Non-Gaussian diffusion profiles caused by mobile impurity-vacancy pairs in the five frequency model of diffusion

TL;DR

This paper extends the five-frequency model to derive a 3D integro-differential equation for impurity diffusion via mobile impurity-vacancy pairs, predicting non-Gaussian diffusion profiles in FCC hosts, and validates the model with simulations and literature data.

Contribution

The study develops a 3D integro-differential equation for impurity diffusion via impurity-vacancy pairs within the five-frequency model, enabling accurate simulation of non-Gaussian diffusion profiles.

Findings

Derived a 3D integro-differential equation for impurity diffusion.

Predicted non-Gaussian diffusion profiles in FCC hosts.

Identified impurity-host systems suitable for observing NGDPs.

Abstract

Vacancy-mediated diffusion of impurities under strong impurity-vacancy (I-v) attraction has been studied in the framework of the five-frequency model (5FM) for the FCC host. The system of impurities and tightly bound I-v pairs has been treated in the framework of the rate-equations approach of Cowern et al., Phys. Rev. Lett. 65, 2434 (1990), developed for the description of the non-Gaussian diffusion profiles (NGDPs) observed in dopant diffusion in silicon. In the present study this approach has been extended to derive a three-dimensional (3D) integro-differential equation describing the pair-mediated impurity diffusion. The equation predicts the same 1D NGDPs as in Cowern et al. but can be also used for the simulation of 3D profiles of arbitrary geometry in the systems where the diffusion proceeds via a mobile state. The parameters of the theory has been calculated within the 5FM on the basis of available literature data. The database on impurities in aluminum host has been analyzed and promising impurity-host systems for the observation of NGDPs has been identified. The diffusion profiles for an impurity where NGDPs are expected to be easily detectable have been simulated. It has been argued that with the input parameters calculated on the basis of experimental diffusion constants the simulated NGDPs can be accurate enough to serve as a quantitative test of the 5FM.