SiC-based microelectronics is a candidate for a future replacement of the current Si-based technology. One of the main advantages of SiC over other wide band-gap semiconductor materials is the existence of a native oxide (SiO$₂$). We present our theoretical study of the very first stages of oxidation on the clean and H-saturated Si-rich 3C-SiC(001) surface. Total-energy density functional theory (DFT) calculation of different on- and near-surface O adsorption sites on both clean and hydrogenated surfaces were performed. All calculations were done with the {\tt siesta} code using GGA and a large basis set. We determine both the most favorable and stable adsorption sites and correlate the adsorption energy with the lattice distortion. We find that the near-surface adsorption is strongly favored and can arise both as intra-bond and interstitial oxygen incorporation. Finally, we use extensive DFT calculations to study the double-oxygen adsorption and test for correlation effects in the clean SiC surface oxidation process.

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