Temperature dependence of divacancy spin coherence in implanted silicon carbide

Spin defects in silicon carbide (SiC) have attracted increasing interest due to their excellent optical and spin properties, which are useful in quantum information processing. In this paper, we systematically investigate the temperature dependence of the spin properties of divacancy defects in implanted $4H$-SiC. The zero-field splitting parameter $D$, the inhomogeneous dephasing time $T_2^{*}$, the coherence time $T_2$, and the depolarization time $T_1$ are extensively explored in a temperature range from 5 to 300 K. Two samples implanted with different nitrogen molecule ion fluences $({\mathrm{N}}_2{}^{+},$ $1\times {10}^{14}/{\mathrm{cm}}^2 \mathrm{and} 1\times {10}^{13}/{\mathrm{cm}}^2)$ are investigated, whose spin properties are shown to have similar temperature-dependent behaviors. Still, the sample implanted with a lower ion fluence has longer $T_2$ and $T_1$. We provide possible theoretical explanations for the observed temperature-dependent dynamics. Our work promotes the understanding of the temperature dependence of spin properties in solid-state systems, which can be helpful for constructing wide temperature-range thermometers based on the mature semiconductor material.

Figure 1

Experimental setup. The sample is mounted on a metal circuit board (MCB), which is attached to the stage in a cryogenic vacuum chamber (CVC). The temperature is controlled by a heater controller (HC). The pump laser modulated by an acousto-optic modulator (AOM) is focused by an objective to the sample. The fluorescence is collected by the same objective and filtered by a dichroic mirror (DM) and an interference filter (IF), which is then coupled by a fiber coupler (FC) and sent through the fiber to a superconducting single-photon detector (SSPD). The pump laser and microwave (MW) pulse sequences are controlled by a computer. The magnetic field is provided by a permanent magnet in the cryogenic chamber.

Figure 2

Temperature dependence of the ODMR spectrum and the ZFS parameter $D$ of sample A implanted with a $1\times {10}^{14}/{\mathrm{cm}}^2$ nitrogen molecule ion fluence along with the simulation result of the vacancy defect's depth distribution by using SRIM. In (a) and (b) the dots are experimental data and the solid lines are fitting lines, while in (c) the solid line is the simulation curve. (a) The ODMR spectra of PL6 at 5, 140, and 300 K in a $1.80\times {10}^{-2}$ T static magnetic field. The fitting lines are Lorentzian lines. ${\omega }_1$ and ${\omega }_2$ are the two corresponding resonant frequencies, respectively, and $D=({\omega }_1+{\omega }_2)/2$. (b) Temperature dependence of $D$. The fitting line is the Debye-model fitting line with a determination coefficient of 0.9997. $D$ decreases monotonically as the temperature increases. The error bars are deduced from the fitting errors. (c) The simulation result that shows the normalized vacancy concentration generated by the ${\mathrm{N}}_2{}^{+}$ ion implantation as a function of the depth from the sample surface. This result demonstrates that most vacancy defects, including PL6 defects, are distributed within 50 nm from the sample surface.

Figure 3

Temperature dependence of Ramsey interference and the inhomogeneous dephasing time $T_2^{*}$ of sample A implanted with a $1\times {10}^{14}/{\mathrm{cm}}^2$ nitrogen molecule ion fluence. (a)–(c) Ramsey interference curves at 50, 150, and 300 K with $T_2^{*}$ derived from the fitting formula, respectively. The dots are experimental data and the solid lines are the fitting lines. (d) Temperature dependence of $T_2^{*}$ from 5 to 300 K. $T_2^{*}$ remains stable at different temperatures. Error bars are deduced from the fitting errors.

Figure 4

Temperature dependence of the coherence time $T_2$ and the depolarization time $T_1$ of sample A implanted with a $1\times {10}^{14}/{\mathrm{cm}}^2$ nitrogen molecule ion fluence. (a) The spin echo oscillation at 5 K with $T_2=30.7\mu \mathrm{s}$ derived from the fitting formula (the solid line). (b) Temperature dependence of $T_2$ from 5 to 300 K. An anomalous revival of $T_2$ occurs at around 250 K. (c) The depolarization curve at 5 K with $T_1=567\mu \mathrm{s}$ derived from the fitting formula (the solid line). (d) Temperature dependence of $1/T_1$ from 5 to 300 K, which transits from a linear relationship to a polynomial relationship. The dots are experimental data. Error bars are deduced from the fitting errors.

Figure 5

Experimental results of sample B implanted with a nitrogen molecule ion fluence of $1\times {10}^{13}/{\mathrm{cm}}^2$. (a) Typical ODMR spectra at 5, 140, and 300 K. The ODMR signals of the low-dose implanted sample B have smaller intensities, smaller signal-to-noise ratios, and narrower full width at half maxima (FWHM) than those of the high-dose implanted sample A. (b) Temperature dependence of $D$. The solid line is the Debye-model fitting curve with the determination coefficient $R^2=0.9986$. (c) Temperature dependence of $T_2^{*}$. $T_2^{*}$ remains stable at different temperatures. (d) Temperature dependence of $T_2$. An anomalous revival of $T_2$ occurs at around 250 K. (e) Temperature dependence of $1/T_1$, which transits from a linear relationship to a polynomial relationship. At the same temperature, sample B has longer $T_2$ and $T_1$ than those of sample A implanted with an ion fluence of $1\times {10}^{14}/{\mathrm{cm}}^2$. Error bars are deduced from the fitting errors.