Generalized linear-parabolic law: a mathematical model for thermal oxidation of silicon

Silicon dioxide growth curves under a variety of oxidation conditions are analyzed. The results indicated that the growth curve is not the linear-parabolic equation as predicted by the Deal-Grove model. Instead, a generalized form of the linear-parabolic equation in which the coefficients are allowed to accommodate the change in the sign and thickness dependency is desirable to describe the silicon oxidation process. It is also shown that the thickness dependence of the rate constant with appropriate approximations can be expressed explicitly in a functional form.<
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