Muon Interaction with Negative- U and High-Spin-State Defects: Differentiating Between C and Si Vacancies in 4H - SiC

Low-energy muon-spin-rotation spectroscopy (LE-$\ensuremath{\mu}\mathrm{SR}$) is employed to study silicon and carbon vacancies in proton-irradiated $4H$-$\mathrm{Si}\mathrm{C}$. We show that the implanted muon is quickly attracted to the negative $\mathrm{Si}$ vacancy (${V}_{\mathrm{Si}}$), where it forms a paramagnetic muonium (${\mathrm{Mu}}^{0}$) state, resulting in a reduction of the diamagnetic fraction. In samples with predominantly $\mathrm{C}$ vacancies (${V}_{\mathrm{C}}$), on the other hand, the formation of ${\mathrm{Mu}}^{0}$ is very short lived and the muon quickly captures a second electron to form a diamagnetic ${\mathrm{Mu}}^{\ensuremath{-}}$ state. The results are corroborated by density-functional calculations, where significant differences in the relaxation mechanism of the nearest-neighbor dangling bonds of the vacancies are discussed. We propose that the LE-$\ensuremath{\mu}\mathrm{SR}$ technique is capable of differentiating between high-spin and negative-$U$ behavior in semiconducting materials. Finally, our findings emphasize the large potential of LE-$\ensuremath{\mu}\mathrm{SR}$ to probe near-surface semiconductor defects, a capability that is crucial for further development of many electronic and quantum technology applications.