ASYMPTOTIC ANALYSIS OF A MODEL FOR SUBSTITUTIONAL-INTERSTITIAL DIFFUSION

A substitutional-interstitial model for impurity diffusion in semi-con ductors is discussed. In particular we consider a surface-source probl em and obtain asymptotic solutions in the limit of the surface concent ration of impurity being much greater than the equilibrium vacancy con centration. In the absence of vacancy generation, a double error funct ion impurity curve is obtained. These double profiles reproduce some o f the qualitative features of diffusion in many III-V semiconductor sy stems. We also discuss how vacancy generation modifies the analysis an d show that in the limit of high vacancy generation, the problem becom es one of linear diffusion with the diffusion curves then being single error function complements.