Observation and manipulation of charge carrier distribution at the SiO$_2$/Si interface

Using low-energy muons, we map the charge carrier concentration as a function of depth and electric field across the \SiOSi interface up to a depth of \SI{100}{\nano\meter} in Si-based MOS capacitors. The results show that the formation of the anisotropic bond-centered muonium \MuBCz state in Si serves as a direct measure of the local changes in electronic structures. Different band-bending conditions could be distinguished, and the extension of the depletion width was directly extracted using the localized stopping and probing depth of the muons. Furthermore, electron build-up on the Si side of the \SiOO/Si interface, caused by the mirror charge induced by the fixed positive charge in the oxide and the image force effect, was observed. Our work represents a significant extension of the application of the muon spin rotation technique ($\mu$SR) and lays the foundation for further research on direct observation of charge carrier density manipulation at technologically important semiconductor device interfaces.