Saturation of front propagation in a reaction-diffusion process describing plasma damage in porous low-k materials
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 \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.
Keywords
Cite
@article{arxiv.1102.3084,
title = {Saturation of front propagation in a reaction-diffusion process describing plasma damage in porous low-k materials},
author = {Soghra Safaverdi and Gerard T. Barkema and Eddy Kunnen and Adam M. Urbanowicz and Christian Maes},
journal= {arXiv preprint arXiv:1102.3084},
year = {2015}
}
Comments
Accepted for publication in Phys. Rev. B