Mathematical model for a radioactive marker in silicide formation

A mathematical model is constructed to interpret the profiles of radioactive Si tracers in a computer simulation proposed by R. Pretorius and A. P. Botha [Thin Solid Films 91, 99 ( 1982)]. This model assumes that only Si moves in the silicide, that the Si moves interstitially and convectively, and that the moving Si can exchange sites with the stationary Si in the silicide lattice. An analytical solution of this model is given and confirms the published computer simulation data. However, it is shown that the model is physically inadequate. Solutions of another model which assumes that metal, instead of Si, is the moving species for silicide formation (either interstitially, or substitutionally, or both), with self-diffusion of Si in the silicide during silicide formation. Almost all the experimental data can be fitted by solutions of both models. These examples demonstrate that radioactive tracer experiments alone are insufficient to determine the moving species when a solid binary compound film forms by reaction of adjacent elemental layers. Both inert marker and tracer data are needed to identify the moving species and the mechanisms.