Wavelength-accurate and wafer-scale process for nonlinear frequency mixers in
thin-film lithium niobate

C. J. Xin1,†,∗, Shengyuan Lu1,†, Jiayu Yang1,†, Amirhassan Shams-Ansari1,2,†,
Boris Desiatov1,3, Letícia S. Magalhães1, Soumya S. Ghosh1,4, Erin McGee1,5,
Dylan Renaud1, Nicholas Achuthan1, Arseniy Zvyagintsev1, David Barton III1,6,
Neil Sinclair1, Marko Lončar1,∗,

1 John A. Paulson School of Engineering and Applied Sciences, Harvard
University, Cambridge, MA, USA

2 DRS Daylight Solutions, 164565 Via Esprillo, San Diego, CA, USA

3 Faculty of Engineering, Bar-Ilan University, Ramat-Gan, Israel

4 Department of Physics, Harvard University, Cambridge, MA, USA

5 Department of Physics, Stevens Institute of Technology, Hoboken, NJ, USA

6 Department of Materials Science and Engineering, Northwestern University,
Evanston, IL, USA

† These authors contributed equally

∗ Corresponding authors<EMAIL_ADDRESS><EMAIL_ADDRESS>

Abstract:  Recent advancements in thin-film lithium niobate (TFLN) photonics
have led to a new generation of high-performance electro-optic devices,
including modulators, frequency combs, and microwave-to-optical transducers.
However, the broader adoption of TFLN-based devices that rely on all-optical
nonlinearities have been limited by the sensitivity of quasi-phase matching
(QPM), realized via ferroelectric poling, to fabrication tolerances. Here, we
propose a scalable fabrication process aimed at improving the wavelength-
accuracy of optical frequency mixers in TFLN. In contrast to the conventional
pole-before-etch approach, we first define the waveguide in TFLN and then
perform ferroelectric poling. This sequence allows for precise metrology
before and after waveguide definition to fully capture the geometry
imperfections. Systematic errors can also be calibrated by measuring a subset
of devices to fine-tune the QPM design for remaining devices on the wafer.
Using this method, we fabricated a large number of second harmonic generation
devices aimed at generating $737~{}$\mathrm{nm}$$ light, with $73\%$ operating
within $5~{}$\mathrm{nm}$$ of the target wavelength. Furthermore, we also
demonstrate thermo-optic tuning and trimming of the devices via cladding
deposition, with the former bringing $\sim 96\%$ of tested devices to the
target wavelength. Our technique enables the rapid growth of integrated
quantum frequency converters, photon pair sources, and optical parametric
amplifiers, thus facilitating the integration of TFLN-based nonlinear
frequency mixers into more complex and functional photonic systems.

## Introduction

The thin-film lithium niobate (TFLN) on insulator integrated photonics
platform has experienced rapid growth within the last decade due to the
commercial availability of high-quality ion-sliced substrates, as well as the
development of optimized etching processes for fabricating low-loss,
nanophotonic waveguides [1]. Underpinning these developments are the excellent
material properties of lithium niobate (LN) including a wide transparency
window, spanning near-ultraviolet to mid-infrared, and strong second-order
nonlinearities ($\chi^{(2)}$).[2] This has enabled many technologically
relevant devices, such as electro-optical modulators and optical frequency
mixers that convert light between widely separated wavelength bands. Compared
to their bulk counterparts [3, 4, 5], TFLN devices feature significant
improvements in key figures of merit such as modulation speed [6, 7], optical
bandwidth [8], and efficiency [9, 10], due to high optical mode confinement in
nanophotonic waveguides. Moreover, reduced device footprints in TFLN and
wafer-scale processing [11] using standard microfabrication techniques provide
a solid foundation for mass production and integration of many individual
components into more complex photonic circuits. For instance, circuits
comprising arrays of electro-optic modulators in TFLN have already been used
to demonstrate functionalities such as large-scale matrix-vector
multiplications [12].

On the other hand, $\chi^{(2)}$-based optical frequency mixers, which are used
in applications ranging from frequency up-/down-conversion [13] to optical
parametric amplification [14, 15] to quantum light sources [16], have thus far
been implemented mostly as standalone components or in relatively simple
circuits featuring at most two mixers operating in concert [17, 18, 19]. This
is despite ongoing interest in developing these components for applications
such as quantum frequency conversion for interfacing with solid state single
photon emitters and memories [20] and multiplexed photon pair sources [21].

One obstacle towards the scaling and integration of $\chi^{(2)}$-based optical
frequency mixers in TFLN is the extreme sensitivity of conventional quasi-
phase matched (QPM) three-wave mixing processes—namely, sum- and difference-
frequency generation (SFG and DFG), and spontaneous parametric downconversion
(SPDC)—to device geometry [22]. QPM is implemented by periodically inverting
domains of TFLN waveguide which changes the sign of $\chi^{(2)}$. The momentum
of such grating is then used to compensate for mismatch between wave vectors
of different waves participating in the nonlinear mixing process. In
particular, nanometer-level local geometry variations in the waveguide cross-
section can lead to a reduction in device efficiency at even moderate device
lengths [23, 24]. Recent work has shown that this issue can be effectively
mitigated by using extensive metrology of the initial thickness of the device
layer to perform fine adjustments to the QPM grating design [10].
Additionally, a less metrology-intensive mitigation approach based on post-
fabrication trimming using spatially varying thermo-optic tuning has also been
demonstrated, albeit at the cost of high power consumption and sacrificing
low-temperature compatibility [25].

However, in larger samples (e.g. wafers), long range waveguide geometry
variations become a salient issue in addition to the aforementioned local
geometry fluctuations. This drift arises from imperfections in the dry etch
process—often using an argon-based physical etch—that is used to realize TFLN
devices, and can cause shifts in the operating wavelength of devices well
beyond the thermo-optic tuning range. Thus, for applications requiring
accuracy in the operating wavelength—such as for interfacing with atom-like
single-photon emitters that have fixed emission wavelengths (e.g. silicon-
vacancy center in diamond at $737~{}$\mathrm{nm}$$ with $\sim
80~{}$\mathrm{GHz}$$ demonstrated tuning range [26])—the conventional approach
is to sweep the design parameters to guarantee at least one device that meets
specifications [27, 28]. While this is viable for standalone devices and small
photonic circuits, the number of trial circuits that must be fabricated to
guarantee one meets specifications scales geometrically with the number of
frequency mixing devices in each circuit even if one assumes unity yield on
all other components in the circuit.

Here, we propose a scalable process for $\chi^{(2)}$-based optical frequency
mixers in $x$-cut TFLN featuring high wavelength accuracy. In our approach,
QPM gratings are defined after waveguide etching, allowing for fine-tuning of
the grating parameters by taking into account variations in waveguide geometry
parameters. Furthermore, systematic errors can be calibrated out using a small
subset of calibration devices defined on the same wafer. The approach is
experimentally validated by realizing second harmonic generation (SHG) mixers
producing 737 nm light. This wavelength corresponds to the optical transition
of silicon-vacancy color center in diamond, a leading solid-state quantum
memory [29]. We show that $73\%$ of devices out of $84$ tested across a
$4^{\prime\prime}$ wafer support SHG of $(737\pm 5)~{}$\mathrm{nm}$$.
Furthermore, we demonstrate on a separate wafer that wavelength trimming and
tuning, using SiO2 deposition and thermal tuning respectively, can bring
$96\%$ of tested devices within the same range.

## Conventional pole-before-etch-process for quasi-phase matching in TFLN

The most basic $\chi^{(2)}$-based optical frequency mixers in TFLN rely on a
rib waveguide oriented orthogonal to the material’s crystallographic z-axis
(Fig. 1a). For efficient parametric three-wave mixing to occur in the device,
the vacuum wavelengths, $\lambda_{i}$, and effective propagation constants,
$k_{i}=2\pi n_{\text{eff},i}/\lambda_{i}$ ($i\in\\{1,2,3\\}$) (where
$n_{\text{eff},i}$ is the effective index for $\lambda_{i}$), of the three
interacting guided modes must satisfy energy conservation,
$\lambda_{3}^{-1}=\lambda_{1}^{-1}+\lambda_{2}^{-1}$, and momentum
conservation, $\Delta k\equiv k_{1}+k_{2}-k_{3}=0$. The latter condition is
also known as “phase matching” and is not, in general, satisfied for most
processes due to material and modal dispersion of waveguide modes of interest.
However, in LN—and other ferroelectric materials—a nonlinear three-wave mixing
process can be “quasi-phase matched” by periodically flipping the sign of the
second order coefficient, $\chi^{(2)}$, with period,
$\Lambda\quantity(n_{\text{LN}},t,w,d,\theta)=2\pi/\quantity(\Delta
k(n_{\text{LN}},t,w,d,\theta))$.[30] The grating period depends on material
indices of LN (buried oxide) layer at the wavelengths of interest, $n_{\rm
LN(SiO_{2})}$; TFLN thickness, $t$; waveguide rib height, $d$; waveguide top
width, $w$; and sidewall angle, $\theta$ (Fig. 1a). In $x$-cut TFLN, which is
the crystal orientation of choice for compatibility with high-performance
electro-optic devices, the QPM grating is typically fabricated by applying a
strong electric field along the crystallographic $-z$ direction using coplanar
finger electrode gratings with a period that matches the desired QPM grating
(Fig. 1b, inset); this is known as “ferroelectric poling”[31]. This creates a
QPM grating with spatial frequency, $K=2\pi/\Lambda$, along the direction of
propagation to compensate for the phase mismatch.

In the majority of works featuring QPM three-wave mixing devices, poling takes
place near the beginning of the fabrication process, before the waveguide is
defined, and thus without the knowledge of the values of $d$, $w$, and
$\theta$. The TFLN waveguide is defined using dry etching, which results in
$\pm 10~{}$\mathrm{nm}$$ uncertainty for $d$ and $w$, and $\pm$$$ for $\theta$
(Fig. 1b). Therefore, to guarantee devices operating at desired wavelengths,
fabrication uncertainties are compensated for by sweeping the poling period
across many devices to guarantee phase-matching over a wide wavelength
range[27, 28]. This, however, results in a low yield and makes it very
difficult to fabricate more complex nonlinear devices (Fig. 1e).

## Etch-before-pole process for wavelength-accurate frequency mixers in TFLN

In this work, we propose an alternative fabrication process in which
ferroelectric poling to define the QPM grating occurs after waveguide etching
(Fig. 1c). In this case, wafer-scale ellipsometry can be used both before and
after etching to determine $t$ and $d$, respectively, as well as to obtain the
material dispersion, $n_{\text{LN}}$. Furthermore, atomic force microscopy
(AFM) can also be carried out to precisely measure the cross-sectional profile
of the waveguide and thus obtain $\theta$ and $w$. Thus, the etch-before-pole
process allows for QPM gratings to be designed with full knowledge of the
waveguide geometry and material parameters. Assuming perfectly accurate
metrology tools, this allows for all devices on a wafer to operate at the
target wavelength. Thus, the proposed fabrication process can be both high-
yield and robust to fabrication imperfections.

In practice, however, systematic errors can be present in every parameter used
to calculate the phase mismatch. Conveniently, the etch-before-pole process
flow allows a small subset of calibration devices to be completed and
characterized to calibrate the metrology tools (ellipsometer and AFM)
themselves (Fig. 1d). Figure 1e provides an illustration of how different
metrology and calibration steps impact the distribution of operating
wavelengths of devices relative to a target operating wavelength,
$\lambda_{0}$.

## Experimental results

To evaluate the efficacy of our etch-before-pole approach, in enhancing device
yield while reducing the necessity for sweeping QPM grating periods, we
fabricated a total of $660$ ($360$) QPM waveguides targeting SHG of
$737~{}$\mathrm{nm}$$ light on a wafer implementing periodic (aperiodic)
poling. All the fabrication and metrology steps up to the extraction of
calibration devices are performed on $4^{\prime\prime}$ 5% MgO-doped TFLN
wafers. Calibration devices are positioned near the wafer flat so that they
can easily be separated from the wafer by dicing (Fig. 1d).

Ellipsometry performed before and after waveguide etching shows $\sim
20~{}$\mathrm{nm}$$ variations in $t$ and $d$ (corresponding to “pre-etch
thickness” and “film etched” respectively in Fig. 2a) across the wafer. Film
thicknesses are sampled at multiple points along every waveguide (Fig. 2b). A
relatively fine sampling grid of $100~{}$\mathrm{\SIUnitSymbolMicro m}$$ along
each waveguide was chosen to allow us to compare the anticipated yield for
periodic QPM gratings and aperiodic QPM grating designs, discussed below. In
the latter, poling periods are adapted to geometry fluctuations along a single
device as in Ref. [10]. We note that although local etch depth fluctuations
along a single waveguide are only on the order of several nanometers, long-
range variation across the full wafer is an order of magnitude larger. This
indicates that while the assumption of uniform etch depth may be valid at chip
scale which is that used by most demonstrations to date, it may not
necessarily hold for larger sample sizes, which could be used for novel device
geometries and co-integration of PPLN.

In addition to film thickness measurements, the waveguide cross-section
profile is measured via tapping mode AFM at multiple points across the wafer,
with one witness structure measured per 60 QPM waveguides. Combining the AFM
traces with film thickness maps provides complete knowledge of the waveguide
geometry both locally (along each QPM waveguide) and across the entire wafer.
This information is then used in finite difference eigenmode (FDE) simulations
to find the phase mismatch $\Delta k^{\rm(sim)}$ for the SHG of
$\lambda_{0}=737~{}$\mathrm{nm}$$ light. Both the fundamental and second
harmonic occupy the fundamental pseudo-transverse electric (TE00) guided mode.

Next, we theoretically investigate possible strategies to design QPM gratings
and compare their ability to produce SHG close to $\lambda_{0}$ (Fig. 3a). In
the absence of measured substrate and fabrication imperfections Method I
assumes the same and uniform QPM grating period (calculated for
$t=600~{}$\mathrm{nm}$$, $w=1.5~{}$\mathrm{\SIUnitSymbolMicro m}$$ ,
$d=300~{}$\mathrm{nm}$$, and $\theta=$$$) applied along each waveguide on the
wafer. However, due to variations in LN thickness and waveguide geometry, this
approach would result in waveguides with SHG spread across $\sim
60~{}$\mathrm{nm}$$ range around $\lambda_{0}$, resulting in poor yield.
Leveraging the knowledge of measured $t$ to design QPM gratings considerably
narrows the distribution of SHG produced by different waveguides. Two
approaches are considered: periodic (Method IIa) which uses uniform
$\Lambda(t_{0})$ based on TFLN thickness ($t_{0}$) sampled at a single point
in the middle of the waveguide, and aperiodic (Method IIb) which uses
$\Lambda\quantity[t(y)]$, the function of the position along the waveguide
length ($y$) due to measured thickness variations obtained from measurements.
However, in both cases, the center of the distribution is displaced from
$\lambda_{0}$ due to the unknown $n_{\rm LN}$, $d$, $w$, and $\theta$.
Finally, when measured values are used for all waveguide parameters, the
distribution of SHG generated by different waveguides can be re-centered on
the $\lambda_{0}$. This is true even when a periodic QPM grating
$\Lambda(n_{\rm LN},t_{0},w_{0},d_{0},\theta_{0})$ is used (Method IIIa) based
on a single waveguide geometry sample in the middle of the waveguide. The
width of the distribution is also expected to narrow compared to Method IIa
since fluctuations from device to device, due to non-uniform etch depths, are
accounted for. Finally, when aperiodic poling is used, by taking into account
all measured parameters along each waveguide (Method IIIb) to obtain the QPM
grating $\Lambda\quantity[n_{\rm LN},t(y),w(y),d(y),\theta(y)]$, all
waveguides on the wafer should produce SHG at $737~{}$\mathrm{nm}$$.

In summary, QPM grating design based on the conventional pole-before-etch
process results in wide distributions of SHG wavelengths produced by different
waveguides (I), even when the knowledge of TFLN thickness is available (IIa,
IIb). On the other hand, the etch-before-pole process reported in this work
allows complete information of the waveguide cross-section geometry to be
considered for the QPM grating design (IIIa, IIIb), and thus are expected to
improve yield on devices meeting target operating wavelength specifications.
Finally, we note that while aperiodically poled QPM designs (IIb and IIIb) are
expected to yield devices with more ideal SH spectra (Fig. 3b) and improve
yield on devices meeting specifications, its advantages must be balanced
against the significant metrology overhead (Supplementary Information)
incurred compared to periodically poled designs (II/IIIa), which only require
coarse mapping of the LN film thickness (e.g. only one measured point near the
middle of the waveguide).

The preceding analysis makes the assumption that the measurement tools and
strategies used are perfectly accurate and precise. However, in practice, both
random and systematic errors can be present in measured data, thus providing
inadequate simulation inputs. While random errors are hard to calibrate out
and will result in a finite width of the measured SHG distribution, the
systematic errors that result in displacement of the measured wavelength from
the $737~{}$\mathrm{nm}$$ target can be calibrated out. This can be
accomplished by poling and measuring a subset of calibration devices that are
processed under identical etch and metrology conditions from the full sample
to obtain a calibration curve that is used to adjust the fabricated grating
periods on all remaining devices.

The calibration sample, fabricated on the same wafer, consists of a number of
QPM waveguides with QPM grating period
$\Lambda^{\text{(sweep)}}=2\pi/\quantity(\absolutevalue{\Delta
k^{\text{(sim)}}}+\Delta k_{\text{sweep}})$ which is intentionally swept, with
$\Delta k_{\text{sweep}}$ taking on values from
$-0.0785$\mathrm{\SIUnitSymbolMicro m}$^{-1}$ to
$+0.0785~{}$\mathrm{\SIUnitSymbolMicro m}$^{-1}$. Therefore, the expected SHG
wavelength changes as a consequence of the varying sweep value, as shown by
the orange markers in Fig. 3d. In the case of perfect metrology, the measured
SHG wavelength (Fig. 3d, green markers) should be the same as the expected SHG
wavelength. However, we find that the QPM grating spatial frequency,
$K=2\pi/\Lambda$, for a device generating peak SH at $\lambda_{\text{SH}}$ is
displaced from the simulated phase mismatch for that device by $\Delta
k_{\text{offset}}\sim-0.645~{}$\mathrm{\SIUnitSymbolMicro m}$^{-1}$ (Fig. 3d).
This is a result of systematic errors that could be attributed to calibration
errors in metrology or lithography tools, or inaccuracies in the index model
used for the waveguide materials. To account for these errors, we correct the
QPM periods of all devices on the same wafer as

$\Lambda^{\text{calibrated}}=\frac{2\pi}{\absolutevalue{\Delta
k^{\text{(sim)}}}+\Delta k_{\text{offset}}}$ (1)

in order to ensure that the measured SHG spectrum peak coincides with the
expected SHG wavelength. Here, we assume that $\Delta k_{\text{offset}}$ is
constant for all waveguides on the wafer.

Using this calibration approach, we show that $73\%$ of devices out of $84$
measured (total of $280$ devices on Wafer A fabricated without error and not
used for calibration) support SHG of $(737\pm 5)~{}$\mathrm{nm}$$ without
additional tuning (Fig. 3, upper panel) despite implementing a simple periodic
poling. Devices sampled from a separate $4^{\prime\prime}$ wafer run
implementing aperiodic poling (Wafer B) have a somewhat narrower distribution
of operating wavelengths (Fig. 3e, lower panel). They are also blue-shifted by
$\sim 4~{}$\mathrm{nm}$$ from the target wavelength, likely due to changes in
metrology tool conditions during processing (Supplementary Information). These
devices are used in subsequent wavelength tuning and trimming experiments.

## Post-fabrication wavelength trimming and tuning

Thermal tuning leveraging the thermo-optic effect in TFLN is the conventional
approach to control the operating wavelength of QPM device [28, 32, 33]. In
our approach, we use a large heater to increase the temperature of Wafer B by
$\Delta T_{\text{max}}=120~{}$\mathrm{K}$$ above room temperature and measure
the wavelength of SHG signal (Fig. 4a).

This allows us to experimentally measure the thermo-optic tuning rate which is
$\frac{\differential\lambda_{\text{SH}}}{\differential
T}=0.1~{}$\mathrm{n}\mathrm{m}\mathrm{/}\mathrm{K}$$. Since increasing
temperature can only red-shift the SHG wavelength, it is advantageous to start
with blue-shifted QPM devices, like those found in our Wafer B. Indeed, Figure
4b shows that a device yield for Wafer B is $\sim 96\%$ at the maximum tested
temperature. Here, we define device yield as the fraction of devices within
tuning range.

In addition to cooling (not demonstrated here), we show that blue-shifting the
operating wavelength of TFLN QPM devices can be achieved by depositing top
cladding. We experimentally find that the operating wavelength can be blue-
shifted by $\sim 50~{}$\mathrm{nm}$$ by depositing only $25~{}$\mathrm{nm}$$
of silica cladding. The blue-shifting effect saturates at silica cladding
thicknesses above $200~{}$\mathrm{n}\mathrm{m}$$, since the optical mode is
entirely contained within TFLN and silica, and its overlap with the air layer
approaches zero (Fig. 4c, lower panel). The trimming range of this approach
($>100~{}$\mathrm{nm}$$) is massive compared to thermo-optic tuning, and the
amount trimmed can be very precisely controlled using atomic layer deposition.
However, it must be noted that this cladding trimming approach will also
modify waveguide dispersion, which can be inferred from the SHG spectra
becoming narrower as more cladding is added (Fig. 4c, upper panel). Thus for
many dispersion-engineered QPM devices[8, 33, 34, 35], care must be taken when
applying cladding trimming to ensure dispersion engineering goals are still
met.

## Summary and outlook

In conclusion, we develop an etch-before-pole process flow for QPM three-wave
mixing devices optimized for scalability and wavelength-accurate operation
within the limits of standard processing and metrology conditions. Wafer-scale
fabrication of large arrays of QPM devices for SHG of
$\lambda_{0}=737~{}$\mathrm{nm}$$ shows robustness to variations in etch depth
and systematic errors in input parameters used in QPM grating design due to
our calibration process. Where thermal tuning is possible, we demonstrate up
to $96\%$ operating at the $737~{}$\mathrm{nm}$$ using an off-chip heater;
future integration with efficient on-chip heaters [36] will allow individual
devices to be tuned without affecting the remaining circuit. For applications
where thermal tuning is not possible, such as interfacing with single-photon
emitters at cryogenic temperatures [37], we also demonstrate cladding trimming
to blue-shift operating wavelengths by $>100~{}$\mathrm{nm}$$. We note that by
making further improvements in the accuracy of the ellipsometer and AFM, it
may be possible to eliminate the systematic errors and may render calibration
step and trimming unnecessary.

Additionally, we also note that for the current poling electrode configuration
used in our etch-before-pole approach, the expected maximum normalized SH
conversion efficiency is expected to be reduced to $\sim 23\%$ compared to the
conventional pole-before-etch approach because poling only occurs in the
waveguide slab. Initial results that use a modified poling electrode geometry
for the etch-before-pole approach to ensure that poling also occurs in the
waveguide ridge have been demonstrated [38], and provide a promising path
towards recovering ideal conversion efficiency.

Improvements to wavelength-accurate QPM device yields in TFLN can accelerate
the integration of QPM devices into more complex photonic integrated circuits
or with other devices with relatively inflexible operating wavelength ranges,
such as solid-state defect centers [20]. This can be especially helpful in the
near- to medium-term while more precise fabrication techniques for the
platform, such as atomic layer etching [39], and process control best-
practices are still under development. In particular, the SHG process chosen
for the demonstrations in this work serves as a suitable proxy for identifying
whether a device is a compatible frequency conversion module for
$737~{}$\mathrm{nm}$$ emission from silicon-vacancy centers in diamond for
most waveguide geometries in TFLN. Thus, this work has immediate applications
in scalable quantum frequency conversion for realizing large-scale, low-loss,
fiber-based quantum networks.

## Acknowledgements

This work was supported in part by AFOSR FA9550-20-1-01015 (D.R., N.S.),
A*STAR National Science Scholarship (S.L.), AWS Center for Quantum
Networking’s research alliance with the Harvard Quantum Initiative (C.X.,
J.Y., A.S., L.M., D.R., M.L.), Ford Foundation Fellowship (D.R.), Harvard
University Dean’s Competitive Fund from Promising Scholarship (M.L.), Harvard
Quantum Initiative (N.A.), NASA 80NSSC22K0262 (J.Y., S.G., N.S.), NASA
80NSSC23PB442 (A.S.), NSF Engineering Research Center for Quantum Networks No.
EEC-1941583 (C.X., E.M., A.Z., N.S.), NSF GRFP-1745303 (D.R.), NSF OMA-2137723
(C.X., D.B.), NSF OMA-2138068 (S.G., N.S.), and ONR N00014-22-C-1041 (S.G.,
M.L.). Device fabrication was performed at the Center for Nanoscale Systems
(CNS), a member of the National Nanotechnology Coordinated Infrastructure
Network (NNCI), which is supported by the National Science Foundation under
NSF Grant No. 1541959.

## Author contributions

C.X. developed the fabrication process, designed the devices and experiments.
C.X. and B.D. optimized the ferroelectric poling process. A.S., S.L., and J.Y.
fabricated devices and performed measurements with the assistance of N.A.
C.X., S.L., and J.Y. analyzed the data. S.G. assisted with second harmonic
imaging. D.R. and A.Z. assisted with the construction of the second harmonic
imaging system. A.S. and L.M. developed the wafer scale process for etching
lithium niobate. E.M. and D.B. assisted with developing film thickness and
index measurement recipes. M.L. and N.S. supervised the project. C.X., S.L.,
J.Y., A.S., and M.L. wrote the manuscript in collaboration with the remaining
co-authors. These authors contributed equally: C.X., S.L., J.Y., and A.S.

## Competing interests

M.L. is involved in developing lithium niobate technologies at HyperLight
Corporation. The remaining authors declare no competing interests.

Figure 1: Etch-before-pole fabrication process flow for nonlinear frequency
mixers in thin-film lithium niobate (TFLN).  a, Illustration of a conventional
quasi-phase matched (QPM) waveguide for parametric three-wave mixing in
$x$-cut TFLN. Alternating dark and light bands along the waveguide correspond
to the alternating signs of optical $\chi^{(2)}$. The QPM period, $\Lambda$,
required to phase match three wavelengths of interest is dependent on the LN
(silica) material index, $n_{\rm LN(SiO_{2})}$, as well as the waveguide
cross-section. The latter crucially depends on TFLN thickness, $t$; etch
depth, $d$; top width, $w$; and sidewall angle, $\theta$. We note that QPM
designs are far less sensitive to $n_{SiO_{2}}$ than the remaining labeled
parameters; nonetheless, we label it here for completeness. b, Schematic of
conventional pole-before-etch fabrication process flow, where $n_{\text{LN}}$
and t are the only measured parameters. Ferroelectric poling via a high
voltage (HV) pulse applied to coplanar finger electrodes is used to pattern
the QPM grating before etching to define the waveguide profile (inset). c,
Schematic of etch-before-pole process proposed here. Film thickness is
measured both pre- and post-waveguide etching. Atomic force microscopy (AFM)
is used to evaluate the waveguide cross-section profile. $\Lambda$ thus can be
designed using complete information of the waveguide cross-section geometry.
Ferroelectric poling is carried out by applying a HV pulse to coplanar
electrodes, with the resulting domain inversion only occurring in the
waveguide slab (inset). d, Schematic of systematic error calibration carried
out using a small subset of total devices (left) with an example of how this
is implemented on a $4^{\prime\prime}$ wafer (right). Dotted lines indicate
the location of the target operating wavelength, $\lambda_{0}$. Calibration
devices, comprising $<20\%$ of the total relevant QPM devices in each wafer
run, are positioned near the wafer flat, separated from the remaining devices
by dicing, and measured first to calibrate out systematic errors. $\Lambda$
only needs to be swept in the calibration devices and can be fixed at the
calibrated $\Lambda$ for the target process. e, Illustrations of the how
distribution of device operating wavelengths is expected to deviate from the
target wavelength, $\lambda_{\text{target}}$, when QPM grating periods are
designed with (I) no metrology information, (II) only pre-etch film thickness,
(III) complete measured waveguide cross-section geometry, and (IV) complete
measured waveguide cross-section geometry with systematic error calibration.

Figure 2: Device geometry variation in a representative wafer run. a, Non-
contact optical measurements of LN film thickness before etching (left) and
the amount etched (right) from a representative wafer run. The amount etched
is calculated from the film thickness difference between pre- post-etch wafer
maps (see Supplementary Information for post-etch data) and shows global
variation on the order of $\sim 20~{}$\mathrm{nm}$$. Black outlines indicate
locations of dies containing QPM devices relevant to this work; locations of
dies corresponding to other work are outlined in light gray for completeness.
Devices below the horizontal dotted line are used for systematic error
calibration, and thus are poled and measured prior to the remaining test
devices on the wafer. b, Not-to-scale diagram of film thickness measurement
locations on a QPM device die. Blue markers indicate the location of scan
points relative to QPM devices, represented by purple lines (left). Local pre-
etch film thickness and etch depth variation along a single waveguide (top
right). Simulated fundamental transverse electric (TE00) mode profile at the
target second harmonic (SH) wavelength,
$\lambda_{\text{target}}=737~{}$\mathrm{nm}$$; waveguide profile from the
nearest AFM measurement site is used in the simulation (lower right). Scan
pattern shown is for a wafer implementing aperiodic QPM designs; a less dense
scan pattern is used for a separate wafer run implementing periodic QPM to
reduce metrology overhead (Extended Data Fig. 1).

Figure 3: Estimated and measured device operating wavelength distributions. a,
Simulated distribution of $\lambda_{\text{SH}}$ for the $N=360$ QPM devices in
the wafer pictured in Fig. 2a for five different types of QPM grating. The QPM
grating design methods considered are: (I) periodic poling based on ideal
waveguide cross-section geometry ($t=600~{}$\mathrm{nm}$$,
$h=300~{}$\mathrm{nm}$$, $w=1.5~{}$\mathrm{\SIUnitSymbolMicro m}$$,
$\theta=$$$); (IIa) periodic poling using a single-point pre-etch film
thickness measurement; (IIb) locally varying period calculated using data at
each film thickness measurement location; (IIIa) periodic poling based on the
measured waveguide geometry at a single point along the waveguide, and (IIIb)
locally varying period calculated using measured waveguide geometry at each
film thickness measurement location. Methods I and II can be used in the
conventional pole-before-etch process, whereas Method III is only possible for
the etch-before-pole process. Dotted lines indicate the position of
$\lambda_{0}$. b, Example SH spectra for each QPM design method considered in
(a). IIa (IIIa) has a wider spread relative to IIb (IIIb) due to a more
displaced $\lambda_{\text{SH}}$ (markers). c, Comparison of estimated and
measured SH spectra for a calibration device with QPM grating designed using
Method IIIb. Simulated phase mismatches are given a swept offset, $\Delta
k_{\text{sweep}}$, in the calibration device (Eq. 1) to deliberately produce a
QPM design where $\lambda_{\text{SH}}$ is red-shifted relative to
$\lambda_{0}$ (orange curve). Measured data (green curve) reproduces the ideal
sinc-squared SH spectrum well but is blue-shifted relative to the theoretical
estimate. d, Estimated and measured $\lambda_{\text{SH}}$ for a set of
calibration devices. Estimation lacks curvature present in the measured data
due to first-order estimation (Methods). Dotted line indicates the position of
${\lambda_{0}}$, while the arrow indicates $\Delta k_{\text{offset}}$ used for
calibration of remaining devices on the same wafer. e, Distributions of
measured $\lambda_{\text{SH}}$ for test devices on two wafer runs relative to
$\lambda_{0}$ (dotted line) after systematic error calibration is applied.
$n=84$ ($n=144$) devices are sampled for periodically poled Wafer A
(aperiodically poled Wafer B) out of a population of $N=280$ ($N=240$) non-
calibration devices without known non-poling processing defects (Methods). The
total number of non-calibration devices fabricated in Wafer A (B) is $600$
($300$).

Figure 4: Device yields vis-à-vis tunability of target three-wave mixing
process. a, Thermo-optic tuning up to $\Delta
T_{\text{max}}=120$\mathrm{\SIUnitSymbolCelsius}$$ above room temperature. SH
spectra maintain approximately the same shape over the tuning range (upper
panel). Red-shifting of up to $12.1~{}$\mathrm{nm}$$ is demonstrated (lower
panel) using an off-chip ceramic heater (inset). b, Yield on devices with
operating wavelengths within thermo-optic tuning range of $\lambda_{0}$ as a
function of the maximum achievable temperature for measured distributions in
Fig. 3d. c, Tuning of device operating wavelength via deposition of thin
layers of cladding oxide, $d_{\rm SiO_{2}}$(lower panel inset). Experimental
data showing $>100~{}$\mathrm{nm}$$ blue-shift of the operating wavelength
observed, with the rate of blue-shift decreasing as more silica cladding is
deposited (lower panel). At large cladding thicknesses, widths of the SH
spectra decrease as operating wavelengths are blue-shifted, indicating
increasing group velocity mismatch between the fundamental and second harmonic
of the quasi-phase matched process (upper panel); the impact of this is minor,
however, for the small amounts of wavelength trimming ($<50~{}$\mathrm{nm}$$)
necessary in most cases.

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## Methods

### Device fabrication

Devices are fabricated on commercially available $4^{\prime\prime}$ thin-film
lithium niobate on insulator wafers (NanoLN). The nominal material stack
consists of a $600~{}$\mathrm{nm}$$ device layer ($x$-cut 5% MgO-doped lithium
niobate) on $2~{}$\mathrm{\SIUnitSymbolMicro m}$$ of buried oxide on a silicon
handle. Prior to processing, variable angle spectroscopic ellipsometry is used
to measure the refractive index of the material as a function of wavelength.

Alignment markers are first patterned on the wafer via photolithography and
metal lift-off. An aligned ellipsometry step is then carried out to produce a
map of device layer film thickness. For periodic poling, film thickness is
sampled with a step size of $1~{}$\mathrm{mm}$$ in between pairs of adjacent
QPM waveguides (Extended Data Fig. 1) to minimize metrology overhead. For
aperiodic poling, film thickness is sampled with a step size of
$100~{}$\mathrm{\SIUnitSymbolMicro m}$$ along each QPM waveguide (Fig. 2b).

Following pre-etch metrology, a hard mask of $600~{}$\mathrm{nm}$$ of silicon
dioxide is deposited on the wafer via plasma-enhanced chemical vapor
deposition (PECVD). Electron beam lithography is then used to pattern the
waveguide layer using a negative tone resist (ma-N 2400). The pattern is then
transferred to the hard mask and the device layer via dry etching. The nominal
etch depth of $300~{}$\mathrm{nm}$$ is targeted by calibrating the etch time
in situ.

Post-etch ellipsometry is carried out to map the amount of remaining slab in
the device layer at the same points sampled during the pre-etch measurement.
Remaining waveguide geometry parameters, such as etch angle and measured top
width, are extracted by AFM on a witness feature on each QPM device die (each
comprising $60$ QPM devices). A high-aspect ratio probe (Nanosensors AR5-NCLR)
is used to minimize the impact of distortions introduced by the probe tip
profile. The measured waveguide geometry parameters are used in FDE
simulations to calculate local variations in the expected phase mismatch of
the target $\chi^{(2)}$ frequency conversion process.

Coplanar finger electrodes (Fig. 1b, inset) for ferroelectric poling are
patterned via electron beam lithography using standard positive resist (PMMA
C4) and metal lift-off ($130~{}$\mathrm{nm}$$ gold on $25~{}$\mathrm{nm}$$
chromium). Following metal lift-off, a cap layer of photoresist (Microposit
S1800 series) is spun on to prevent dielectric breakdown through air during
poling. Contact pad windows are lithographically defined to allow probing.
High-voltage pulses are applied to the finger electrodes to create the QPM
grating for the target $\chi^{(2)}$ frequency conversion process. Second
harmonic microscopy is used to validate the poling quality. Electrodes are
removed via wet etch prior to measurement.

In each wafer run, the small wafer segment containing calibration devices is
cleaved or diced from the full wafer after waveguides are etched so that they
can be poled and measured separately from the test devices. All devices in the
remaining segment are processed simultaneously after the calibration parameter
is extracted from measurements of the calibration devices. For cladding
trimming, the same PECVD silica was deposited in $\sim 25~{}$\mathrm{nm}$$
increments.

### Waveguide cross-section geometry metrology

Pre- and post-etch film thickness measurements are carried out using a
variable-angle spectroscopic ellipsometer (SE). Film thickness map
measurements were carried at a fixed angle of $None$. Focusing probes are used
to reduce the spot size to $<100~{}$\mathrm{\SIUnitSymbolMicro m}$$ to resolve
fine local film thickness variations for aperiodic poling. Film thickness data
is extracted from raw ellipsometric data by fitting to in-house index models
for both the device and buried oxide layers. The in-house index models are
developed by fitting multi-angle SE measurements of an as-received wafer to
Sellmeier index models in the $500~{}$\mathrm{nm}$$ to $2,500~{}$\mathrm{nm}$$
wavelength range.

We note that both ellipsometry and AFM provide measurements of etch depth,
$d$. Under ideal tool conditions, the etch depth extracted from these two
measurement approaches should give the same results. However, we find that
this is generally not the case, which indicates the existence of calibration
errors. We find that data obtained from ellipsometry results in better
predictions of the SHG wavelength. For this reason, we also use ellipsometry
measured etch depth to calibrate the AFM obtained one, which also calibrates
that sidewall measurement obtained by AFM (waveguide width AFM measurements
are not affected).

### Simulation of phase-mismatch at the target three-wave mixing process

After calibration, ellipsometry and AFM data are combined to produce a
complete waveguide cross-section profile (Fig. 2b, lower right) for FDE
simulations (Lumerical MODE). FDE simulations are performed at the second
harmonic wavelength $\lambda_{\text{SH}}=\lambda_{0}$ and fundamental harmonic
wavelength $\lambda_{\text{FH}}=2\lambda_{0}$ to find the phase mismatch,
$\Delta k^{\text{(sim)}}=k_{\text{SH}}-2k_{\text{FH}}$, where
$k_{\text{SH(FH)}}$ is the propagation constant of the TE00 mode at the SH
(FH) wavelength.

One AFM measurement is carried for per set of $60$ QPM devices due to AFM
being significantly more time intensive. For each set of devices that share
the same AFM waveguide profile, only pre- and post-etch LN thickness from the
ellipsometry from point-to-point. For aperiodic poling, $3060$ points are
measured for each set of devices. An exhaustive simulation at the requisite
FDE mesh size ($5~{}$\mathrm{nm}$\times 5~{}$\mathrm{nm}$$) is computationally
intensive. To mitigate this, the $2$-dimensional parameter space of post-etch
LN thickness and the etch depth for devices using the same AFM profile is
binned into a 2-dimensional histogram with $0.5~{}$\mathrm{nm}$\times
0.5~{}$\mathrm{nm}$$ bins. The coordinates of the vertices of each non-empty
bin are recorded and simulated (Extended Data Fig. 2a), reducing the number of
simulations for similar geometries. Since $\Delta k^{\text{(sim)}}$ is smooth
and continuous, bilinear interpolation based on simulation results at the
vertex coordinates (Extended Data Fig. 2b) can be used to calculate $\Delta
k^{\text{(sim)}}$ at each measured point (Extended Data Fig. 2c).

### Theoretical estimates of SH spectra

Theoretical estimates of the SH spectra, such as those in Fig. 3a, are
numerically calculated using FDE-simulated propagation constants,
$k_{\text{eff}}=k_{\text{eff}}(\lambda,y)$ of the TE00 mode at wavelength
$\lambda$ using the measured waveguide cross-section geometry at position $y$
along a QPM device the method described in Ref. [10]. Fluctuations in
$k_{\text{eff}}$ below the the film thickness map resolution of $\Delta
y=100~{}$\mathrm{\SIUnitSymbolMicro m}$$ are ignored. To ensure
$\lambda_{\text{SH}}$ can be correctly identified for a wide range of geometry
parameters, a wide simulation range of
$\lambda_{\text{SH}}=600~{}$\mathrm{nm}$$ to $850~{}$\mathrm{nm}$$ was chosen.
To reduce simulation complexity for the large number of waveguide geometries
in each wafer run, $k_{\text{eff}}$ is only simulated for two wavelengths:
$\lambda_{\text{SH,0}}=\lambda_{0}$ and $\lambda_{\text{FH, 0}}=2\lambda_{0}$.
For SH (FH) wavelengths other than $\lambda_{\text{SH(FH),0}}$, a first-order
estimate of $k_{\text{eff}}$ is used:

$k_{\text{eff}}\quantity(\lambda_{\text{SH(FH)}},y)\approx
k_{\text{eff}}\quantity(\lambda_{\text{SH(FH), 0}},y)-\frac{2\pi
n_{g}\quantity(\lambda_{\text{SH(FH),0}},y)}{{\lambda_{\text{SH(FH),0}}}^{2}}\Delta\lambda,$

where $\Delta\lambda=\lambda_{\text{SH(FH)}}-\lambda_{\text{SH(FH), 0}}$, and
the group index, $n_{g}\quantity(\lambda_{\text{SH(FH)}},0,y)$, is also
extracted from the FDE simulation at $\lambda_{\text{SH(FH), 0}}$. At large
$\Delta\lambda$, higher-order dispersion terms must be taken into account for
a more accurate calculation of $k_{\text{eff}}(\lambda_{\text{SH(FH)}},y)$,
and consequently $\lambda_{\text{SH}}$. This is evident in Fig. 3d, where the
theoretical estimate of $\lambda_{\text{SH}}$ does not reflect the curvature
present in the measured data. Notwithstanding, the first-order estimate is
sufficient for identifying qualitative differences in the
$\lambda_{\text{SH}}$ for different methods of designing the QPM grating (Fig.
3b).

### Measurement of SH spectra

The SH spectrum of a QPM device is measured by measuring the SH power output
as a function of input FH wavelength. Two FH sources are combined for
continuous wavelength coverage from the telecommunications E-band (Santec
TSL-550; $1355~{}$\mathrm{nm}$$ to $1485~{}$\mathrm{nm}$$) to L-band (Santec
TSL-710; $1480~{}$\mathrm{nm}$$ to $1640~{}$\mathrm{nm}$$). Light is coupled
into and collected from the device under test (DUT) using lensed fibers (OZ
Optics). A fiber polarization controller at the output of each FH laser is
used to ensure TE input into the device under test (DUT) in order to measure
the target type-0 SHG process. The FH wavelength is stepped with a resolution
of 0.2 nm and the SH power is recorded at each FH wavelength step using a
fiber-coupled visible power meter (Thorlabs S150C). A reference curve of the
FH power at the DUT output as a function wavelength is also acquired (Thorlabs
S155C) in a separate sweep following the SH spectrum measurement.

All measurements are performed at room temperature with the exception of the
thermal tuning experiment. The thermal tuning experiment is performed by
heating the device die using an off-chip $20~{}$\mathrm{W}$$ metal ceramic
heater; device temperature is measured using a
$100~{}$\mathrm{\SIUnitSymbolOhm}$$ platinum resistance temperature detector.

### Device sampling

The distribution of operating wavelengths of devices in each wafer run is
estimated by measuring the SH spectra of a subset of the population of test
devices without known non-poling processing defects. An accounting of the
total number of devices fabricated in each wafer run, and known processing
defects is provided below:

#### Wafer A

A total of 660 devices relevant to this work are fabricated in this wafer run,
with $600$ ($60$) devices designated as test (calibration) devices. Of the
test devices, 40 devices with anomalous top widths (Extended Data Fig. 3a) due
to stitching errors in the electron beam lithography step are excluded from
consideration. A further $280$ devices’ waveguide profiles are measured with a
different AFM tip than the calibration devices’ due to damage to the original
tip, and are thus excluded since the assumption of consistent systematic
errors does not hold. The population of test devices without known non-poling
processing defects in Wafer A is $N=280$; the location of excluded devices is
indicated in Extended Data Fig. 3b. During measurement, a total of $n=84$
($35\%$) devices are sampled to estimate the distribution of
$\lambda_{\text{SH}}$ shown in Fig. 3e (upper panel). A subset of devices
measured with a different AFM tip were tested to verify that the systematic
error from waveguide profiling changes with AFM tip used (Extended Data Fig.
3c).

#### Wafer B

A total of $360$ devices relevant to this work are fabricated in this wafer
run, with $300$ ($60$) devices designated as text (calibration) devices. Of
the test devices, an error in the extraction of the post-etch film thickness
data during QPM design resulted in anomalous $\lambda_{\text{SH}}$ for $60$
devices. The error in the post-etch film thickness is identified by comparing
the fine wafer map data against a reference coarse wafer map (Extended Data
Fig. 3d). The correct post-etch film thickness is subsequently extracted
during post-mortem analysis (Extended Data Fig. 3d, right panel), and the
devices designed with erroneous film thickness data are excluded from the
population of the valid test devices. The population of test devices without
known non-poling processing defects in Wafer A is $N=240$. During measurement,
a total of $n=144$ ($60\%$) devices are sampled to estimate the distribution
of $\lambda_{\text{SH}}$.

Extended Data Figure 1: Film thickness map for Wafer A implementing periodic
poling.  Pre-etch film thickness and amount of film etched for wafer run
implementing periodic QPM grating designs (Wafer A). The number of measured
points—and therefore metrology overhead—is reduced by an order of magnitude by
sampling along each device with a step size of $1~{}$\mathrm{mm}$$ rather than
the $100~{}$\mathrm{\SIUnitSymbolMicro m}$$ step size used for Wafer B, which
implements aperiodic QPM grating designs (Fig. 2b).

Extended Data Figure 2: Simulation of phase mismatch for target SHG process.
a, Distributions of pre- and post-etch LN thickness and etch depth for a set
of $60$ QPM devices using the same AFM cross-sectional data for simulation
(upper panel). A $2$-D distribution of post-etch thickness and etch depth
(lower left). Phase mismatch for the target process, $\Delta
k^{\text{(sim)}}$, is simulated for the coordinates at the corners of each
occupied bin (lower right, markers). b, $\Delta k^{\text{(sim)}}$ at selected
coordinates are smooth and continuous and therefore can be interpolated. c,
Bilinear interpolation of simulated points to the each measured waveguide
geometry is used to extract the $\Delta k^{\text{(sim)}}$ values used to
design QPM gratings. Each point in the scatter plot represents a measured
waveguide geometry, which is defined by its slab thickness (post-etch
thickness) and rib height (etch depth).

Extended Data Figure 3: Non-poling processing defects.  a, Comparison of AFM
profile of waveguides on Wafer A with and without EBL stitching error. The
waveguide top width is noticeably dilated relative to the nominal top width
(dotted lines) for waveguides affected by stitching error (lower panel),
whereas unaffected waveguides have close to nominal top width (upper panel).
b, Wafer A devices in locations highlighted in magenta feature non-poling
processing defects and are excluded from the aggregate shown in Fig. 3e (upper
panel). All devices located within magenta boxes are excluded because a new
AFM tip had to be used for waveguide profiling instead of the original tip
used to profile the calibration devices, and therefore feature different
systematic errors compared to the calibration devices. c, $n=75$ ($27\%$)
devices with waveguide profiles taken using the new AFM tip are measured. We
verify that the distribution $\lambda_{\text{SH}}$ for these devices are
indeed shifted relative to the correctly calibrated devices (original tip),
reflecting a different systematic error introduced by using the new tip.

Extended Data Figure 4: Impact of reduced overlap between poled region and
optical modes on conversion efficiency.  a, False-color scanning electron
micrograph of an etch-before-pole waveguide after dry-etching to expose LN
$z$-faces and wet etching using $49\%$ hydrofluoric acid (HF) to expose
structure of inverted domains. The region that is dry-etched to expose LN
$z$-faces is bounded by dashed yellow lines. The position of the waveguide
ridge is highlighted in purple. Only the region immediately below the
waveguide ridge, corresponding to the waveguide slab, shows corrugation
indicative of differential etching of $+z$\- and $-z$-faces in HF. This shows
that domain inversion in the etch-before-pole process only propagates through
the waveguide slab. b, Measured waveguide profile along with the simulated
$1/e$ contours of the fundamental TE SH (FH) electric fields,
$E_{\text{SH(FH)}}$, for a fully poled waveguide (upper panel) and a partially
poled waveguide (lower panel) with the poled region shaded in black.
$d_{\text{poled}}$ indicates the thickness of poled LN measured from the
bottom of the LN film. c, Estimated normalised conversion efficiency for the
target SHG process as a function of $d_{\text{poled}}$. Marker indicates the
normalised conversion efficiency for a configuration in which only slab of the
waveguide is poled for the waveguide geometry shown in (b).