Asymptotic analysis of a model for substitutional-interstitial diffusion

A substitutional-interstitial model for impurity diffusion in semi-conductors is discussed. In particular we consider a surface-source problem and obtain asymptotic solutions in the limit of the surface concentration of impurity being much greater than the equilibrium vacancy concentration. In the absence of vacancy generation, a double error function impurity curve is obtained. These double profiles reproduce some of the qualitative features of diffusion in many III-V semiconductor systems. We also discuss how vacancy generation modifies the analysis and show that in the limit of high vacancy generation, the problem becomes one of linear diffusion with the diffusion curves then being single error function complements.