Exact solution of the five frequency model of the vacancy-assisted   impurity diffusion in the limit of vanishing vacancy concentration
  The van Hove autocorrelation function of the impurity is obtained which is exact to the first order in the vacancy concentration. It is found that in the case of strong vacancy-impurity binding a singularity in the van Hove function corresponding to a resonant bound state develops on the unphysical sheet in the complex frequency plane close to the real axis. It is argued that this bound state corresponds to the defect-impurity pairs widely used in models of diffusion in semiconductors. 
V. I. Tokar