Electron spin coherence of silicon vacancies in proton-irradiated 4H-SiC

We report $T_2$ spin coherence times for electronic states localized in Si vacancies in $4H\text{−}\mathrm{SiC}$. Our spin coherence study included two SiC samples that were irradiated with 2 MeV protons at different fluences (${10}^{13}$ and ${10}^{14}\mathrm{c}{\mathrm{m}}^{-2}$) in order to create samples with unique defect concentrations. Using optically detected magnetic resonance and spin echo, the coherence times for each sample were measured across a range of temperatures from 8 to 295 K. All echo experiments were done at a magnetic field strength of 0.371 T and a microwave frequency of 10.49 GHz. The longest coherence times were obtained at 8 K, being $270\pm 61\mu \mathrm{s}$ for the ${10}^{13}\mathrm{c}{\mathrm{m}}^{-2}$ proton-irradiated sample and $104\pm 17\mu \mathrm{s}$ for the ${10}^{14}\mathrm{c}{\mathrm{m}}^{-2}$ sample. The coherence times for both samples displayed unusual temperature dependencies; in particular, they decreased with temperature until 60 K, then increased until 160 K, then decreased again. This increase between 60 and 160 K is tentatively attributed to a motional Jahn-Teller effect. The consistently longer lifetimes for the ${10}^{13}\mathrm{c}{\mathrm{m}}^{-2}$ sample suggest that a significant source of the spin dephasing can be attributed to dipole-dipole interactions between Si vacancies or with other defects produced by the proton irradiation. The lack of a simple exponential decay for our ${10}^{14}\mathrm{c}{\mathrm{m}}^{-2}$ sample indicates an inhomogeneous distribution of defect spins.

Figure 1

Photoluminescence of the two main SiC samples with 870 nm excitation. Note the order-of-magnitude increased strength of the spectral peaks for the ${10}^{14}\mathrm{c}{\mathrm{m}}^{-2}$ sample as compared to the ${10}^{13}\mathrm{c}{\mathrm{m}}^{-2}$ sample, due to the increased number of vacancy defects. The spectra were both taken at low temperature (5 and 6 K for the ${10}^{14}$ and ${10}^{13}\mathrm{c}{\mathrm{m}}^{-2}$ samples, respectively).

Figure 2

Depth-dependent photoluminescence of the ${10}^{12}\mathrm{c}{\mathrm{m}}^{-2}$ sample at the V2 wavelength. The large peak at 34 μm indicates the stopping position of the protons. The spatial resolution was 1 μm.

Figure 3

(a) Schematic of the optical experiment. (b) View of microwave coupling loop (black) and sample (gray) in cryostat, with static magnetic field (green arrows), microwave field (blue arrow tails), and laser beam (red dot, vertically polarized) indicated.

Figure 4

Representative optically detected magnetic resonance of the ${10}^{14}\mathrm{c}{\mathrm{m}}^{-2}$ proton-irradiated sample, at 80 K and 0.3708 T. Two peaks are observed. The signal strength is plotted as a percentage of the total photoluminescence reaching the detector. Inset: Energy levels of the spin 3/2 system, with the two observed transitions indicated. The $+3/2\leftrightarrow +1/2$ transition was used for all echo scans.

Figure 5

Representative Rabi oscillation data, for the ${10}^{14}\mathrm{c}{\mathrm{m}}^{-2}$ sample at 80 K. The vertical lines (green) represent the π and π/2 pulse times deduced from the experiment for those conditions. The horizontal dashed line (red) indicates the zero polarization value. Inset: The laser and microwave pulse sequences for the Rabi experiments.

Figure 6

Representative spin echo data, for the ${10}^{14}\mathrm{c}{\mathrm{m}}^{-2}$ sample at 80 K and with a $T_{\mathrm{fixed}}$ value of 6 μs. The data is normalized so that the $y$ axis is the ODMR signal divided by the ODMR baseline. The red line represents a Gaussian fit of the data with a linear baseline. The echo strength is defined to be how far the echo changes from 100% towards zero. Inset: The laser and microwave pulse sequences for the spin echo experiments.

Figure 7

Representative echo decays for both samples. (a) The ${10}^{13}\mathrm{c}{\mathrm{m}}^{-2}$ sample at 60 K. The red line is an exponential decay fit as per Eq. (1). (Noise prohibited data collection in for $T_{\mathrm{fixed}}$ values longer than 35 μs.) (b) The ${10}^{14}\mathrm{c}{\mathrm{m}}^{-2}$ sample at 80 K. The red line is an exponential decay fit [Eq. (1)]; the green line is a biexponential decay fit [Eq. (2)]; the blue line is a stretched exponential fit [Eq. (3)], which overlaps the biexponential fit for most of the decay.

Figure 8

Temperature dependence of spin lifetimes in SiC. The black connecting lines serve as guides to the eye. (a) $T_2$ coherence times of ${10}^{13}\mathrm{c}{\mathrm{m}}^{-2}$ $4H\text{−}\mathrm{SiC}$ sample. (Noise prohibited data collection for temperatures higher than 190 K.) (b) $T_2$ coherence times of ${10}^{14}\mathrm{c}{\mathrm{m}}^{-2}$ $4H\text{−}\mathrm{SiC}$ sample (biexponential ${\tau }_{\mathrm{long}}$ values). (c) ${T_2}^{*}$ times of SiC $hh$ divacancies. Figure 7 adapted with permission from Ref. [21]. Copyrighted by the American Physical Society.