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On modelling thermal oxidation of Silicon I: theory
Author(s) -
Rao Vinay S.,
Hughes Thomas J. R.
Publication year - 2000
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(20000110/30)47:1/3<341::aid-nme774>3.0.co;2-z
Subject(s) - conservation law , conservation of mass , silicon , mechanics , work (physics) , thermal , continuum mechanics , momentum (technical analysis) , deformation (meteorology) , oxide , balance equation , classical mechanics , materials science , thermodynamics , mathematics , physics , mathematical analysis , composite material , metallurgy , statistics , markov model , finance , markov chain , economics
This work focuses on a new mathematical framework to model the process of thermal oxidation in silicon. The mathematical model is derived from the fundamental conservation equations of mechanics. The mass balance law provides the description of the oxidant transport and the Si–SiO 2 interface motion, and momentum balance provides the framework to model the displacements and stresses in the bulk and the oxide. The displacements define the geometry of the final oxide structure. The large expansion is treated within a mathematically exact formulation following a split of the deformation gradient. A thermodynamically consistent constitutive equation for silicon dioxide is suggested to represent recent experimental data. Copyright © 2000 John Wiley & Sons, Ltd.