Time-Dependent Power-Law Growth of Oxide with Anomalous Diffusion in the Thermal Oxidation of 4H-SiC(11(2)over-bar0) and 4H-SiC(000(1)over-bar)

A model for the oxide growth in the thermal oxidation of SiC with a non-polar surface orientation is proposed. It is based on the reaction-diffusion equations (RDEs), in which the diffusion of both SiO and O-2 molecules is considered. By taking the 4H-SiC(11 (2) over bar0) a-face as an example, the RDEs are integrated numerically at the oxidation temperature of T = 1150 degrees C and the partial pressure of oxygen molecules in the ambient environment of P-ox = 0.25, 0.5, 1, 2, and 4 (atm). By analyzing the simulation results on the evolution of the oxide thickness x(o), it is found that x(o) obtained by the simulations and those of the experiments reported in the literature collapse onto a single curve when they are plotted against the rescaled time t ' = (omega(p)/omega(1))t, where t denotes the oxidation time and omega(p) is defined as omega(p) = Theta(s)(P-ox)nu(inc). Here, Theta(s)(P-ox) and nu(inc) denote the steady-state density of the oxygen molecules chemisorbed on the oxide surface and the prefactor for the incorporation rate of the oxygen molecules from the oxide surface into the oxide layer, respectively; omega(1) is a constant, which is given by omega(1) = omega(p)|(Pox)=1(atm). The curve yielded by the collapse is found to follow the time-dependent power law (TDPL) as x(o)(t) proportional to (t/tau)(nu(t)), where the exponent nu(t) is given by nu(t) = 0.565 + 0.2=(1 + root 2t/tau) with tau [= 1 (h)] a constant. This property is found to be valid also for the oxidation of a polar surface, 4H-SiC(000 (1) over bar), by comparing the results of the calculations according to x(o)(t) proportional to (t/tau)(nu(t)) with the experiments reported in the literature. Therefore, the oxide growth in these systems follows the TDPL with the anomalous diffusion of nu(D) = 0.565, which is larger than the normal diffusion of nu(D) = 0.5 observed in the thermal oxidation of Si. In addition, the transition between the etching mode at low P-ox and the oxidation mode at high P-ox on the 4H-SiC(11 (2) over bar0) a-face is found to occur at P-c similar or equal to 0.73 (atm) at T = 1150 degrees C.