Saturation of front propagation in a reaction diffusion process describing plasma damage in porous low-kmaterials

Abstract

We propose a three-component reaction-diffusion system yielding an asymptotic logarithmic time dependence for a moving interface. This is naturally related to a Stefan problem for which both one-sided Dirichlet-type and von Neumann-type boundary conditions are considered. We integrate the dependence of the interface motion on diffusion and reaction parameters and we observe a change from transport behavior and interface motion $~{t}^{1/2}$ to logarithmic behavior $~\mathrm{ln}t$ as a function of time. We apply our theoretical findings to the propagation of carbon depletion in porous dielectrics exposed to a low temperature plasma. This diffusion saturation is reached after about one minute in typical experimental situations of plasma damage in microelectronic fabrication. We predict the general dependencies on porosity and reaction rates.