Room-temperature coherent control of implanted defect spins in silicon carbide

Recently, vacancy-related spin defects in silicon carbide (SiC) have been demonstrated to be potentially suitable for versatile quantum interface building and scalable quantum network construction. Significant efforts have been undertaken to identify spin systems in SiC and to extend their quantum capabilities using large-scale growth and advanced nanofabrication methods. Here we demonstrated a type of spin defect in the 4H polytype of SiC generated via hydrogen ion implantation with high-temperature post-annealing, which is different from any known defects. These spin defects can be optically addressed and coherently controlled even at room temperature, and their fluorescence spectrum and optically detected magnetic resonance spectra are different from those of any previously discovered defects. Moreover, the generation of these defects can be well controlled by optimizing the annealing temperature after implantation. These defects demonstrate high thermal stability with coherently controlled electron spins, facilitating their application in quantum sensing and masers under harsh conditions.


INTRODUCTION
Previously, deep defects in semiconductors were considered harmful elements that needed to be eliminated. Nowadays, with the development of quantum information, several optically addressable defect spins have played important roles in optical/ spin interface. Some of these defect spins can be individually and coherently controlled at room temperature. Among these, the negatively charged nitrogen-vacancy (NV) center in diamond is a leading platform through which significant achievements have been accomplished in quantum communications 1 , quantum computation [2][3][4] , and quantum sensing [5][6][7][8] . However, scalable quantum network construction for NV centers in diamond still encounter considerable challenges 9 . To further extend such defect-based applications, many attempts have been made to explore similar defects in other materials; vacancy-related defects in silicon carbide (SiC) are attractive candidates [10][11][12][13][14][15][16][17][18][19] .
As SiC is a promising wide-bandgap semiconductor material with well-established inch-scale growth and device-engineering protocols, it is widely used in high-power electronic devices. Highquality bulk and epitaxial single crystals of SiC can be commercially purchased. There are many different polytypes for SiC with 3C-SiC, 4H-SiC, and 6H-SiC symmetries; 4H-SiC is the most common among them 10 . Similar to NV centers in diamond, certain defects in SiC, such as divacancies (PL1-PL7) and silicon vacancies (V Si ) in 4H-SiC, can be optically identified and coherently controlled at room temperature [18][19][20] . Furthermore, their nearinfrared (NIR) fluorescence signals can be used for biological sensing 21 and optical fiber transmission. Moreover, the Hahn echo coherence time of divacancy defect spins in 4H-SiC has been demonstrated to be 1.3 ms, i.e., the longest coherence time in a naturally isotopic crystal 16 . Apart from intrinsic defects, different implanted methods have been used to generate different types of defects on-demand in SiC with similar optical and spin properties [22][23][24][25][26] . Defect spins in SiC have important applications in many quantum information tasks 11,12,27 .
Recently, significant efforts have been undertaken to investigate more spin systems embedded in SiC to extend their quantum functionalities 10,11,27 . Herein, we demonstrated new optically addressable paramagnetic point spin defects in the 4H-SiC epitaxy layer generated by implanting 170-keV hydrogen ions (H + ) with a fluence of up to 5 × 10 16 cm −2 and annealing at 1300°C for 2 h (see "Methods" for more details). The NIR zero-phonon line (ZPL) of defects is at 1007 nm, which is suitable for biological sensing and located between the first and second communication windows of the fiber. According to the optically detected magnetic resonance (ODMR) spectrum, the ground-state structure of the defect spins is classified as a c-axis three-level system. The ODMR contrast of these ensemble defects is similar to that of the divacancy in SiC (reported to be~0.7%), but the resonant frequencies are different from those of any known defects (see the comparison in Supplementary Table 1; refer to the Supplementary Information for more details). The density of the generated defects is largely dependent on the fluence of the implanted ions and annealing temperature. The defects are further shown to be controllably generated by optimizing the annealing temperature. By increasing the implanted fluence, the concentration of these defects (similar to divacancies, the defects are labeled PL8 according to the photoluminescence (PL) spectrum) can be further increased to a sufficiently high level to 1 CAS be useful for high-sensitivity quantum sensing 28 and maser development 29 .

RESULTS
The PL spectra of the sample at temperatures 20-300 K are shown in Fig. 1a. The sample was excited using a 920-nm laser (see "Methods" for details), and the peak at 1007 nm of the lowtemperature spectra belonged to ZPL of PL8 defects. Several other peaks in the spectrum were deduced to be unrelated to PL8 defects (see Supplementary Fig. 1; refer to the Supplementary Information for more details). Figure 1b displays the ODMR spectrum without a magnetic field applied at room temperature that was fitted using two Lorentz functions. Two obvious ODMR peaks centered at 1383.8 and 1391.8 MHz are shown. They were different from the ODMR signals of the divacancy defects in SiC 10,18 (refer to the Supplementary Information for more details). Based on the ODMR spectrum's features, the ground-state electronic structure was inferred to be a three-level system (shown in the inset of Fig. 1b). The spin ground-state Hamiltonian under the external magnetic field (B 0 ) can be described as the zero-field-splitting parameters and S x , S y , and S z are the three components of the spin (S). From the Lorenz fittings in Fig. 1b, the zero-field parameters |D| = 1387.8 MHz and |E| = 4 MHz were obtained at room temperature. To confirm that the ground state of PL8 defects were the c-axis symmetry, the ODMR signals were measured as a function of the c-axis magnetic field. As shown in Fig. 1c, the two transitions of PL8 defects were measured to split at a slope of ±2.8 MHz/G, demonstrating the c-axis spin orientation. The property was similar to that of PL6 defects in 4H-SiC 10,19 . Further, we detected the ODMR signals with polarized microwaves implemented using two crossed copper wires with a 90°phase difference 30 at 12.8-G external magnetic field. The experimental results are shown in Fig. 1d. The higher resonant frequency represented the transition between m s = 0 and m s = +1, while the lower resonant frequency represented the transition between m s = 0 and m s = −1. Comparing the transition intensities with a clockwise circular polarized microwave (σ − , green triangles, transition mainly occurred for Δm s = −1), anticlockwise circular polarized microwave (σ + , red dots, transition mainly occurred for Δm s = +1), and linearly polarized microwave (L, black squares, both transitions occurred almost equally), we concluded that PL8 defect spins were primarily initialized to m s = 0, with 920-nm laser pumping (similar to PL6 defects). Moreover, we investigated the coherent manipulation of PL8 defect spins at 20 K. Figure 2a shows the ODMR spectrum obtained by collecting all PL from the sample using a 1000-nm longpass filter. Several weak ODMR signals of other previously reported defects (PL2, PL5, and PL6) were also observed 10 . The ODMR spectrum was further detected by only collecting the PL around ZPL at 1007 nm with a band-pass filter from 1000 to 1024 nm. The result is shown in the inset of Fig. 2a. Only the signal of PL8 defect spins was observed, confirming ZPL at 1007 nm. The resonant frequency of the ODMR spectrum at 20 K increased by 10 MHz compared with that at room temperature, as clearly shown in Fig. 2b. This behavior was similar to that of the divacancy   15 . Similar to that of PL5 defects in SiC 15 , when the temperature increased, the zerofield parameter |E| remained the same. A Ramsey pulse sequence 18 was used to measure the free induction decay time T Ã 2 . Figure 2c shows the Ramsey oscillation at 84G with a detuning frequency δf = 10 MHz, which revealed an inhomogeneous spin coherence time T Ã 2 ¼ 184 ± 10 ns for ground-state spins. The fit function was a power-dependent attenuation oscillation function 5 . A Hahn echo pulse was implemented to detect the homogenous spin coherence time 18 ; the result is shown in Fig. 2d. From the oscillation decay fitting 18 , we obtained T 2 = 15.6 ± 0.5 μs. The oscillation was driven by nuclear spins ( 13 C and 29 Si).
PL8 defect spins can also be coherently controlled at room temperature. Figure 3a shows the Rabi oscillation at room temperature. The Rabi frequency was demonstrated to be proportional to the square root of the microwave power in the copper wire 20 (inset of Fig. 3a). The Ramsey oscillation was also measured at room temperature; the result is shown in Fig. 3b. The inhomogeneous spin coherence time T Ã 2 ¼ 180 ± 9 ns was deduced from the fitting. Compared with the result shown in Fig. 2c, T Ã 2 was nearly constant and independent of the sample temperature. Figure 3c shows the room temperature spin echo decay time of 6.1 ± 0.1 μs at 25-G external magnetic field. The result was fitted with two frequency components equal to Larmor frequencies of 13 C and 29 Si. The decoherence effect can be suppressed using the dynamical decoupling method. In Fig. 3d, the Carr-Purcell-Meiboom-Gill (CPMG)-3π pulse is implemented 18,31 . Compared with 6.1-μs decay time in Fig. 3c, the decay time here was extended to 14.7 μs at the same magnetic field. The decay time in Fig. 3c was shorter than T 2 owing to the perturbation of the nuclear spin environment at the magnetic field. We further increased the magnetic field 16 , and the homogenous spin coherence time was measured (Fig. 3c) at 157G, revealing that T 2 = 9.1 ± 0.9 μs at room temperature, which is longer than that of the implanted PL1 defects in SiC (T 2 = 6 μs) 10 . Compared with Fig.  2d, T 2 at a lower temperature was longer than that at room temperature. We also measured T 2 of the implanted PL6 defects for T 2 = 9.7 ± 0.8 μs (see Supplementary Fig. 3; refer to the Supplementary Information for more details), which was almost the same as that of PL8 defects. However, T 2 of PL6 in the sample from Cree company reached~40 μs 18 , indicating that T 2 can be improved upon optimizing the sample. The longitudinal spin relaxation time T 1 was also measured. The result is shown in Fig. 3f for 230 ± 53 μs, which is longer than that of the divacancies in SiC at room temperature 18 . This indicates that we can extend T 2 to be longer time (~T 1 ) using the CPMG-n secquence 32 .
Further, we investigated the conditions required to generate PL8 defects. Figure 4a, b shows the optical spectra at 20 K and ODMR spectra at room temperature for the samples annealed at 1200°C (red line and squares), 1300°C (black line and dots), and 1400°C (blue line and triangles). All annealing was implemented in a high-vacuum environment (1.1 × 10 −6 Pa) for 2 h. The samples were implanted with the same fluence of 2 × 10 16 cm −2 using 170-keV H + . We found that PL8 defects were very sensitive to the annealing temperature. For the sample annealed at 1200°C, ZPL and ODMR signals of PL8 defects were not observed; however, they were clearly detected when the sample was annealed at 1300°C. When the annealing temperature increased to 1400°C, both optical and ODMR signals considerably reduced. Signals of divacancy defects were also observed in the sample annealed at 1300°C, but they were considerably weaker than those of PL8 defects. Therefore, the controllable generation of PL8 defects in 4H-SiC can be realized by optimizing the annealing temperature. The spin coherent properties of PL8 defects were further investigated as a function of the implanted fluences. The results of T 2 and T Ã 2 are shown in Fig. 4c, d, respectively. T 2 was nearly constant, while T Ã 2 decreased as the implanted fluences increased owing to inhomogeneous broadening. In Supplementary Information, we further measured the optical decay time, which was deduced to be 6.0 ± 0.1 ns. By including the spin initialization and measuring the subsequent lifetime, we determined the spin polarization to be approximately 97.5% (see Supplementary Fig. 1; refer to the Supplementary Information for more details).

DISCUSSION
In this study, we demonstrated a type of defect spin in 4H-SiC which has not been previously reported by implanting high-fluence H + and annealing at 1300°C. The PL and ODMR spectra of PL8 defects were different from those of any known defects in 4H-SiC (the optical spectrum excited by 532-nm laser is shown in Supplementary Fig. 2; refer to the Supplementary Information for more details) 18,33 . To identify the possible origins of PL8 defects, we implanted the 4H-SiC sample with high-fluence helium ions (He + ) and detected the same ODMR signals as those of PL8 defects (see Supplementary Fig. 3; refer to the Supplementary  Information for more details). Thus, we conclude that they were not hydrogen-related defects. Other possible candidates were multivacancy 34 , stacking faults 35 , and silicon vacancy-related defects (Si 0 V and Si 2À V ) with the same spin state as the neutral silicon vacancy in diamond 27,36 . Moreover, further theoretical and experimental researches are required to confirm PL8 defect structures. In this study, the spin coherence time T 2 of PL8 defects was equal to that of implanted PL6 defects in our sample (see Supplementary Fig. 3; refer to the Supplementary Information for more details). That is, we could extend T 2 by optimizing the sample 18   of PL8 defects with thermal stability for harsh conditions can be increased to a level that is sufficiently high to be used for maser development 29 .

Sample preparation
The sample used herein was a commercially available high-purity 4H-SiC epitaxy layer purchased from Xiamen Powerway Advanced Material Co. Ltd. The epitaxy thickness was approximately 7 μm, and the N-doping was 5 × 10 15 cm −3 . The epitaxy wafer was implanted with 170-keV H + , and the fluence ranged from 1 × 10 16 to 5 × 10 16 cm −2 . The sample was annealed at varying high temperatures (1200, 1300, and 1400°C) for 2 h. For comparison, the sample was also implanted with high-fluence He + (5 × 10 15 and 2 × 10 16 cm −2 ) and carbon ions (C + ) (1× 10 14 cm −2 ). The experimental results are shown in the Supplementary Information.

Experimental setup
A 920-nm laser modulated by an acousto-optic modulator was used to excite these defects. The laser was reflected by a dichroic mirror (Semrock, Di02-R980) and passed through an objective (N.A. = 0.85 for roomtemperature measurement and 0.65 for low-temperature measurement) and focused on the epitaxy SiC sample. The PL was collected using the same objective and detected by a femtowatt photoreceiver (OE-200-IN1) or spectrometer (Horiba, iHR550) after a 1000-nm longpass interference filter (Thorlabs, FELH1000). In the ODMR experiment, the microwave was applied using a 20-μm-diameter copper wire post modulation by 70-Hz pulses from a lock-in amplifier (SRS, SR830). The different PL intensity (ΔPL) between the cases with and without resonant microwave excitation was extracted. The spin signals, which were modulated by 70 Hz, were extracted by the same lock-in amplifier. A microwave generator (minicircuit, SSG6000) was used to generate the microwave, which was further amplified using a microwave amplifier (mini-circuit, ZHL-30W-252+). The pulse sequences used in the experiment were controlled through a pulse generator (PBESR-PRO-500, Spincore) via a computer. The corresponding ODMR signals with red squares (1200°C annealing), black dots (1300°C annealing), and blue triangles (1400°C annealing) at room temperature. There were no detectable ODMR signals of PL8 defects for 1200°C annealing. c Room temperature T 2 (at 157G) of PL8 defect spins as a function of the implanted fluence and annealing at 1300°C. d Room temperature T Ã 2 (at 157G) as a function of the implanted fluence and annealing at 1300°C, which decreased as the implanted fluence increased. Error bars represent the standard deviations of the corresponding fitting values for (c) and (d).