  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 \sim t^1/2 to logarithmic
behavior \sim 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 1 minute
in typical experimental situations of plasma damage in microelectronic
fabrication. We predict the general dependencies on porosity and reaction
rates.
