Room-temperature single-photon emission from β-Ga_2O_3

Domain: physics
Published: 2025-12-02
Editorial outcome: minor_revision

Abstract
Single photon emitters (SPEs) hosted by the wide bandgap semiconductors have the great potential to enable quantum applications at room temperature. Recently, many defect-based SPEs have been discovered in various wide bandgap materials, such as diamond, AlN, SiC, h-BN, GaN and ZnO. Beta-phase gallium oxide (β-Ga2O3) is an emerging ultra-wide bandgap semiconductor with promising electronic and optoelectronic properties, however, there has been no report on single-photon emission from β-Ga2O3 to date. Herein, we present the demonstration of room-temperature photostable single-photon emission from β-Ga2O3. We find that the SPEs can be found in a variety of β-Ga2O3 including homoepitaxial and heteroepitaxial β-Ga2O3 films and commercially available β-Ga2O3 wafers. The observed emitters have excellent photophysical characteristics including high purity, high brightness, and linear polarization. First-principles calculations predict that a localized neutral divacancy defect, generated by plasma treatment and activated by annealing, is responsible for the SPEs in β-Ga2O3. The high-performance room-temperature SPEs embedded in a technologically mature semiconductor are promising for on-chip scalable integrated devices and quantum technologies.

Introduction
Single photon sources are key elements for various scalable quantum information technologies, including quantum communication, quantum computing, quantum sensing and measurement1–3. So far, single photon emission has been observed from various quantum emitters such as single molecules4, atoms5, ions6, quantum dots7, and point defects in semiconductors8,9. Among them, color centers in wide bandgap semiconductors are considered to be one of the most promising single photon emitters (SPEs) due to their unique properties of stable emission at room temperature or even at high temperature, as well as a wide range of single-photon emission wavelengths9. Furthermore, the SPEs based on wide bandgap semiconductors are compatible with mature semiconductor technologies, which is beneficial for the integration of optoelectronic devices. In recent years, defect-based SPEs have been discovered in various wide bandgap materials, such as diamond10–12, silicon carbide (SiC)13–15, silicon nitride (SiN)16, zinc oxide (ZnO)17,18, gallium nitride (GaN)19,20, aluminum nitride (AlN)21,22, and hexagonal boron nitride (h-BN)23–26.

Beta-phase gallium oxide (β-Ga2O3) has emerged as a potentially disruptive ultra-wide bandgap semiconductor for next-generation electronic and optoelectronic applications27–30, as it has a wide bandgap of ~4.9 eV, high breakdown electric field of 8 MV cm−1, excellent chemical and thermal stability, and large Baliga’s figure of merit of 3444. To date, β-Ga2O3 has well-established growth and device engineering protocols, and β-Ga2O3 wafers up to 8-inch are now commercially available. Unlike traditional semiconductors, β-Ga2O3 possess a low-symmetry monoclinic crystal structure (C2/m space group), characterized by two crystallographically nonequivalent Ga3+ and three nonequivalent O2- ions in the unit cell. The abundance of possible natural defects makes β-Ga2O3 a flexible and scalable material platform for defect-based SPEs. Recently, Stehr et al. reported a transition-metal color center in β-Ga2O3 that emits in the telecom range and has an electronic structure suitable for quantum information applications31. However, there are no reports on single-photon emission from β-Ga2O3 yet.

In this work, we demonstrate the single-photon emission from β-Ga2O3 at room temperature. The samples we used are homoepitaxial β-Ga2O3 films, heteroepitaxial β-Ga2O3 films on sapphire substrates, and bulk β-Ga2O3 wafers, which were irradiated with plasma then annealed at high temperatures to generate SPEs. Second-order correlation measurements reveal strong photon antibunching, which unambiguously establishes the single-photon nature of the emission. The SPEs in β-Ga2O3 exhibit high purity and brightness, excellent stability, as well as spatially uniform distribution. The prevalence of SPEs in different β-Ga2O3 samples indicates that the intrinsic defects are responsible for the observed quantum emissions. We performed first-principles calculations to identify the possible origin of the observed SPEs. This work provides a reliable and scalable platform for further technological development, which may open promising avenues for photonic quantum devices based on β-Ga2O3.

Results
Characterization of epitaxial β-Ga2O3 thin films

The homoepitaxial and heteroepitaxial β-Ga2O3 thin films were grown by low pressure chemical vapor deposition (LPCVD) on single crystal β-Ga2O3 (−201) and sapphire substrates, respectively. The atomic force microscopy (AFM) image (Fig. 1a) demonstrates that the surface of the polished β-Ga2O3 substrates is rather smooth and uniform with a root mean square (RMS) roughness of 0.48±0.04 nm (Supplementary Fig. 1a). The homoepitaxial β-Ga2O3 film exhibits a clear step-flow growth mode (Fig. 1b) with an RMS roughness of 2.5±0.31 nm (Supplementary Fig. 1b), which is in good agreement with the previously reported β-Ga2O3 homoepitaxial films32,33. In contrast, the heteroepitaxial β-Ga2O3 film grown on a sapphire substrate follows the island-growth model and displays coral-like morphology (Fig. 1c) with a relatively large RMS roughness of 3.1±0.22 nm (Supplementary Fig. 1c). Both Raman spectra of the homoepitaxial and heteroepitaxial β-Ga2O3 films show a set of characteristic Raman peaks at 113.2, 143.8, 168.9, 199.3, 319.7, 345.6, 416.0, 657.5 and 765.3 cm−1 (Fig. 1d), which are well consistent with the previously reported data32,34. Furthermore, X-ray photoelectron spectroscopy (XPS) measurements confirm that the homoepitaxial β-Ga2O3 films have high chemical purity and their chemical composition is close to the ideal stoichiometry (Supplementary Fig. 2). The thickness of epitaxial β-Ga2O3 film is about 200 nm, as revealed by the low magnification cross-sectional transmission electron microscopy (TEM) image (Supplementary Fig. 3).

We conducted high-resolution TEM (HRTEM) measurements to investigate the interfacial microstructure and crystalline quality of the homoepitaxial β-Ga2O3 films, taken along the zone axis <102> of β-Ga2O3 (Fig. 1e). The atomically sharp interface between the epitaxial layer/substrate almost cannot be distinguished (the interface indicated by the dashed line is determined from the global large-scale TEM image in Supplementary Fig. 4), revealing the high-quality homoepitaxy of the β-Ga2O3 film. As shown in the magnified interfacial region (Fig. 1f), the d-spacing of lattice structure is 4.68 Å, matching the (−201) planes of β-Ga2O3, while the lateral lattice distance of β-Ga2O3 is about 1.52 Å, corresponding to the lattice spacing of β-Ga2O3 (020) planes. These results are aligning with the observed sharp and bright diffraction spots of the selected area electron diffraction (SAED) pattern taken from the interface (the inset of Fig. 1e). In addition, the interface structure of the heteroepitaxial β-Ga2O3 film was also investigated (Supplementary Fig. 5), and the epitaxial relationship between the β-Ga2O3 epilayer and the sapphire substrate is determined as follows: β-Ga2O3 (−201)[010]//sapphire (0001)[1–100]. The orientation relationship of β-Ga2O3 film is also confirmed by the corresponding X-ray diffraction (XRD) patterns (Supplementary Fig. 6a). The XRD rocking curve of (−201) peak displays a full width at half maximum (FWHM) of 0.007° (25 arcsec) and 1.21° for the homoepitaxial and heteroepitaxial β-Ga2O3 layers (Supplementary Fig. 6b), respectively, suggesting that the crystalline quality of homoepitaxial β-Ga2O3 layer is much higher than that of the heteroepitaxial counterpart.

Photophysical properties of SPEs in β-Ga2O3

The spectroscopy measurements on all β-Ga2O3 samples were conducted using a homemade confocal microscopy system equipped with an objective lens with high numerical aperture (NA=0.9) and a 532 nm continuous-wave laser at room temperature. Several plasma-treatment combined with annealing processes have been attempted to generate isolated point-defects in β-Ga2O3. Similar to the as-grown β-Ga2O3 films without any treatment, both plasma treatment alone and plasma treatment with air-annealing don’t cause PL emission, and only two Raman peaks of β-Ga2O3 are observed (Supplementary Fig. 7a). By applying plasma treatment followed by vacuum annealing, the β-Ga2O3 film exhibits PL defect-emission with strong fluorescence background (Supplementary Fig. 7b). When these β-Ga2O3 films were further annealed in air at 850 °C for 30 min, the fluorescence background is substantially reduced (Supplementary Fig. 7c). Thus, we introduced isolated point-defects in β-Ga2O3 films through plasma treatment and activated them using vacuum annealing, and followed by air annealing to eliminate the fluorescence background. Unless otherwise specified, this treatment procedure was employed in all subsequent experiments. The normalized confocal photoluminescence (PL) intensity maps for the homoepitaxial and heteroepitaxial β-Ga2O3 films are shown in Fig. 2a, b, respectively, where the local bright spots marked by red boxes are isolated emission points. As revealed by an analysis using Ripley’s K function (Supplementary Fig. 8), these emission points are uniformly and randomly distributed in both samples. The density of SPEs is estimated to be 0.02 counts μm−2, which is comparable with previously reported quantum emitters in SiN16, GaN19 and AlN22. The PL spectra of two representative SPEs in the homoepitaxial and heteroepitaxial films are shown in Fig. 2c. Both PL spectra exhibit an asymmetric zero-phonon line (ZPL), possibly due to interactions with phonons23. As revealed by the fitting results, the spectra are composed of a prominent ZPL centered at ~565 nm (~2.19 eV) and a lower-intensity phonon sideband (PSB) red-shifted by ~34 meV, as well as a weak peak at ~610 nm due to multi-phonon scattering and/or anharmonic process35. The sharp peaks at ∼530/550 nm (marked by hash symbols) and 690 nm (marked by asterisk) in the PL spectra originate from the Raman mode of β-Ga2O3 and sapphire substrate, respectively. The Debye–Waller (DW) factors (i.e., the probability of coherently emitting into the ZPL) are calculated to be 77% (homoepitaxial) and 70% (heteroepitaxial), which are higher than the values of several commonly SPEs, such as G-center in Si (∼15% @ 10 K)36, AlN (∼29% @ 10 K)37, and negatively charged nitrogen vacancy (NV−) center in diamond (2.55% @ room temperature)38. The emitters with a higher DW factor could be directly enhanced via coupling to an optical cavity, achieving better single-photon emission characteristics.

Next, we investigated the single photon purity of the emitters by second-order autocorrelation g2(τ) measurements with a Hanbury Brown-Twiss (HBT) interferometer. The normalized second-order correlation function g2(τ) of SPEs in the homoepitaxial and heteroepitaxial β-Ga2O3 films is shown in Fig. 2d, e, respectively. The experimental g2(τ) data were fitted (red lines) using a three-level model without background correction25,39: g2(τ)=1-(1+a)e−|τ|/τ1+be−|τ|/τ2, where a and b are fitting parameters, τ1 and τ2 are the lifetimes of the excited and metastable states, respectively. From the fitting, we obtained the g2(τ) value of 0.24±0.08 and 0.32±0.08 at zero delay time for the homoepitaxial and heteroepitaxial β-Ga2O3, respectively, which is well below the threshold of 0.5, unambiguously proving its nature of single-photon emission. The real quantum emission purity could be higher than the g2(0) values shown in Fig. 2d, e since they were obtained without any background correction. In addition, because the g2(τ) measurements were performed at a high excitation power of ∼5 mW, bunching behavior was also observed with a τ2 of a couple of tens ns. The emission intensity of SPEs from both β-Ga2O3 films as a function of excitation power is presented in Fig. 2f. The saturation data were fitted with the power model: I(P)=I∞×P/(P+Psat), where I∞ and Psat are fitting parameters corresponding to the maximum emission counts and saturation power, respectively16,19. The fitted saturation curve yields a saturation count rate of I∞=1.6×104 counts s−1 and a saturation power of Psat=3.3 mW for the homoepitaxial β-Ga2O3. Similarly, we obtain a I∞ of 6.9×103 counts s−1 and a Psat of 2.4 mW for the heteroepitaxial β-Ga2O3 film. These results show that both the emission rate and the purity of single photons emitted from the homoepitaxial β-Ga2O3 are higher compared to the heteroepitaxial β-Ga2O3, indicating the superiority of high crystallinity of β-Ga2O3 as a host of SPEs. It should be noted that the PL spectra were recorded using the charge-coupled device detector of the spectrometer in this work, which leads to a decrease in fluorescence intensity by approximately 50-fold. After correction for the reduced PL intensity, the saturation brightness of β-Ga2O3-based SPEs can reach around 105 counts s−1, which is comparable to the other solid-state SPEs40,41.

Photostability of the quantum emitters was investigated by recording PL spectra under continuous wave excitation and an integration time of 1 s. As shown in Fig. 3a, there is almost no change in the PL intensity and position for more than 300 s of continuous acquisition, demonstrating the long-term stability of the SPEs in the homoepitaxial β-Ga2O3. To further examine the blinking and photobleaching, the time-dependent PL intensity of the emitter with a sampling time bin size of 200 ms is displayed in Fig. 3b. The emitter exhibits stable emission without obvious blinking or bleaching over a measurement period of 180 s even under near-saturation excitation power (5 mW), revealing the emitter’s absolute photostability at room temperature. The photostability of the quantum emitters hosted by heteroepitaxial β-Ga2O3 is similar to that of its homoepitaxial counterpart with occasional blinking (Supplementary Fig. 9).

We measured the excitation polarization of emitters by rotating a half-wave plate after the polarizer in the excitation path of the confocal set-up while fixing the emission polarization measurements. Figure 3c illustrates the normalized polarization-dependent contour map of PL spectra for the emitter in the homoepitaxial β-Ga2O3, and the corresponding waterfall plot of PL spectra is shown in Supplementary Fig. 10. These PL spectra exhibit an obvious periodic variation with the change of polarization angle. Figure 3d shows the corresponding polar coordinate plot of the PL intensity and the polarization angle θ, where the experimental data is perfectly fitted by the function I(θ)=Imin+Imax cos2(θ+θ0), exhibiting a two-lobed shape. The excitation polarization visibilities H=(Imax−Imin)/(Imax+Imin) is calculated to be 54%, indicating that the quantum emitters in the homoepitaxial β-Ga2O3 have a single linearly polarized dipole transition. Similarly, the linear polarization feature is also observed in the heteroepitaxial β-Ga2O3 film (Supplementary Fig. 11).

The above results indicate that the quantum emitters can be generated in both homoepitaxial and heteroepitaxial β-Ga2O3 films through the plasma treatment and annealing. To examine whether SPEs are prevalent in various types of β-Ga2O3, single-crystal β-Ga2O3 wafers were also plasma treated and subsequently annealed for further characterization. As shown in Supplementary Fig. 12a, the bright spots marked by red boxes in the PL map are attributed to single-defect centers hosted by the single-crystal β-Ga2O3 wafer. The representative PL spectrum consists of a sharp ZPL and a weak and broad PSB (Supplementary Fig. 12b), and a clear antibunching is demonstrated with a very low multiphoton probability of g2(0)=0.18 (Supplementary Fig. 12c). The SPEs in the single-crystal β-Ga2O3 also show high stability (Supplementary Fig. 12d) and linearly polarized characteristics (Supplementary Fig. 12e). The fitted saturation curve yields a saturation emission rate of I∞=5.7×103 counts s−1 at a saturation power of 4.5 mW (Supplementary Fig. 12f). Apparently, the emitters in single-crystal β-Ga2O3 wafers and epitaxial films show similar luminescence characteristics.

To further investigate the statistics of the optical properties of these SPEs, we collected a large number of PL spectra in three series: 101/88 emitters in a homoepitaxial/heteroepitaxial β-Ga2O3 film and 95 emitters in a single-crystal β-Ga2O3 wafer, and extracted the ZPL positions and linewidths by fitting the spectra with two Lorentzian functions. The histograms in Fig. 4a show the ZPL wavelength distribution with a bin width of 5 nm. The red curve represents the Gaussian fitting for ZPL wavelengths. Distribution of the full width at half maximum (FWHM) of ZPL (b) and the ZPL-PSB energy separation (c). These histograms show that the SPE wavelengths vary over a wide range of 550–650 nm, with most of the emitters exhibiting a ZPL around 560–590 nm. Nevertheless, there are some differences between different types of β-Ga2O3. For the single-crystal β-Ga2O3 wafer and homoepitaxial β-Ga2O3 film, about 72% of the emitters have ZPL wavelengths within the range of 575±15 nm, indicating a relatively narrow spectral distribution. By contrast, only 60% of the investigated emitters are located in the spectral range from 560 to 590 nm for the heteroepitaxial β-Ga2O3. Figure 4b summarizes the distribution of the ZPL linewidth of the quantum emitters in three types of β-Ga2O3. The majority of SPEs have a ZPL FWHM less than 15 nm with an average FWHM of 9.7 nm, suggesting the excellent monochromaticity of emitters hosted by β-Ga2O3. Figure 4c shows the distribution of ZPL-PSB energies of the quantum emitters, where the ZPL-PSB energies of the majority SPEs are distributed in the range of 20–60 meV with a mean value of 37 meV. This energy separation is in good agreement with the energies of phonon modes of β-Ga2O3 (20–90 meV) reported in the literatures42 and our calculations on the phonon density of states (Supplementary Fig. 13). The statistics of Huang–Rhys (S) factor (the number of phonons emitted during vibrational relaxation) are displayed in Supplementary Fig. 14. These S factors are all less than 0.90 with an average value of ~0.50, signifying that pure electronic transitions dominate in β-Ga2O3. The similarity of luminescence characteristic of the SPEs in different β-Ga2O3 samples demonstrates that these defects have similar crystallographic structure.

Origin of SPEs in β-Ga2O3

To gain insight into the origin of the quantum emitters observed in β-Ga2O3, we conducted systematic theoretical studies of defect structures via density functional theory (DFT). As is well-known, there are two crystallographically inequivalent gallium sites (labelled GaI and GaII) and three inequivalent oxygen sites (labelled OI, OII, and OIII) in monoclinic β-Ga2O3 (Fig. 5a). Due to its low symmetry, β-Ga2O3 harbors a diverse array of defects. The pervasiveness of the SPEs in different β-Ga2O3 samples suggests that intrinsic defects rather than extrinsic defects are responsible for the observed quantum emissions. Ga or O interstitials are metastable and are expected to diffuse at higher temperatures. Actually, there is limited experimental evidence for Ga or O interstitials under normal conditions43. Therefore, in this work, four main intrinsic vacancy defects, including gallium vacancies (VGa), oxygen vacancies (VO), Ga-O divacancies (VGaI-VOIII), and O-O divacancies (VO-VO) in their neutral, negatively, and positively charged states are considered. The formation energies for various vacancy defects with different charge states as a function of the Fermi energy were calculated previously44. Firstly, we calculated the Kohn-Sham (KS) energy levels, ZPL energies, and S factors only for these stable charge states of various defects44 using the Perdew–Burke–Ernzerhof (PBE) functional45, as listed in Supplementary Table 1. To rapidly identify potential candidate defects for SPEs, two preliminary screening rules are applied to exclude some defects. (i) Defects capable of emitting single photon usually require the formation of a two-level system between the conduction band minimum (CBM) and the valence band maximum (VBM). These defects without a two-level system are excluded as candidates for SPEs, and they are marked by “×” in Supplementary Table 1. (ii) These defects with calculated S > 1.80 (marked by “-” in Supplementary Table 1) are also dismissed to refine these remaining candidates, since experimentally statistically S factors are all less than 0.90 with an average value of 0.50. Further, we employed the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional46 to obtain accurate ZPL energies, which is a key predictor to evaluate the origin of the experimentally observed quantum emitters. As summarized in Supplementary Table 1, the predicted ZPL energy (2.34 eV) of neutral VGaI-VOIII defects (Fig. 5b) align closely with the experimental values (2.20 eV), indicating a possible SPE candidate. The KS energy levels of the VGaI-VOIII defect in different charge states are shown in Fig. 5c and Supplementary Fig. 15. Among them, when the defect charge state is −3, there is no two-level system suitable for optical transitions. The +2 and −1 charge states are also discarded due to the calculated high S factors. To further identify the candidate defects, the calculated optical properties of the neutral VGaI-VOIII defect, including ZPL energy, longitudinal optical (LO) phonon energy (ELO), DW and S factors, excited-state lifetime (τr) are compared with the typical experimental results. As seen from Table 1, the theoretically predicted optical properties are fully consistent with the experimental data, indicating that the neutral VGaI-VOIII defect is the most promising SPE candidate. The calculated electron-phonon spectral density, from which the S factor and ELO can be derived, is shown in Supplementary Fig. 16. Furthermore, the predicted excited-state lifetime of the neutral VGaI-VOIII is about 1.12 ns, and such short lifetime can be understood by its wavefunctions of the highest occupied orbital and the lowest unoccupied orbital related to optical transitions. As shown in Fig. 5d, e, both wavefunctions show typical localization characteristics, corresponding to deep-level defects. Their similar spatial distribution implies a large transition dipole moment between the two levels, which explains the short excited-state lifetime. Additionally, the calculated emission spectrum of the neutral VGaI-VOIII is shown in Fig. 5f, which has been horizontally shifted from the ZPL energy to match the experimental result. The similarity between the theoretical and experimental lineshapes is remarkable, especially, the PSB accounts for the asymmetric broadening of the PL spectrum. Based on these calculations, we identified the neutral VGaI-VOIII as a suitable defect to explain the observed single-photon emissions in β-Ga2O3.

Methods
Sample fabrication

The homoepitaxial and heteroepitaxial β-Ga2O3 thin films were grown on the β-Ga2O3 (−201) single crystal substrates and sapphire (0001) substrates by LPCVD, respectively. The LPCVD system consists of a two-inch tubular quartz reactor and has two independently controlled temperature zones. Before the growth process, single-side polished β-Ga2O3 (−201) substrates (1 mm thick) and sapphire (0001) substrates (0.5 mm thick) were sequentially cleaned by acetone, ethanol, and deionized water in an ultrasonic bath, followed by drying with N2 gas. High purity Ga pellets and O2 with a flow rate of 10 sccm were used as precursors. The Ga-source and substrate temperatures were fixed at 830 and 800 °C, respectively. Ar with a flowing at 50 sccm acted as the carrier gas, and the growth was conducted at a pressure of 40 Pa for 30 min. Finally, the furnace was cooled down to room temperature in an Ar atmosphere.

The plasma treatment was carried out in a home-made system equipped with a 13.56 MHz radio frequency (RF) plasma generator. The cleaned β-Ga2O3 samples were first loaded into the plasma treatment chamber, then it was evacuated to a pressure of less than 1 Pa. Afterward, the plasma treatment was performed at room temperature and a constant RF power of 100 W for 10 min. Finally, the plasma-treated β-Ga2O3 samples were annealed in a tube furnace at 850 °C and an atmospheric pressure of less than 1 Pa for 30 min to promote the formation of optically active defects. A further annealing at 850 °C under air atmosphere for 30 min is usually performed to reduce the influence of spectral background fluorescence.

Characterization

The surface morphology of β-Ga2O3 samples was characterized by atomic force microscope (AFM) with a NT-MDT solver P47 microscope in the semi-contact mode. Raman spectra were collected by a Smart-Raman confocal-micro Raman system (Horibai HR550 spectrometer) under the backscattering geometry with a 532 nm laser in the region of 100–800 cm−1. XRD measurements were carried out with a Rigaku D/MAX-2500 diffractometer with a Cu Kα (λ=1.5406 Å) radiation source operating at 40 kV and 40 mA. X-ray photoelectron spectroscopy (XPS) core levels were acquired with an ESCALAB 250Xi spectrometer using monochromatized Al Kα source (1486.6 eV). The microstructures of epitaxial β-Ga2O3 films were analyzed by transmission electron microscopy (TEM) using a Talos F200S microscope operating at 200 kV.

The optical spectroscopy measurements on all β-Ga2O3 samples were conducted using a custom-built micro-area confocal PL setup equipped with an objective lens of high numerical aperture (0.9) and a 532 nm continuous-wave (CW) laser at the room temperature. PL spectra were acquired with the charge-coupled device detector of Andor Kymera 328i-B1 spectrometer and a CCD camera, resulting in an approximate 50-fold reduction in fluorescence intensity. The excitation polarizations were measured by placing a broadband polarizer (Thorlabs) and a half-wave plate in the excitation path. Second-order autocorrelations (g2(τ)) were measured using a Hanbury Brown-Twiss system excited by a 532 nm continuous wave laser and connected to a time-correlated single photon counting module with two avalanche photodiodes (APDs).

DFT calculations

DFT calculations were performed using the projector augmented wave (PAW) method as implemented in the Vienna Ab initio Simulation Package (VASP)47. For defect modeling, a 160-atom supercell was constructed, and self-consistent calculations were carried out with a single Γ-point. The energy convergence criterion and force convergence criterion for structural relaxation were set to 0.02 eV/Å and 10−5 eV, respectively. All DFT calculations utilized a plane-wave cutoff energy of 520 eV. To predict optical properties, we calculated ΔQ and S using constrained DFT based on the PBE ground-state and excited-state geometries. The ΔSCF method was employed to predict ZPL energies under both PBE and HSE functionals. By adjusting α to 0.39, we calculated the bandgap of bulk β-Ga2O3 as 4.87 eV, which is in excellent agreement with experimental values28. The radiative lifetime τr associated with ZPL was determined using Fermi’s golden rule48. PL line shapes were simulated using the PyPhotonics package49, and phonon energies were determined via the finite displacement method implemented in the Phonopy code50.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The study reports the discovery of room-temperature single-photon emitters in the emerging semiconductor Ga₂O₃. The\nauthors observe visible single-photon emission in various samples following plasma and annealing treatments, and employ\ntheoretical modeling to identify the intrinsic defect responsible for this behavior. These findings are of significant importance\nto the field and are likely to stimulate a new line of research on Ga₂O₃ for quantum applications.\nThe nature of the work raises questions regarding the robustness of the single-photon emitters and the role of the sample\ntreatments in enabling them. It is essential that the authors present the luminescence spectra of the samples prior to any\ntreatment. Additionally, it would be valuable to discuss the parameter space for engineering these single-photon emitters—\nfor instance, how the emission properties depend on annealing conditions.\nHere are a few minor points:\n- Given that the films are only 200 nm thick and that photoluminescence is done below bandgap excitation, how confident\nare the authors that the luminescence comes from the film and not the substrate?\n- RMS roughness values in page 3 should be given with error bars.\n- I would recommend avoiding words like “obviously”\n- “Crystallo-graphic” should be written “crystallographic”\n- Figure 3c, the y-axis should be “Angle”\n- Figure 4c would benefit to have the y-axis in meV\n- Page 10, line 275: the sentence “Actually, … conditions.” doesn’t make sense grammatically", "reviewer_2": "In the manuscript titled “Room-temperature single-photon emission from β-Ga2O3”, Shi et al demonstrate the first reports of\nsingle photon emitters in β-Ga2O3 in homoepitaxial, heteroepitaxial and bulk samples. Photophysical measurements similar\nto other such works in literature are presented to an acceptable standard to definitively identify this new SPE. Density\nfunctional theory evidence is presented to offer a physical origin for the SPE with a convincing conclusion. The manuscript is\nwell written and features sufficient references and I believe this result will be of interest to those in the wider research\ncommunity.\nSubject to the following amendments being satisfied, it is my recommendation that this work is published.\nOn line 130, the authors make reference to the spatial distribution of emitters being uniform and random. Whilst not heavily\nexamined in similar works, this point can be reinforced by an analysis using Ripley’s K function to determine if the emitters\nare clustered or diffuse.\nThe autocorrelation functions presented in Figure 2. D and E, are somewhat noisy. Could the authors experiment with\nrebinning the data and quote the error in g^((2) ) (0) to ensure that these results are consistent with single-photon emission?"}, "author_response": "Point-by-Point Response to the Reviewers’ Comments for NCOMMS-25-61281\nDear Editors and Reviewers:\nWe would like to thank the Reviewers for their insightful comments and valuable\nsuggestions on our manuscript entitled “Room-temperature single-photon emission from\nβ-Ga O ”. Those comments are all valuable and very helpful for revising and improving\n2 3\nour paper, as well as the important guiding significance to our researches. We have made\ncareful revision of our manuscript based on comments suggested by the Reviewers.\nBelow is our point-by-point response to these comments. For ease of tracking, the\nreviewers’ comments are reproduced by verbatim in italics, followed with our responses\nin purple and the revisions in blue.\nReviewer #1 Comments:\nThe study reports the discovery of room-temperature single-photon emitters in the\nemerging semiconductor Ga O . The authors observe visible single-photon emission in\n2 3\nvarious samples following plasma and annealing treatments, and employ theoretical\nmodeling to identify the intrinsic defect responsible for this behavior. These findings are\nof significant importance to the field and are likely to stimulate a new line of research on\nGa O for quantum applications. The nature of the work raises questions regarding the\n2 3\nrobustness of the single-photon emitters and the role of the sample treatments in enabling\nthem.\nResponse: We are very grateful for your thoughtful and positive assessment of our\nmanuscript. We sincerely thank the reviewer for the recognition of our demonstration of\nroom-temperature photostable single-photon emission from β-Ga O . According to your\n2 3\nvaluable suggestions, we have made a few corrections to our previous draft as listed below.\nComment #1-1: It is essential that the authors present the luminescence spectra of the\nsamples prior to any treatment.\nResponse on comment #1-1: Many thanks for the reviewer’s valuable comments. We\nagree that it is necessary to display the PL spectra of β-Ga O thin films without treatment.\n2 3\nAccording to the reviewer’s suggestion, the PL spectrum of the homoepitaxial β-Ga O\n2 3\nfilms without any treatment has been added in the revised manuscript as Supplementary\nFig. 7a, in which only two Raman peaks from β-Ga O were observed. It can be concluded\n2 3\n1\nthat the single photon emitter is introduced by plasma treatment and subsequent annealing\nprocess.\n[... Supplementary Fig. 7a description ...]\nOur revision to the manuscript:\nPage 5, lines 128-131: “Similar to the as-grown β-Ga O films without any treatment,\n2 3\nboth plasma treatment alone and plasma treatment with air-annealing don’t cause PL\nemission, and only two Raman peaks of β-Ga O are observed (Supplementary Fig. 7a).”\n2 3\nhas been added.\nComment #1-2: Additionally, it would be valuable to discuss the parameter space for\nengineering these single-photon emitters—for instance, how the emission properties\ndepend on annealing conditions.\nResponse on comment #1-2: Thanks for the reviewer’s valuable suggestions. According\nto the reviewer’s suggestion, the parameter spaces for engineering these single-photon\nemitters have been discussed in the revised manuscript. As shown in Supplementary Fig.\n7a, the individual plasma treatment does not cause any PL defect-emission in β-Ga O ,\n2 3\nand the situation remains similar even with subsequent air annealing. To activate the\ndefects induced by plasma treatment, the plasma treated β-Ga O was annealed at 850 °C\n2 3\nfor 30 min under a pressure of <1 Pa (vacuum annealing), leading to PL defect-emissions\nwith strong background fluorescence (Supplementary Fig. 7b). In order to suppress the\nbackground fluorescence, the β-Ga O film after plasma treatment and vacuum annealing\n2 3\nwas further annealed in air at 850 °C for 30 min. Indeed, the PL defect-emissions with a\n2\nsubstantially reduced fluorescence background is clearly observed for the β-Ga O after\n2 3\nplasma treatment combined with vacuum annealing and air annealing (Supplementary\nFig. 7c). Furthermore, the plasma treatment power of 100-150 W is appropriate as\nindicated by the stronger PL emission.\nOur revision to the manuscript:\nPage 5, lines 127-138: “Several plasma-treatment combined with annealing processes\nhave been attempted to generate isolated point-defects in β-Ga O . Similar to the as-\n2 3\ngrown β-Ga O films without any treatment, both plasma treatment alone and plasma\n2 3\ntreatment with air-annealing don’t cause PL emission, and only two Raman peaks of β-\nGa O are observed (Supplementary Fig. 7a). By applying plasma treatment followed by\n2 3\nvacuum annealing, the β-Ga O film exhibits PL defect-emission with strong fluorescence\n2 3\nbackground (Supplementary Fig. 7b). When these β-Ga O films were further annealed\n2 3\nin air at 850 °C for 30 min, the fluorescence background is substantially reduced\n(Supplementary Fig. 7c). Thus, we introduced isolated point-defects in β-Ga O films\n2 3\nthrough plasma treatment and activated them using vacuum annealing, and followed by\nair annealing to eliminate the fluorescence background. Unless otherwise specified, this\ntreatment procedure was employed in all subsequent experiments.” has been added.\n[... Supplementary Fig. 7 description ...]\nComment #1-3: Given that the films are only 200 nm thick and that photoluminescence\nis done below bandgap excitation, how confident are the authors that the luminescence\ncomes from the film and not the substrate?\ndiscussed in Response on comment #1-2, the PL emission of β-Ga O is generally\n2 3\nbelieved to come from point-defects caused by plasma treatment. The physical effect\ndepth of plasma treatment is relatively shallow, typically ranging from 1 to several tens\nof nanometers, mainly due to the ion bombardment on the material surface. Since the\nthickness of our β-Ga O films is about 200 nm, which is much larger than the depth of\n2 3\nplasma treatment, we believe that the single photon emitters generated in both\nhomoepitaxial and heteroepitaxial β-Ga O samples come from the epitaxial film rather\n2 3\nthan the substrate.\nComment #1-4: RMS roughness values in page 3 should be given with error bars.\nResponse on comment #1-4: Many thanks for the reviewer’s suggestions. According to\nthe reviewer’s suggestion, AFM images of the single crystal β-Ga O wafer, the\n2 3\nhomoepitaxial β-Ga O and heteroepitaxial β-Ga O were measured at five positions to\n2 3 2 3\nobtain the average value and the standard deviation (SD) of RMS roughness\n(Supplementary Fig. 1). Then, the RMS roughness values in Page 3 are given by the\naverage value with error bars.\n[... Supplementary Fig. 1 description ...]\nOur revision to the manuscript:\nPage 3, line 79: “root mean square (RMS) roughness of 0.47 nm.” has been changed to\n“root mean square (RMS) roughness of 0.480.04 nm (Supplementary Fig. 1a)”. line 81:\n“RMS roughness of 2.4 nm” has been changed to “RMS roughness of 2.50.31 nm\n(Supplementary Fig. 1b)”. lines 84-85: “RMS roughness of 2.8 nm” has been changed to\n“RMS roughness of 3.10.22 nm (Supplementary Fig. 1c)”\nComment #1-5: I would recommend avoiding words like “obviously”\nResponse on comment #1-5: Many thanks for the reviewer’s suggestions. The sentences\nhave been revised to avoid using the word “obviously”.\nOur revision to the manuscript:\nPage 5, line 141: “Obviously,” has been changed to “As revealed by an analysis using\nRipley’s K function (Supplementary Fig. 8),”.\nPage 8, line 228: “Obviously,” has been changed to “indicating that …”\nComment #1-6: Crystallo-graphic” should be written “crystallographic”\nResponse on comment #1-6: Many thanks for the reviewer’s suggestion. All words\n“crystallo-graphic” have been written as “crystallographic” in the revised manuscript.\nComment #1-7: Figure 3c, the y-axis should be “Angle”\nResponse on comment #1-7: Many thanks for the reviewer’s kind remind. The y-axis of\nFigure 3c has been revised as “Angle”.\nComment #1-8: Figure 4c would benefit to have the y-axis in meV\nResponse on comment #1-8: Many thanks for the reviewer’s helpful suggestions, the y-\naxis in Figure 4c is represented as “meV” in the revised manuscript.\n[... Figure 4c description ...]\nComment #1-9: Page 10, line 275: the sentence “Actually, … conditions.” doesn’t make\nsense grammatically\nResponse on comment #1-9: Many thanks for the reviewer’s comments. The related\nsentence has been rewritten to correct grammatical errors.\nOur revision to the manuscript:\nPage 10, lines 286-287: “Actually, there is limited experimental evidence for under\nnormal conditions.” has been changed to “Actually, there is limited experimental evidence\nfor Ga or O interstitials under normal conditions.”\nReviewer #2 Comments:\nIn the manuscript titled “Room-temperature single-photon emission from β-Ga O ”, Shi\n2 3\net al demonstrate the first reports of single photon emitters in β-Ga O in homoepitaxial,\n2 3\nheteroepitaxial and bulk samples. Photophysical measurements similar to other such\nworks in literature are presented to an acceptable standard to definitively identify this\nnew SPE. Density functional theory evidence is presented to offer a physical origin for\nthe SPE with a convincing conclusion. The manuscript is well written and features\nsufficient references and I believe this result will be of interest to those in the wider\nresearch community. Subject to the following amendments being satisfied, it is my\nrecommendation that this work is published.\nResponse: We sincerely appreciate the reviewer’s positive assessment of the significance\nof our work. We are delighted that the reviewer found our progress meaningful, the\nmanuscript well-written, and the references sufficient, as well as the potential applications\ndiverse. We are also grateful for the reviewer’s insightful comments and constructive\nsuggestions, and we have carefully addressed each point in the following responses to\nfurther improve the manuscript.\nComment #2-1: On line 130, the authors make reference to the spatial distribution of\nemitters being uniform and random. Whilst not heavily examined in similar works, this\npoint can be reinforced by an analysis using Ripley’s K function to determine if the\nemitters are clustered or diffuse.\nResponse on #2-2: Many thanks for the reviewer’s valuable suggestion. According to the\nreviewer’s suggestion, the distribution of emitters in homoepitaxial and heteroepitaxial\nβ-Ga O thin films was analyzed using the Ripley’s K-function. As shown in\n2 3\nSupplementary Fig. 8, the observed K values consistently fluctuating within the\nconfidence interval, indicating that the emitters are randomly distributed and do not\nexhibit obvious clustering or dispersion trends.\nOur revision to the manuscript:\nPage 5, lines 141-142: “Obviously, these emission points are uniformly and randomly\ndistributed in both samples.” has been changed to “As revealed by an analysis using\nRipley’s K function (Supplementary Fig. 8), these emission points are uniformly and\nrandomly distributed in both samples.”\n[... Supplementary Fig. 8 description ...]\nComment #2-2: The autocorrelation functions presented in Figure 2. D and E, are\nsomewhat noisy. Could the authors experiment with rebinning the data and quote the\nerror in g^((2) ) (0) to ensure that these results are consistent with single-photon emission?\nResponse on #2-2: Many thanks for the reviewer’s helpful suggestions. Indeed, the\nautocorrelation function g2(τ) shown in Fig. 2d,e is a little noisy. To improve the signal-\nto-noise ratio of data, the g2(τ) were remeasured by increasing measurement time and\nmanipulated by rebinning the data. To ensure that these results are consistent with single-\nphoton emission, the error in g2(0) has also been quoted. From the fitting, we obtained\nthe g2(τ) at zero delay time of g2(0)=0.24±0.08 for the homoepitaxial β-Ga O and\n2 3\ng2(0)=0.32±0.08 for the heteroepitaxial β-Ga O , respectively. Both g2(0) values are well\n2 3\nbelow the threshold of 0.5, unambiguously proving its nature of single-photon emission.\n[... Figure 2 description ...]\nOur revision to the manuscript:\nPage 6, lines 165-167: “From the fitting, we obtained the g2(τ) value of 0.23 and 0.35 at\nzero delay time for the homoepitaxial and heteroepitaxial β-Ga O , respectively, …” has\n2 3\nbeen changed to “From the fitting, we obtained the g2(τ) value of 0.24±0.08 and 0.32±0.08\nat zero delay time for the homoepitaxial and heteroepitaxial β-Ga O , respectively, …”\n2 3"}, {"round": 2, "reviewer_comments": {"reviewer_1": "Thank you for addressing my comments adequately.", "reviewer_2": "I thank the authors for taking my comments into consideration. I am satisfied my comments have been sufficiently addressed\nand can now fully recommend this for publication in Nature Comms."}, "author_response": ""}]

Decision letter