Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold

XINGCHEN JI, FELIPPE A. S. BARBOSA, SAMANTHA P. ROBERTS, AVIK DUTT, JAIME CARDENAS, YOSHITOMO OKAWACHI, ALEX BRYANT, ALEXANDER L. GAETA, AND MICHAL LIPSON* School of Electrical and Computer Engineering, Cornell University, Ithaca, New York 14853, USA Department of Electrical Engineering, Columbia University, New York, New York 10027, USA Current address: Instituto de Física, Universidade Estadual de Campinas, 13083-970 Campinas, SP, Brazil Current address: The Institute of Optics, University of Rochester, Rochester, New York 14627, USA Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA *Corresponding author: ml3745@columbia.edu


INTRODUCTION
Low-propagation-loss silicon nitride (Si 3 N 4 ) ring resonators are critical for a variety of photonic applications such as low-threshold frequency combs [1][2][3][4][5], optical clocks [6], and high-precision sensing [7][8][9][10].High confinement is critical for tailoring the waveguide dispersion to achieve phase matching in nonlinear processes as well as for tighter bends in large-scale photonic systems.A microresonator's quality factor (Q) is extremely sensitive to losses.To date, ultrahigh Qs have been demonstrated only in discrete resonators based on platforms such as polished calcium fluoride (CaF 2 ) and magnesium fluoride (MgF 2 ) or silica microresonators [11][12][13][14][15][16][17] with typical cross-sectional mode field diameters much larger than the wavelength.Spencer et al. have recently demonstrated ring resonators with a high Q of up to 80 million using extremely thin (40 nm) Si 3 N 4 films [18], which can be useful for narrowband filtering or building reference cavities for laser stabilization.However, they suffer from highly delocalized optical modes and millimeter-scale bending radii, making it challenging to use these thin-film ring resonators for compact photonic routing or nonlinear applications requiring dispersion engineering.High confinement combined with low propagation loss is the key for efficient nonlinear optical processes.The highest intrinsic Q in high-confinement Si 3 N 4 ring resonators reported to date is 17 million [19].However, as Xuan et al. mention in their conclusion, a fabrication process that can predictably achieve an intrinsic Q larger than 10 million has not been achieved [19].

EFFECTS OF SURFACE ROUGHNESS ON HIGH-CONFINEMENT WAVEGUIDES
In this work, we show that surface roughness, rather than absorption from the bulk material, plays a major role in the loss limitations of Si 3 N 4 , thereby enabling a path for achieving ultra-low-loss devices by addressing the surface quality.Absorption loss is mainly due to O-H bonds in SiO 2 , and N-H and Si-H bonds in Si 3 N 4 [20].Scattering loss comes primarily from the interaction of light with the roughness of all the surfaces in a high-confinement waveguide.Mode simulations show that light propagating in the waveguide significantly interacts and scatters from both the patterned sidewalls and the top and bottom surfaces [see Fig. 1(c)].Several groups have been working on reducing losses by improving the properties of the bulk material to achieve high Q [21][22][23].However, to date, it has not been clear whether surface interactions or material absorption is the main source of the high loss in the integrated platform.

A. Sidewall Roughness Reduction
In order to reduce surface scattering from the sidewalls, we minimize the roughness introduced during the pattern transfer step of the processing by eliminating in situ polymer formation typical in the dry etching processes.Standard waveguide fabrication methods consist of patterning a masking layer, typically a photoresist or an electron-beam resist, and transferring this pattern into the photonic waveguide device layer using some form of plasma etching.Polymer formation is a common by-product of plasma etching [24,25].In situ polymer deposition passivates the sidewalls and enables anisotropic etching, with vertical sidewalls desirable for fabrication of rectangular waveguides [26,27].It also enables pattern transfer to thick waveguide device layers by enhancing the selectivity between the mask layer and the films.The polymer formed during this process, while critical for surface passivation and anisotropic etching, often leaves residue on the sidewalls, which introduces sidewall roughness.This roughness adds to the roughness introduced by the lithography itself [28,29].Since the roughness is generally of the order of nanometers, it usually introduces negligible loss; however, it becomes significant in the high-Q regimes that we are aiming for here [20,30].Trifluoromethane (CHF 3 ) and oxygen (O 2 ) gases are widely used as standard etchants in Si 3 N 4 fabrication, and this etching chemistry is always accompanied by a polymer residue left on the sidewalls [31,32].In order to reduce this polymer residue on sidewalls, we used a higher oxygen flow to remove in situ polymer formation, since oxygen reacts with the polymer residue to form carbon monoxide (CO) and carbon dioxide (CO 2 ).Oxygen also reacts with the photoresist, which is generally used in standard etching as the mask to transfer patterns.As a result, higher oxygen flow decreases the etching selectivity, degrading the ability to transfer patterns.To compensate for this effect, we use a silicon dioxide hard mask instead of a photoresist to maintain the ability to transfer waveguide patterns while eliminating in situ polymer formation on the sidewalls using a higher oxygen flow.Nitrogen is also added to increase the nitride selectivity over oxide [33,34].
In contrast to standard silicon-based waveguides with losses of the order of 1 dB∕cm [35][36][37], where sidewall roughness plays the main role in inducing scattering loss, in ultra-low-loss Si 3 N 4 , top surface roughness also plays a major role.Typically, roughness on the top and/or bottom surfaces has not attracted much attention due to the facts that sidewall roughness was quite significant and many of the previous studies relied on polished wafers or oxidized wafers from silicon photonics.Here we focus on reducing scattering loss from the top surface since the Si 3 N 4 films are deposited using low-pressure chemical vapor deposition, and are not as inherently smooth as polished single-crystal wafers or oxidized wafers.Bottom surface roughness is not addressed here since its roughness, governed by thermal oxidation, is lower than the one governed by Si 3 N 4 deposition.

B. Top Surface Roughness Reduction
In order to reduce scattering from the top surfaces, we reduce the roughness by chemical mechanical polishing (CMP) of the Si 3 N 4 after deposition [as shown in Fig. 2(d)].Atomic-force microscopy (AFM) scans before and after the polishing step are shown in Fig. 2. The root-mean-squared (RMS) roughness has decreased from 0.38 nm to 0.08 nm (AFM scans of different CMP Si 3 N 4 films are shown in Supplement 1).

C. Lithography-Induced Roughness Reduction
To further decrease the loss, we apply multipass lithography to reduce line edge roughness known to contribute to scattering loss [38][39][40].Electron-beam (e-beam) lithography, used extensively for pattering optical waveguides, creates a line edge roughness, which introduces extra roughness to the sidewalls.During e-beam lithography, any instability, such as beam current fluctuations, beam jitter, beam drift, stage position errors, and mechanical vibrations, can generate statistical errors, which result in extra line edge roughness in the patterns, which will add roughness to the sidewalls.The principle of multipass lithography [39,40] consists of exposing the same pattern multiple times at a lower current to reduce line edge roughness by averaging statistical errors.

OPTICAL MEASUREMENTS AND COMPARISONS
We measure an intrinsic Q of 37 6 million in highconfinement Si 3 N 4 ring resonators using the techniques described above.Mode splitting, commonly observed in ultrahigh-Q systems such as whispering-gallery-mode microresonators [41][42][43], is induced due to backscattering of light from fabrication imperfections or surface roughness.When Q is high and the mode is highly confined, extremely small defects or roughness can induce a visible splitting.We measured the transmission of four sets of fabricated ring resonators: (1) using the standard process we reported in Ref. [44] [Fig.3(a)], (2) using our optimized etch process but without CMP and without multipass lithography [Fig.3(b)], (3) using both the optimized etch recipe and CMP but without multipass lithography [Fig.3(c)], and (4) using all the techniques, including the optimized etch recipe, surface smoothing technique, and multipass lithography [Fig.3(d)].All the rings have a radius of 115 μm, height of 730 nm, and width of 2500 nm, and are coupled to a waveguide of the same dimensions.The transmission spectra and linewidth of the resonator [full width at half-maximum (FWHM)] are measured using a laser scanning technique.We launch light from a tunable laser source, which is then transmitted through a fiber polarization controller and coupled into our device via an inverse nanotaper [45] using a lensed fiber.We collect the output of the ring resonator through another inverse nanotaper and an objective lens.We monitor the output on a high-speed InGaAs photodetector.The frequency of the laser is measured using a wavemeter with a precision of 0.1 pm and the laser detuning is calibrated by monitoring the fringes of a reference fiber-based Mach-Zehnder interferometer with a known free spectral range (FSR).
Figure 3 shows the measured transmission spectra of different ring resonators.We measured the ring resonators in the undercoupled regime so that the measured Q is close to their intrinsic Q.
The measured intrinsic Qs, estimated by measuring the transmission [46,47] for rings fabricated using processes (1)-( 4) described above, are 5.6 0.7 million, 16.2 2.9 million, 28 4.7 million, and 37 6 million, which correspond to propagation losses of 5.2 0.6 dB∕m, 1.8 0.3 dB∕m, 1.1 0.2 dB∕m, and 0.8 0.1 dB∕m, respectively [48].Note that these estimated propagation losses are the upper bounds on the losses in straight waveguides since in a ring the optical mode interacts more strongly with the sidewalls due to bending.

SUB-MILLIWATT OPTICAL PARAMETRIC OSCILLATION
In order to illustrate the importance of simultaneous high-Q and high-confinement ring resonators, we demonstrate a strong decrease in the threshold for optical parametric oscillation down to the sub-milliwatt level with decrease of optical losses.To determine the threshold for parametric oscillation, we measured the output power in the first generated four-wave-mixing sideband for different pump powers.Figure 4(a) shows the data for a device pumped at the resonance near 1557 nm with a loaded Q of 35 million.The average threshold power is 330 70 μW, comparable to the theoretically estimated threshold power of 206 μW using the expression [49,50] where λ is the pump wavelength, n is the linear refractive index, n 2 is the nonlinear refractive index (n 2 2.4 × 10 −19 m 2 ∕W) [51], V is the resonator mode volume, and Q c and Q L are, respectively, the coupling and loaded quality factors of the resonators.This, to the best of our knowledge, is the lowest and the first sub-milliwatt power threshold parametric oscillation reported in planar nonlinear platforms [5,19,[52][53][54] (Comparisons are shown in Supplement 1).In addition, this threshold power is close to the lowest threshold reported in ultrahigh-Q microresonators such as CaF 2 [55] and silica microtoroids [1].We also measure and plot the thresholds for rings with various loaded quality factors in Fig. 4(b).The threshold powers follow the theoretically predicted trend of being inversely proportional to Q 2 L .

FUNDAMENTAL LOSS LIMIT EXTRACTION
In order to extract the fundamental limit of achievable loss in silicon nitride waveguides, we compare the losses of two different structures, which have different mode interactions with the sidewalls.We estimate the bulk absorption limitation in our Si (2) η 1 , η 2 , and η 3 are factors that account for the interaction of the field with the waveguide core, the top and bottom surfaces, and the sidewalls, respectively, for the wider waveguides relative to the narrower waveguide [59] and are calculated using Finite element method simulations (performed with COMSOL) to be 1.010, 1.002, and 0.138, respectively.In our simulation, we have taken different bending radii into account.α top_scatter ∼ 0.007 dB∕m (0.001 dB∕m) and α bottom_scatter ∼ 0.24 dB∕m (0.02 dB∕m) are, respectively, the losses due to scattering at the top and bottom interfaces estimated from the Payne-Lacey model [60], which relates scattering loss to the surface's RMS (σ) roughness and correlation length (L c ), which are both extracted from the AFM measurements (AFM scans of the bottom SiO 2 film are shown in Supplement 1).The scattering losses due to the sidewalls, α sidewalls_scatter , and the bulk loss are then extracted to be 0.41 0.05 dB∕m and 0.13 0.05 dB∕m, respectively.Note that we are assuming here that both sidewalls have the same loss as they experience the same e-beam lithography and plasma etching conditions, and the loss in the oxide cladding is negligible when compared with the loss in the Si 3 N 4 due to the high degree of confinement.

CONCLUSIONS
In conclusion, we drastically and systematically reduced losses in high-confinement resonators by using methods for reducing roughness from waveguide interfaces.Moreover, we demonstrate optical parametric oscillation in an on-chip microresonator, with sub-milliwatt pump powers.We extract the absorption-limited Q of the ring resonator to be at least 170 million, which indicates that we are still limited by the scattering loss, thereby providing a path for achieving ultra-low-loss resonators simply via addressing the scattering loss.From our AFM measurements, one possible path for further decreasing these scattering losses is by addressing the roughness at the bottom cladding-core interface generated by the thermal oxidation process.Our work provides an on-chip platform for devices with performance that could be comparable to the performance achieved in discrete large devices.

Fig. 1 .
Fig. 1.Microscope images and mode simulation of the fabricated devices.(a) Top view optical microscope image of a 115 μm radius ring resonator.(b) Scanning electron microscopy image of a fabricated waveguide with smooth surfaces.(c) Mode simulation of a 730 nm tall and 2500 nm wide waveguide showing the mode is highly confined in the geometry we have chosen.

Fig. 2 .
Fig. 2. AFM measurement of the top surface of Si 3 N 4 .(a) 3D AFM scan of the top surface of Si 3 N 4 before CMP with RMS roughness of 0.38 nm and correlation length of 29 nm.(b) 2D image of the top surface of Si 3 N 4 before CMP and scaled to −1.4 to 1.4 nm with RMS roughness of 0.38 nm and correlation length of 29 nm.(c) 3D image of the top surface of Si 3 N 4 after CMP with RMS roughness of 0.08 nm and correlation length of 8.76 nm.(d) 2D image of the top surface of Si 3 N 4 after CMP and scaled to −1.4 to 1.4 nm with RMS roughness of 0.08 nm and correlation length of 8.76 nm.Note the different scale bars in (a) and (c).

Fig. 3 .Fig. 4 .
Fig.3.Normalized transmission spectra of ring resonators fabricated using different processes.(a) Device fabricated using the standard process reported in Ref.[44] with a measured FWHM of 47 MHz.(b) Device fabricated using the optimized etch process, but without our new surface smoothing technique and multipass lithography with a measured FWHM of 12.8 MHz.(c) Device fabricated using both the optimized etch recipe and surface smoothing techniques, but without multipass lithography with a measured FWHM of 7.6 MHz.(d) Device fabricated using all the techniques including the optimized etch recipe, surface smoothing technique, and multipass lithography with a measured FWHM of 5.6 MHz.

3 N 4
films to be 0.13 0.05 dB∕m, which corresponds to an absorption-loss-limited Q of at least 170 million.We fabricated two devices with waveguide widths of 2.5 μm and 10 μm on the same wafer to ensure that the fabrication processes are identical.Both rings have the same height of 730 nm and they are coupled to a waveguide of the same dimensions (730 nm × 2500 nm).The radius of the 2.5 μm ring is 115 μm and the radius of the 10 μm ring is 369 μm [mode simulations shown in Figs.5(a) and 5(b)].Figures5(c) and 5(d) show, respectively, the measured transmission spectra for the 10 μm wide ring with in TE and TM polarizations.The measured intrinsic Q is 67 7 million for the TE mode and 59 12 million for the TM mode.At these ultrahigh Q s , one is operating near the limits of Q, which can be reliably estimated by scanning a laser across a resonance.Hence, we corroborate these Q measurements by performing a cavity ring-down experiment for the TM mode[56][57][58]15,16].As shown in Fig.5(e), the measured lifetime is 25.6 1.3 ns, which corresponds to an intrinsic Q of 63 3 million, consistent with our measurement of the Q, using a laser scanning technique.We estimate the fundamental loss limit given by the bulk absorption of Si 3 N 4 in our films (α total_absorption ) by comparing the losses for the two structures extracted from the transmission measurements (α ring ∼ 0.79 0.14 dB∕m and α wide_ring ∼ 0.43 0.046 dB∕m) and considering the absorption of the rings with narrower and wider waveguides to, respectively, be α ring α total_absorption α top_scatter α bottom_scatter α sidewalls_scatter ;

Fig. 5 .
Fig. 5. Mode simulation and normalized transmission spectra for ring resonators with different interaction strengths with sidewalls.(a) TE mode profiles of waveguides that are 2.5 μm and 10 μm wide and 730 nm high using Si 3 N 4 with a refractive index of 1.996 as the core material and SiO 2 with a refractive index of 1.446 as the cladding material.(The mode simulations have taken the bending radius into account).(b) Same as (a) but for TM.(c) Measured normalized TE transmission spectra of the ring resonator composed of the 2.5 μm wide waveguide (left) with a measured FWHM of 6.2 MHz and the measured spectra of the ring resonator composed of the 10 μm wide waveguide (right) with a measured FWHM of 3.3 MHz in TE polarization using the optimized fabrication process.(d) TM transmission spectra of the rings with the narrower (left) and the wider (right) waveguides with FWHMs of 6.8 MHz and 5.8 MHz, respectively.(e) Cavity ring-down measurement in TM mode.The measured lifetime extracted from the exponential fit is 25.6 1.3 ns.