An approximate model for boron drive diffusions in oxidizing ambients

Abstract

The linear diffusion equation may be transformed to a moving reference frame which corresponds to a linear-parabolic or experimental oxide growth law. The resulting partial differential equation is separable and may be Laplace transformed. If the initial distribution is piecewise constant the solutions may be written in terms of Kummer functions in the transform domain. Use is made of this fact for a drive diffusion in an oxidizing ambient. The initial distribution is approximated by a rectangle and a two-region solution is used to determine all coefficients. The inversion of the solution to the time domain is accomplished by numerical residue techniques. The amount of boron which is lost to the oxide is computed and approximate relationships are given which allow its computation without the aid of a computer. It is found that boron leaching is controlled by the first few minutes of oxidation and may involve as much as 90% of the boron due to the deposition. Experimental data is presented which supports the theory.