Chemically etched ultrahigh-Q wedge-resonator on a silicon chip

Ultrahigh-Q optical resonators are being studied across a wide range of fields, including quantum information, nonlinear optics, cavity optomechanics and telecommunications1,2,3,4,5,6,7. Here, we demonstrate a new resonator with a record Q-factor of 875 million for on-chip devices. The fabrication of our device avoids the requirement for a specialized processing step, which in microtoroid resonators8 has made it difficult to control their size and achieve millimetre- and centimetre-scale diameters. Attaining these sizes is important in applications such as microcombs and potentially also in rotation sensing. As an application of size control, stimulated Brillouin lasers incorporating our device are demonstrated. The resonators not only set a new benchmark for the Q-factor on a chip, but also provide, for the first time, full compatibility of this important device class with conventional semiconductor processing. This feature will greatly expand the range of possible ‘system on a chip’ functions enabled by ultrahigh-Q devices. Using only conventional semiconductor processing on a silicon wafer, researchers successfully fabricate an on-chip resonator with a record Q-factor of 875 million — around 20 times higher than previous results. They also demonstrate stimulated Brillouin lasers as an example application to emphasize the size control feature of the fabrication method and the ultrahigh-Q available from these resonators.

Ultrahigh-Q optical resonators are being studied across a wide range of fields, including quantum information, nonlinear optics, cavity optomechanics and telecommunications [1][2][3][4][5][6][7] . Here, we demonstrate a new resonator with a record Q-factor of 875 million for on-chip devices. The fabrication of our device avoids the requirement for a specialized processing step, which in microtoroid resonators 8 has made it difficult to control their size and achieve millimetre-and centimetre-scale diameters. Attaining these sizes is important in applications such as microcombs and potentially also in rotation sensing. As an application of size control, stimulated Brillouin lasers incorporating our device are demonstrated. The resonators not only set a new benchmark for the Q-factor on a chip, but also provide, for the first time, full compatibility of this important device class with conventional semiconductor processing. This feature will greatly expand the range of possible 'system on a chip' functions enabled by ultrahigh-Q devices.
Achieving a long photon storage time (high Q-factor) in microcavities relies critically on the use of low-absorption dielectrics and the creation of very smooth (low-scattering) dielectric interfaces. Although crystalline resonators currently provide the highest Q-factors [9][10][11] , in chip-compatible devices silica has by far the lowest intrinsic material loss. Microtoroid resonators combine this low material loss with a reflow technique in which surface tension is used to smooth lithographic and etch-related blemishes 8 . However, reflow smoothing makes it very challenging to fabricate larger-diameter ultrahigh-Q (UHQ) resonators or to leverage the full range of integration tools and devices available on silicon. The devices reported here attain UHQ performance using only conventional semiconductor processing methods on a silicon wafer. Moreover, the best Q performance occurs for diameters greater than 500 mm, a size range that is difficult to access with microtoroids because of the limitations of the reflow process. Microcombs will benefit from a combination of UHQ and largerdiameter resonators (microwave-rate free spectral range, FSR) to create combs that are efficient in turn-on power and can be selfreferenced 6 . Two further applications that can benefit from larger (1-50 mm diameter) UHQ resonators are integrated reference cavities and ring gyroscopes.
We also demonstrate excellent control of the FSR, opening the possibility of precision repetition rate control in microcombs or precision control of the FSR. The latter is important in stimulated Brillouin lasers (SBLs), which have been demonstrated recently in UHQ silica microspheres, in calcium fluoride resonators 12,13 and in rib-waveguide Fabry-Perot resonators 14 . As an application of this control, SBLs are demonstrated here using these new resonators. The devices feature very low threshold turn-on power, milliwattscale output power and very high coherence.
Earlier work investigated the Q-factor in a wedge-shaped resonator fabricated from silica on a silicon wafer, and Q-factors as high as 50 million were obtained 15 . That approach isolated the mode from the lithographic blemishes near the outer rim of the resonator by using a shallow wedge angle. In the current work, we boost the optical Q by a factor of 20 beyond these earlier results through a combination of process improvements. Although the present devices resemble the earlier geometry 15 , they derive their UHQ performance from changes to the etch process and oxide growth and not from the physical principle at work in the earlier structures, namely a shallow wedge angle to provide roughness isolation. Indeed, and in contrast to that earlier work, larger wedge angles are now desirable.
A top-view optical micrograph is provided in Fig. 1 to illustrate the basic geometry. The process flow begins with thermal oxide on silicon, followed by lithography and oxide etching with buffered hydrofluoric acid. Figure 1b (inset) presents scanning electron micrographs of devices with 128 and 278 wedge angles. Empirically, this angle can be controlled by adjustment of the photoresist adhesion using commercially available adhesion promoters. The oxide disk structures function as an etch mask for an isotropic dry etch of the silicon using XeF 2 . During this dry etch, the silicon undercut is set to reduce coupling of the optical mode to the silicon support pillar. This value is typically set to 100 mm for 1-mm-diameter structures and over 150 mm for 7.5-mm-diameter disks; however, smaller undercuts are possible while still preserving UHQ performance. Further information on processing is provided in the Methods.
To measure the intrinsic Q-factor, devices were coupled to SMF-28 optical fibre using a fibre taper 16,17 , and spectral lineshape data were obtained by tuning an external cavity semiconductor laser across the resonance while monitoring transmission on an oscilloscope. The taper coupling could be adjusted to both overcouple and undercouple the resonator 17 . All measurements were performed in the 1,500 nm band. To accurately calibrate the laser scan in this measurement, a portion of the laser output was also monitored after transmission through a calibrated Mach-Zehnder interferometer with an FSR of 7.75 MHz. Figure 2 (inset) presents a spectral scan obtained on a device with a record Q-factor of 875 million. In these measurements, the taper coupling was applied on the upper surface of the resonator near the centre of the wedge region (Fig. 1b). Modelling shows that the fundamental mode has its largest field amplitude in this region. Moreover, this mode is expected to feature the lowest overall scattering loss resulting from the three dielectric-air interfaces as well as from the silicon support pillar. An additional test that can be performed to verify the fundamental mode is to measure the mode index by monitoring the FSR. The fundamental mode features the largest mode index and hence smallest FSR. To expedite the measurement of the Q-factor in these devices, an automated system was devised in which a broad spectral scan (exceeding a full FSR) was performed and recorded onto a fast digital oscilloscope (1 GHz). The spectrum was then analysed using a fitting algorithm to identify and fit the resonator modes. This made a rapid acquisition (and identification) of the highest Q The typical coupled power in all measurements was maintained at 1 mW to minimize thermal effects. However, there was little or no evidence of thermal effects in the optical spectrum (up to coupled power levels as high as 1 mW). Typically, these appear as an asymmetry in the lineshape and also a scan-direction-dependent (to higher or lower frequency) spectral linewidth. As a further check that thermal effects were negligible, ring-down measurements 18 were also performed on a range of devices for comparison with the spectral-based Q measurement. For these, the laser was tuned into resonance with the cavity and a lithium niobate modulator was used to abruptly switch off the input. The output cavity decay rate was then monitored to ascertain the cavity lifetime. Ringdown data and spectral linewidths were consistently in good agreement. This insensitivity to thermal effects is a result of the larger mode volumes of these devices in comparison to the microtoroids used in earlier work (for which thermal effects must be carefully monitored). The mode volumes in the present devices are typically 100-1,000 times larger.
Measurements showing the effects of oxide thickness and device diameter on Q-factor are presented in Fig. 2. Four oxide thicknesses are shown (2, 4, 7.5 and 10 mm) over diameters ranging from 0.2 mm to 7.5 mm. All data points, with the exception of the red points, correspond to a wedge angle of 108. The uppermost (highest Q at a given diameter) data correspond to a wedge angle of 278. It is interesting to note that there was a high level of consistency in the Q-values measured on devices from a single chip. A complete data set for the red curve in Fig. 2 is provided in the caption to Fig. 2 to indicate the low dispersion in the Q data. The solid curves are a model of optical loss caused by surface scattering on the upper, wedge, and lower oxide-air interfaces and by bulk-oxide loss. In the model, surface roughness was measured independently on each of these surfaces using an atomic force microscope (AFM) (r.m.s. roughness values and additional information on the model are given in the Methods). Data corresponding to the 108 wedge angle show that Q increases for thicker oxides and also larger diameters. Using the model, this trend can be understood to result from loss caused primarily by scattering at the oxide-air interfaces. Specifically, both thicker oxides and larger-diameter Blue circles indicate the approximate locations of the taper during measurements. c, Calculated fundamental-mode intensity profiles in resonators with 108 and 308 wedge angles at two wavelengths. As a guide, the centre-of-motion of the mode is provided to illustrate how the wedge profile introduces a normal dispersion that is larger for smaller wedge angles.  show the Q-factor predicted by a model that accounts for surfaceroughness-induced scattering loss and also material loss (fitting gives a material Q of 2.5 billion). The r.m.s. roughness is measured using an atomic force microscope (see Methods for values). Red data points correspond to a wedge angle of 278. All other data are obtained using a wedge angle of 108. Inset: spectral scan for the case of a record Q-factor of 875 million. In this spectrum, the resonator is undercoupled so that the linewidth is close to the intrinsic value. However, both critical coupling and strong overcoupling are also possible by adjusting the air gap between the taper and the resonator. The sinusoidal curve accompanying the spectrum is a calibration scan performed using a fibre interferometer.
structures feature a reduced field amplitude at the dielectric-air interface, leading to reduced scattered power. An overall boost to the Q-factor is possible by increasing the wedge angle. In this case, the mode experiences reduced upper and lower surface scattering compared to the smaller angle case. As noted before, this behaviour contrasts with earlier work in which the wedge was used to isolate the mode from edge roughness 15 . Specifically, the larger angle case in Fig. 1b leads to higher Q-values, and a record Q-factor of 875 million for any chip-based resonator is obtained under these conditions. In general, there is reasonably good agreement between the model and the data, except in the case of the thinner oxides. For these thinner structures, there is a tendency for stress-induced buckling to occur at larger radii. This is believed to create the discrepancy with the model. The trend of improving Q with increasing wedge angle that is apparent in Fig. 2 is also confirmed by the model (Supplementary Section I).
The ability to lithographically define UHQ resonators rather than rely on the reflow process enables a multi-order-of-magnitude improvement in the control of resonator diameter and FSR. This feature is especially important in microcombs and certain nonlinear sources 12,13 . As a preliminary test of the practical limits of FSR control, two studies were conducted. In the first, a series of resonator diameters were set in a CAD file that was to be used to create a photomask. A plot of the measured FSR (fundamental mode) versus CAD file target diameter is provided in Fig. 3. The variance from ideal linear behaviour measured on five devices from different locations on the same four-inch wafer is 2.4 MHz, giving a relative variance of better than 1:4,500 (FSR ≈ 11 GHz). The inset to Fig. 3 shows that for a second set of four devices from different locations on a separate wafer, but having the same target diameter, the variance is further improved to a value of 0.45 MHz or 1:20,000. More data runs will be accumulated over time to provide better statistics, but these preliminary findings are nonetheless very encouraging. There is an overall size reduction that occurs between the mask and final etch diameter of 10 mm (10 mm oxide). However, the above data suggest that this size reduction can be accurately calibrated.
As an application of the combination of size control and ultrahigh Q-value available using these new resonators, we then demonstrated SBLs. Although Brillouin scattering is well known in optical fibre communication, including its use for gain in narrow-linewidth fibre lasers 19 , generation of slow light 20,21 and information storage 22 , the realization of microcavity-based SBLs is very challenging because of the requirement to precisely match the Brillouin shift to a pair of cavity modes. Specifically, the narrow linewidth of the Brillouin gain requires better than 1:1,000 control of the resonator diameter to obtain a match, and more realistically it requires 1:10,000 control for consistent low threshold turn-on power.
To test the resonators as SBLs, pump power was coupled into the resonator through the fibre taper coupler. SBL emission was coupled into the opposing direction and routed via a circulator into a photodiode and optical spectrum analyser to monitor both the laser output power and the spectrum. The transmitted pump wave was monitored using a balanced homodyne receiver so as to implement a Hänsch-Couillaud locking of the pump to the resonator 23,24 . The threshold for SBL action is given by the expression where n is the refractive index, V eff is the mode volume, l p (l b ) is the pump (lasting) wavelength, and Q p (Q b ) is the loaded Q-factor of the pump (lasting) mode. Beyond the importance of the high cavity Qfactor evident in this expression, it is essential to maintain a large SBL gain parameter, g b (Dv -V B ) (where gain ¼ g b P pump , Dv is the FSR and V B is the Brillouin shift). Because the gain spectrum is relatively narrow (typical full-width at half-maximum of 20-60 MHz; refs 19,25), this requires a precise match of the FSR to the Brillouin shift. V B depends on the pump wavelength l p and phonon velocity V a through the relation V B /2p ¼ 2nV a l p . An illustration of the control possible using the new resonator geometry is provided in Fig. 4a, in which four devices with diameters of 6,020, 6,044, 6,062 and 6,080 mm (lithography mask size) were tested at a series of pump wavelengths in the 1,500 nm band. In each device, the pump wavelength was sequentially tuned along resonances belonging to the same azimuthal mode family. The minimum threshold for each device corresponds to excitation at the Brillouin gain maximum (that is, g b (Dv -V B ¼ 0)). The rise in threshold away from the minimum (for a given resonator diameter) reflects tuning of the Brillouin shift frequency with pump wavelength as noted above. A typical spectrum showing the emitted laser line and the pump are given in Fig. 4c. As an indication of the consistency in size and Q that is possible, all devices tested lased with minimum threshold values below 200 mW. Moreover, because of the narrow Brillouin gain bandwidth, the side mode suppression at 1 mW output power was in excess of 60 dB (measured by mixing the pump and laser waves on a photodetector and monitoring the electrical power in the beat note). The coherence properties of these Brillouin lasers are excellent and are studied in Supplementary Section II (for example, they feature subhertz Schawlow-Townes linewidths).
The Q-factor for these new resonators is not only higher in an absolute sense than what has been possible with microtoroids, but it also accesses an important regime of resonator FSR that has not been possible using microtoroids. To date, the smallest FSR achieved with the toroid reflow process is 86 GHz (D ¼ 750 mm) and the corresponding Q factor is 20 million 26 . The present structures achieve their best Q-factors for FSRs that are complementary to microtoroids (FSRs less than 100 GHz). As well as the application to SBLs described, this range has become increasingly important in applications such as microcombs where self-referencing is important. Specifically, low turn-on power and microwave-rate repetition are conflicting requirements in these devices because of the inverse 11.00 8  dependence of threshold power on FSR. However, such increases can be compensated using ultrahigh Q-values because turn-on power depends inverse-quadratically on Q (ref. 27). The wedge angle can be shown to provide control over the zero dispersion point in spectral regions where silica exhibits anomalous dispersion. Specifically, beyond 1.3 mm, silica features anomalous dispersion; however, the wedge structure introduces a geometrical component of dispersion that is normal (Fig. 1c). Calculations show that the overall zero dispersion falls within the 1.5 mm band for the structures tested here. UHQ performance in large-area resonators is also important in rotation sensing 28 and for on-chip frequency references 29,30 . In the former case, the larger resonator area enhances the Sagnac effect. In the latter, the larger mode volume lowers the impact of thermal fluctuations on the frequency noise of the resonator 31 . There may also be potential applications of these structures to cavity optomechanics 2,3 , where the ability to define the whispering gallery and a mechanical support in one lithographic step could provide an improved method to both boost optical Q while controlling mechanical eigenmodes and their damping. For example, spoke structures have been implemented in toroids to minimize clamping losses 32 . By applying the methods described here, structures like these could be implemented in the same step used to define the whispering gallery.
Although not demonstrated here, there are several ways to incorporate waveguides into these devices. For example, wafer bonding has recently been used to apply a thermal oxide structure to a second wafer containing a nitride resonator with Q-factors in  the range of 20 million 33 . We are studying an adaptation of this approach to create a nitride-waveguide-coupled UHQ resonator. Such a device does not currently exist and would have a major impact on the many applications of UHQ devices. Key to this approach would be achieving precise resonator size control, which would make it possible for lithographically defined fiducial locators to register mating parts. Finally, it is important to note that an upper bound to the material loss of thermal silica has been established in this work. The value of 2.5 billion for material Q bodes well for further application of thermal silica to photonic devices. Also, while the ability to leverage thermal silica on silicon in this way is important, the techniques reported here could equally well be applied to high-quality silica deposited onto other substrates.

Methods
Disks were fabricated on (100) prime-grade float-zone silicon wafers. Photoresist was patterned using a GCA 6300 stepper on thermally grown oxide with a thickness in the range 2-10 mm. A post-exposure bake was then used to cure the surface roughness of the photoresist pattern, which acted as an etch mask during immersion in buffered hydrofluoric solution (Transene, buffer-HF improved). Careful examination of the wet etch revealed that the vertex formed by the lower oxide surface and upper surface contained an etch front distinct from that associated with the upper surface (see 'foot' region in Fig. 5, left inset). This region has a roughness level that is higher than any other surface and is a significant contributor to Q degradation. By extending the etch time beyond what is necessary to reach the silicon substrate, this foot region can be eliminated, as shown in Fig. 5 (main panel). With elimination of the foot etch front, the isotropic and uniform etching characteristic of buffered hydrofluoric solution results in oxide disks and waveguides with very smooth wedge-profiles, which enhance the Q-factors. Additionally, the oxide used in these studies was prepared in such a way as to reduce optical loss. Although the oxide layers were prepared using wet oxidation, it was found that a final dry oxidation step (24 h) at 1,000 8C was required to reliably achieve the highest Q factors. This additional step is believed to drive down the water content in the silica oxide. After a conventional cleaning process to remove photoresist and organics, silicon was isotropically etched by xenon difluoride to create an air-cladding whispering-gallery resonator. An atomic force microscope was used to measure the surface roughness of the three silica-air dielectric surfaces. For the lower surface, the resonators were detached by first etching the silicon pillar to a few micrometres in diameter and then removing the resonator using tape. The r.m.s. roughness values on 108 wedge-angle devices were 0.15 nm (upper), 0.46 nm (wedge) and 0.70 nm (lower); for the 278 wedge-angle devices these values were 0.15 nm (upper), 0.75 nm (wedge) and 0.70 nm (lower). The morphology of the lower surface is complex and the roughness is an estimate. The correlation length is on the order of a few hundred nanometres. The difference in the wedge surface roughness obtained for the large and small wedge angle cases is not presently understood. By conducting Q versus resonator diameter studies, we conclude that scattering losses are the dominant source of loss in these resonators (Fig. 2). To estimate these losses, we adapted a general approach reported elsewhere [34][35][36] .