# Tailoring Broadband Kerr Soliton Microcombs via Post-Fabrication Tuning of
the Geometric Dispersion

Gregory Moille<EMAIL_ADDRESS>Joint Quantum Institute, NIST/University of
Maryland, College Park, MD 20742, USA  Microsystems and Nanotechnology
Division, National Institute of Standards and Technology, Gaithersburg, MD
20899, USA  Daron Westly  Microsystems and Nanotechnology Division, National
Institute of Standards and Technology, Gaithersburg, MD 20899, USA  Ndubuisi
George Orji  Microsystems and Nanotechnology Division, National Institute of
Standards and Technology, Gaithersburg, MD 20899, USA  Kartik Srinivasan
Joint Quantum Institute, NIST/University of Maryland, College Park, MD 20742,
USA  Microsystems and Nanotechnology Division, National Institute of Standards
and Technology, Gaithersburg, MD 20899, USA

(August 27, 2024)

###### Abstract

Geometric dispersion in integrated microresonators plays a major role in
nonlinear optics applications, especially at short wavelengths, to compensate
the natural material normal dispersion. Tailoring of geometric confinement
allows for anomalous dispersion, which in particular enables the formation of
microcombs which can be tuned into the dissipative Kerr soliton (DKS) regime.
Due to processes like soliton-induced dispersive wave generation, broadband
DKS combs are particularly sensitive to higher-order dispersion, which in turn
is sensitive to the ring dimensions at the nanometer-level. For microrings
exhibiting a rectangular cross section, the ring width and thickness are the
two main control parameters to achieve the targeted dispersion. The former can
be easily varied through parameter variation within the lithography mask, yet
the latter is defined by the film thickness during growth of the starting
material stack, and can show a significant variation (few percent of the total
thickness) over a single wafer. In this letter, we demonstrate that controlled
dry-etching allows for fine tuning of the device layer (silicon nitride)
thickness at the wafer level, allowing multi-project wafers targeting
different wavelength bands, and post-fabrication trimming in air-clad ring
devices. We demonstrate that such dry etching does not significantly affect
either the silicon nitride surface roughness or the optical quality of the
devices, thereby enabling fine tuning of the dispersion and the spectral shape
of the resulting DKS states.

Integrated microresonators have been demonstrated in a variety of different
materials in which the frequency spacing of a set of optical modes, the free
spectral range (FSR), increases with the optical frequency, a behavior termed
as anomalous dispersion [1, 2]. This allows for compensation of the intensity-
dependent Kerr frequency shift, enabling the fundamental conservation of both
energy and momentum - or frequency and angular momentum in the special case of
periodic whispering gallery modes structures. This fundamental dispersion
property allows for a variety of $\chi^{(3)}$ nonlinear processes to be
effectively realized [3, 4]. In particular, four-wave mixing (FWM) and optical
parametric oscillation from a continuous-wave pump can occur, seeding the so-
called modulation instability frequency microcomb [5], which is a first step
in obtaining a stable pulse state in the dissipative Kerr soliton (DKS) regime
[6]. In photonic platforms where DKS states have been demonstrated, for
example in microrings [7, 8, 9, 10, 11], material dispersion (which is normal)
is compensated by geometric dispersion, i.e. the confinement of the guided
mode within the structure relative to the wavelength, to obtain anomalous
dispersion [12]. The amount of dispersion compensation needed is particularly
acute at shorter wavelengths as photonic materials, such as Si3N4, SiO2, AlN
or LiNbO3, exhibit pronounced normal dispersion in the visible range.

However, obtaining anomalous dispersion is usually not sufficient for
supporting a DKS state that suits application needs. In particular, for full
comb stabilization requiring an octave of bandwidth, the DKS spectrum has to
be extended using dispersive waves (DWs) [13, 14, 15], a phenomenon relying on
higher-order dispersion [8, 16]. In this case, a DKS comb tooth overlaps with
a cavity resonance far away from the pumped mode, exhibiting resonant
enhancement at this particular wavelength, and increasing the comb power
locally. The spectral positions of such DWs are highly sensitive to the
geometric dispersion, which in turn is controlled primarily through the ring
width [14] and the ring thickness [17]. Dimensional control down to the few
nanometer level is required for precise targeting of DW spectral locations.
The ring width, being an in-plane parameter, can be addressed at the design
level where different structures on the same chip are given a slight variation
in their ring width. However, thickness is defined during growth and requires
subsequent post-growth processes if it is to be adjusted.

Figure 1:  A 100 mm wafer of Si3N4/SiO2 on a Si substrate that is divided into
several cells, each containing a certain number of die in a multi-project
fabrication run. The heat map corresponds to the Si3N4 thickness measured by a
spectroscopic ellipsometer and exhibiting a variation of more than $\approx$
30 nm ($\pm$3.5 % of the mean thickness of 445 nm) across the whole wafer.
Cells can be selectively masked for dry-etch trimming of particular areas of
the wafer, allowing for different controlled thicknesses across the wafer to
accommodate different projects. For devices that lack a top-cladding material
(air-clad structures), fine trimming can also occur after the completed device
fabrication, with measurement feedback guiding the level of trimming needed.
In our case, we lift-off the SiO2 (right image) to uncover the rings for
dispersion and fine trimming purposes while keeping SiO2 at the facets for
improved fiber input/output coupling. Figure 2:  (a)-(b) Insertion loss
calculation computed through finite element simulations, assuming a spot-size
diameter of the lensed fiber of 2.5 $\mu$m and assuming 430 nm thick Si3N4,
for (a) a fully SiO2-clad waveguide and (b) an air top-cladding waveguide. For
each structure, TE (purple) and TM (teal) insertion losses are calculated and
the mode profile for the optimized dimension for TE polarization are
showcased, along with the structure (black) and the lensed fiber spot size
(dashed white). The measured insertion losses for SiO2 clad waveguides is
between 3.5 dB to 4.0 dB per facet.(c) Scanning electron microscope (SEM)
image and (d) optical microscope image of the dual-layer resist used to lift-
off the low-temperature PECVD SiO2 to create selectively-clad photonic chips.
(e) Optical microscope and (f) SEM images after the SiO2 lift-off process,
which uncovers the ring area while keeping the SiO2 at the chip facets for low
insertion losses. The SEM image in (f) highlights smooth transition between
the air and oxide clad regions.

In this letter, we demonstrate a dry etch trimming approach that enables fine
tuning of the thickness of Si3N4 microresonator frequency comb devices with a
resolution down to the few nanometer level (Fig. 1). One application of this
trimming is in chip-to-chip compensation of the natural thickness variation
across a wafer, which is typically at the percent level or higher for growth
via low pressure chemical vapor deposition [18]. The dry etch trimming can
also be used to realize thickness differences of several tens of nanometers,
enabling multi-project wafers in which different thicknesses are needed to
target, for example, frequency combs operating in different spectral bands or
other $\chi^{(3)}$ nonlinear nanophotonic devices. Working in an air-clad
system in which the Si3N4 device layer remains accessible after fabrication
(see Fig. 1), we perform optical characterization of the microcomb devices
before and after trimming steps. We show that the frequency shift of the
resonator modes due to dry etch trimming can be repeatably controlled and does
not adversely impact their optical quality factor ($Q$). We further show how
DKS microcomb states, and in particular, DW positions, are modified through
thickness trimming, with the DW shift predictable based on the impact of
device layer thickness on higher-order dispersion.

Most of the reported DKS microcombs in Si3N4 resonators have been demonstrated
in devices that are fully clad with SiO2 [8, 14]. This approach has the
advantages of making the resonator relatively insensitive to its environment
and allows for better heat dissipation. However, post-fabrication steps to
modify the geometry based on measurement results are made impossible as the
resonator is not directly accessible. Here, we use a system where the ring
resonator does not have any material as the top cladding. Such air-clad
resonators have been demonstrated to support high-$Q$ and octave-spanning
microcombs [19, 20], as well as other wide-band nonlinear processes [19, 21].
Yet in our system, the facet waveguides are still embedded in SiO2 (Fig. 2).
This selectively-clad chip thus enables direct access to the microresonator
section for trimming purposes, while providing more optimized facet coupling
regions for improved insertion losses from/to lensed optical fibers (Fig.
2(a)). In particular, the full SiO2 cladding both provides for a more
symmetric mode than what would be possible with an air-clad waveguide and
ensures that a guided mode is supported even when inverse tapers are used to
expand the mode size to best match that of lensed optical fibers
(asymmetrically clad waveguides are not guaranteed to support even a
fundamental guided mode if the taper width is too small). Together, this
results in insertion losses that are predicted to be as low as 2 dB per facet
at 1060 nm (Fig. 2(a)), an improvement on the 6 dB per facet loss that could
be reached in air-clad waveguides tapered to a larger width at the chip facets
(Fig. 2(b)). In practice, we typically measure insertion losses between 3.5 dB
to 4 dB per facet for a nominal inverse taper width of 150 nm (see
supplementary material). We note that the Fresnel reflection between the two
cladding regions, which could potentially lead to other insertion losses, is
negligible and in the 0.1 dB range (see supplementary material). The selective
SiO2 cladding is realized through a photoresist lift-off process (Fig.
2(c)-(d)), where removal of the top SiO2 cladding over the microring is made
possible through low-temperature (180∘C) inductively-coupled plasma enhanced
chemical vapor deposition (PECVD) of SiO2, allowing photoresist to be used
without polymerization that would occur at high temperature. We use a dual
layer of LOR5-A and nLOF resists [22] (one spin coating of LOR5-A, two spin
coatings of nLOF), thicker than the targeted deposited SiO2 thickness of 3 µm,
and optically expose them over the microring regions of the chip. Optical and
scanning electron microscope images of a completed chip are shown in Fig.
2(e)-(f).

Figure 3:  (a) Atomic force microscopy measurement across a 1 $\mu$m2 area of
the top surface of a Si3N4 film before and after RIE trimming steps, the
latter of which vary in duration and radio frequency (RF) power. b Root-mean
square (RMS) roughness comparison for different etch duration (horizontal
scale) and a RF power of 60 W (green) and 75 W (red). The roughness standard
deviation for each sample is between 38 pm and 45 pm and is too small to be
displayed here. The black dashed line indicates the RMS roughness prior to
trimming.

As the above method leaves selected regions of the Si3N4 layer accessible, a
reactive ion etch (RIE) can be used to trim the Si3N4 thickness in those
regions. In comparison to wet etching of Si3N4, which can be done through
dilute hydrofluoric acid or heated phosphoric acid but are isotropic (and
hence impact both resonator in-plane dimensions and thickness), we emphasize
that dry etching can be tailored to predominantly impact thickness. In
particular, we use a CF4 and O2 plasma mixture at 2 Pa (15 mTorr) chamber
pressure, with $5\times 10^{7}$ m3.s-1 (30 sccm) and $3.33\times 10^{7}$
m3.s-1 (20 sccm) flow respectively, at room temperature. In comparison to
inductively-coupled plasma dry etching with a significant chemical component,
this RIE etch is mostly physical and only affects the top surface and not the
sidewalls of the microrings. To ensure that the RIE does not adversely impact
microring top surface roughness, we perform atomic force microscope (AFM)
measurements of the Si3N4 surface for several films that have been etched for
times ranging between 30 s to 120 s and for two different radio frequency (RF)
powers (Fig. 3). The AFM measurements were made in tapping mode using wear-
resistant high density diamond-like carbon tips of 2 nm radius. To further
minimize tip wear and ensure imaging consistency, each surface map was
acquired using a fresh tip. These measurements across a region of a reference
(unetched) Si3N4 sample are shown in Fig. 3(a), where the root-mean square
(RMS) of the surface roughness is 0.39 nm. The etched samples show a slight
increase in RMS roughness to $\approx$ 0.46 nm, with approximately no increase
in rms roughness for longer etch times or the higher RF power (Fig. 3(b)).
Importantly, this rms roughness remains significantly below the sidewall
roughness measured for high-$Q$ Si3N4 devices [23], and is comparable to the
Si3N4 roughness after film growth (and before chemical-mechanical polishing)
reported by Ji et al. (0.38 nm) [24].

Figure 4:  (a) Linear transmission data for a microring resonator ($RW=920$
nm) with an initial thickness of $H=430$ nm, after several different trimming
steps, where for each step the trim was for 20 s and with 45 W of RF power.
The frequency-split mode indicated in-between the dashed black lines is the
result of an inner sidewall modulation whose period was set to target a
specific mode of the ring (azimuthal mode number $M=237$), providing an easy
reference by which mode frequencies can be tracked. (b) Frequencies of the
tracked microring mode for several different $RW$ values and several different
trim steps, showing a nearly constant frequency shift per step. (c) Average
intrinsic quality factor ($Q_{\text{i}}$) of 14 different resonances at each
trim step and for $RW=945$ nm and $RW=1015$ nm. The error bars represent one
standard deviation values based on the spread in the $Q_{\text{i}}$ values.
Figure 5:  (a) Dispersion parameter of the Si3N4 microring resonator for
$RR=23$ µm, $RW=1050$ nm, and for different thicknesses between $H$=410 nm and
$H$=465 nm, highlighting the crossover from normal to anomalous dispersion for
sufficiently thick films. (b) Integrated dispersion of the same ring resonator
at 305 THz (983 nm) pump frequency. (c) Position of the DWs from the
integrated dispersion zero crossing for a 305 THz pump frequency. (d) DKS
microcomb state measured by driving the same pumped mode at each trimming step
of -4 nm in thickness (every other DKS spectrum is displayed, i.e., after -8
nm steps). The DW at high frequency (short wavelength) is tuned at a rate of
$\approx$ -73 GHz/nm. The dashed lines represent the obtained spectra through
LLE simulations, where the only change in input for each spectrum is the shift
in dispersion corresponding to a change of -4 nm thickness per trimming step.
The theoretical and experimental DWs agree closely. The power discrepancy is
due to the chromatic coupling of the straight waveguide coupler, resulting in
undercoupling at short wavelengths. Soliton stabilization is provided by a
counterpropagating 283 THz (1060 nm) pump.

While the AFM suggests that RIE trimming results in at most a small increase
in the Si3N4 film roughness, it is still important to understand the impact of
the trimming on the optical properties of the resonator modes, in particular,
the influence on resonator $Q$ and modal frequencies, and the extent to which
the trimming can be repeatably applied. To do so, we need to track the same
resonator modes before and after trimming, which can be difficult in microring
resonators due to the large number of modes present. We use the selective mode
splitting technique employed in Ref. 25, where the ring resonator has an inner
sidewall modulation with a period set to couple and frequency split the
initially degenerate clockwise and counterclockwise traveling wave modes with
a specific azimuthal mode number. Here, we target the azimuthal mode number of
237 ($2\times 237$ periods along the ring inner circumference), resulting in a
resonance frequency that is split close to 287.5 THz (Fig. 4(a)). Using the
trim etch recipe presented earlier, we perform a series of seven trims for
devices which have been designed with different nominal ring width ($RW$)
varying from 920 nm to 1015 nm on the same chip, with each trim step lasting
20 s and at 45 W of RF power. The reduced RF power relative to that used in
the AFM measurements in Fig. 3 provided finer trimming resolution, while
ensuring that the induced surface roughness was minimized. We observe a nearly
uniform frequency shift of $\approx$ 0.29 THz with each step for each of the
considered $RW$ values (Fig. 4(b)), though there are some small discrepancies
from this trend, for example, the first trim step produced a somewhat smaller
shift than the subsequent ones. Using finite element method eigenmode
simulations, we retrieve the thickness dependence of the resonance frequencies
${\partial}f_{\mathrm{res}}/{\partial}H=-73.2$ GHz/nm for the $RW$ range under
study (from 900 nm to 1100 nm), and from the frequency shifts measured in Fig.
4(b), we estimate that each 20 s trim step reduces the thickness by 4 nm. Even
finer trimming steps (e.g., 2 nm for a 10 s etch) should be possible; however,
we note that a linear scaling of etched amount with etch time should not
necessarily be assumed due to plasma ignition delay (for short etch times) and
sample heating (for long etch times). Finally, we consider the intrinsic
quality factor ($Q_{\text{i}}$) for 14 resonances in our linear frequency scan
for each trimming step. We find that the average $Q_{\mathrm{i}}$ remains
about the same (within the one standard deviation uncertainty values
determined by the spread in the $Q_{\text{i}}$ data). This is consistent with
the AFM measurements indicating that the top surface roughness is only
slightly increased by the trimming, and suggests that the post-fabrication
trimming process can provide a method to tune the geometric dispersion of
devices without significantly impacting their losses, which is critical for
nonlinear applications.

Fine tuning of the thickness of a ring resonator not only allows for fine
shifting of the frequency of resonances - which can be of interest for post-
fabrication tuning to overlap with atomic transitions or other frequencies of
interest - but also impacts the overall dispersion of the resonator, in
particular the higher order dispersion coefficients responsible for dispersive
wave creation [8]. For such microcombs, it is convenient to introduce the
integrated dispersion
$D_{\mathrm{int}}(\mu)=\omega_{\mathrm{res}}(\mu)-\omega_{\mathrm{DKS}}$,
where $\mu$ is the mode number relative to the pumped mode (i.e.
$\mu_{\mathrm{pmp}}=0$), which effectively measures the discrepancy between
the resonator mode frequencies and the supported DKS frequency comb teeth
$\omega_{\mathrm{DKS}}\approx\omega_{pmp}+D_{1}\mu$, which are spaced by the
resonator free spectral range that is approximately given by $D_{1}/2\pi$. As
the modal confinement is partly set by the resonator thickness, the resonator
dispersion (calculated in Fig. 5(a)) and therefore its integrated dispersion
(calculated in Fig. 5(b)) can be significantly impacted by modifying its
thickness for a fixed ring width. This ultimately results in a variation in
the frequency of the DWs (Fig. 5(c)) on both the low and high frequency sides
of the spectrum. DWs are crucial elements in realizing octave spanning DKS
frequency combs that can be self-referenced [13] and reach atomic transition
frequencies [14], and control of their spectral positions is important to
optimize the power available for the $f$-2$f$ technique. Post-fabrication
trimming thus provides the option of being able to measure a device, determine
its DW positions, and then trim its thickness to move them closer to the
targeted values.

To demonstrate the possibility to post-process tune a DW through thickness
trimming, we measure a DKS state obtained in a ring resonator with a starting
thickness $H$=459 nm and $RW$=1040 nm and pumped at 976 nm in the fundamental
transverse electric mode, while actively-cooled using a counter-propagative
wave cross-polarized at 1060 nm, which allows for adiabiatic tuning onto the
soliton state [26, 27]. Here, we proceed to monitor the DKS state as we trim
the thickness by more than 30 nm, which corresponds to the full variation of
Si3N4 thickness over a 100 mm wafer (Fig. 1). We use the same recipe as for
the trimming calibration, namely a 20 sec RIE etch at 45 W RF power. By
pumping the exact same mode, which is slightly shifted in wavelength for each
trim step from approximately 307 THz (976 nm) to 309.5 THz (969 nm), a clear
and constant red shift of the DW is observed for each trimming step. Assuming
the previously calibrated trimming amount of 4 nm per step, the dispersion at
each trimming step can be found theoretically, and the linear approximation of
the DW position based on the zero-crossing of the integrated dispersion (Fig.
5(b)-(c)) provides a reasonable estimate of the observed DW shift. It is
important to note that for an asymmetric integrated dispersion profile (odd
dispersion coefficients dominating), the linear approximation of predicting
the DW position based on the zero-crossing of the integrated dispersion will
present a discrepancy with respect to the actual DW frequency [16, 28]. To
address this, we also present rigorous simulation data of the expected comb
envelope using the Lugiato Lefever equation model [29], where the only
modified parameter at each trimming step is the dispersion profile, chosen to
be consistent with the expected thickness, and with the same in-waveguide pump
power and pump detuning of 180 mW and -1.932 GHz respectively. The simulated
comb spectra closely match the measured ones (Fig. 5(d)), confirming that the
RIE etching process is mostly physical and does not affect the ring width. The
power discrepancy between the theoretical and experimental DWs are due to the
straight waveguide coupling system used for injecting and extracting light
from the microring resonators, which exhibits a strong chromatic dependence
and undercouples the resonator at short wavelengths [30].

In conclusion, we have demonstrated a dry etch technique that allows for fine
control of the thickness of Si3N4 microring resonators with a thickness step
as low as 4 nm and over a range of 30 nm. The post-processing trimming does
not significantly impact the Si3N4 surface roughness or resonator quality
factors. By using an air-clad structure with oxide cladding still present at
the chip facets, we are able to measure the resonator performance in-between
trimming steps while retaining low insertion losses to lensed optical fibers.
We demonstrate the utility of such fine trimming in microcomb engineering by
showing how a dissipative Kerr soliton comb pumped in the 980 nm band can have
its dispersive wave tuned across a total range of 40 THz in few THz steps.
This trimming approach has numerous potential uses in the development of
microresonator frequency combs and related Kerr nonlinear optical devices. For
example, it can enable multi-project wafer runs in which different thickness
are needed across the wafer; recent demonstrations of four-wave mixing Bragg
scattering [31] and $\chi^{(3)}$ optical parametric oscillation [21] were
realized for Si3N4 thicknesses (480 nm and 500 nm, respectively) that could be
combined with the microcomb devices shown in this work. Finally, the trimming
technique also makes it possible to compensate for the natural thickness
variation of the Si3N4 material across a full wafer, so that the number of
devices exhibiting a desired dispersion can be greatly increased.

See the supplementary material for information related to the insertion losses
of the dual air/oxide cladding structure.

Acknowledgments \- The authors acknowledge funding from the DARPA APHI and
NIST-on-a-chip programs, and thank David Carlson and Feng Zhou for helpful
comments.

Data Availability \- The data that support the findings of this study are
available from the corresponding author upon reasonable request.

## References

  * Kippenberg  _et al._ [2018] T. J. Kippenberg, A. L. Gaeta, M. Lipson, and M. L. Gorodetsky, “Dissipative Kerr solitons in optical microresonators,” Science 361 (2018), 10.1126/science.aan8083.
  * Ilchenko  _et al._ [2003] V. S. Ilchenko, A. A. Savchenkov, A. B. Matsko, and L. Maleki, “Dispersion compensation in whispering-gallery modes,” J. Opt. Soc. Am. A 20, 157–162 (2003).
  * Ferrera  _et al._ [2009] M. Ferrera, D. Duchesne, L. Razzari, M. Peccianti, R. Morandotti, P. Cheben, S. Janz, D.-X. Xu, B. E. Little, S. Chu, and D. J. Moss, “Low power four wave mixing in an integrated, micro-ring resonator with q $=$ 1.2 million,” Opt. Express 17, 14098–14103 (2009).
  * Liang  _et al._ [2011] W. Liang, A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, D. Seidel, and L. Maleki, “Generation of near-infrared frequency combs from a mgf2 whispering gallery mode resonator,” Opt. Lett. 36, 2290–2292 (2011).
  * Savchenkov  _et al._ [2008] A. A. Savchenkov, A. B. Matsko, V. S. Ilchenko, I. Solomatine, D. Seidel, and L. Maleki, “Tunable optical frequency comb with a crystalline whispering gallery mode resonator,” Phys. Rev. Lett. 101, 093902 (2008).
  * Chembo and Yu [2010] Y. K. Chembo and N. Yu, “Modal expansion approach to optical-frequency-comb generation with monolithic whispering-gallery-mode resonators,” Phys. Rev. A 82, 033801 (2010).
  * Suh and Vahala [2018] M.-G. Suh and K. Vahala, “Gigahertz-repetition-rate soliton microcombs,” Optica 5, 65–66 (2018).
  * Brasch  _et al._ [2016] V. Brasch, M. Geiselmann, T. Herr, G. Lihachev, M. H. P. Pfeiffer, M. L. Gorodetsky, and T. J. Kippenberg, “Photonic chip–based optical frequency comb using soliton cherenkov radiation,” Science 351, 357–360 (2016).
  * Gong  _et al._ [2018] Z. Gong, A. Bruch, M. Shen, X. Guo, H. Jung, L. Fan, X. Liu, L. Zhang, J. Wang, J. Li, J. Yan, and H. X. Tang, “High-fidelity cavity soliton generation in crystalline aln micro-ring resonators,” Opt. Lett. 43, 4366–4369 (2018).
  * He  _et al._ [2019] Y. He, Q.-F. Yang, J. Ling, R. Luo, H. Liang, M. Li, B. Shen, H. Wang, K. Vahala, and Q. Lin, “Self-starting bi-chromatic linbo3 soliton microcomb,” Optica 6, 1138–1144 (2019).
  * Moille  _et al._ [2020] G. Moille, L. Chang, W. Xie, A. Rao, X. Lu, M. Davanço, J. E. Bowers, and K. Srinivasan, “Dissipative kerr solitons in a iii-v microresonator,” Laser & Photonics Reviews 14, 2000022 (2020).
  * Okawachi  _et al._ [2014] Y. Okawachi, M. R. E. Lamont, K. Luke, D. O. Carvalho, M. Yu, M. Lipson, and A. L. Gaeta, “Bandwidth shaping of microresonator-based frequency combs via dispersion engineering,” Optics Letters 39, 3535 (2014).
  * Spencer  _et al._ [2018] D. T. Spencer, T. Drake, T. C. Briles, J. Stone, L. C. Sinclair, C. Fredrick, Q. Li, D. Westly, B. R. Ilic, A. Bluestone, N. Volet, T. Komljenovic, L. Chang, S. H. Lee, D. Y. Oh, M.-G. Suh, K. Y. Yang, M. H. P. Pfeiffer, T. J. Kippenberg, E. Norberg, L. Theogarajan, K. Vahala, N. R. Newbury, K. Srinivasan, J. E. Bowers, S. A. Diddams, and S. B. Papp, “An optical-frequency synthesizer using integrated photonics,” Nature 557, 81–85 (2018).
  * Yu  _et al._ [2019] S.-P. Yu, T. C. Briles, G. T. Moille, X. Lu, S. A. Diddams, K. Srinivasan, and S. B. Papp, “Tuning Kerr-Soliton Frequency Combs to Atomic Resonances,” Physical Review Applied 11, 044017 (2019).
  * Gong  _et al._ [2020] Z. Gong, X. Liu, Y. Xu, and H. X. Tang, “Near-octave lithium niobate soliton microcomb,” Optica 7, 1275–1278 (2020).
  * Cherenkov, Lobanov, and Gorodetsky [2017] A. Cherenkov, V. Lobanov, and M. Gorodetsky, “Dissipative Kerr solitons and Cherenkov radiation in optical microresonators with third order dispersion,” Physical Review A 95, 033810 (2017).
  * Black  _et al._ [2021] J. A. Black, R. Streater, K. F. Lamee, D. R. Carlson, S.-P. Yu, and S. B. Papp, “Group-velocity-dispersion engineering of tantala integrated photonics,” Opt. Lett. 46, 817–820 (2021).
  * Gumpher, Bather, and Wedel [2003] J. Gumpher, W. Bather, and D. Wedel, “LPCVD silicon nitride uniformity improvement using adaptive real-time temperature control,” IEEE Transactions on Semiconductor Manufacturing 16, 26–35 (2003).
  * Li  _et al._ [2017] Q. Li, T. C. Briles, D. A. Westly, T. E. Drake, J. R. Stone, B. R. Ilic, S. A. Diddams, S. B. Papp, and K. Srinivasan, “Stably accessing octave-spanning microresonator frequency combs in the soliton regime,” Optica 4 (2017), 10.1364/OPTICA.4.000193.
  * Moille  _et al._ [2019a] G. Moille, X. Lu, A. Rao, Q. Li, D. A. Westly, L. Ranzani, S. B. Papp, M. Soltani, and K. Srinivasan, “Kerr-microresonator soliton frequency combs at cryogenic temperatures,” Phys. Rev. Applied 12, 034057 (2019a).
  * Lu  _et al._ [2020a] X. Lu, G. Moille, A. Rao, D. A. Westly, and K. Srinivasan, “On-chip optical parametric oscillation into the visible: generating red, orange, yellow, and green from a near-infrared pump,” Optica 7, 1417 (2020a).
  * [22] Certain commercial products or names are identified to foster understanding. Such identification does not constitute recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the products or names identified are necessarily the best available for the purpose.
  * Roberts  _et al._ [2017] S. P. Roberts, X. Ji, J. Cardenas, A. Bryant, and M. Lipson, “Sidewall roughness in si3n4 waveguides directly measured by atomic force microscopy,” Conference on Lasers and Electro-Optics , SM3K.6 (2017).
  * Ji  _et al._ [2017] X. Ji, F. A. S. Barbosa, S. P. Roberts, A. Dutt, J. Cardenas, Y. Okawachi, A. Bryant, A. L. Gaeta, and M. Lipson, “Ultra-low-loss on-chip resonators with sub-milliwatt parametric oscillation threshold,” Optica 4, 619–624 (2017).
  * Lu  _et al._ [2020b] X. Lu, A. Rao, G. Moille, D. A. Westly, and K. Srinivasan, “Universal frequency engineering tool for microcavity nonlinear optics: multiple selective mode splitting of whispering-gallery resonances,” Photon. Res. 8, 1676–1686 (2020b).
  * Zhou  _et al._ [2019] H. Zhou, Y. Geng, W. Cui, S.-W. Huang, Q. Zhou, K. Qiu, and C. Wei Wong, “Soliton bursts and deterministic dissipative Kerr soliton generation in auxiliary-assisted microcavities,” Light: Science & Applications 8, 50 (2019).
  * Moille  _et al._ [2021] G. Moille, E. F. Perez, A. Rao, X. Lu, Y. Chembo, and K. Srinivasan, “Ultra-Broadband Soliton Microcomb Through Synthetic Dispersion,” arXiv:2102.00301 [physics] (2021), arXiv:2102.00301 .
  * Jang  _et al._ [2014] J. K. Jang, M. Erkintalo, S. G. Murdoch, and S. Coen, “Observation of dispersive wave emission by temporal cavity solitons,” Optics Letters 39, 5503 (2014).
  * Moille  _et al._ [2019b] G. Moille, Q. Li, X. Lu, and K. Srinivasan, “pylle: a fast and user friendly lugiato-lefever equation solver,” Journal of Research of NIST 124, 124012 (2019b).
  * Moille  _et al._ [2019c] G. Moille, Q. Li, T. C. Briles, S.-P. Yu, T. Drake, X. Lu, A. Rao, D. Westly, S. B. Papp, and K. Srinivasan, “Broadband resonator-waveguide coupling for efficient extraction of octave-spanning microcombs,” Optics Letters 44, 4737–4740 (2019c).
  * Li, Davanço, and Srinivasan [2016] Q. Li, M. Davanço, and K. Srinivasan, “Efficient and low-noise single-photon-level frequency conversion interfaces using silicon nanophotonics,” Nature Photonics 10, 406–414 (2016).

## Supplementary Materials

###  Insertion Losses in Selectively Clad Devices – Experimental Data

Figure S1:  (a) Experimentally measured per facet insertion losses for the
same material thickness as in Fig. 2(a) from the main text and inverse taper
widths from 150 nm to 250 nm. (b) Chromatic dispersion of the per facet
insertion losses in the 1020 nm to 1070 nm band. The one standard deviation
uncertainty in per facet insertion loss is at the $\pm 0.5$ dB level and is
due to measured variations in coupling for nominally identical devices.

Our system utilizes a selective SiO2 cladding, with the absence of cladding
over the microresonator region allowing direct access for post-processing,
while keeping an SiO2 cladding at the facets that is useful for reduced
insertion losses. Here we present experimental data supporting the simulations
presented in the main article, which show that the insertion losses are lower
than that in an air-clad system. We perform measurement of the insertion
losses with the inverse taper width (Fig. S1(a)). As expected from the
simulation, the insertion losses for the first order transverse electric mode
increase with the inverse taper width, where the optimum value is at 150 nm
width (smaller tapers are limited by the fabrication process; in particular,
the ability to realize high-aspect ratios for thick Si3N4 films). Finally, we
measured that such inverse tapers present very low chromatic dispersion in
their losses across the pump band, and present similar insertion losses
($\approx$ 3.5 dB per facet) across the range between 1020 nm to 1070 nm (Fig.
S1(b)).

###  Losses from the Cladding Transition

Figure S2:  (a) Schematic of silicon nitride waveguide cladding transition
between oxide-clad and air-clad regions. (b) Mode profile of $y$-oriented
electric field component of the first order transverse electric mode in the
oxide clad region for a waveguide cross section of 550 nm width and 420 nm
thickness. (c) Mode profile for the same polarization and waveguide cross-
section, but with an air top/side cladding. (d) Finite-difference time-domain
simulation results for the transmission between the oxide and air-clad
regions.

In order to estimate the potential Frensel losses from the oxide-clad to air-
clad transition (Fig. S2(a)), we perform finite-difference time-domain
simulation of the structure, where a silicon nitride waveguide of 550 nm width
and 420 nm thickness is halfway embedded in SiO2 at the left edge, and then
transitions to a waveguide that has only a bottom SiO2 cladding and a top and
side air cladding. Although the mode profile of the first order transverse
electric mode presents some disparity between the two regions (Fig. S2(b)),
due to the difference of refractive index gradient in the two regions that
modifies the confinement of the mode, the simulated transmission from the
oxide-clad region to the air-clad region remains well above 90 % (i.e. losses
lower than 0.1 dB). This level of losses is negligible in comparison to the
facet coupling loss.