High-yield wafer-scale fabrication of ultralow-loss, dispersion-engineeredsilicon nitride photonic circuits

Junqiu Liu,1 Guanhao Huang,1 Rui Ning Wang,1 Jijun He,1 Arslan S.Raja,1 Tianyi Liu,1 Nils J. Engelsen,1 and Tobias J. Kippenberg1, ∗

1Institute of Physics, Swiss Federal Institute of Technology Lausanne (EPFL), CH-1015 Lausanne, Switzerland

Low-loss photonic integrated circuits (PIC)and microresonators have enabled novel appli-cations ranging from narrow-linewidth lasers1,2,microwave photonics3,4, to chip-scale opticalfrequency combs5,6 and quantum frequencyconversion7,8. To translate these results into awidespread technology9, attaining ultralow op-tical losses with established foundry manufac-turing is critical. Recent advances in fabri-cation of integrated Si3N4 photonics10–14 haveshown that ultralow-loss, dispersion-engineeredmicroresonators can be attained at die-levelthroughput. For emerging nonlinear applica-tions such as integrated travelling-wave paramet-ric amplifiers15–18 and mode-locked lasers19, PICsof length scales of up to a meter are required,placing stringent demands on yield and perfor-mance that have not been met with current fabri-cation techniques. Here we overcome these chal-lenges and demonstrate a fabrication technologywhich meets all these requirements on wafer-levelyield, performance and length scale. Photonicmicroresonators with a mean Q factor exceeding30 × 106, corresponding to a linear propagationloss of 1.0 dB/m, are obtained over full 4-inchwafers, as determined from a statistical analysisof tens of thousands of optical resonances and cav-ity ringdown with 19 ns photon storage time. Theprocess operates over large areas with high yield,enabling 1-meter-long spiral waveguides with 2.4dB/m loss in dies of only 5× 5 mm2 size. Using amodulation response measurement self-calibratedvia the Kerr nonlinearity, we reveal that, strik-ingly, the intrinsic absorption-limited Q factorof our Si3N4 microresonators exceeds 109. Thisabsorption loss is sufficiently low such that theKerr nonlinearity dominates the microresonator’smodulation response even in the audio frequencyband. Transferring the present Si3N4 photon-ics technology to standard commercial foundries,and merging it with silicon photonics using het-erogeneous integration technology20–22, will sig-nificantly expand the scope of today’s integratedphotonics and seed new applications.

Silicon photonics23 has evolved into a mature technol-ogy enabling the generation, modulation and detectionof optical signals on-chip, via heterogeneous or hybridintegration of different material platforms20–22. Withinthe past two decades, it has been transferred from aca-

demic research to large-volume commercial deploymentin datacenter interconnects. A second revolution is cur-rently under way in which, the optical nonlinearitiesof PIC - accessed with continuous-wave lasers at sub-milliwatt power - become relevant for applications, i.e.integrated nonlinear photonics. The Kerr, χ(2) or Bril-louin nonlinearities enable novel schemes for nonlinearoptical signal generation and processing3,6,24. Major ef-fort has been made in the past decade in developingvarious integrated nonlinear photonic platforms rangingfrom Si3N4

10–14, diamond25, Ta2O526, SiC27 to highly

nonlinear AlGaAs28,29 and GaP30 on insulator, as wellas electro-optic platforms such as LiNbO3

24,31–33 andAlN34–37. Significant progress has been achieved on har-nessing the Kerr nonlinearity which enables the gen-eration of dissipative Kerr soliton microcombs in inte-grated optical microresonators5,6. Microcombs consti-tute chip-scale frequency combs with broad bandwidthsand repetition rates in the microwave domain, amenableto heterogeneous or hybrid integration with III-V/Silasers38,39, and have been used in system-level demon-strations including coherent telecommunications40, inte-grated frequency synthesizers41, astronomical spectrom-eter calibration42,43, ultrafast ranging44,45, low-noise mi-crowave generation46,47 and massively parallel coherentLiDAR48.

For nonlinear integrated photonics, Si3N453–55 has

emerged as a leading material due to its ultralow lin-ear and nonlinear optical losses, strong Kerr nonlin-earity, high refractive index, and high power handlingcapability56. To date, among all integrated photon-ics platforms57, optical losses near or below 1 dB/mhave only been demonstrated in Si3N4 waveguides. Firstachieved in thin-core waveguides (e.g. waveguide heighth < 100 nm)49,50,58, ultralow losses have later also beenattained in thick-core (i.e. h > 700 nm)10–12 waveg-uides enabling negligible bending loss, dispersion engi-neering and significantly higher Kerr nonlinearity, as out-lined in Fig. 1. Many system-level demonstrations ofsoliton microcombs40,42,44,47,48 have been based on thistype of Si3N4 PICs. Figure 1(a) highlights the lowest-loss nonlinear (ref.10,11 and this work) and linear49,50Si3N4 waveguides in terms of their optical losses and ef-fective area of the fundamental optical mode, in compar-ison with the state-of-the-art, lowest-loss silicon51, InP52

and AlGaAs29 waveguides. The tight confinement sig-nificantly relaxes the bending loss, a key parameter fordevice footprint and photonic integration, as outlined inFig. 1(b). Though the desirable combination of tight

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Figure 1. Comparison of ultralow-loss linear and nonlinear Si3N4 platforms with state-of-the-art silicon, InPand AlGaAs platforms. (a) Comparison of optical losses and effective mode areas (in the telecommunication band of1550 nm) in state-of-the-art, lowest-loss waveguides, including nonlinear (ref.10,11 and this work) and linear (ref.49,50) Si3N4

waveguides, 220 nm silicon-on-insulator (SOI) waveguides51, 1000 nm InP rib waveguides52, nonlinear AlGaAs waveguides29.The insets show the waveguide geometry and optical mode profile of the Si3N4 waveguides. (b) Comparison in device size forlinear and nonlinear Si3N4 waveguides and single-mode fibers. (c) Simulated GVD parameter Dλ as a function of the waveguideheight h, with a fixed waveguide width of w = 2.1 µm. (d) Simulated bending loss as a function of the waveguide height, witha fixed bending radius of d/2 = 25 µm and waveguide width of w = 2.1 µm. Anomalous GVD region is brown-shaded, whichis accessed with h > 700 nm.

confinement, ultralow loss and anomalous GVD has beenachieved to date10,11, it has only been attained in indi-vidual chips, i.e. with die-level throughput. Meanwhile,the fabrication of densely packed, meter-long PIC hasnot been achieved. Nor has wafer-level fabrication yield,reliability and reproducibility, required for widespreadadoption in CMOS foundries, been demonstrated. Yet,densely packed, meter-long nonlinear Si3N4 PIC couldenable a new class of devices, ranging from integratedtravelling-wave parametric amplifiers15–18 to integratedmode-locked-lasers based on rare-earth doping19.

Here we report a high-yield wafer-scale fabricationtechnology to build tight-confinement, ultralow-loss,dispersion-engineered Si3N4 waveguides of length scalesup to more than a meter. It is based on the photonicDamascene process59 using standard CMOS fabricationtechniques such as DUV stepper lithography, dry etchingand low-pressure chemical vapor deposition (LPCVD).Figure 2(a) shows process flow and scanning electron mi-crographs (SEM) for selected key steps. The waveguidesand stress-release filler patterns59 are written directly on

the SiO2 substrate via DUV stepper lithography based on248 nm KrF excimer laser. The use of DUV, in contrastto the commonly employed electron-beam lithography,enables dramatic increase in throughput, stability andreproducibility, essential to large-volume manufacturing.The patterns are then dry-etched to the SiO2 substrateto create waveguide preforms. We note that our SiO2

dry etching does not introduce a trade-off between theetch verticality and surface roughness. Figure 2(d) topshows the sidewall bottom angle 90◦ < β < 92◦. Tofurther reduce the waveguide sidewall roughness (rootmean square) to sub-nanometer level, the entire sub-strate is annealed at 1250◦C (“preform reflow”)60. Im-portantly, this reflow process can further reduce the scat-tering loss, and does not lead to prominent deformationof the waveguide preform. Figure 2(d) bottom shows themeasured sidewall bottom angle β ≈ 93◦. An LPCVDSi3N4 film of 1000 nm thickness is deposited on the pat-terned substrate, filling the preform trenches and form-ing the waveguides. A novel etchback planarization pro-cess is applied, combining photoresist coating, dry etch-

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Figure 2. The photonic Damascene process flow and highlighted features. (a) Process flow of the photonic Damasceneprocess including DUV stepper lithography, preform etching, preform reflow, LPCVD Si3N4 deposition, planarization, and SiO2

cladding deposition. The blue shaded part is Si3N4. (b) Photograph showing Si3N4 photonic chips with ring resonators of 10to 1000 GHz free spectral range. (c) Optical micrograph showing the bus waveguide, microring resonator, and filler patterns(used to prevent crack formation). Inset: simulated tightly confined optical mode. (d) Transmission electron micrographs(TEM) of the waveguide cross-sections, before (top) and after (bottom) the preform reflow. The reflow preserves the waveguidedimensions accurately, while removing high-frequency spatial roughness.

ing and chemical-mechanical planarization (CMP). Thisprocess enables full control of polishing depth and wafer-scale uniformity with variation below 3%. Afterwards,the entire substrate is thermally annealed at 1200◦C todrive out the residual hydrogen impurities in the Si3N4

film12. Top SiO2 cladding composed of TEOS and low-temperature oxide (LTO) are deposited on the wafer, fol-lowed by SiO2 thermal annealing. Finally, the wafer isseparated into chips via deep dry etching followed by dic-ing or backside grinding, to attain chip facets with supe-rior quality which is critical for edge coupling39,61,62.

Figure 2(b) shows the final Si3N4 chips containingmultiple ring resonators of different free spectral ranges(FSR). Figure 2(c) shows the optical micrograph of theSi3N4 ring resonator, bus waveguide and filler patterns,as well as the tightly confined waveguide mode. The re-sulted negligible bending loss allows microresonators ofsmall radii below 23 µm (i.e. 1 THz FSR), which findwide applications in optical filters and coupled-resonator-based delay lines63,64. The filler patterns consist of hori-zontal and vertical bars uniformly distributed over theentire wafer area, and can significantly relax the as-deposited LPCVD Si3N4 film stress for crack prevention.These filler patterns are also required for etching andCMP uniformity.Statistical analysis of microresonator Q factors:We fabricate Si3N4 microresonators of 40.6 GHz FSR,

2200 nm width and 950 nm height, and systemati-cally study the microresonator Q factors (i.e. loss).Frequency-comb-assisted diode laser spectroscopy65,66 isused to characterize the resonance frequency ω/2π andlinewidth κ/2π, which relate to the resonance Q factor asQ = ω/κ. Here we mainly study the fundamental trans-verse electric (TE00) mode. The total (loaded) linewidthκ/2π = (κ0 + κex)/2π, the intrinsic loss κ0/2π and thecoupling strength κex/2π are extracted from each res-onance fit. Figure 3(a) shows the κ0/2π histogram of10,197 TE00 resonances measured from twenty-six mi-croresonators. The most probable value is κ0/2π = 6.5MHz, corresponding to an intrinsic Q factor of Q0 =30 × 106. In comparison, κ0/2π = 9.5 MHz is foundfor the fundamental transverse magnetic (TM00) mode,corresponding to Q0 = 20 × 106. Finally, as the thresh-old power for soliton formation scales as 1/Q2, such highmicroresonator Q allows soliton formation of 40 GHz rep-etition rate with only 10 mW optical power, without us-ing an optical power amplifier (The measured GVD isD2/2π ∼ 224 kHz).

Next, we demonstrate wafer-scale yield of our fabri-cation technology. Figure 3(b) shows our mask layoutcomprising 4 × 4 chip designs on the DUV stepper reti-cle. Each chip has a 5×5mm2 size, and contains multiplemicroresonators as shown in Fig. 2(b). The DUV stepperwrites the reticle pattern uniformly over the full 4-inch

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Figure 3. Statistic study of microresonator Q factors using multiple techniques. (a) Histogram of 10,197 TE00

resonances from twenty-six resonators, showing the most probable value of κ0/2π = 6.5 MHz and Q0 = 30 × 106. (b) DUVstepper exposure layout, and the most probable value κ0/2π of the C7 chips at different positions on the wafer. The reticledesign containing sixteen chips is uniformly exposed in discrete fields over a 4-inch wafer. NA: not applicable, due to visiblephotoresist coating defects or missing C7 chips in fields near the wafer edge. (c) Linewidth measurement of the same resonanceat 1550.6 nm using frequency-comb-assisted diode laser spectroscopy (left, κ/2π = 7.75 MHz and κ0/2π = 5.87 MHz) andsideband modulation technique (right, κ/2π = 7.95 MHz and κ0/2π = 6.05 MHz). This resonance does not present a visiblemode split. (d) Cavity ring-down measurement. An intensity modulator (IM) is used to switch off the pump field. The cavityring-down signal is averaged 1000 times. The exponential fit gives an optical field decay time of τ = 37.8 ns, corresponding toa photon decay time of 18.9 ns and a loaded linewidth of κ/2π = 8.4 MHz. arb.u.: arbitrary unit. AWG: arbitrary functiongenerator. OSC: oscilloscope.

wafer in discrete fields. The calibration chips of 40 GHzFSR studied here are the C7 chips. The most probablevalue of κ0/2π histograms of C7 chips is measured andplotted in each exposure field, as shown in Fig. 3(b). Inmost fields, κ0/2π 6 7.5 MHz is found. While excep-tionally narrow linewidth has been reported previouslyon individual resonances, our statistics based on tens ofthousands of analyzed resonances from dozens of samplesat different wafer positions, shows wafer-scale fabricationthroughput and yield.

In addition, sideband modulation technique67 is per-formed to measure the resonance linewidth κ/2π andto fit κ0/2π. Two sidebands, each separated from thecarrier by 100 MHz, are used to calibrate the resonancelinewidth. Figure 3(c) compares the measured κ/2π andfitted κ0/2π of the same resonance which does not presenta visible mode split, using both the frequency-comb-assisted diode laser spectroscopy (κ/2π = 7.75 MHz andκ0/2π = 5.87 MHz) and the sideband modulation tech-nique (κ/2π = 7.95 MHz and κ0/2π = 6.05 MHz). Bothmethods agree with each other, and show Q0 > 32×106.

Furthermore, cavity ring-down measurement is per-formed to validate the measured linewidth (see Method).Figure 3(d) shows the schematic of the experimentalsetup and a representative ring-down measurement data.The fitted optical field decay time is 37.8 ns, correspond-ing to 18.9 ns photon storage time. The calculated loaded

linewidth is κ/2π = 8.4 MHz, showing consistency be-tween the three characterization methods used here.Meter-long spiral waveguides: In addition to high-Q microresonators, we also fabricate and characterizemeter-long spiral waveguides that are key elements tobuild photonic true-time delay lines. Previously, sil-ica suspended wedge waveguides68 and thin-core Si3N4

waveguides58 have been studied to build delay lines withlosses below 0.1 dB/m. However, as a result of avoid-ing bending losses, these waveguides occupy more than20 cm2 areas, thus suffering from significant device foot-prints. While tight optical confinement can reduce thefootprint, losses approaching even 1 dB/m have not beenachieved in any nonlinear waveguide including thick-coreSi3N4. Here, we demonstrate meter-long Si3N4 waveg-uides featuring ultralow loss and small footprint, whichcan enable key applications for travelling-wave paramet-ric amplifiers15–18, rare-earth-doped mode-locked lasers19and optical coherence tomography (OCT)69.

Figure 4(a) shows a photograph of photonic chips con-taining Si3N4 waveguides of physical lengths L longerthan 1 m. Figure 4(b, c, d) shows the spiral layout.The waveguides are densely packed in Archimedean spi-rals, with waveguide width w = 2.1 µm and gap distanceg = 4 µm. Three lengths are studied here: a 0.5-meter-long spiral contains 50 coils and covers 3.1 mm2 area;a 1.0-meter-long spiral contains 106 coils and covers 6.6

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Figure 4. Small-footprint, meter-long, ultralow-loss Si3N4 spiral waveguides. (a) Photograph showing Si3N4 chipscontaining two 1.0-meter-long and one 1.4-meter-long spiral waveguides. (b, c) Optical micrographs of the densely packed Si3N4

waveguides in Archimedean spirals, with yellow light camera (b) and IR camera (c). When 1550 nm laser light is coupled intothe waveguide, light-scattering defects are observed under the IR camera (highlighted with a red circle). (d) Schematic showingthe waveguide width and spacing. (e) Measured and calibrated optical losses in 0.5 m, 1.0 m and 1.4 m long spiral waveguides.(f) Measured and calibrated losses measured at different wavelengths for four selected samples.

mm2 area; and a 1.4-meter-long spiral contains 130 coilsand covers 20.2 mm2 area. Compared with the previousreport based on thin-core Si3N4 waveguides58 showing adevice footprint of more than 20 cm2 area for 1 m physicallength, our devices represent a footprint reduction of 300times, critical for photonic integration. Figure 4(e) showsthe measured losses in multiples samples, calibrated us-ing the adjacent 5-millimeter-long waveguide which hasa fiber-chip-fiber through coupling efficiency of 33% (4.8dB for two chip facets). The lowest loss values found are1.7 dB/m for 0.5 m length, 2.4 dB/m for 1.0 m length,and 4.1 dB/m for 1.4 m length. These loss values arehigher than the value extrapolated from microresonatorQ characterization (1.0 dB/m). Meanwhile, the over-all trend shows higher losses in longer waveguides. Weattribute both observations to the extra light-scatteringdefects. Light-scattering defects are found under an in-frared (IR) microscope, as shown in Fig. 4(c). By count-ing the number of defects in high-loss spirals, we estimatethat each defect causes 1–2 dB extra loss. The proba-bility of defects depends on the waveguide area. Thesedefects are likely caused by particle contamination on thewafer, as we have verified that these defects are not onthe DUV reticle which would generate the same defectsin the same position in each exposure field. Figure 4(f)shows the calibrated losses measured at different wave-

lengths for four selected samples. A trend showing ahigher loss at a shorter wavelength is observed.Quantitative analysis of loss limit: Next, we investi-gate quantitatively the intrinsic absorption and scatter-ing losses of our Si3N4 waveguides. The optical lossesin the telecommunication band have two main contri-butions: the Rayleigh scattering loss caused mainly bythe waveguide sidewall roughness, and the absorptionloss due to e.g. hydrogen impurities. While the hy-drogen absorption loss can be efficiently eliminated viarepeated thermal annealing of Si3N4 at high tempera-ture ∼ 1200◦C12,70, efforts on loss reduction have mainlyfocused on reducing waveguide roughness via optimizeddry etching11, wet etching71, and etchless process72,73.In addition, the large mode area of thin-core Si3N4

waveguides49,50,58 results in reduced optical mode inter-action with waveguide sidewall roughness, and therebyreduced scattering losses.

To quantify the thermal absorption loss of our Si3N4

waveguides, a modulation response measurement30 isperformed. The experimental setup is shown in Fig. 5(a),with two lasers, the pump and probe. The pump laser istuned to an optical resonance whose frequency is fm, andthe thermal absorption loss κabs in this resonance is tobe characterized. Meanwhile, the pump laser is intensity-modulated with frequency ω. The probe laser is loosely

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Figure 5. Probing the ultimate absorption loss limit of Si3N4 microresonators via Kerr-nonlinearity-calibratedthermal response measurements. (a) Experiment setup. ECDL: external-cavity diode lasers. IM: intensity modulator.VNA: vector network analyzer. PBS: polarization beam splitter. (b) Thermal simulation of the temperature distribution in thewaveguide structures. (c, d) Measured frequency response χ(ω) normalized to χKerr, of two representative resonances at 1515nm and 1598 nm. The fitted thermal cutoff frequency ωtherm/2π and cavity cutoff frequency κ/4π are, ωtherm/2π = 14.2 kHzand κ/4π = 6.2 MHz in (c), and ωtherm/2π = 14.9 kHz and κ/4π = 6.5 MHz in (d). (e) Calculated absorption loss κabs/2πof different resonances from different samples. The black solid circles correspond to the data shown in (c, d). (f) Comparisonof loss values measured using the linear response measurement and the frequency-comb-assisted diode laser spectroscopy, ona partially annealed sample. This particular samples features prominent hydrogen absorption losses. The green-shaded zoommarks a wavelength-independent scattering loss of 20 MHz.

locked (i.e. low-bandwidth locking) to another opticalresonance whose frequency is f ′m. The principle of thelinear microresonator response measurement is to charac-terize the resonance frequency shift δfm′ = χ(ω)δnph ofthe probe mode fm′ induced by the intensity modulationof the pump mode fm. This intensity modulation causesintracavity power modulation (i.e. photon number mod-ulation nph), which modulates the resonance frequencyof the probe mode fm′ via Kerr and thermal nonlinear-ities. The pump power is maintained sufficiently low,such that the steady-state frequency shift of the probemode is small compared to the resonance linewidth κ,i.e. δfm′ � κ. In this linear regime, the frequency re-sponse to the modulating pump power is given by30

χ(ω) =δfm′

δnph= χtherm(ω) + χKerr(ω) (1)

The total response χ(ω) consists of two parts: theKerr response χKerr(ω) with infinite bandwidth, and the

thermal response χtherm(ω) with a bandwidth below 20kHz. Therefore, by calibrating the response χ(ω) as afunction of the modulation frequency ω, χtherm(ω) andχKerr(ω) can be individually identified. Using the valuesof χtherm(ω) and χKerr(ω) at DC (ω = 0), the absorptionrate is calculated as

κabs =2cnmatn2

n2gVeff

dTdPabs

dnmatdT

χtherm(0)

χKerr(0)(2)

where Veff is the effective optical mode volume, n2 =2.4 × 10−19m2/W is the nonlinear index of Si3N4, ng =2.1 is the group index, nmat = 2.0 is the material in-dex and dnmat/dT = 2.5 × 10−5/K is the thermo-opticcoefficient74, and Pabs is the absorbed power.

The frequency response δfm′ to the pump modulationis transduced into the probe laser’s phase modulation.The phase response is measured using a balanced homo-dyne detection, with the pump laser being filtered out be-fore detection (see Methods). To evaluate the absorption

7

rate κabs, the factor χtherm(0)/χKerr(0) is retrieved bya two-pole fitting of the measured response χ(ω), whichpresents a thermal cutoff frequency ωtherm and a cavitycutoff frequency κ/2. The fitting exploits the fact thatthe thermal response χtherm(ω) dominates at frequencybelow 10 kHz and has a cutoff frequency ωtherm/2π < 20kHz. At higher frequency, the Kerr response χKerr(ω)dominates. Figure 5(c, d) present two examples of mea-sured and fitted χ(ω). Finite-element simulations of op-tical mode profiles and bulk absorption heating are per-formed to calculate the coefficients Veff and dT/dPabs.Figure 5(b) shows the temperature profile from the ther-mal simulation (see Method).

Figure 5(e) shows the calculated absorption rates κabs

of different resonances from four 40-GHz-FSR Si3N4 sam-ples featuring Q0 > 30×106, in comparison with 10- and100-GHz-FSR samples fabricated using the same pro-cess but from different wafers. All samples show similartrends, and present two conclusions. First, the mean ab-sorption loss is only κabs/2π ≈ 0.2 MHz, correspondingan absorption-loss-limited Q factor of 109. Therefore, theoptical losses of our Si3N4 waveguides (κ/2π = 6.5 MHz)are currently dominated by scattering losses. Second,κabs/2π is higher (≈ 0.4 MHz) around 1520 nm, com-pared to the value at e.g. 1600 nm (< 0.2 MHz). This iscaused by the residual hydrogen impurities in our ther-mally annealed Si3N4. Note that, only standard LPCVDSi3N4 / SiO2 films and thermal annealing are used in ourfabrication to achieve such low absorption losses.

To validate our findings, we further benchmark the lin-ear response measurement by characterizing a partiallyannealed Si3N4 sample whose resonance linewidth datahave been published in ref.12. We characterize againthis particular sample, using both the response measure-ment and the frequency-comb-assisted diode laser spec-troscopy, and compare the results using both methods inFig. 5(f). Assuming a wavelength-independent scatter-ing loss of 20 MHz, the measured hydrogen absorptionloss using the response measurement agrees with the to-tal loss measured using the other method.Conclusion: We have demonstrated a fabricationtechnology enabling high-yield and reproducible wafer-scale manufacturing of ultralow-loss, high-confinement,anomalous-GVD Si3N4 PIC. We present a statisticalstudy of microresonator losses based on tens of thou-sands of analyzed resonances. We further reveal thatour waveguide losses are dominated by scattering losses,which could be further reduced via e.g. optimized lithog-raphy and etching. In the ideal case limited only by thethermal absorption loss, the potential microresonator Qis calculated to exceed 109 (corresponding to a linear lossof 0.03 dB/m). The optimized photonic Damascene fab-rication technology allows tight-confinement, ultralow-loss, high-yield, meter-scale, nonlinear PIC, and is suit-able for adoption in CMOS foundries.Methods

Cavity ringdown: An intensity modulator (IM) is used to rapidlyswitch on and off the pump field. The ring-down signal of the trans-

mitted light is recorded by a 1-GHz-bandwidth low-noise photode-tector. A 50-kHz square wave electrical drive signal is generatedusing a fast arbitrary waveform generator, ensuring that the lightis switched off significantly faster than the resonance linewidth.The upper and lower voltage levels of the square wave are adjustedto match the maximum and minimum transmission voltage of theIM, such that the electrical overshoot and undershoot of the squarewave signal do not twist the ring-down slope. Due to the finite ex-tinction ratio of the IM, the residual pump field beats with theleakage of the intracavity field, producing a field ring-down signalwhich is affected by the detuning of the laser from the cavity moderesonances75. At small detunings (κ� ∆), the effective ring-downrate is increased by the laser’s detuning from cavity resonance, andthus the directly inferred quality factor is less accurate than thesideband fitting result. Therefore, the ring-down results can onlyserve as a lower bound of the loaded Q factor of the measured res-onances. The estimated loaded linewidth κ/2π = 8.4 MHz is inagreement with the sideband fitting results, showing consistencybetween the three characterization methods used here.Thermal simulations: We use COMSOL Multiphysics to sim-ulate the thermal response due to bulk absorption heating of ourSi3N4 samples. The main material property coefficients of interestused in the current simulation are identical to the ones used in ref.76for simulating the Si3N4 thermal refractive noise. We first simu-late the waveguide optical mode profile (TE00 mode), from whichthe effective mode volume Veff is calculated. Bulk absorption heat-ing is introduced whose power distribution is proportional to theintensity distribution of the optical mode fm. From the station-ary study of the sample heating, the dependence of temperaturechange on absorbed power, dT/dPabs, is retrieved from an absorp-tion power sweep. The combined value of Veff · dT/dPabs is calcu-lated as 2.09 × 10−12 K ·m3/W in the case of full SiO2 claddingfor samples used in Fig. 5(c, d, e), and is 3.84 × 10−12 K ·m3/Win the case of missing top SiO2 cladding for samples used in Fig.5(f).Response calibration: In order to extract the actual microres-onator response χ(ω) from the experimentally photodetected χ′(ω),the frequency response χdet(ω) of our entire experiment setup anddetection chain needs to be calibrated first. This is realized by di-rect detection of the pump power modulation δP (ω) ∝ χdet(ω) inthe absence of the probe laser and the pump filter. The measuredresponse χ′(ω) is normalized to the setup response χdet(ω), andthus the actual microresonator response χ(ω) = χ′(ω)/χdet(ω) isretrieved, with an uncertain constant factor. This constant factoris removed when retrieving χtherm(0)/χKerr(0) from the two polefitting of χ(ω) using a fitting function

χ(ω) =χKerr(0)√1 + (2ω/κ)2

· (1 +χtherm(0)

χKerr(0)

1

1 + i(ω/ωtherm)γ)

with ωtherm/2π and κ/4π being the thermal and cavity cutoff fre-quencies, γ being the parameter accounting for the material inho-mogeneity (that is, the Si3N4 waveguide has a finite dimension andis surrounded by SiO2 cladding). In Fig. 5(c, d), only the normal-ized response χ(ω)/χKerr(0) is shown, with the uncertain constantfactor removed.Funding Information: This work was supported by Con-tract HR0011-15-C-055 (DODOS) from the Defense Advanced Re-search Projects Agency (DARPA), Microsystems Technology Office(MTO), by the Air Force Office of Scientific Research, Air ForceMateriel Command, USAF under Award No. FA9550-15-1-0250,and by Swiss National Science Foundation under grant agreementNo. 176563. (BRIDGE).Acknowledgments: We thank Bahareh Ghadiani for the assis-tance in the fabrication process development in the early stage, andQi-Fan Yang for the fruitful discussion. The Si3N4 microresonatorsamples were fabricated in the EPFL center of MicroNanoTechnol-ogy (CMi).Data Availability Statement: The code and data used to pro-duce the plots within this work will be released on the repositoryZenodo upon publication of this preprint.

8

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