We have performed electronic state calculations to clarify the initial stage of the oxidation of the Si- and C-faces in 4H-SiC based on the density-functional theory. We investigate how each Si and C atomic site is oxidized on C- and Si-face, and explore most probable reaction pathways, corresponding energy barriers, and possible defects generated during the oxidation. We have found that carbon annihilation process is different between on Si- and on C-face, and this difference causes different defects in interface; In C-face case, (1), carbon atoms are dissociated directly from the substrate as CO molecules. (2), after CO dissociation, 3-fold coordinated oxygen atoms (called Y-lid) are observed at the interface. (3), high density of C-dangling bonds can remain at the interface. In Si-face case, (1), C atoms inevitably form carbon nano clusters (composed of a few atoms) in interface to reduce the number of dangling bonds there. Moreover, we have found that the carbon nano clusters are composed of not only single but also double chemical bonds. (2), We have observed that CO molecules are dissociated from the carbon nano clusters in MD simulations. Furthermore, we have investigated whether H$_2$ and NO molecules react with the defects found in this study.
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