Reparametrization-Invariant Reaction–Diffusion Equation as the Model of the Thermal Oxidation of Si

The thermal oxidation of Si with a planar interface in the dry oxidation condition is studied by constructing a continuum model based on a reparametrization-invariant reaction–diffusion equation. By analyzing the simulation results, it is found that the growth of the oxide thickness xo follows a tim...

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Bibliographic Details
Published in:Journal of the Physical Society of Japan 2020-06, Vol.89 (6), p.64601
Main Author: Itoh, Makoto
Format: Article
Language:English
Subjects:
Computer simulation
Continuum modeling
Invariants
Oxidation
Power law
Reaction-diffusion equations
Silicon carbide
Time dependence
Wet oxidation
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Summary:The thermal oxidation of Si with a planar interface in the dry oxidation condition is studied by constructing a continuum model based on a reparametrization-invariant reaction–diffusion equation. By analyzing the simulation results, it is found that the growth of the oxide thickness xo follows a time-dependent power law, xo ∼ (t/τ)ν, with the temporal exponent given by ν = 2−1 + (5(1 + √2t/τ))−1, where t denotes the oxidation time and τ [= 1 (h)] is a constant. The validity of this property is confirmed by comparing the evolution curves of xo according to the power law given above with the experimental data on the thermal oxidation of Si(100) in both dry and wet oxidation conditions and also those of SiC(0001) C-face, SiC(1120) a-face, and SiC(0001) Si-face in the dry oxidation condition. The implication of our results to the self-limiting oxidation of a Si nano wire is discussed additionally.
ISSN:0031-9015
1347-4073
DOI:10.7566/JPSJ.89.064601