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Construction of an Asymptotic Model for the Oxidation Process of Silicon
Author(s) -
Merz W.,
Pulverer K.,
Stoth B.
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199810)78:10<711::aid-zamm711>3.0.co;2-3
Subject(s) - silicon , uniqueness , ode , process (computing) , oxidation process , materials science , mathematics , mathematical analysis , computer science , chemical engineering , metallurgy , engineering , operating system
In this article we consider a model which describes the oxidation process of silicon. The two phases, silicon and silicon‐dioxide, are separated by a moving mixed zone of thickness O(ε), ε being a small parameter. We use the techniques of formal asymptotic analysis to derive a model with a sharp reaction front between the two phases. The resulting model agrees with other existing oxidation models on the basis of a sharp interface. In addition we give a proof for the existence, uniqueness, and qualitative behaviour of the solution to the system of ODEs obtained to leading order of the interfacial expansion.