Carbon clusters as possible defects at the SiC-SiO$_{2}$ interface*

High state densities in the band gap of the SiC-SiO$_{2}$ interface significantly reduce the channel mobilities in SiC-based high-temperature/high-power microelectronics. Investigations of the nature of the interface defects are thus of great importance. While several possible defects including very small carbon clusters with up to four carbon atoms have been identified by first-principles theory, larger carbon clusters as possible defects have attracted less attention. Here, we report first-principles quantum-mechanical calculations for two larger carbon clusters, the C$_{10}$ ring and the C$_{20}$ fullerence, at the SiC-SiO$_{2}$ interface. We find that both carbon clusters introduce significant states in the band gap. The states extend over the entire band gap with higher densities in the upper half of the gap, thus accounting for some of the interface trap densities observed experimentally.