Interaction of low-energy muons with defect profiles in proton-irradiated Si and $4H$-SiC

Muon spin rotation $\left(\mu \text{SR}\right)$ with low-energy muons is a powerful nuclear method where electrical and magnetic properties of thin films can be investigated in a depth-resolved manner. Here, we present a study on proton-irradiated Si and 4H-SiC where the formation of the hydrogen-like muonium (Mu) is analyzed as a function of the proton dose. While the Mu formation is strongly suppressed in the highly defective region of the shallow proton stopping profile, the Mu signal quickly recovers for higher muon energies where the muons reach the untreated semiconductor bulk. A lower sensitivity limit of low-energy $\mu \text{SR}$ to crystal defects of around ${10}^{17}$ to ${10}^{18}{\mathrm{cm}}^{-3}$ is estimated. Our results demonstrate the high potential of this technique to nondestructively probe near-surface regions without the need for electronic device fabrication and to provide valuable complementary information when investigating defects in semiconductors.

Figure 1

Muon implantation profiles for energies between 5 and $21\mathrm{keV}$ (shaded areas) and proton stopping profile (circles), calculated with Trim.SP [11, 12] for silicon (a) and silicon carbide (b).

Figure 2

Temperature scans performed on the Si samples at $B=10\mathrm{mT}$ for three different muon implantation depths. While muons at (a) $5\mathrm{keV}$ and (b) $13\mathrm{keV}$ probe only regions within the proton-irradiated region, muons at $19\mathrm{keV}$ are implanted deep enough to also partially probe the area behind this damaged region (c).

Figure 3

(a) Diamagnetic fraction of the Si samples as a function of implantation energy for different proton-irradiation doses. $B=10\mathrm{mT},T=50\mathrm{K}$. (b) Change of $F_D$ compared to the nonirradiated sample.

Figure 4

(a) Diamagnetic and (b) $\text{Mu}{}_{BC}^0$ asymmetries as a function of the muon implantation energy for the nonirradiated and two proton-irradiated Si samples with doses of $1\times {10}^{15}{\mathrm{cm}}^{-2}$ and $1\times {10}^{16}{\mathrm{cm}}^{-2}$, taken at $B=0.15\mathrm{T}$. (c) Low-field measurement of $A_D$ and $A_{MuT}$ for the nonirradiated Si sample with $B=0.5\mathrm{mT}$. All measurements were performed at $T=50\mathrm{K}$.

Figure 5

Diamagnetic fraction of the 4H-SiC samples, taken at $10\mathrm{mT}$ and two different temperatures: (a) $5\mathrm{K}$ and (b) $200\mathrm{K}$.

Figure 6

(a) Diamagnetic and (b) Mu fractions of the 4H-SiC samples, measured at $0.5\mathrm{mT}$ and $200\mathrm{K}$. A stronger transition of $\text{Mu}{}_T^0$ to ${\mathrm{Mu}}^{+}$ for increasing defect densities is again observed. The missing fraction is around 40%.