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Integration of Single-Photon Emitters into 3C-SiC Microdisk Resonators Alexander Lohrmann,† Timothy James Karle,‡ Vikas Kanayalal Sewani,§ Arne Laucht,§ Matteo Bosi,⊥ Marco Negri,⊥ Stefania Castelletto,∥ Steven Prawer,† Jeffrey Colin McCallum,† and Brett Cameron Johnson*,# †

School of Physics, University of Melbourne, Melbourne, Victoria 3010, Australia The Florey Institute of Neuroscience and Mental Health, University of Melbourne, Melbourne, Victoria 3052, Australia § Centre for Quantum Computation and Communication Technology, University of New South Wales, Kensington, NSW 2052, Australia ⊥ IMEM-CNR Institute, Parco Area delle Scienze 37/A, 43124 Parma, Italy ∥ School of Engineering, RMIT University, Melbourne, Victoria 3001, Australia # Centre for Quantum Computing and Communication Technology, School of Physics, University of Melbourne, Melbourne, Victoria 3010, Australia ‡

S Supporting Information *

ABSTRACT: We demonstrate the integration of bright, fully polarized single-photon emitters readily created by thermal oxidation of cubic silicon carbide (SiC) into microdisk resonators. The resonators are created by a direct laser beam writing lithography technique that is used to align the position of the resonator to a preselected single defect. Quality factors as high as 1900 are measured. We show the presence of whispering gallery modes in the emission spectrum of a single defect and an increase in the detected emission intensity. The experimental work is supported by numerical calculations of the electric field distribution in the resonators. KEYWORDS: single-photon sources, optically active defects, silicon carbide, microdisk resonator, nanophotonics, optical lithography

A

These defects can be created by the thermal oxidation of the SiC surface13 and can be optically and electrically driven at room temperature,14 which strongly increases their practicality. Although no spin control has yet been achieved with these particular defects, their bright and stable emission may prove useful for quantum key distribution or bioimaging. Cavity structures rely on internal reflection or gap guiding to confine light in a small optical volume, for example, in a photonic crystal cavity or a microdisk resonator. In particular, microdisk resonators exhibit whispering gallery modes (WGMs), with quasi-transverse electric (TE) and quasitransverse magnetic (TM) modes. Dipole emission with the correct spatial position, polarization, and wavelength can couple to a WGM and undergo Purcell enhancement, to a degree determined by the modal quality (Q) factor (the ratio between the energy stored to energy lost per cycle) and the modal volume, V.15,16 For an emitter with a narrow zero-phonon line (ZPL), the Purcell factor, P, is given by

key challenge in emerging quantum technologies, such as quantum sensing, quantum computing, and quantum communication, is the isolation and control of single defects in semiconductors.1 Integration of single defects into a solid-state cavity may further allow the enhancement of the emission rate, spectral properties, and collection efficiency. This increases the number of usable single photons for such quantum applications. Great progress has been achieved with the integration of single NV centers in diamond microcavities.2 Another promising wide-band-gap semiconductor that has been used for the fabrication of photonic structures is silicon carbide (SiC).3−6 SiC has the added advantage over diamond that it can be grown as 6 in. wafers and is amenable to electrical and optical device fabrication. Additionally, SiC exists in a variety of different polytypes with unique properties. Very recently paramagnetic defects in SiC with long spin coherence times were isolated on a single-defect level.7−9 The possibility for optical spin control and read-out of these defects was shown to have immediate applications in magnetometry and temperature sensing.10,11 The key problems for the further development of these SiC defect centers, however, is their low emission rate7,8 and their cryogenic temperature requirements.9 A separate class of single-photon emitters (SPEs), which are ultrabright and fully polarized, was recently observed in SiC.12 © 2017 American Chemical Society

Received: November 16, 2016 Published: February 28, 2017 462

DOI: 10.1021/acsphotonics.6b00913 ACS Photonics 2017, 4, 462−468

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2 3 3 ⎛⎜ λ ⎞⎟ Q ⎛ |μE| ⎞ 1 ⎜ ⎟ 4π 2 ⎝ n ⎠ V ⎝ |μ||Emax | ⎠ 1 + 4Q 2 λzpl − 1 λ

(

)

(1)

where λ denotes the mode position, λzpl the emitter zerophonon line position, μ the dipole moment, E the electric field, and n the refractive index of the material (n(SiC) = 2.6)). Due to improvements in the material quality and processing, the fabrication of microdisk resonators in SiC has been successfully explored theoretically and experimentally in recent years. Disk resonators fabricated in hexagonal SiC optimized for emission in the visible spectral region have yielded Q-factors of up to 9200.17 In cubic (3C)-SiC, previous investigations of disk resonators fabricated in 3C-SiC by electron-beam lithography exhibited Q-factors of up to 2300.18 Recent progress in the integration of SiC defects into cavities has yielded high Purcell factors for silicon vacancy defects located in 1D photonic crystal cavities19 and non-Purcell-related emission enhancement from SiC nanopillars.20 Similarly, emission enhancement of silicon vacancy and chromium related color centers in nanodiamonds atop 3C-SiC microdisk resonators has recently been demonstrated.21 However, single-photon sources integrated into nano- or microcavities have not yet been demonstrated in SiC. The key to successful integration of individual defects into resonators is the exact alignment of the dipole with the E-field maximum of a WGM. Such alignment can be achieved by a direct beam writing technique consisting of a probe and exposure beam, a successful method previously applied for micropillars aligned to single quantum dots at cryogenic temperatures.22−24 The advantage of using such a technique for SiC-based defects is that the lithography can be performed at room temperature, drastically reducing the complexity of the fabrication method. In the present work, SPEs in 3C-SiC created by thermal oxidation13 were integrated into microdisk resonators fabricated by a specifically developed direct laser beam writing lithography technique. The ease of alignment demonstrated in the present work can be applied to other materials and defects. In systems for which deterministic defect placement is challenging or not possible, the technique demonstrated here allows registration of the optical cavity to the SPE.

Figure 1. (a) Fabrication scheme of the direct beam-writing lithography. (i) Imaging of SPEs buried under an SU8 resist layer with 633 nm excitation. (ii) High-power exposure with a 532 nm beam. (iii) RIE after development. The disks are subsequently undercut using HF/HNO3. (iv) Removal of the SU8 in piranha acid. (b) SEM image of a test array of resonators.

steps were performed under ambient conditions and are transferable to SPEs in other materials. Details are provided in the Supporting Information. The co-registration of the exposure and imaging beams can be probed by overexposing a single point in the SU8 layer to create a brighter fluorescence region (∼Mcps) without the need for resist development. The center of this overexposed region can then be determined with an accuracy of 10 nm and can be used as a high-resolution alignment marker. With this strategy, a resonator placement accuracy of about 50 nm can be achieved (see Supporting Information) without the use of predeposited high-resolution markers, thus further simplifying the lithography technique. The dipole emission from our defects lies in the plane of the SiC layer. Optimal modal coupling relies on measuring the dipole orientation before exposure. Then an appropriate offset is selected to position the resonator relative to the defect. In addition to individual alignment, large arrays of resonators can be fabricated with relative ease. A scanning electron microscopy (SEM) image of one of these arrays is displayed in Figure 1b. SPEs may be stochastically created in these arrays before or after the resonator fabrication. The resolution of this technique is mainly determined by the size of the laser spot in the SU8 (fwhm ≤880 nm, see Supporting Information). In addition, the etching process introduced angled side walls, with angles between 10° and 50° as determined by SEM. The angle can be controlled by the etching conditions.

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FABRICATION OF MICRODISK RESONATORS Microdisk resonators were fabricated with 160−190 nm thick nominally undoped 3C-SiC films heteroepitaxially grown on ⟨100⟩ silicon.25 This material exhibited a low background luminescence and was therefore an ideal host for SPEs stochastically formed by thermal oxidation as outlined previously.13 Note that the oxidation of the SiC surface is not expected to have a negative impact on the Q-factor of a resonator. We developed a direct beam-writing technique that allowed for the alignment of a resonator to a precharacterized singlephoton source. The process is outlined in Figure 1. A confocal microscope (see Methods) with a probe laser beam (633 nm, 150 μW) was first used to characterize the SPEs13 under an SU8 resist layer (Figure 1). Subsequently, a laser (532 nm, 7− 10 mW) was used to expose the resist and define the resonator pattern (ii). After exposure and resist cross-linking, the SiC on silicon can be etched using dry reactive ion etching techniques in fluorinated gases26 and subsequently undercut in HF/ HNO327 to create a SiC disk supported by a Si pedestal. All

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ELECTRIC FIELD DISTRIBUTION In order to investigate the behavior of SPEs in microdisk resonators, finite-difference time-domain simulations (see Methods) were performed with resonator dimensions determined from the corresponding SEM images. Several key points have to be addressed when SPEs are to be integrated into microdisk resonators. First, it is critical that the defect is located close to the E-field maximum of the TE or TM WGMs with an expected defect position close to or at the disk surface.14 We modeled the quasi-TE and TM modes, as displayed in Figure 2a. The defect’s dipole orientation is crucial for the coupling of the emission to the WGMs. Most defects are located in the surface plane with two major polarization 463

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with the present fabrication technique, may shift the modes spectrally several nanometers, making exact alignment of resonant cavity frequency and ZPL challenging. This may be resolved by using in situ tuning methods of the ZPL or mode position, such as electrical control28 or gas condensation methods.29

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CHARACTERIZATION OF MICRODISK RESONATORS A conventional μ-photoluminescence (PL) system with a high laser power of 50 mW with 532 nm excitation using a 100× objective (0.95 NA) was employed to characterize an array of resonators. The high power density excited a bright visible fluorescence possibly arising from surface states.18 This broadband and broadly polarized fluorescence was used to simultaneously probe many WGMs. A typical emission spectrum of a high-quality resonator with a nominal diameter of 1.8 μm is displayed in Figure 3a. The spectrum exhibited periodic peaks throughout the whole investigated spectral region, which indicated the presence of WGMs. The distinct peaks are narrow and high in intensity, indicating excellent Q-factors. The theoretical positions for TE (TM) modes are indicated by the gray dashed (dotted) lines. The experimentally measured mode spacing lies between 19 and 21 THz and is in fair agreement with the calculations. The quality factors were determined by fitting a Voigt profile, which accounts for the spectral resolution of the spectrometer, to the modes as indicated in Figure 3b. We find that the Qfactors have an apparent maximum for lower emission wavelengths and decrease for longer wavelengths (see Figure 3c). This is in good agreement with the previous results18 and also our theoretical calculations. The mode spacing and Q-factors of 29 resonators were measured and compared for different disk diameters. The mode spacing, as shown in Figure 4a, is in good agreement with the theoretical calculations for both TE and TM modes. The highest Q-factor measured was 1900 and therefore slightly lower but comparable to that achieved by using electron beam lithography (230018). In previous works, Q-factors greater than 106 have been calculated; however, the experimental values were 3 orders of magnitude lower.18 The main factors for loss and therefore low Q-factors are absorption and the high surface roughness. Another reason could be ascribed to the quality of the 3C-SiC/ Si film. The heteroepitaxy of the highly mismatched 3C-SiC on a Si substrate generates a lot of defects (mainly twins and stacking faults) near the interface in particular for thin films.25 Slanted side walls may further reduce the Q-factors. The Qfactors may therefore be increased by improving the fabrication and, in particular, the RIE process.

Figure 2. (a) Absolute values of the electric field components, Er, Eϕ, and Ez for a TE (top) and TM mode (bottom) with the mode orders (15,1) and (13,1) and mode volumes of 7 and 10 λ3/n3, respectively. The simulated resonator structure is indicated by the white line. The disk top diameter was 1.8 μm, the thickness 170 nm, and the slant angle 15°. (b, c) Z-profile of (b) |Er| and (c) |Eϕ| of the TE and TM mode, respectively, for the radial position with the highest field component at the top surface (dotted line). (d) Radial field profile of the modes in (b) (solid line) and (c) (dotted line). The dashed line indicates the surface and the arrow the full-width at half-maximum of the |Er| component. (e) Top view of the field distribution with the red line indicating the disk perimeter and the blue line the radial field maximum of the TE mode at the surface. The green and red arrows denote two dipole emitters with a radial and azimuthal dipole orientation, respectively.

orientations of 0° and 90° with respect to the in-plane lattice vectors.13 Defects at the surface can couple most strongly to TE modes if radially aligned and TM modes if azimuthally aligned. If we consider the field components that are strongest at the surface, it is apparent that the TE mode exhibits only Er components at the surface, while the Eϕ component is the largest for the TM mode. The Ez component cannot be used for coupling due to the in-plane dipole orientation of the SPEs. The vertical E-field profiles, normalized to Emax, for the TE Er and TM Eϕ field components are displayed in Figure 2b and c, and both exhibit a non-negligible field strength at the surface (dotted line). This suggests that defects located at the disk surface can couple effectively to TE or TM WGMs depending on their dipole orientation. At the same time, the two radial field distributions as displayed in Figure 2d have a broad maximum that requires a defect positioning accuracy of less than 200 nm, which can be easily achieved with the positioning accuracy of the confocal lithography technique. Figure 2e shows a top view of the resonator, with the blue line indicating the ideal defect position for a radially polarized dipole. The two possible dipole orientations are indicated by the red (Eϕ direction) and green (Er direction) arrows. Finally, the spectral overlap of the ZPL of the defect and at least one mode is required to achieve coupling. However, even nanometer errors in the resonator size, which are inevitable

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RESONATOR ALIGNMENT The advantage of the lithography technique reported here over electron beam lithography is the possibility to individually align a resonator to an SPE in a single step. Figure 5a shows a confocal fluorescence map (see Methods) of a resonator (the actual size is 1.5 ± 0.1 μm) that was aligned to a precharacterized single defect. After fabrication, the single defect showed bright single-photon emission with a saturation count rate of 4.3 ± 0.6 Mcps and remained photostable throughout the measurements over several days. The count rate increased by a factor of 1.7 after fabrication, which can be 464

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Figure 3. (a) Photoluminescence spectrum of a 1.8 μm diameter resonator taken under 50 mW 532 nm illumination. The TM and TE modes are indicated by red triangles and black squares, respectively. The dashed (dotted) lines indicate the numerically calculated mode position for each TE (TM) mode. (b) Zoom-in of the region marked with a rectangle in (a). A Voigt function with a Gaussian width corresponding to the spectrometer response function was fitted to each peak. Quality factors of 1700 and 1000 were extracted from the fit. (c) Q-factors for the modes displayed in (a) plotted as a function of wavelength. (d) SEM image of the resonator.

Methods). The antibunching for τ = 0 indicates that the emission indeed originated from a single emitter. The excitedstate lifetime was 2.7 ± 0.3 ns as extracted from a series of power-dependent measurements of g(2)(τ). Importantly, the spectra of the emission before and after fabrication of the resonator were compared (see Figure 5c). The prefabrication spectrum exhibited a strong ZPL at 667 nm with a high Debye−Waller factor (the fraction of light emitted into the ZPL) of 0.25. About 10% of the defects have comparably sharp emission spectra, albeit with a great variability in their ZPL position.13,14 After fabrication of the resonator, distinct modes with low Qfactors (∼300−600) are visible in the spectrum. These values are in agreement with the lower range of values displayed in Figure 3c and Figure 4b. The exact mode positions and Qfactors were determined under 532 nm excitation (green dots), which did not excite the single-defect emission. The mode spacing was found to be 22.8 and 22.6 THz for the modes between 650 and 700 nm for TE and TM modes, respectively. This is in fair agreement with the mode spacing determined from the other resonators of the same size. The TM WGM at 666 nm is close to the ZPL and enhances and shifts its position slightly. This enhancement is counterintuitive based on the defect’s dipole orientation (inset of Figure 5c), but can be explained by the non-negligible Er component of the quasi-TM mode. Additionally, there is a slight overlap of the ZPL with a TE WGM at 662 nm. With the dipole orientation and the resonator’s radial mode profile, the targeted ideal position of the defect inside the resonator is indicated by the blue annular region. The defect is located close to the maximum of the calculated radial E-field profile (displacement: ∼60 nm). This therefore shows that the single defect was successfully integrated into the resonator for

Figure 4. Comparison of (a) the mode spacing and (b) the maximum Q-factor in the spectral region from 650 to 700 nm of 29 resonators located in the same array with five different targeted resonator diameters. The error bars indicate the standard deviation. TE and TM modes are indicated by black squares and red triangles (experimental data) and black crosses and red circles (simulation), respectively.

attributed to an enhancement of the collection efficiency due to the removal of the SiC substrate or Purcell enhancement. Figure 5b shows the second-order autocorrelation function, g(2)(τ), determined from a time-correlation measurement after correction for the 18% uncorrelated background emission (see 465

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region, showed similar Q-factors to those fabricated by electron-beam lithography18 and, moreover, were aligned to single photoluminescent defects. The fabrication and characterization were supported by numerical simulations of the resonators’ electric field distribution. WGMs were observed in the emission spectrum of a single defect integrated into a deterministically placed microdisk resonator. At the same time, the detected emission rate was increased after fabrication due to an enhanced collection efficiency. The alignment demonstrated here can easily be transferred to other defect centers, such as the divacancy defect in 3C-SiC,31 which exhibits accessible spin sublevels. Similarly, the technique can be adapted to create disk resonators in the hexagonal polytypes via electrochemical etching17 optimized for silicon vacancy,7,8 divacancy,9 and possibly nitrogen vacancy defects.32 Moreover, the technique is adaptable to fabrication of a wide range of microstructures, including cantilevers, micropillars, and microring resonators. A reduction in the resonator size variability to yield more predictable WGM positions is required. This may be achieved by combining the technique with highresolution lithography methods, for example electron beam lithography. In this case, the present approach could be used to produce high-resolution markers to enable alignment of a resonator fabricated by electron beam lithography to a single defect.

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METHODS Confocal Microscope. The custom-built confocal microscope was equipped with a 100× infinity corrected air objective with an NA of 0.95. The sample was mounted vertically on a piezoelectric translation stage with nanometer positioning accuracy. A 633 nm helium neon laser was used to excite defect luminescence, and a 532 nm diode laser was used to expose the resist. The spectrally filtered fluorescence light was focused onto a multimode fiber (50 μm) that acted as the confocal pinhole. The light was then split 50/50 and guided onto a single-photon counting module (SPCM) and either to a spectrometer (Acton Spectra Pro 2300i) or to a second SPCM. The time correlation measurements were performed with the two SPCMs in a Hanbury-Brown and Twiss configuration. The confocal system has an overall detection efficiency of about 1.5%. In this work, the emission intensity of SPEs is measured as detector counts per second (cps). The histogram, H(τ), obtained for the time correlation measurement was first normalized by Hn(τ) = H(τ)/(N1N2T δt), where Ni labels the detector count rates, T the acquisition time, and δt the time binning. The normalized histogram was then corrected for the uncorrelated background as measured in the vicinity of the defect by g(2)(τ) = (Hn(τ) − (1 − ρ2))/ρ2, where ρ = S/(S + B), with the signal, S, and the background intensity, B. For the g(2)(τ) presented in Figure 5, ρ was 0.72. Prior to background correction, the g(2)(0) was less than 0.5. FDTD Simulations. All simulations were performed with the finite-difference time-domain (FDTD) method, using the freely available software package MEEP.33 Both the SiC disk and the Si pedestal were approximated as truncated cones (with a constant slant angle) along with their appropriate material dispersions. Around the dielectric structure, we defined a perfectly matched layer of thickness 2.0 μm for the simulations in Figure 2 and 1.0 μm for all other simulations, at least 1.0 μm away from disk or pedestal, acting as boundary. The top view electric field profile shown in Figure 2 was calculated using a 3D simulation with a resolution of 60 μm−1. All other

Figure 5. (a) Confocal fluorescence map of a resonator that was aligned to a bright SPE (green arrow) under 633 nm excitation with 1 mW. The blue circle indicates the ideal alignment as determined by the full-width at half-maximum of the radial mode profile. The resonator perimeter is indicated by the white dashed circle. (b) Measurement of the second-order autocorrelation function of the defect in the fully fabricated resonator (corrected for the uncorrelated background), proving that the bright emitter is an SPE. (c) Preexposure and postfabrication PL spectrum of the defect shown in (a) using identical excitation conditions, vertically offset for clarity. The green PL spectrum was measured under 532 nm excitation to extract the TE and TM mode positions. The TE modes are indicated by the black boxes. The inset shows a polarization measurement of the emitter. The squared sinusoidal fit indicates a dipole orientation with a 2° offset with respect to Er.

the goal of improving its emission properties. On the basis of the numerical simulations shown in Figure 2 we can estimate the Purcell factor using eq 1. Due to the finite width of the emitter, the cavity Q-factor is replaced with the effective Qfactor of the system:30 Qeff = λ/(Δλem + Δλcav) = 280, where Δλcav and Δλem are the cavity and emitter line width, respectively. Also including the Debye−Waller factor of 0.25, we estimate a Purcell factor of 0.12 ± 0.08 for the TM and 0.06 ± 0.02 for the TE mode. These values do not support that the increased brightness after fabrication is due to Purcell enhancement. Instead calculations indicate that it is caused by a higher collection efficiency after removal of the silicon substrate underneath the SiC film.

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CONCLUSION In conclusion, we have fabricated microdisk resonators in 3CSiC with a specifically designed optical lithography technique. These resonators, optimized for emission in the visible spectral 466

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(7) Widmann, M.; Lee, S.; Rendler, T.; Son, N. T.; Fedder, H.; Paik, S.; Yang, L.; Zhao, N.; Yang, S.; Booker, I.; Deniseko, A. Coherent control of single spins in silicon carbide at room temperature. Nat. Mater. 2015, 14, 164−168. (8) Fuchs, F.; Stender, B.; Trupke, M.; Simin, D.; Pflaum, J.; Dyakonov, V.; Astakhov, G. V. Engineering near-infrared singlephoton emitters with optically active spins in ultrapure silicon carbide. Nat. Commun. 2015, 6, 1−7. (9) Christle, D. J.; Falk, A. L.; Andrich, P.; Klimov, P. V.; Hassan, J. U.; Son, N. T.; Janzen, E.; Ohshima, T.; Awschalom, D. D. Isolated electron spins in silicon carbide with millisecond coherence times. Nat. Mater. 2014, 14, 160−163. (10) Kraus, H.; Soltamov, V. A.; Fuchs, F.; Simin, D.; Sperlich, A.; Baranov, P. G.; Astakhov, G. V.; Dyakonov, V. Magnetic field and temperature sensing with atomic-scale spin defects in silicon carbide. Sci. Rep. 2014, 4, 1−8. (11) Simin, D.; Fuchs, F.; Kraus, H.; Sperlich, A.; Baranov, P. G.; Astakhov, G. V.; Dyakonov, V. High-Precision Angle-Resolved Magnetometry with Uniaxial Quantum Centers in Silicon Carbide. Phys. Rev. Appl. 2015, 4, 014009. (12) Castelletto, S.; Johnson, B.; Ivády, V.; Stavrias, N.; Umeda, T.; Gali, A.; Ohshima, T. A silicon carbide room-temperature singlephoton source. Nat. Mater. 2014, 13, 151−156. (13) Lohrmann, A.; Castelletto, S.; Klein, J. R.; Ohshima, T.; Bosi, M.; Negri, M.; Lau, D. W. M.; Gibson, B. C.; Prawer, S.; McCallum, J. C.; Johnson, B. C. Activation and control of visible single defects in 4H-, 6H-, and 3C-SiC by oxidation. Appl. Phys. Lett. 2016, 108, 021107. (14) Lohrmann, A.; Iwamoto, N.; Bodrog, Z.; Castelletto, S.; Ohshima, T.; Karle, T. J.; Gali, A.; Prawer, S.; McCallum, J. C.; Johnson, B. C. Single-photon emitting diode in silicon carbide. Nat. Commun. 2015, 6, 1−7. (15) Faraon, A.; Barclay, P. E.; Santori, C.; Fu, K.-M. C.; Beausoleil, R. G. Resonant enhancement of the zero-phonon emission from a colour centre in a diamond cavity. Nat. Photonics 2011, 5, 301−305. (16) Vahala, K. J. Optical microcavities. Nature 2003, 424, 839−846. (17) Magyar, A. P.; Bracher, D.; Lee, J. C.; Aharonovich, I.; Hu, E. L. High quality SiC microdisk resonators fabricated from monolithic epilayer wafers. Appl. Phys. Lett. 2014, 104, 051109. (18) Radulaski, M.; Babinec, T. M.; Muller, K.; Lagoudakis, K. G.; Zhang, J. L.; Buckley, S.; Kelaita, Y. A.; Alassaad, K.; Ferro, G.; Vuckovic, J. Visible photoluminescence from cubic (3C) silicon carbide microdisks coupled to high quality whispering gallery modes. ACS Photonics 2014, 2, 14−19. (19) Bracher, D. O.; Zhang, X.; Hu, E. L. Selective Purcell enhancement of two closely linked zero-phonon transitions of a silicon carbide color center. arXiv preprint arXiv:1609.03918, 2016,. (20) Radulaski, M.; Widmann, M.; Niethammer, M.; Zhang, J. L.; Lee, S.; Rendler, T.; Lagoudakis, K. G.; Son, N. T.; Janzen, E.; Ohshima, T.; Wrachtrup, J. Scalable Quantum Photonics with Single Color Centers in Silicon Carbide. arXiv preprint arXiv:1612.02874, 2016,. (21) Radulaski, M.; Tzeng, Y.; Zhang, J. L.; Lagoudakis, K. G.; Ishiwata, H.; Dory, C.; Alassaad, K.; Ferro, G.; Shen, Z.; Melosh, N.; Chu, S. Hybrid Microresonator Enhanced Emission from SiliconVacancy and Chromium-Related Color Centers in Diamond. arXiv preprint arXiv:1610.03183, 2016,. (22) Dousse, A.; Lanco, L.; Suffczyński, J.; Semenova, E.; Miard, A.; Lemaître, A.; Sagnes, I.; Roblin, C.; Bloch, J.; Senellart, P. Controlled light-matter coupling for a single quantum dot embedded in a pillar microcavity using far-field optical lithography. Phys. Rev. Lett. 2008, 101, 267404. (23) Dousse, A.; Suffczyński, J.; Beveratos, A.; Krebs, O.; Lemaître, A.; Sagnes, I.; Bloch, J.; Voisin, P.; Senellart, P. Ultrabright source of entangled photon pairs. Nature 2010, 466, 217−220. (24) Lee, K. H.; Green, A. M.; Taylor, R. A.; Sharp, D. N.; Scrimgeour, J.; Roche, O. M.; Na, J. H.; Jarjour, A. F.; Turberfield, A. J.; Brossard, F. S. F.; Williams, D. A. Registration of single quantum

simulations were performed as 2D simulations with a resolution of 150 to 200 μm−1 assuming cylindrical symmetry of the structure to increase the accuracy and speed of computation. For each simulation, we further specified the rotational symmetry of the mode we would like to simulate, which MEEP uses to restrict the computed field to a particular angular momentum (angular dependence). In order to determine the whispering gallery mode frequencies, and hence the mode spacing, of a particular disk geometry, a broadband TE or TM source (Gaussian pulse with 150 THz spectral bandwidth) at a center frequency of 450 THz was used for excitation, while specifying the mode order from 8 to 25. Quality factors, mode volumes, and electric field distributions were determined by exciting the same computational cell with a narrowband source (9 THz spectral bandwidth) at the center frequency of each particular mode.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.6b00913. Technical details of the fabrication method and the demonstration of stochastic creation of SPEs in a resonator array by postfabrication oxidation (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Alexander Lohrmann: 0000-0001-8966-1443 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Australian Research Council Center for Quantum Computation and Communication Technology (No. CE110001027). This work was performed in part at the Melbourne Centre for Nanofabrication (MCN) in the Victorian Node of the Australian National Fabrication Facility (ANFF). A.L. further acknowledges the financial support of the Albert Shimmins Fund. This work was partially funded by a University of Melbourne Early Career Researcher award.

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REFERENCES

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ACS Photonics

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DOI: 10.1021/acsphotonics.6b00913 ACS Photonics 2017, 4, 462−468