Interstitial and vacancy concentrations in the presence of interstitial injection

Abstract

In processes such as thermal oxidation and phosphorus diffusion, where self-interstitials are generated in excess, what happens to the vacancy concentration may significantly affect many diffusion processes which occur via dual mechanisms. Most authors in diffusion modelling have assumed as self-evident that, for a very long time or in steady state, the product of the vacancy and the interstitial concentrations should be a constant. It is shown here that this assumption is generally invalid. The fallacy in the analogy between this case and the solubility product is pointed out. A correct relationship is first derived on a uniform defect concentration approximation. Then rigorous expressions for both the vacancy and the interstitial concentrations are given from an exact solution of simultaneous vacancy and interstitial continuity equations that include diffusion, recombination, and generation terms, under appropriate boundary conditions. The errors in the results from previous speculations are especially severe in the surface region.