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

摘要

We propose a three-component reaction-diffusion system yielding an asymptoticlogarithmic time-dependence for a moving interface. This is naturally relatedto a Stefan-problem for which both one-sided Dirichlet-type and vonNeumann-type boundary conditions are considered. We integrate the dependence ofthe interface motion on diffusion and reaction parameters and we observe achange from transport behavior and interface motion \sim t^1/2 to logarithmicbehavior \sim ln t as a function of time. We apply our theoretical findings tothe propagation of carbon depletion in porous dielectrics exposed to a lowtemperature plasma. This diffusion saturation is reached after about 1 minutein typical experimental situations of plasma damage in microelectronicfabrication. We predict the general dependencies on porosity and reactionrates.