Multiple-pathway diffusion with traps was analyzed within the kinetic approach, where the diffusion terms in the diffusion-kinetic equations were replaced by kinetic ones. As the solutions were linear combinations of exponents, both the components and the pre-exponential factors were taken into account. As an example, Au diffusion into a Si film was studied, and account was taken of both dissociative and kick-out mechanisms. In order to analyze thin-film diffusion, thin-film surfaces were considered to be substantial sources and/or sinks of point defects in addition to terms which described diffusional transport in crystals of infinite size. The various diffusion mechanisms and regimes, and the conditions for transitions from one mechanism and/or regime to another, were determined. Expressions were obtained for the critical sample thickness, dislocation density, swirl and vacancy cluster densities when transitions in the diffusion transport mechanisms and regimes occurred. Quantitative criteria for the critical values of temperature, dislocation density and thin-film thickness transitions of the Au-Si diffusion transport mechanisms were obtained. It was found that, for fairly long times, the results which were obtained using the kinetic approach coincided with those of the diffusion-kinetic approach. However, the set of pure kinetic equations was much simpler to solve. It was concluded that the kinetic approach was a valuable approximation to multiple-pathway diffusion with traps.

M.G.Goldiner, A.V.Vaysleyb: Physical Review B, 1995, 52[14], 10060-8