High-frequency and high-quality silicon carbide optomechanical microresonators

Silicon carbide (SiC) exhibits excellent material properties attractive for broad applications. We demonstrate the first SiC optomechanical microresonators that integrate high mechanical frequency, high mechanical quality, and high optical quality into a single device. The radial-breathing mechanical mode has a mechanical frequency up to 1.69 GHz with a mechanical Q around 5500 in atmosphere, which corresponds to a fm · Qm product as high as 9.47 × 1012 Hz. The strong optomechanical coupling allows us to efficiently excite and probe the coherent mechanical oscillation by optical waves. The demonstrated devices, in combination with the superior thermal property, chemical inertness, and defect characteristics of SiC, show great potential for applications in metrology, sensing, and quantum photonics, particularly in harsh environments that are challenging for other device platforms.

In this letter, we demonstrate the first SiC optomechanical microresonators that exhibit significant optomechanical coupling with a coefficient up to |g om |/2π ≈ (61 ± 8) GHz/nm, which enables us to efficiently actuate and characterize the mesoscopic mechanical motions by optical means. By optimizing the device structure and the fabrication process, we are able to achieve high optical quality, large mechanical frequency, and high mechanical quality simultaneously in a single device. The whispering-gallery modes exhibit high optical qualities around ~3.8 × 10 4 . The radial-breathing mechanical modes show frequencies up to 1.69 GHz and mechanical qualities around 5500. The corresponding f m ⋅ Q m product is 9.47 × 10 12 , which is the highest value for the fundamental bulk acoustic mode in SiC demonstrated to date [36][37][38][39][40][41][42][43][44][45][46][47] , to the best of our knowledge.
The high performance of the demonstrated optomechanical microresonators shows that SiC devices are now ready for broad optomechanical applications. With the superior thermal and chemical properties of SiC material 15 , SiC optomechanical devices are particularly attractive for optomechanical sensing, such as displacement, force, mass, and inertial sensing, especially in harsh environments that are challenging for other device platforms. On the other hand, the SiC optomechanical microresonators, in combination with SiC's significant optical nonlinearities 26,28 and unique defect characteristics 31,32 , are of great promise for realizing hybrid micro/nanophotonic circuits for nano-optomechanics, integrated nonlinear photonics, and quantum photonics.

Results
Optomechanical device. The devices we employed are cubic-type (3C) silicon carbide (SiC) microresonators sitting on silicon pedestals. The device fabrication process is described in Methods. Figure 1(a) shows the fabricated devices of different radii with smooth sidewalls and fine-controlled undercuts. The fabrication process is optimized to produce smooth sidewalls, which are critical for minimizing the scattering loss of the optical modes. The device undercuts are optimized to reduce the clamping loss, which improves the mechanical qualities of the radial-breathing modes.
The microresonator exhibits whispering-gallery optical modes (Fig. 1b) that produce radiation pressure along the radial direction to actuate the fundamental radial-breathing mechanical modes (Fig. 1c), which in turn changes the cavity length and thus shifts the optical resonance frequency. The resulting dynamic backaction between the optical field and mechanical motion can be used to excite and probe the coherent mechanical motion, with efficiency dependent on the optomechanical coupling strength. Optical Q characterization. The optical properties of devices are tested by a fiber-device coupling setup shown in Fig. 2. A tunable laser is launched into the devices by evanescent coupling through a tapered optical fiber. The cavity transmission is coupled out by the same tapered fiber and then recorded by fast detectors. The laser wavelength is calibrated by a Mach-Zehnder interferometer. A typical cavity transmission trace is shown in Fig. 3(a) with multiple high-Q optical modes. Three optical modes from different mode families all show optical qualities around 3.8 × 10 4 ( Fig. 3(b)). The coupling conditions of these modes can be easily tuned from under coupled, critical coupled to over coupled by tuning the fiber-device distance. For example, the cavity modes located around 1528 nm and 1553 nm are nearly critically coupled in this case.
Optomechanical excitation and sensing. The high optical quality of the whispering gallery modes, combined with the strong optomechanical coupling, enables efficient excitation and probing of the mechanical motion. To do so, we launch an optical wave (the pump wave) into a cavity resonance, with power sinusoidally modulated at a frequency around the mechanical resonance frequency. The operation principle is illustrated in Fig. 2(b). A sinusoidal modulation of the optical power leads to a sinusoidally time varying radiation pressure that actuates the radial-breathing mechanical motion coherently via the strong optomechanical coupling. To probe such optomechanical excitation, we launch a weak continuous-wave optical wave (the probe wave) at a different cavity resonance. The coherent optomechanical excitation modulates the probe field inside the cavity via the optomechanical coupling, which is in turn transduced to the cavity output. Figure 2(a) shows schematically the experiment testing setup, with more detailed information given in the Methods. The devices are tested at room temperature in the atmospheric environment.
A detailed analysis of the optomechanical dynamics shows that the modulated probe power, δP s (Ω ), at the modulation frequency Ω , detected at the cavity transmission is given by   ficient of SiC, respectively. ω 0s is the resonance frequency of the probe mode and V eff represents the effective volume of the optical mode. Our devices fall into the sideband unresolved regime, where the mechanical frequency is much smaller than the optical linewidth 6 . In this regime, Eq. (1) can be simplified to where δP d (Ω ) stands for the modulated pump power dropped inside the cavity. Γ 0p is the intrinsic photon decay rate of the pump mode. Γ 0s and Γ ts represent intrinsic and total photon decay rate of the probe mode, respectively. Γ es represents its external coupling rate. Δ s = ω s − ω 0s is the laser-cavity detuning of the probe wave.
In the experiments, the optical mode is typically near critical-coupling conditions, Γ 0s = Γ es , and the laser detuning for the probe mode is set around the half of total cavity linewidth Δ s ~ Γ ts /2. As a result, Eq. 2 reduces considerably to Equation (3) clearly shows the linear dependence of the transduced probe signal on the optical qualities of the pump and probe modes. Moveover, it depends quadratically on the optomechanical coupling coefficient g om since the optomechanical effect not only drives the mechanical mode by the modulated pump beam, but also transduces the mechanical motion to the probe beam. Consequently, significant optomechanical coupling and high optical quality in the devices would lead to efficient optomechanical excitation and transduction by the pump and probe waves. Equations (1)- (3) show that, by scanning the modulation frequency, we can obtain the mechanical response of the radial-breathing mode. Figure 4 frequencies in these devices but all with a mechanical Q above 5000. The slight spectral asymmetry on the mechanical spectra is primarily due to the Fano-type interference between the narrow-band mechanical response and the broadband background of optical Kerr nonlinear response (see Eq. (2)). A comparison of the recorded optomechanical spectra with the theory infers an optomechanical coupling coefficient of |g om |/(2π) = (61 ± 8) GHz/nm for the 2 μm device. This is smaller than the FEM simulated value (89 GHz/nm), which accounts for the radiation pressure of the shifting dielectric boundary. The discrepancy is likely from the electrostrictive contribution in the dielectric material 48 . We also characterize the devices with different radii to map out the dependence of mechanical frequency. As shown in Fig. 4(a), the mechanical frequency of the radial-breathing mode scales inversely with the device radius.
Comparing the experimental data (blue dots) with the theoretical prediction (red curve), we infer the Young's modulus to be 390 GPa, which is consistent with previous measurements of 3C-SiC epitaxial films on silicon substrates 49 . One critical figure of merit for mechanical resonators is the f m ⋅ Q m product, which quantifies the degree of decoupling of mechanical motion from the environmental thermal reservoir 6 . Figure 5 summarizes the f m ⋅ Q m product reported to date for SiC micro/nanomechanical resonators [36][37][38][39][40][41][42][43][44][45][46][47][50][51][52][53] . In general, bridge-and cantilever-type SiC micro/nanomechanical resonators exhibit low f m ⋅ Q m products, with a mechanical damping dominated by the mechanical clamping loss. To mitigate the clamping loss, high-order overtone-bulk-acoustic-resonator (OBAR) modes are employed to store mechanical energy over many mechanical wavelengths [50][51][52][53] , which, however, requires a large device size significantly greater than the mechanical wavelength that seriously limits the device miniaturization and integration.
In contrast, our optomechanical resonators operate in the fundamental radial-breathing acoustic mode, with a small device size comparable to the mechanical wavelength. For example, the device with a radius of 2 μm exhibits a frequency of 1.69 GHz and a mechanical Q of 5589 ( Fig. 4(b)), which corresponds to a f m ⋅ Q m product of 9.47 × 10 12 Hz. This product is among the largest values reported up to date of SiC devices [36][37][38][39][40][41][42][43][44][45][46][47][50][51][52][53] , as shown in Fig. 5. In fact, our device has the largest f m ⋅ Q m product among whispering-gallery-type optomechanical microresonators made from various materials 7,10,11,13,14,54,55 , as shown in Table 1. This value is still about an order of magnitude lower than the theoretical f m ⋅ Q m product [33][34][35] , implying that the current limitation is not on intrinsic mechanical loss of SiC material, but on practical factors such as device etching, pillar clamping, and air damping. We thus expect improvement of the f m ⋅ Q m product in the future after further optimization of the device structure and fabrication process. Table 1 also shows that current SiC devices have lower optical qualities than the state-of-the-art optomechanical devices in other materials. We are currently optimizing the fabrication process to improve the optical quality of SiC for practical optomechanical applications.

Discussions
We have demonstrated the first SiC optomechanical resonators in 3C-SiC microdisks that exhibit strong optomechanical coupling and excellent mechanical qualities, with a f m ⋅ Q m product as high as 9.47 × 10 12 Hz. The high performance of the demonstrated devices infers that the SiC optomechanical devices are of great potential for metrology and sensing applications, particularly in detecting displacement, force, mass, and acceleration/rotation with high sensitivity. In combination with SiC's superior thermal property, chemical inertness, hand high breakdown voltage, SiC optomechanical devices are of great promise for applications in various harsh environments, such as those with high temperature, reactive chemicals, biological fluid, or high electric field 15,16,42,[56][57][58] , that are challenging for other device platforms.
On the other hand, the SiC optomechanical microresonators exhibit a mechanical frequency scalable by the device radius. In particular, the SiC microdisk with a radius of 2.5 μm exhibits a mechanical frequency of 1.33 GHz (see Fig. 4), which matches the zero-field splitting of spin ground states of the point defects in 3C-SiC 31,32 . Therefore, the high-Q collective mechanical mode is potentially able to coherently interact with the ground states of the defect spin via stress-induced coupling. This mechanism, in combination with the photon-spin coupling in SiC 24,25 and photon-photon interaction via SiC's significant χ (2) and χ (3) nonlinearities 26,28 , is of great potential to form a hybrid micro-/nano-photonic circuit that mutually couples photon, defect spin, and acoustic phonon for nonlinear optical, quantum optical, and optomechanical functionalities.

Methods
Device fabrication. The device structure we employed is cubic-polytype silicon carbide (3C-SiC) microdisks sitting on silicon pedestals. A high-definition electron-beam resist (ZEP520A) is used to pattern Chromium (Cr) mask with chlorine-based plasma by reactive-ion etching (RIE). The Cr mask is later used as a hard mask to etch SiC with fluorine-based plasma by inductively coupled-plasma RIE. The residue of Cr is then released by CR-14, a Cr etchant, and the silicon substrate is undercut by potassium hydroxide. The device is annealed afterwards at 1100 °C for 2 hours. Figure 1 shows the fabricated devices of different radii with smooth sidewalls and fine-controlled undercuts. More fabrication details can be found in ref. 25. Pump-probe setup. The experimental setup is shown in detail in Fig. 2(a). An intensive laser wave is sinusoidally modulated in amplitudes by a lithium niobate modulator. The frequency of modulation is scanned by a network analyzer. The pump laser is attenuated by a variable optical attenuator (VOA) to ~80 μW. The probe laser is kept 10 dB smaller than the pump beam by another VOA. The thermal effect is negligible for the operating powers in the devices. The polarization controllers are used to change the polarizations of the laser beams to the employed cavity modes. A coarse-wavelength-division-multiplexing (CWDM) multiplexer is used to combine the pump and probe beams and launch them into the cavity. The modulated pump beam drives the mechanical mode, with the mechanical displacement transduced to the jittering of the cavity resonance frequencies. The pump and probe beam are then separated by the CWDM demultiplexer. Detector 1, with 90% transmission of probe beam, is collected by the network analyzer. The network analyzer scans the modulation frequencies and detects the signal at the same frequencies simultaneously. Detectors 2 and 3 are used for locking laser cavities to probe and pump modes, respectively. The optical modes we employed in the experiments are high order modes, which can be easily critically coupled by the current tapered fiber. The optomechanical coupling can be improved by accessing the fundamental modes through thinner tapered fiber or waveguide coupling.