Exact solution of the five frequency model of the vacancy-assisted impurity diffusion in the limit of vanishing vacancy concentration

TL;DR

This paper derives an exact first-order solution for impurity diffusion considering vacancy interactions, revealing a resonant bound state linked to defect-impurity pairs in semiconductors.

Contribution

It provides an exact analytical expression for the van Hove autocorrelation function in a five-frequency vacancy-assisted diffusion model at low vacancy concentrations.

Findings

Identification of a resonant bound state near the real axis in the complex frequency plane.

Connection of the bound state to defect-impurity pairs in semiconductor diffusion models.

Exact first-order solution applicable to low vacancy concentrations.

Abstract

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.