  We introduce a first-principles study to clarify the carrier-scattering
property at the SiC/SiO$_2$. Interestingly, the electron transport at the
conduction-band edge is significantly affected by the introduction of oxygen,
even though there are no electrically active defects. The origin of the large
scattering is explained by the behavior of the internal-space states (ISSs).
Moreover, the effect of the ISSs is larger than that of the electrically active
carbon-related defects. This result indicates that an additional scattering not
considered in a conventional Si/SiO$_2$ occurs at the SiC/SiO$_2$.
