On concentration dependence of arsenic diffusivity

TL;DR

This paper analyzes arsenic diffusion in silicon, showing that a single effective diffusion coefficient can model the process well at moderate concentrations but deviates at higher doping levels due to complex impurity flows.

Contribution

It demonstrates that arsenic diffusion can be modeled by Fick's law with an effective diffusivity considering two impurity flows, clarifying the conditions for accurate modeling.

Findings

Effective diffusivity agrees with experimental data near intrinsic concentration

Deviations occur at higher impurity concentrations

Discrepancies may be due to nonuniform vacancy and interstitial distributions

Abstract

An analysis of the equations used for modeling thermal arsenic diffusion in silicon has been carried out. It was shown that for arsenic diffusion governed by the vacancy-impurity pairs and the pairs formed due to interaction of impurity atoms with silicon self-interstitials in a neutral charge state, the doping process can be described by the Fick's second law equation with a single effective diffusion coefficient which takes into account two impurity flows arising due to interaction of arsenic atoms with vacancies and silicon self-interstitials, respectively. Arsenic concentration profiles calculated with the use of the effective diffusivity agree well with experimental data if the maximal impurity concentration is near the intrinsic carrier concentration. On the other hand, for higher impurity concentrations a certain deviation in the local regions of arsenic distribution is observed. The difference from the experiment can occur due to the incorrect use of effective diffusivity for the description of two different impurity flows or due to the formation of nonuniform distributions of neutral vacancies and neutral self-interstitials in heavily doped silicon layers.