Closed-Loop Electron-Beam-Induced Spectroscopy and Nanofabrication Around Individual Quantum Emitters

Color centers in diamond play a central role in the development of quantum photonic technologies, and their importance is only expected to grow in the near future. For many quantum applications, high collection efficiency from individual emitters is required, but the refractive index mismatch between diamond and air limits the optimal collection efficiency with conventional diamond device geometries. While different out-coupling methods with near-unity efficiency exist, many have yet to be realized due to current limitations in nanofabrication methods, especially for mechanically hard materials like diamond. Here, we leverage electron-beam-induced etching to modify Sn-implanted diamond quantum microchiplets containing integrated waveguides with width and thickness of 280 nm and 200 nm, respectively. This approach allows for simultaneous high-resolution imaging and modification of the host matrix with an open geometry and direct writing. When coupled with the cathodoluminescence signal generated from the electron-emitter interactions, we can monitor the enhancement of the quantum emitters in real-time with nanoscale spatial resolution. The operando measurement and manipulation of single photon emitters demonstrated here provides a new foundation for the control of emitter-cavity interactions in integrated quantum photonics.


D Introduction
Diamond color centers, notably the nitrogen-vacancy (NV) and group-IV color centers like the tin-vacancy (SnV -), have emerged as crucial components in quantum information technology [Y]- [\].They serve as photonic interfaces to electron and nuclear spin ground states, driving research in applications such as quantum sensing, quantum computing, and quantum networking []]- [P].Nevertheless, a significant challenge in this field lies in fabricating photonic nanostructures, such as waveguides and photonic crystal nanocavities, to efficiently manipulate and couple photons to the spin of color centers.[^] The obstacle is particularly pronounced in diamond due to its unique properties, including high hardness and chemical stability.Conventional methods like electron-beam lithography (EBL) and reactive ion etching (RIE) have demonstrated remarkable progress over the past few years, enabling the development of diamond quantum microchiplets (QMCs) [YQ] and nanobeam waveguides [YY].However, RIE requires the development of a hard mask and the resolution is limited to YQQ nm.Focused ion beam (FIB) milling, on the other hand, induces a damage layer in diamond that is \Q nm in depth for gallium sources and up to \QQ nm in depth for lighter species such as oxygen; this FIB-induced damage is known to quench color center emission in diamond [YO].Femtosecond laser writing enabled the fabrication of diamond-based three-dimensional (eD) waveguides[Ye], [Yf], and micro-pillar structures [Y\], but the structure size is limited to the microscale and can be highly dependent on spherical aberrations [Y]].Recently, electron-beam-induced etching (EBIE) has emerged as an effective etching method for patterning diamond substrates, evidenced by the low damage and absence of graphitization [Yg].In this method, the ions in FIB are replaced with a focused electron beam in a water vapor environment; the electron beam doesn't etch the material directly, but it initiates a surface reaction for material removal in a relatively pure chemical environment [YP], [Y^].This technique has enabled direct-write eD sculpting with a high resolution on the order of YQ nm[OQ], [OY].However, challenges in spatially and spectrally aligning nanoscale photonic cavities with sparsely distributed single photon emitters (SPEs) in diamond remain a substantial obstacle to the development of high quality-factor diamond quantum photonic platforms.
Here, we manipulate the optical properties of SPEs in diamond QMCs using in-situ mask-less EBIE and hyperspectral cathodoluminescence (CL) microscopy performed simultaneously (Figure Ya).While conventional optical probes of SPEs are limited by the optical diffraction limit, CL microscopy relies on a sub-nm converged electron-beam probe and offers spatial resolution limited only by secondary electron scattering and free-carrier migration.
We show here that we can deterministically etch photonic cavities using EBIE around individual SPEs identified by CL.Collecting the photons from in-situ CL while etching a SnV -SPE embedded in a suspended diamond QMC waveguide, we observed up to ~O.\x emission enhancement followed by emission quenching as the SPE was etched away.These results show that the EBIE induces minimal damage, if any, and the emitter remained active until it was removed from the OQQ-nm thick waveguide.Further, we showed the feasibility of fabricating an array of cavities approximately OQ nm in diameter with minimal variations along the waveguide.This highly integrated approach can serve as a rapid testbed for various complex designs with in-situ testing and imaging, establishing a direct correlation between design attributes and performance metrics.While this method is not meant to address the is sue of scalability or entirely replace RIE, it can nicely complement it, especially for sub-YQQ nm features and in-situ emitter enhancement tests.This method facilitates rapid iterations and refinements in the development process, significantly reducing the time from concept to application.

O.D Gas-assisted EBIE and CL in diamond
The EBIE and CL microscopy was performed in an FEI Quattro environmental scanning electron microscope (SEM) using a Delmic Sparc CL module to collect luminescence generated by the electron beam into an Andor Kymera Y^ei spectrograph.A flip mirror was used to redirect the collected CL away from the spectrograph and into a \Q/\Q fiber splitter for photon correlation function measurements performed with a pair of superconducting nanowire single photon detectors and a Swabian TimeTagger Ultra used to time tag photon detection events.
The emitter was first located and characterized in no water vapor (i.e.pressures below YE-] Torr).Then, the EBIE was performed in a Q.g\ Torr water vapor background.CL was acquired concurrently during the EBIE process, and reference CL measurements were taken at pressures of less than YE-] Torr, where no etching was observed even with extended electron-beam dwell times.A Gatan cryostage was used to acquire CL spectra at PK, though, because the water vapor background is incompatible with cryogenic operation, no EBIE was observed at cryogenic temperatures.Notably, cooling the sample to PK immediately after switching to high-vacuum operation results in ice formation on the diamond QMC at PK, but this water reservoir is quickly removed by electron-beam exposure, and it provides an insufficient environment to facilitate cryogenic EBIE.In this room temperature (O^e K) experiment, the HOO vapor injected into the chamber adsorbs onto the diamond surface, forming bonds with the diamond surface mediated by the oxygen atoms.The incident and emitted electrons then interact with these adsorbed molecules, dissociating them and generating reactive radicals (i.e., H + and OH -) that facilitate local chemical dry etching.The reaction products, such as COO and CO, formed in this process are volatile and spontaneously desorb from the surface, leaving behind etched areas[Yg], [OQ].Several factors, including the dose of the electron beam, the kinetics of the reaction and the nature and pressure of the injected gas, determine the spatial resolution and etch depth in EBIE.The subnm electron beam spot size allows for the local etching of specific structures, enabling the direct writing of a wide range of photonic cavities and structures within a single system that also serves as a photonic interface for quantum technologies.EBIE has been used with various combinations of gases and substrate materials[YP], [OO], including recent efforts focused on nanoscale

O.O Diamond QMC fabrication
To prepare the diamond substrate for color center creation, we etched the top YQ μm of the [QQY] electronic-grade single crystal diamond using Ar/ClO plasma etching followed by OO etching to alleviate surface strain.Implantation of YOQ Sn ions was done at Innovion with a dose of \ x YQ YY ions/cm O at e\Q keV, targeting a depth of g] nm as deduced from stopping and range of ions in matter (SRIM) simulations.The diamond underwent annealing at YOQQ°C in a vacuum furnace at YQ -g mbar.We cleaned the diamond with a boiling mix of sulfuric, nitric, and perchloric acid to remove any graphitic residue from the annealing process.The purpose of high-dose implantation was to ensure, on average, more than one quantum emitter per quantum channel.
Following the color center implantation in diamond, we coated the diamond with a silicon nitride (SieNf) hard mask via plasmaenhanced chemical vapor deposition, patterned by ZEP-\OQA electron beam resist combined with ESpacer conductive polymer and CFf reactive-ion etching (RIE).This was followed by a conformal deposition of an YP nm alumina atomic layer.Alumina breakthrough was achieved using CFf RIE, and an oxygen plasma was employed to undercut the diamond QMC uniformly.Finally, the silicon nitride and alumina masks were removed with hydrofluoric acid.

O.W Optical measurements
We pre-characterized the diamond QMC quantum emitters using cryogenic free-space confocal photoluminescence (PL) microscopy at f K equipped with an objective lens (ZEISS, NA = Q.^,YQQx).The collected signal is sent to either an avalanche photodiode (APD) for initial intensity mapping (Figure Yb) and for high resolution photoluminescence excitation (PLE) spectroscopy measurements, or to the spectrometer (SP-O\QQi, Princeton Instruments) for initial spectral analysis.Figure Yd shows a representative PLE spectrum of the SnV -quantum emitters from the chiplets.The corresponding g (O) characterization shows an average (g) (O)

W.D Simultaneous EBIE and CL around SnV -in QMC
Figure Yc presents an SEM micrograph alongside a CL hyperspectral map of a diamond QMC obtained at an accelerating voltage of YQ keV.A spatially isolated color center was selected for the analysis to enable the independent examination of individual photon-cavity coupling and the emission characteristics of the SnV -color center.The CL hyperspectral map revealed a distinct emission peak at ]Y^ nm, indicative of localized emission at room temperature (O^e K) from the SnV -color centers.This emission manifests as a broad spectral feature, composed of several overlapping peaks.Upon cooling the system to P K, a pronounced enhancement of the SnV -emission peak was observed, along with a significant narrowing of the spectral full-width at half-maximum (FWHM), suggesting enhanced emission purity at reduced temperatures.To investigate the coupling between fabricated photonic cavities and SnV -color centers, time-dependent CL measurements were performed in an a HOO environment (Q.g\ Torr) with a beam energy of eQ keV and a current of O.P nA for an electron beam incident on the SnV -color center shown in Figure Oa.The resulting CL time series spectra in Figure Oc illustrate the change in SnV -luminescence as a function of electron beam etching time; the time-dependent CL and secondary electron signals are consistent with etching rates of roughly fnm/s for these beam conditions.Interestingly, as we etch through the diamond chiplet at the location of the SnV -color center, we observed a gradual increase in the ]OQ nm emission.Figure Od-I shows the spectral fitting results within the f.\ s to YO s timeframes to investigate the CL enhancement further.Three emission peaks were fitted and deconvoluted, where red, green, and blue correspond to diamond emission from lattice disorder (e.g.A-band emission from dislocations and grain boundaries)[eY], [eO], SnV -color center, and potentially other defects complexes with different charged states, respectively.The key effect observed in Figure Od-i is the marked emission enhancement from the SnV -color center at ]OQ nm (green curve).This is in contrast to the red peak from the host matrix that showed almost constant emission throughout the process.Thus, EBIE can be used to dynamically control and locally optimize the coupling from a single diamond color center in a diamond photonic cavity.
While the ability to locally optimize the emission from a single color center in a prepatterned QMC using operando EBIE and CL microscopy, as shown in Figure O is certainly compelling, the approach described here also allows for the direct writing of nanophotonic structures in diamond QMCs around single color centers.As an initial proof of principle of this approach, the morphology of photonic cavities patterned by RIE and EBIE on this diamond QMC are compared in  illustrates a similar cavity design with reduced hole diameter of \] nm achieved by dwelling the electron beam at a single point for a user-defined time.The ability to fabricate holes and vertical cavities on these length scales provides a critical testbed for complex photon cavity designs in diamond with in-situ subdiffraction-limited optical feedback that is not accessible with modern nanofabrication tools.

W.O Origin of SnV -CL enhancement
To identify the origin of CL enhancement at ]OQ nm during the etching shown in Figure O and to better understand how the EBIE modifies the photonic local density of states (LDOS) around the emitter, we performed finite-difference time-domain (FDTD) simulations of the diamond QMC.The FDTD simulations were designed to replicate the experimental conditions as closely as possible.We modeled a SnV -embedded in a diamond waveguide, incorporating the geometric dimensions as determined by SEM and optical measurement: a width (w) of OPQ nm, a height (h) of OQQ nm, and a depth for the SnV -centers of YQQ nm (Figure fa).The emitter was positioned near the simulated etched dimple, offset from the center by δx and δy in the x and y directions, respectively, to account for potential misalignments (Figure fd-f).To examine the spectral characteristics, we monitored the normalized intensity of the emission peak at ]OQ nm.
The FDTD simulations accounted for the emitter's assumed circular polarization and the collection optics' high numerical aperture (NA), set to Q.^g, to ensure accurate collection efficiencies.By varying the etch depth, δx, and δy, we evaluated the impact of these parameters on the collection efficiency.The results indicated that the collection efficiency of the emission does not significantly change as the LDOS is modified by the etching process-less than OQ% change in collection efficiency is expected for a wide range of structural parameters.
Therefore, we conjecture that the CL enhancement is from changes in electronic excitation efficiency as a function of etching depth rather than photonic modification.Further studies are needed to identify the exact dynamics.For example, the implantation energy of Sn defects can be swept to vary the depth of the emitters and to identify the correlation with the emission intensity.Alternatively, photonic crystal cavity structures that can significantly modify LDOS can be used to see the photonic enhancement by increased LDOS[ee].

[ Discussion
Exciting future directions include fabricating one-dimensional (YD) photonic crystals, and milling a vertical half-bowtie with a parabolic profile on (YYY) diamond, in which we could align the photonic mode with the emitter's polarization (polarization of SnV -is on the plane orthogonal to the defect orientation, [YYY]) [ef].Using hermetic fiber feedthroughs to collect luminescence from fiber-pigtailed diamond QMCs could offer more refined control over light collection and delivery, ensuring that a greater proportion of emitted photons are captured and analyzed[e\] while maintaining all of the advantages of in situ EBIE and CL described here.
Through the precise control offered by gas-assisted EBIE, we successfully demonstrated deterministic patterning of Sn-implanted diamond QMCs, substantially enhancing the CL emission intensity.The observed enhancement in SnV - color center emission is attributed to the combination of proximity to the etched surface, LDOS enhancement, and other potential electron-emitter interactions.Further studies are needed to reveal the role of the electronemitter interaction on the CL signal and fabrication-induced strain in diamond photonic structures fabricated using this method[e]].Tailoring the gas precursors can enable selectivity over the crystal planes and, therefore, the etching pathway (i.e., isotropic vs. anisotropic) and change the surface topology [OY].indicate that the collection efficiency of the emitter, which depends on the etch depth, δx, and δy, is not significantly affected by the local electromagnetic environment.The emission is assumed to be circularly polarized, with the numerical aperture (NA) of the optics being 0.97.

Figure 1 :
Figure 1: Experimental design for diamond QMC etching and analysis.(a) SEM-CL setup: converged electron beam incident on a diamond QMC through a pinhole in a parabolic mirror in an environmental SEM operating in 100 Pa water vapor environment at a temperature of 300K.(b) Diamond QMC image overlaid with the location of SPEs characterized by the widefield PLE at 4 K.Each circle denotes an SPE.(c) SEM image of a diamond QMC indicating area of interest (red box) with CL map displaying emission at 620 nm from the emitter.(d) PLE spectrum centered around 620 nm from SnV -represented in panels (b,c ; inset shows a representative autocorrelation measurement of single SnV -.(e) CL spectrum for an individual SPE at room temperature (grey) and 8 K (purple).
confirming the presence of single-photon emission.A representative autocorrelation measurement of the SnV -emitters is presented in Figure Yd.The extended optical system design is illustrated by Linsen Li et al. [OP].

Figure 2 :
Figure 2: Cavity fabrication with in-situ cathodoluminescence.Hyperspectral cathodoluminescence mapping (top panel) with concurrent scanning electron microscopy (bottom panel) before etching (a) and after etching (b).(c) Time resolved cathodoluminescence with 1.5s time interval.Start and stop time is indicated by blue and red, respectively.(d-i) Individual spectra acquired from 4.5s to 12s highlighting the enhancement at 620nm.The spectra were fitted and deconvoluted with three peaks corresponding to extended defects in diamond, SnV -, and potential transition-radiation induced by the electron-beam.
Because the high-energy electron-beam excitation can excite multiple excited states that are inaccessible in resonant or nearresonant PL microscopy, no antibunching was observed in CL photon correlation function measurements, and broadband background fluorescence contaminated many of the measurements[O^], [eQ].However, the close correlation between the PL map shown in Figure Yb and CL maps acquired on each QMC together with the low temperature CL spectrum shown in Figure Ye provided strong confidence that the localized CL observed in Figure Yc and Ye was from a single SnV -center.
Figure e.A large area image of the QMC is shown in Figure ea, and images of the same cavity design fabricated by RIE and EBIE are shown in Figure eb.Note, the cavities fabricated via EBIE were created by rastering the electron beam in a circular pattern to intentionally increase the cavity diameter, matching that of the RIE process.
Figure ec

Figure 3 :
Figure 3: Patterning of nanophotonic structures in diamond waveguides.(a) diamond QMC suspended on holey carbon support films for E-beam in-situ fabrication.(b) photonic cavities fabricated by reactive ion etching (RIE) (top panel) and electron beam etching (bottom panel).(c) Ultimate resolution limit for periodic photonic cavities achieved with electron beam etching.Scale bars are 200 nm.

Acknowledgments:
The diamond QMCs fabrication was carried out in part through the use of MIT.nano's facilities.J.A. acknowledges the support from KACST-MIT Ibn Khaldun Fellowship for Saudi Arabian Women at MIT, and from Ibn Rushd Postdoctoral award from King Abdullah University of Science and Technology (KAUST).D.E. acknowledge HSBC, Mekena Metcalf, Zapata Computing, and Yudong Cao for MIT QSEC collaboration.H.C. and D.E. also acknowledge Honda Research Institute and Avetik Harutyunyan.H.C. acknowledges the Claude E. Shannon Fellowship and the Samsung Scholarship Research funding: The work was supported by the U.S. Department of Energy, Office of Science, Materials Sciences and Engineering Division.The scanning electron microscopy research was performed and partially supported at Oak Ridge National

Figure 4 :
Figure 4: Single photon emission enhancement.(a) Illustration of an etched dimple in a diamond waveguide.Characterization with Scanning Electron Microscopy (SEM) and optical measurement revealed a width (w) of 280 nm, a height (h) of 200 nm, and a depth for the SnV -centers of approximately 100 nm.The location of the emitter is offset from the center of the etch by δx and δy in the x and y directions, respectively.(b) Normalized intensity versus electron beam etching time for emission peak at 620 nm showing over 2.5x increase in emission intensity and (c) reference peak at 405 nm.(d-f) Finite-difference time-domain (FDTD) simulation resultsindicate that the collection efficiency of the emitter, which depends on the etch depth, δx, and δy, is not significantly affected by the local electromagnetic environment.The emission is assumed to be circularly polarized, with the numerical aperture (NA) of the optics being 0.97.