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K. Parto, S. I. Azzam, N. Lewis, S. D. Patel, S. Umezawa, [K. Watanabe](https://orcid.org/0000-0003-3701-8119), [T. Taniguchi](https://orcid.org/0000-0002-1467-3105), G. Moody

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[Cavity-Enhanced 2D Material Quantum Emitters Deterministically Integrated with Silicon Nitride Microresonators](https://mdr.nims.go.jp/datasets/724c9aca-d0d2-475a-93a9-cab3bb21b6fc)

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Cavity-Enhanced 2D Material Quantum Emitters Deterministically Integrated with Silicon Nitride MicroresonatorsCavity-Enhanced 2D Material Quantum Emitters DeterministicallyIntegrated with Silicon Nitride MicroresonatorsK. Parto,△ S. I. Azzam,△ N. Lewis, S. D. Patel, S. Umezawa, K. Watanabe, T. Taniguchi, and G. Moody*Cite This: Nano Lett. 2022, 22, 9748−9756 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: Optically active defects in 2D materials, such ashexagonal boron nitride (hBN) and transition-metal dichalcogenides(TMDs), are an attractive class of single-photon emitters with highbrightness, operation up to room temperature, site-specific engineer-ing of emitter arrays with strain and irradiation techniques, andtunability with external electric fields. In this work, we demonstrate anovel approach to precisely align and embed hBN and TMDs withinbackground-free silicon nitride microring resonators. Through thePurcell effect, high-purity hBN emitters exhibit a cavity-enhancedspectral coupling efficiency of up to 46% at room temperature,exceeding the theoretical limit (up to 40%) for cavity-free waveguide-emitter coupling and demonstrating nearly a 1 order of magnitudeimprovement over previous work. The devices are fabricated with a CMOS-compatible process and exhibit no degradation of the 2Dmaterial optical properties, robustness to thermal annealing, and 100 nm positioning accuracy of quantum emitters within single-mode waveguides, opening a path for scalable quantum photonic chips with on-demand single-photon sources.KEYWORDS: quantum emitter, microresonator, silicon nitride, Purcell enhancement, hexagonal boron nitrideSolid-state single-quantum emitters (SQEs) integrated withchip-scale photonic circuitry are key building blocks forquantum information technologies, including linear opticalcomputing, cluster state generation, quantum key distribution,and quantum random number generation.1−3 Numerous SQEscapable of high-purity single-photon emission have beendiscovered in several materials, including semiconductorquantum dots,2 diamond,4 silicon nitride,5 and two-dimen-sional materials.6 The integration of SQEs with CMOS-compatible photonics would address a longstanding need forcombining the manufacturability and scalability inherent tosilicon-based photonics with materials that host high-qualitySQEs. Heterogeneous integration techniques have led tosuccessful demonstrations at cryogenic temperatures, includingarrays of diamond SQEs coupled to aluminum nitride photonicintegrated circuits (PICs)7 and self-assembled quantum dotsintegrated with silicon nitride.8,9 Yet, scalable strategies for theintegration of SQEs with silicon-based PICs have not yet beendemonstrated. Four key requirements are necessary to addressthis challenge: (1) a host material with high purity, highindistinguishability (V), and bright emitters, (2) the ability tointegrate the SQE host material with the PIC platform withoutdegrading the optical properties, (3) control of the emissionwavelength and precise alignment within low-loss andbackground-free single-mode waveguide structures, and (4)integration with microresonators to enable Purcell enhance-ment of single-photon extraction efficiency (η) and indis-tinguishability (maximizing η × V) into a single optical mode.Of the SQE platforms, defect-type emitters in 2Dmaterials6,10−12 have emerged as an attractive approach forengineering single-photon sources. SQEs have been identifiedin several 2D materials spanning ultraviolet to telecommuni-cations wavelengths, including hexagonal boron nitride(hBN),13−15 transition-metal dichalcogenides (TMDs),16−23and heterostructures.23,24 In hBN and WSe2, >10 MHzemission rates25,26 and 95% single-photon purity have beenreported. Through strain and defect engineering, emitters canbe aligned into arrays,27,28 and nanophotonic integrationfurther enhances their brightness.29,30 SQEs in hBN areparticularly appealing due to a 5.7 eV band gap, which enablesroom-temperature generation of single photons with up to 93%purity.25 The observation of mechanically decoupled emittersin hBN with transform-limited line widths shows a promisingpath toward the emission of indistinguishable photons atcryogenic temperatures.31,32 Both indistinguishability and on-chip brightness are important, and thus it is critical tomaximize the coupling efficiency−indistinguishability product(η × V) while maintaining a high purity of the emitters. WhileReceived: August 10, 2022Revised: October 26, 2022Published: November 1, 2022Letterpubs.acs.org/NanoLett© 2022 The Authors. Published byAmerican Chemical Society9748https://doi.org/10.1021/acs.nanolett.2c03151Nano Lett. 2022, 22, 9748−9756Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on December 18, 2022 at 07:16:56 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="K.+Parto"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="S.+I.+Azzam"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="N.+Lewis"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="S.+D.+Patel"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="S.+Umezawa"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="K.+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="T.+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="G.+Moody"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.nanolett.2c03151&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/nalefd/22/23?ref=pdfhttps://pubs.acs.org/toc/nalefd/22/23?ref=pdfhttps://pubs.acs.org/toc/nalefd/22/23?ref=pdfhttps://pubs.acs.org/toc/nalefd/22/23?ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.nanolett.2c03151?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org/NanoLett?ref=pdfhttps://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://acsopenscience.org/open-access/licensing-options/Figure 1. Universal platform for precision integration of 2D quantum emitters in silicon nitride photonics. (a) The family of 2D materials,including hBN emitters at UV15,57 and visible25 wavelengths, TMD monolayers,23,26,52 and TMD heterostructures,24,58 exhibiting a rich spectrumof quantum emitters spanning the ultraviolet-to-telecommunications wavelength transparency window of silicon nitride photonics. The height ofeach bar indicates the reported intensity of the photoluminescence from the class of emitters (the gray data points are brightness-corrected for theobjective extraction efficiency, whereas the blue data points are reported at the detector). (b) Concept for the deterministic integration of a 2Dmaterial quantum emitter embedded within a silicon nitride microresonator with its electric dipole aligned to maximize overlap with the cavitymodes for large Purcell enhancement and coupling efficiency.Figure 2. Site-specific and momentum-aligned integration of hBN SQEs to low-emission silicon nitride. (a) Refractive index of silicon nitride as afunction of decreasing silane/ammonia ratio, R. (b) Background emission of silicon nitride as a function of R. At R = 20, the background emission issufficiently suppressed for high-purity measurements of hBN SQEs. (c) PL spectrum of an hBN SQE covered with 100 nm of low-stressstochiometric PECVD Si3N4. (d) PL spectra of an hBN SQE before (red) and after (blue) 100 nm deposition of nitrogen-rich nonstochiometricPECVD SiN and 1000 °C rapid thermal annealing, acquired at the same excitation power and integration time as in (c). (e) To position the flakewith respect to the photonic structure, thin hBN flakes are exfoliated on PECVD SiN films with an optional thickness (topt) that is either equal to allor half of the designed thickness of the waveguide for top or embedded flakes, respectively. Alternatively, to position the flake on the bottom of thewaveguide, hBN can be exfoliated directly on the SiO2 substrate. Gold alignment markers are patterned with electron-beam lithography in closeproximity to the flake. (f) Position and dipole orientation of quantum emitters determined by high numerical-aperture polarization-resolvedmicroscopy and raster scanning of the sample. (g) Thin-film PECVD SiO2 for protecting TMD flakes from damage during SiN PECVD. (h)Deposition of remaining SiN, if necessary, to complete the photonic layer. (i) Electron-beam lithography and ICP-RIE etching used to define thephotonic circuits. (j) Final PECVD SiO2 for the cladding layer.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.2c03151Nano Lett. 2022, 22, 9748−97569749https://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig2&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.2c03151?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asprevious reports have shown 2D emitters coupled to fiber andplanar cavities for off-chip collection,33−35 2D emittersintegrated with cavities for on-chip collection into waveguideshave not been demonstrated yet. Previous on-chip integrationstrategies that have placed hBN and WSe2 directly onwaveguides suffer from low coupling efficiencies (a fewpercent) due to the random position and dipole orientationof the SQEs. Even for perfectly positioned and aligned emittersin a single-mode waveguide, the finite mode confinement limitsthe maximum simulated coupling efficiency36 up to ∼40%(∼20%) for emitters embedded at the center of (below) thewaveguide (see the Supporting Information for details ofmodeling). Furthermore, commonly used stochiometric siliconnitride, which is an excellent platform for 2DMs due to its lowpropagation loss,37 large refractive index,38 and wide trans-parency window that spans all 2D SQEs (Figure 1a), has astrong fluorescence39 that reduces the single-photon purity ofintegrated SQEs, further complicating their optimal on-chipintegration.Here, we demonstrate a novel method for efficient on-chipcoupling by integrating 2D SQEs with microring resonatorsusing a CMOS-compatible process. Our approach is universalin that it enables the deterministic integration of SQEs withlow autofluorescence and single-mode silicon nitride photoniccircuits with precise control over the emitter placement anddipole orientation within the waveguiding structures�both ofwhich are critical for achieving efficient coupling. Wedemonstrate this approach by integrating hBN SQEsgenerating single photons at room temperature with wave-guide-coupled microring resonators (Figure 1b). Emitter−cavity coupling of up to 46% is measured, which requires onlya modest Purcell factor of 0.86 ± 0.15 to surpass thewaveguide coupling efficiency in prior studies by nearly 1 orderof magnitude.36,39−41 We demonstrate the universality of theapproach by also coupling exciton emission from embeddedWS2, achieving >63% efficiency with a Purcell factor of 1.44 ±0.25. We present various emitter−microresonator designs,coupling schemes, and metrics that provide a roadmap for theintegration of SQEs spanning the UV to telecommunicationswavelength regimes. Guided by a semiclassical cavity−emittermodel, routes toward achieving high-purity, high-indistinguish-ability (η × V) single-photon emission from a variety of 2Dmaterial emitters are proposed, paving the way for enablingscalable and manufacturable integrated quantum photonicswith on-demand sources in silicon nitride. Standard plasma-enhanced chemical vapor deposition (PECVD) of stoichio-metric Si3N4 suffers from significant background fluores-cence5,39,42−44 that overlaps with the emission from many2D materials, including hBN and TMDs. To address thesechallenges, we extend previous developments of nitrogen-richFigure 3. Integration of hBN SQE and microresonator characterization. (a) Optical image of an SQE in an hBN flake near positioning markers.The SQE location is denoted by the bright white dot, which corresponds to the dimmed excitation laser spot. The inset plot depicts the emissiondipole orientation of the emitter. (b) Fabrication of a complete device with an hBN emitter integrated and dipole-aligned to a microring resonatorwith 100 nm precision. The inset plot shows the distribution of the SQE positioning over several trials. (c) Simulated waveguide−emitter couplingefficiency (β) for 2D quantum emitters on top, within, or below the straight waveguide. A maximum of up to 40% coupling efficiency (summedover both waveguide propagation directions) is possible for each type of emitter. (d) Theoretical (lines) and experimental (points) resonatorquality factor as a function of the integrated hBN flake thickness. It is assumed the flake covers 25% of the ring in the simulations. The black dashedline represents the theoretical simulations, which do not take into account the intrinsic loss due to the flake and absorption in the guiding medium.The blue dashed line represents the theoretical simulations corrected with the experimental intrinsic quality factor. (e) Characterization of a ringwith an integrated hBN flake. A broad-band superluminescent diode (centered roughly at 638 nm, dashed line) is coupled to the output port of thewaveguide. Scattered light from the ring (solid line) is collected using a 0.9 NA objective. A free-spectral range (FSR) of 2.1 nm and a loadedquality factor (Q) of 1512 are measured with an embedded flake.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.2c03151Nano Lett. 2022, 22, 9748−97569750https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.2c03151/suppl_file/nl2c03151_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig3&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.2c03151?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-assilicon nitride (SiN) that eliminate the background fluo-rescence. Careful tuning of the PECVD RF power, voltage bias,and silane to ammonia ratio (R) allows for the deposition ofhigh-quality silicon nitride with negligible backgroundfluorescence and a high refractive index, without damagingthe underlying 2D materials.Figure 2 illustrates that, for decreasing R, the fluorescence isquenched with only a moderate reduction in the refractiveindex; however, creating SQEs in hBN is typically achieved45through rapid thermal annealing up to 1100 °C. In previousstudies, annealing has introduced or activated defects, whichenhances the fluorescence background even in nitrogen-richfilms.39 By preconditioning the annealing chamber with anoptimized oxygen/nitrogen environment, we find that thedefect band remains absent for temperatures at least as high as1000 °C. This points to extrinsic defects being introducedfrom the chamber as one of the primary sources of thefluorescence. Figure 2c illustrates the results from this process.A room-temperature photoluminescence spectrum is shown inFigure 2c from a representative hBN emitter in a flake under a100 nm thick low-stress stoichiometric Si3N4 film. Nearly 50%of the emission at the zero-phonon-line (ZPL) wavelength ofthe emitter near 540 nm arises from the Si3N4 emission. Usingthe new thin-film deposition procedure, we observe emissionfrom hBN emitters with negligible background from the SiN,as shown in Figure 2d for bare hBN (red curve) and the samehBN after growth and annealing of 100 nm SiN (blue curve).The fabrication process for deterministically embedding 2Dflakes within SiN photonic structures is illustrated in Figure2e−h, which enables the fabrication of photonic devicesaligned to emitters with 100 nm precision (see the SupportingInformation). This procedure, combined with the ability todeposit and anneal SiN on top of the 2D emitters withoutdamaging them, enables flakes to be integrated throughout thecross-sectional profile of the structures. Figure 3c shows thetheoretical coupling efficiency of an emitter with perfectpolarization alignment integrated with a single-mode SiNwaveguide at different heights for three types of 2D materials.The coupling efficiency of the radiated field into the waveguidemode, normalized to the total radiated field, is defined as β,where β = 1 corresponds to 100% emission into the waveguidemode. Intuitively, the greatest mode overlap occurs whenflakes are embedded in the center of the waveguide; however,care must be taken to avoid etched hBN edges within a fewhundred nanometers of the emitter, which can introduce edgestates and lead to optical dephasing and spectral diffusion.Thus, we also explored the integration of hBN underneath thewaveguide in which the hBN flake is not exposed to any etchedsurfaces. For this configuration, a theoretical couplingefficiency of β = 20% (Figure 2c) is expected. In practice,the measured waveguide coupling efficiency, however, istypically limited to ∼1−3% primarily due to poor emitter-mode overlap and dipole misalignment.36,40,41Alternatively, β can be enhanced relative to waveguides byintegrating the emitter within an optical cavity. For a cavity-coupled emitter, its radiative decay rate is resonantly enhancedand becomes F(1 ) 0= + , where Γ0 is the radiative decayrate in the absence of the cavity and FΓ0 is the radiativeenhancement due to the cavity.46,47 This enhancement can beq u a n t i fi e d t h r o u g h t h e P u r c e l l f a c t o rF n Q V(3/4 )( / ) ( / )2zpl cav3= where ncav, Q, and V are therefractive index, quality factor, and cavity mode volume,respectively. For a cavity-coupled emitter,47,48 β can beexpressed in terms of the Purcell factor as F F/(1 )= + .As we show experimentally below, even for F ≈ 1, the on-chipSQE emission can be significantly enhanced relative to anemitter coupled to a waveguide.The Purcell factor is typically defined in the “good-emitter”regime in which the cavity line width κ is larger than the SQEline width γ; however, in many instances, including hBNemitters at room temperature, phonon-induced dephasingbroadens the ZPL width beyond the radiative limit, and thecavity-coupled system is found in the “bad-emitter” regime, i.e.γ > κ, where only a portion of the ZPL couples into the cavity.This reduces the traditional Purcell factor to Fκ/γ, where κ/γheuristically represents the ratio of the radiated power from theSQE that overlaps with the cavity mode. In the bad-emitterregime, a wavelength-dependent Purcell factor and couplingefficiency can be defined in terms of the spectral power of theemitter, Fs(λ) = Icav(λ)/Ifb(λ) and F F( )/(1 ( ))s s s= + ,where Icav(λ) and Ifb(λ) are the spectral intensities of theemitter into the cavity mode and into free-space, respectively.In effect, this negates the κ/γ factor and allows for theenhancement of the portion of the ZPL that is resonantlycoupled to the cavity to be quantified regardless of theemitter−cavity regime.49 Whether in the good- or bad-emitterregime, ( )s 0 specifies the cavity enhancement at the emissionwavelength λ0, while integration over λ determines the total β.We chose a racetrack resonator configuration with a 100 nmthick and 600 nm wide cross section, a 3 μm long couplerregion that results in a free spectral range (FSR) of 2 nm, and amode volume of ( )30n3at the resonance of interest around610 nm (see Figure 3a,b). The simulated quality factor is 7000,which is comparable to the cryogenic line width of hBNemitters observed in our samples. Light is coupled into/out ofthe waveguide via end-coupling between a single-mode fiberand a tapered waveguide for mode matching. We firstcharacterized resonators without 2D materials to establish abaseline for our quality factor, which we can write asQ Q Q Q1i1c1sc1= + + , where Qi corresponds to thebare resonator, Qc corresponds to the coupling to thewaveguide, and Qsc arises from scattering from an integrated2D flake. Measurements from 10 nominally identicalresonators from three different fabrication runs yield anaverage Qi = 3560 and Qc = 9700, indicating a slightly lower Qvalue than in our simulations likely due to etched sidewallroughness and a larger waveguide−resonator coupling gap.The impact of integrated hBN flakes on the resonator Q isalso examined. With increasing flake thickness, Q decreases,which matches our simulations (Figure 3d). While hBN has arefractive index similar to that of SiN, light scattering at theSiN−hBN interfaces, which has a more pronounced effect forthicker flakes, dominates the loss and reduction of Q in oursimulations. Experimentally, for flakes with a thicknessexceeding 30 nm, Q decreases by 1 order of magnitude.Given that hBN emitters tend to have narrower line width andbrighter emission in thin but multilayer flakes, this resultconfirms an important design tradeoff for resonator integra-tion. We found that emitters with line widths as narrow as 3−4nm at room temperature are routinely identified in ∼15 nmthick flakes. Figure 3e shows the spectrum of the micro-resonator with an hBN flake integrated below the ring,exhibiting a loaded Q = 1512.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.2c03151Nano Lett. 2022, 22, 9748−97569751https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.2c03151/suppl_file/nl2c03151_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.2c03151/suppl_file/nl2c03151_si_001.pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.2c03151?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asFigure 4a shows the photoluminescence (PL) spectrum of arepresentative hBN emitter after the complete devicefabrication using top-down excitation and collection at roomtemperature. As demonstrated in Figures 2d and 4a, theintegration and fabrication do not degrade the quality of theemitter and we retain the background-free emission. Thephoton antibunching behavior verifying single-photon emis-sion is illustrated in Figure 4b in which g (0) 0.22(2) = (0.18with background correction). We next excite the emitter usinga 0.9 NA objective from above the resonator, and emission intothe waveguide is collected into a single-mode fiber and sent toa spectrometer and charge-coupled-device camera. Figure 4cshows the integrated hBN SQE with the ZPL emissioncentered near 610 nm. The solid red line is emission collectedfrom above the emitter, whereas the solid blue line is emissioncollected from the waveguide, which shows the resonatormodes clearly imprinted on the ZPL emission spectrumseparated by an FSR of ∼2 nm. A similar response is observedon the room-temperature exciton emission from bilayer WS2 asshown in Figure 4d, demonstrating the universality of theapproach for 2D material integration.To extract the spectral Purcell enhancement Fs(λ) and thespectral coupling efficiency βs(λ), we follow a procedurepreviously reported for SQEs.36,40,46 Accounting for the opticalloss in our system, the effective Purcell enhancement at theZPL peak wavelength can be expressed asFIIsob topout facet sidecavccdfbccd=(1)where ηob, ηtop, ηout, ηfacet, ηside, Ifbccd, and Icavccd are respectively theportion of the total light collected by the top objective,efficiency of the top collection path, microring out-couplingefficiency, facet coupling efficiency, side path collectionefficiency, spectral intensity measured on the CCD at theZPL wavelength from the top objective, and spectral intensitymeasured from the waveguide output port. From this analysis,we determine a spectral Purcell factor of up to 0.86 ± 0.15corresponding to βs = 46 ± 4% at the ZPL resonance (β = 28± 4% integrated across the entire spectrum). Deviation fromthe theoretical estimate of the effective Purcell factor for thissystem (equal to 1.7) can be attributed to small misalignmentand dipole orientation inaccuracies. Importantly, even thoughFs is close to unity, this results in nearly half of the emissionnow coupled into the cavity mode. This is best reflected in βsof the cavity-coupled system. Here, the lower bound of ourmeasured βs exceeds the maximum theoretical couplingefficiency into a waveguide of the same configuration(∼20%) as shown in Figure 2). For this emitter, we measurea 13% reduction of the lifetime after integration, qualitativelyconsistent with our measured Purcell enhancement; however,we did not rely on lifetime measurements to estimate thePurcell factor due to ambiguities in the quantum yield,nonradiative processes, and whether these are affected byfabrication (see the Supporting Information). Similarly for theintegrated WS2, βs = 63 ± 4% is obtained, amounting to aspectral Purcell factor of Fs = 1.44 ± 0.25. The highermeasured Purcell factor for WS2 is due to the fact that it isthinner and thus does not significantly alter the loaded qualityfactor of the resonator.An important figure of merit of an emitter−cavity system isthe PIC efficiency−indistinguishability product η × V. In thegood-emitter regime, the cavity not only provides enhance-ment in coupling efficiency but also broadens the natural linewidth to increase the indistinguishability. Total PIC efficiencycan be expressed as η = ηqe × β × ηout, where ηqe is thequantum efficiency of the emitter and ηout is the extractionefficiency of the coupled light in the cavity into the buswaveguide.46,50 Maximizing η × V is a multivariable problembecause the individual components of efficiency andindistinguishability cannot be adjusted independently. Forinstance, while a high Q results in a larger β and V, for large Q,Figure 4. Microresonator-integrated hBN quantum emitter with high coupling and Purcell enhancement. (a) PL spectrum of an hBN SQEacquired with top-down excitation and collection after microresonator integration. The emitter properties are preserved after the fabricationprocess. (b) Second-order autocorrelation measurement demonstrating 78% purity and a lifetime of 1.23 ns (82% purity when background-corrected). The data are raw with no correction for the background or detector dark counts. (c) ZPL of the emitter observed from the output portof the waveguide using an aligned fiber array (blue line) and from the top collection (red line). A factor of 10 reduction of the ZPL line width isobserved (from 7.2 nm down to 0.72 nm), as expected from the bandwidth of the microresonator. The peak intensity of the ZPL is misaligned fromthe nearest cavity resonance by ∼0.35 nm. (d) Excitonic response of a bilayer WS2 collected from the waveguide port. The modes of themicroresonator are clearly visible, demonstrating a quality factor of up to 2400.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.2c03151Nano Lett. 2022, 22, 9748−97569752https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.2c03151/suppl_file/nl2c03151_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig4&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.2c03151?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asthe cavity−emitter system can enter the bad-emitter regimewhere only a portion of the ZPL will couple into the microringresonator and η will begin to decrease. Generally, the linewidth of the emitter sets a practical upper bound for the loadedQ. While this can imply that SQEs with the narrowest linewidth are more suitable for cavity integration, the SQEquantum efficiency ηqe also plays an important role in theemitter−cavity design. For instance, ηqe for WSe2 isestimated28,29 to be only ∼1−5% compared to up to 87%reported for hBN.51 Therefore, to optimize the cavity designwith high η × V for different 2D emitters, a holistic approachmust be considered.As shown in Figure 5, we explore the performance of a 2DSQE−cavity system using solutions to a modified Jaynes−Cummings Hamiltonian49,52 for the state of the art 2D SQEsinteracting with a cavity (see the Supporting Information).Figure 5a shows η × V as a function of mode volume and themicroresonator quality factor Q for near-transform-limitedmechanically decoupled hBN emitters at cryogenic temper-atures.31,32 The vertical dashed line sets the boundary of thebad-emitter regime, in which the total quality factor exceedsthe emitter quality factor Qe determined from its line width; asQc becomes larger than Qe, only a portion of the emittercouples to the cavity mode. The horizontal dashed line inFigure 5a indicates the minimum mode volume for our PICs(30(λ/n)3), and slices along this line are shown in Figure 5bfor hBN and TMD emitters. For Q ≈ 16000, an η × V value ofup to 90% is possible with existing hBN emitters at cryogenictemperatures. For Q exceeding Qe, the system enters the bad-emitter regime and η × V begins to decrease.Purcell enhancement can compensate for intrinsic lowquantum efficiency and indistinguishability of some emittertypes, such as WSe2, provided loaded Q > 105 is reached. SuchQ values are orders of magnitude below the fundamentalthermorefractive noise limit for SiN;53 however, furtheroptimization of nonstochiometric growth, side-wall roughness,and engineering emitters in monolayer flakes is required tofurther improve the quality factors. On the other hand,integration of emitters with high quantum efficiency, such ashBN, can be realized at lower Q. Figure 5c shows themaximum attainable η × V for each class of the emitters as afunction of the intrinsic quality factor of the platform. As theintrinsic Q approaches 106, which is already achievable fordifferent SiN waveguide aspect ratios, it is possible to integrate2D quantum emitters with η × V exceeding 80%. These valuesare competitive with some of the best alternative materials forintegrated single-photon emitters, such as self-assembled InAsquantum dots (ranging from η × V = 3% for dots emitting on-chip54 to up to 78% for dots in a nanopillar cavity55) andsilicon vacancy centers in diamond56 (modeling using theMarkovian master equation with dissipative dynamics places η× V near ∼80%).Taken together, our simulations and experiments provide astraightforward approach for deterministically aligning andorienting SQEs in 2D materials to microresonators with aroute toward high coupling efficiency. Already this approachachieves 46% coupling efficiency into the resonator at theemitter ZPL resonance, which is 1 order of magnitude higherthan waveguide coupling for hBN. A systemwide efficiencyapproaching 10% can be attained in the near term with modestimprovements to the microresonator Q and its design forovercoupling. The platform and methods developed in thiswork can serve as a crucial advancement toward futuredemonstrations of on-chip 2D quantum emitter integrationwith high extraction efficiency, brightness, and indistinguish-ability. In the near future, by exploring SiN microresonatorsembedded with other SQEs with narrow line widths, such asWSe2 and MoTe2, new opportunities exist for on-demand andsite-controlled SQEs with silicon-based photonics for chip-scale quantum information applications.■ ASSOCIATED CONTENTData Availability StatementThe data that support the findings in this study are availablefrom the corresponding author upon reasonable request.*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151.Details of the alignment procedure, fabrication methods,numerical modeling of the microresonators, andFigure 5. Projected performance of state of the art 2D material quantum emitters in a SiN heterogeneous platform. (a) Mode volume versuscoupling quality factor Qc for hBN visible emitters (mechanically decoupled near-transform limited line widths32). The red dashed linedemonstrates the mode volume achieved in our SiN microresonators. The blue dashed line demonstrates the intrinsic quality factor Qe of theemitter determined from its line width. (b) Total system efficiency−indistinguishability figure of merit η × V as a function of loaded Q at theminimum achievable mode volume for hBN and WSe2 emitters in the visible wavelength. The intrinsic line width and total dephasing rate are takenfrom previous resonant fluorescence studies to be 50 and 150 MHz (for hBN32) and 100 MHz and 2 GHz (for WSe2 monolayers59), respectively.(c) Maximum figure of merit ηmax × V achievable for each class of emitters as a function of the intrinsic quality factor of the SiN platform.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.2c03151Nano Lett. 2022, 22, 9748−97569753https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.2c03151/suppl_file/nl2c03151_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?goto=supporting-infohttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.2c03151?fig=fig5&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.2c03151?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asanalytical modeling of the emitter−cavity coupling(PDF)■ AUTHOR INFORMATIONCorresponding AuthorG. Moody − Electrical and Computer EngineeringDepartment, University of California, Santa Barbara,California 93106, United States; California NanosystemsInstitute, University of California, Santa Barbara, California93106, United States; orcid.org/0000-0002-6265-2034;Email: moody@ucsb.eduAuthorsK. Parto − Electrical and Computer Engineering Department,University of California, Santa Barbara, California 93106,United StatesS. I. Azzam − Electrical and Computer EngineeringDepartment, University of California, Santa Barbara,California 93106, United States; California NanosystemsInstitute, University of California, Santa Barbara, California93106, United StatesN. Lewis − Electrical and Computer Engineering Department,University of California, Santa Barbara, California 93106,United StatesS. D. Patel − Electrical and Computer EngineeringDepartment, University of California, Santa Barbara,California 93106, United StatesS. Umezawa − Electrical and Computer EngineeringDepartment, University of California, Santa Barbara,California 93106, United StatesK. Watanabe − Research Center for Functional Materials,National Institute for Materials Science, Tsukuba 305-0044,Japan; orcid.org/0000-0003-3701-8119T. Taniguchi − International Center for MaterialsNanoarchitectures, National Institute for Materials Science,Tsukuba 305-0044, Japan; orcid.org/0000-0002-1467-3105Complete contact information is available at:https://pubs.acs.org/10.1021/acs.nanolett.2c03151Author Contributions△K.P. and S.I.A. contributed equally to this work.NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSThis work was supported by NSF Award No. ECCS-2032272and the NSF Quantum Foundry through Q-AMASE-i programAward No. DMR-1906325. Experiments were performed withsupport from DURIP Award No. FA9550-21-1-0257. S.I.A.acknowledges support from the California NanoSystemsInstitute through an Elings fellowship. 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