Analysis of Non-Fickian Diffusion Data Using the Interstitial-Substitutional Equilibrium Model

摘要

A refinement of the Interstitial-Substitutional Equilibrium Model is proposed in which the concentration of holes in the host crystal is replaced by hole activity. The result is a refined model in which the diffusion coefficient is proportional to a power of the diffusant concentration. Unlike past approaches, however, the introduction of hole activity relaxes the restriction that the concentration exponent be an integer. Generalized numerical solutions are presented for a range of concentration exponents. Analyses based on the refined model have been completed using experimental data from the literature for Zn in GaAs, Cu in GaAs, Sb in Ge, and P in Si. In each case, the data reviewed was labeled anomalous or non-fickian. In general, good agreement was found between computed profiles and experimental profiles using two adjustable parameters. A mathematical criterion for computing the deviation of a computed profile from an experimental profile was established and a wide range of parameters was examined. Parameter values corresponding to minimum deviation of computed from experimental data were recorded for each of the data sets examined. (Author)