsic diffusivity of a substitutional impurity in silicon is derived in terms of the self-interstitial and vacancy concentrations. The vacancy mechanism, the exchange mechanism, and two processes associated with the motion of interstitial impurity atoms, the ‘‘kick-out’’ and ‘‘Frank–Turnbull’’ mechanisms, are included in the analysis. These last two contributions to the impurity diffusion are not additive under nonequilibrium point-defect conditions, and may partially cancel each other in certain cases. The general expression can be fitted to data on As diffusion in silicon under nitridation and oxidation conditions, which were previously unexplained. The results indicate the possible presence of substantial vacancy, pushout, and Frank–Turnbull terms, but no significant exchange term. Conditions are proposed for definitive experimental measurements to test the significance of the Frank–Turnbull contribution.