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A modified Deal-Grove thermal oxidation model for silicon wafers
The mathematical model describing $SiO_2$ layer growth presented in this paper is defined by the original Deal-Grove differential equation, used for describing oxide layer growth at constant temperature and by the heat balance equation, which describes the temperature evolution in the sample, when the injected power is constant. In this framework it is shown, that starting with a sample, which has an initial (natural) oxide layer thickness $x'$[m] and a temperature $T'=300$[K], and injecting in the growth system a constant power P[W], the oxide layer thickness x[m] evolves according to a law which is in a good agreement with results reported in the literature, both for thin and large oxide layer thicknesses. The computed evolution reveals that oxide layers of thickness below 10 nm grow in the transition period, i.e. during the period of time when the sample temperature $T$ increases from $T'$ and achieves the constant equilibrium temperature $T_0$ (which depends on the injected power $P$). Numerical examples are given for (100) and (111) oriented Si samples and the computed results are compared to the results reported in the literature.