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 x(o), follows a time-dependent power law, x(o)similar to (t/tau)(upsilon), with the temporal exponent given by v = 2(-1) + (5(1 + root 2t/tau))(-1), where t denotes the oxidation time and tau [= 1 (h)] is a constant. The validity of this property is confirmed by comparing the evolution curves of x o 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(000 (1) over bar) C-face, SiC(11 (2) over bar0) 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.