Generalized Wagner's diffusion model of surface modification of materials by plasma diffusion treatment

A general model of surface modification of materials by plasma diffusion techniques has been developed. This model takes into account the erosion effects at the plasma/solid interface occurring due to the ion bombardment of the surface. For constant sputtering rate, which is the usual situation during plasma treatment, the growth of the sub-layers (and the total compound layer) is well described by the analytical expression g(t) = g(0) f(-1) (t/t(0)), where g(t) is the sub-layer thickness at time t, g(0) and t(0) are parameters that depend on the treated material and plasma characteristics, and f(-1) is the inverse function of f(x) = -(ln(1 - x) + x), where x = g(t)/g(0), 0 less than or equal to x less than or equal to 1. Under negligible erosion effects, the model becomes of Wagner's diffusion model type and the expression for g(t) reduces to the parabolic law. The model can be simplified by considering the compound layer as a united one. The general and simplified models can be used as a method for the experimental determining of the effective diffusion coefficients and the erosion rate during plasma treatment of material surfaces.