A treatment of impurity diffusion in oxidizing ambients

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 semiconductor is initially uniformly doped and semi-infinite, solutions in the Laplace transform domain are expressible as parabolic cylinder functions. Integration constants for constant interface concentration or deposition diffusions as well as leaching boundary conditions may be determined.A space-time solution for the deposition problem is derived. Leaching from a uniformly doped substrate is treated in some detail. Residue techniques are used to develop analytic expressions for the dominant solution term, which is compared to published results. The complete solution may be obtained by using approximate analytic inversion, which requires numerical computations. Results are compared with data from existing theories, which are special cases of the present model.