Diffusion of carbon oxides in SiO$_2$ during SiC oxidation*

SiC is a wide-band-gap semiconductor and has an advantage to fabricate electronic devices such as MOSFETs due to the ability to thermally oxidize to SiO$_2$. Despite many studies conducted on the oxidation of SiC, the kinetics such as diffusion and interface reaction is not fully understood. Here, we focus on the diffusion process during SiC oxidation, and clarify the diffusion mechanism of carbon oxides (CO and CO$_2$) in SiO$_2$ by means of density functional calculations. Our calculations demonstrate that the CO without any chemical bonds with host SiO$_2$ is stabilized while the CO$_2$ is incorporated between Si-O bonds of SiO$_2$ to form a carbonate group. The energy of CO$_2$ is found to be lower than that of CO by 3.7 eV, indicating that the most stable form of carbon oxides in SiO$_2$ is CO$_2$. Furthermore, the calculated energy barriers for diffusion of CO and CO$_2$ are found to be 0.1 and 1.8 eV, respectively. These results thus imply that CO molecules easily react with oxidant such as O$_2$ to form CO$_2$ and the outward diffusion of resultant CO$_2$ is rate-limiting. Indeed, the estimated activation energy for CO$_2$ diffusion (3.5 eV) reasonably agrees with that for Si-face SiC (3.1 eV) obtained by Deal-Grove model considering product gas out-diffusion.