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Bright Room-Temperature Single Photon Emission from Defects in Gallium Nitride

Single photon emitters play a central role in many photonic quantum technologies. A promising class of single photon emitters consists of atomic color centers in wide-bandgap crystals, such as diamond silicon carbide and hexagonal boron nitride. However, it is currently not possible to grow these materials as sub-micron thick films on low-refractive index substrates, which is necessary for mature photonic integrated circuit technologies. Hence, there is great interest in identifying quantum emitters in technologically mature semiconductors that are compatible with suitable heteroepitaxies. Here, we demonstrate robust single photon emitters based on defects in gallium nitride (GaN), the most established and well understood semiconductor that can emit light over the entire visible spectrum. We show that the emitters have excellent photophysical properties including a brightness in excess of 500x10^3 counts/s. We further show that the emitters can be found in a variety of GaN wafers, thus offering reliable and scalable platform for further technological development. We propose a theoretical model to explain the origin of these emitters based on cubic inclusions in hexagonal gallium nitride. Our results constitute a feasible path to scalable, integrated on-chip quantum technologies based on GaN.

In this work, we report room temperature (RT), bright, stable single photon emitters (SPEs) in GaN films that do not require any post-growth sample treatments. The emitters are defects that are optically active in the visible/near-infrared (NIR) spectral range, and the zero-phonon lines (ZPL) span a wide range of wavelengths. They were found in five GaN wafers that have different doping types and levels, and are grown on various substrates using Metal Organic Chemical Vapor Deposition (MOCVD), the most common commercially viable technique for the growth of devicegrade GaN. The pervasiveness of the SPEs in different GaN samples demonstrates that our finding are not limited to a rare defect found in select few ultrapure samples.
To identify and characterize the SPEs, we analyzed 5 GaN samples grown on sapphire and silicon carbide (SiC). Sample A consists of a 4 µm thick Magnesium (Mg)-doped GaN film grown on sapphire. For clarity, we present an optical image and an atomic force microscope (AFM) scan of Sample A in Figure 1(a-b), while a summary of the structural characterization of the other samples is provided in the supporting information (table S1). The crystalline quality of the GaN samples was evaluated by X-ray diffraction (XRD) measurements, confirming their single crystal nature (see table S2). For all samples, surface roughness is below 1 nm (see table S1, S2).
The spectroscopy measurements on all samples were performed using a scanning confocal microscope (microscope objective with numerical aperture 0.9) with green laser excitation (532nm) focused to a laser spot with a diameter of ~ 400 nm. Figure 1c shows a representative 60 µm X 60 µm fluorescence map with localized, bright spots labeled E1-E8, corresponding to isolated emission spots in Sample A. This map is obtained from a 1 cm 2 sample using an excitation power of 300 µ W (measured before the microscope objective). An analysis of other regions of sample A indicate an average of 1 emitter per 25 .  Below, we provide a detailed analysis of sample A and show representative data from the other 4 samples. As shown in Figure 2a, the RT photoluminescence (PL) spectra from emitters E1-E5 show distinct ZPL wavelengths of 640 nm, 657 nm, 681 nm, 703 nm and 736 nm, respectively.
All spectra are obtained with the same excitation power of 100 µW, while all second-order correlation measurements were carried out using a laser power of 50 µW. The 696 nm luminescence peak corresponds to the ruby CrAl 0 emission and is present in all spectra taken from the samples grown on sapphire. Additional representative RT spectra from Sample A are provided in the supporting information ( Figure S2). Figure 2b shows the ZPL wavelength distribution of 93 emitters in Sample A.

The histogram in
This histogram bin width is 10 nm as small differences in peak position can be caused by strain variations throughout the sample [27] . However, the ZPL wavelengths span 180 nm, suggesting a different primary mechanism for the broad distribution seen in Figure 2b. A likely mechanism is proposed below.
The histogram in Figure 2c summarizes the RT ZPL line width distribution of 96 emitters in Sample A, with a median full width at half maximum (FWHM) of ~ 5 nm. Fits of the ZPL peak shape reveal an asymmetry caused by a low energy tail which may be caused by coupling to phonons. The ZPLs are narrower than the RT line width of the NV [28] center in diamond and comparable to other defects in diamond (e.g. the SiV [29] and the Cr-related [30] ).
Photon emission statistics were analyzed using a Hanbury Brown and Twiss (HBT) interferometer. The spots E1-E5 in Sample A (see Figure 1c and 2a) are SPEs, where the second order autocorrelation measurement ( ( at zero delay time ( = 0 shows that (0 <0.5. Spots E6-E8 also exhibit antibunching, but the (0 values exceed 0.5, indicating that they are small ensembles of 2-4 emitters ( ( measurement from all 8 spots are shown in Figure S3).

Figure 2d shows spectra and autocorrelation measurements from typical emitters in Samples
B-E. Data from additional emitters found in these samples is provided in the Supporting Information (Figures S4-S7).
To confirm that the observed fluorescence is indeed from the GaN films, three pieces of Sample A were etched using chlorine reactive ion etching (RIE) to depths of 300 nm, 4 µm and 6 µm. Subsequent PL analyses show that the emitters were still present after the 300 nm etch process, but no localized florescence was observed if the 4 µm GaN epilayer was completely removed by the etch process. This confirms that the emitters do indeed originate from GaN. All the emitters that were investigated are bright and do not exhibit blinking or bleaching.

Figure 3a
shows the saturation behavior of emitter E2 with a ZPL wavelength of 657 nm obtained using two different methods [31] . In the first method, the saturation data are corrected for background and fitted with power model (red points and line) of the form, where is the saturation power and is the corresponding photon detection rate. Fitting the background-corrected data with Equation (1) yields a maximum intensity of 501×10 3 counts/s at a saturation power of 930 µW. This intensity value is comparable with other single emitters in bulk materials.
Alternatively, the single photon emission rate can be estimated using g 2 -corrected data [31] . At an excitation power of 50 µW, Emitter E2 yields an antibunching dip at zero-delay time ( ( = 0 ) of 0.331. The normalized ( can be corrected for background using [31] : where ( is the pure antibunching function and ρ is the ratio of single photon emission rate (!) to total count rate ("). Ideally, antibunching of a SPE such as E2 satisfies the condition Photostability of the SPEs is studied by recording PL intensity versus time under continuous wave excitation. Figure 3b shows an example obtained from emitter E2 using an excitation power of 3 mW over 10 minutes of continuous acquisition. All the emitters studied in this work were stable and did not exhibit blinking or bleaching under our experimental conditions. We now proceed to characterize the SPEs at cryogenic temperatures. Figure 3c shows a PL spectrum from a SPE at ~4 K. The emitter ZPL has a FWHM of 0.98 nm corresponding to a Huang-Rhys factor of 0.46 (defined by S=-ln (Izpl/Itot) where Izpl (Itot) is the ZPL (total) integrated PL intensity [32] ). We did not observe spectrometer-limited linewidths and the broadening is most likely caused by coupling to phonons or ultrafast spectral diffusion. Figure 3d shows the ZPL wavelength and FWHM measured as a function of temperature between 3.5 K and 80 K. Unlike other solid-state emitters that have monotonic T 5 , T 3 , T 7 or exponential dependencies on temperature [33][34][35] , the emitters in GaN exhibit an unusual 'S-shaped' dependence, suggesting that the emitters are not simple atomic defect centers, but have an alternate origin. Furthermore, the broad spectral spread of ZPL wavelengths across individual wafers and between wafers suggests that the emitters are associated with growth defects rather than a particular impurity (such as the NV defect in diamond).
Point defect agglomeration during growth of wurtzite GaN can lead to the formation of stacking faults (SF) with varying widths spanning a few angstrom to 10 nm [36,37] . Figure 4a is a schematic illustration of a 5-bilayer cubic inclusion in a 12-bilayer slab of wurtzite GaN, forming stacking faults. Consequently, localized cubic inclusions introduce a quantum well for conduction band electron due to the narrower band gap of cubic GaN relative to wurtzite GaN. The cubic inclusion is surrounded by the spontaneously polarized wurtzite matrix, resulting in electronic states with a localized electric field [38,39] . These electronic states with a strong electric field act as effective triangular quantum well structures, altering the local optical properties of GaN [39][40][41] The presence of SFs and their role in the observed quantum emissions is supported by the observed "S-shaped" temperature dependence of the ZPL wavelength seen in Figure 3d. The ZPL blue-shifts as T is increased from 10 K to 30 K, and red-shifts as T is increased beyond 30 K. This has been reported previously for band edge excitons in c-and a-plane grown GaN [42][43][44] , where the blue shift is explained by an exciton transition from a shallower energy level of conduction band quantum wells to holes in the valance band. It can occur due to carrier reshuffling within the stacking faults by virtue of lattice strain or location of extrinsic atoms in the vicinity of a stacking fault [42] . The red shift at temperatures greater than 30 K can arise from thermal activation of additional bilayers, allowing deeper quantum-well-potential-bound exciton transitions [45,46] . An alternative explanation for the red shift is a delocalization of holes in the valance band and recombination with stacking-fault-bound electrons [42,47] .
Similarly, we attribute the antibunched photon emissions reported here to the radiative recombination of an exciton bound to a point defect that resides inside or next to a stacking fault.
In our model, the hole is tightly localized to the defect site whereas the electron is loosely bound by a Coulomb interaction introduced by the localized hole in the optically allowed lowest-energy excited state of the point defect. This localization modifies the stacking fault's triangular potential profile acting on the electron as illustrated in Figure 4b. We solve a quasi-one-dimensional Hamiltonian of this potential [48] where we applied fundamental material parameters of wurtzite and cubic GaN such as the band gaps, band alignments, effective masses of the hole and electron, dielectric constants, and steepness of the triangular well caused by spontaneous polarization. The resulting calculated energy of the exciton is assumed to be the ZPL energy of the emitter. It is important to note that the observed emitters are different from GaN or InGaN quantum dots, which have been isolated and shown to exhibit quantum emissions [49,50] . Those sources operate predominantly at cryogenic temperatures, and originate from crystal size confinement of the QDs.
To conclude, we show that GaN is a promising host of bright SPEs in the visible and near infrared spectral ranges. In particular, we demonstrated that these emitters are prevalent in a broad range GaN films grown on sapphire and SiC substrates. Low-temperature studies and subsequent Hamiltonian parametrized calculations suggest that the quantum emitters are defects localized in close proximity to an extended stacking fault formed due to a cubic inclusion. The model suggests that generation and, potentially, control of the emitter wavelengths may be possible by intentional introduction of cubic layers in the GaN growth process. Even at the current stage, the highly photostable SPEs offer a compelling opportunity for scalable nanophotonic devices and quantum information science based on an industrially and commercially important semiconductor material.