Time-Dependent Power-Law Growth of Oxide with Anomalous Diffusion in the Thermal Oxidation of 4H-SiC\((11\bar{2}0)\) and 4H-SiC\((000\bar{1})\)

Abstract

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 O2 molecules is considered. By taking the 4H-SiC\((11\bar{2}0)\) a-face as an example, the RDEs are integrated numerically at the oxidation temperature of T = 1150 °C and the partial pressure of oxygen molecules in the ambient environment of Pox = 0.25, 0.5, 1, 2, and 4 (atm). By analyzing the simulation results on the evolution of the oxide thickness xo, it is found that xo 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′ = (ωp/ω1)t, where t denotes the oxidation time and ωp is defined as ωp = Θs(Pox)νinc. Here, Θs(Pox) and νinc 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; ω1 is a constant, which is given by \(\omega_{1} = \omega_{p}|_{P_{\text{ox}} = 1(\text{atm})}\). The curve yielded by the collapse is found to follow the time-dependent power law (TDPL) as xo(t) ∝ (t/τ)ν(t), where the exponent ν(t) is given by \(\nu (t) = 0.565 + 0.2/(1 + \sqrt{2t/\tau } )\) with τ [= 1 (h)] a constant. This property is found to be valid also for the oxidation of a polar surface, 4H-SiC\((000\bar{1})\), by comparing the results of the calculations according to xo(t) ∝ (t/τ)ν(t) with the experiments reported in the literature. Therefore, the oxide growth in these systems follows the TDPL with the anomalous diffusion of νD = 0.565, which is larger than the normal diffusion of νD = 0.5 observed in the thermal oxidation of Si. In addition, the transition between the etching mode at low Pox and the oxidation mode at high Pox on the 4H-SiC\((11\bar{2}0)\) a-face is found to occur at \(P_{\text{c}} \simeq 0.73\) (atm) at T = 1150 °C.