Deterministic Creation of Identical Monochromatic Quantum Emitters in Hexagonal Boron Nitride

Quantum information science (QIS) is an emerging field at the intersection of quantum physics, computer science, and information theory. It uses the basic rules of quantum mechanics to handle and process information in ways that traditional computing cannot match. There is, however, no dominant platform technology in QIS and many different materials and devices are actively investigated[1, 2, 3, 4, 5, 6, 7]. Key areas within this field are photon-based quantum information processing, communications, and transduction. Photon-based systems offer several advantages, including the ability to maintain their quantum state for a long time, minimal interference from the environment, and the capacity to transmit quantum information over long distances through optical fibers[8, 9, 10, 11]. The essential component of these systems is a quantum emitter (QE), capable of producing single photons that are ideally identical and coherent. There are now many sources of single photon emitters based upon a range of materials platforms and spanning the ultraviolet to infrared spectrum[12, 13, 14, 15]. Although many QEs exhibit excellent properties in isolation, their technological utility also requires deterministic localization and reproducibility across ensembles of QEs.

Two-dimensional (2D) materials, such as transition metal dichalcogenides and hexagonal boron nitride (hBN), have been found to be possible hosts for QEs, attracting significant research interest in the last decade[16, 17, 18, 19, 20, 21, 22]. hBN, in particular, has been extensively studied for QE creation as its large electronic band gap and optical phonon energy, in principle, allow it to host QEs at room temperature with perfect monochromaticity[23, 24, 25, 26, 27, 28]. Existing approaches have successfully achieved spatial control in the creation of QEs; however, most of them have limited control of the spectral properties of generated QEs, limiting practical use. A key factor leading to this problem is insufficient understanding of the true atomic configurations of the defects involved in the observed single photon emission behaviors. To address this issue, many efforts has been undertaken by the global research community[29, 30, 20, 31], and recently, both theoretical and experimental works have suggested that carbon related defects are a major source of the visible (from $435\,\text{nm}$ to $700\,\text{nm}$) QEs in hBN[32, 33, 34, 35, 36]. Therefore, an improved carbon implantation method for hBN with controlled defect creation is valuable to improve the repeatability and quality of the created QEs, but also significantly reduce the difficulty to identify the correlation between the defects atomic structure and observed single photon emission behaviors. In this study, we report a deterministic QE creation process for freestanding hBN flakes through masked-carbon-ion-implantation (MCI) yielding room temperature QEs which satisfies many important properties for ensembles of QEs. The QEs created using this process have remarkable monochromaticity with 2.5 nm standard deviation in zero phonon line (ZPL) wavelengths, and a linewidth of 6.8 nm full-width-half-maximum (FWHM). In addition to known polarization and single-photon behaviors, they are also exceptionally stable (no observable degradation after days with $10^{5}\,\text{W/cm}^{2}$ laser excitation) and bright (1 MHz emission rate). The origins of the QEs was also discussed, where both photoluminescence (PL) and scanning-transmission-electron-microscopy (STEM) based cathodoluminescence (STEM-CL) analysis suggested that the observed QEs could be categorized into two types: single defects and donor-acceptor pairs. First principles density functional theory defect calculations together with Scanning Transmission Electron Microscopy suggest that these QEs consist of four carbon substitutions.

To achieve more consistent creation of carbonaceous defects in hBN with desired ensemble optical properties, typical ion bombardment procedures were modified to minimize lattice damage and generate defects in the middle of the hBN flake. This was achieved by employing an amorphous carbon mask, placed in front of the freestanding hBN flake to decelerate incoming carbon ions (Fig. 1a). The masks were designed and fabricated with a thickness that ensures the carbon ions most probable penetration depth aligns with the middle of the hBN flake, for example, a $100\,\text{nm}$ thick carbon mask was used for a 16 monolayer hBN flake (Fig. 1b) to achieve the maximum stopping efficiency of carbon ions[37]. Such configuration maximized the doping efficiency, leaving less damage due to other defects such as vacancies. Meanwhile, typical contamination caused by the recoiling of the mask elements was automatically precluded as the mask and the implantation ions were made of the same element. To minimize the intrinsic defects of the sample, for instance the defects created during the synthesis, hBN flakes exfoliated from high-quality pristine crystal bulk were used. Since previous work on optical properties of the QEs created by carbon-ion-implantation have found strong substrate dependence[34], in this research, the hBN flakes were stamped on to Si or SiN transmission electron microscopy (TEM) grids with pre-fabricated apertures by the dry-transfer method[38] to eliminate the influence from the substrate. As shown in Fig. 2a, a successful sample preparation resulted in a hBN flake with a freestanding area larger than $100\,\mu\text{m}^{2}$.

During a typical carbon-ion implantation process, a fluence of $2.5\times 10^{6}\,\text{ions per}\,\mu\text{m}^{2}$ with a $40\,\text{keV}$ acceleration energy was applied to achieve a moderate emitter density (around $0.03\,\text{cts per }\mu\text{m}^{2}$ for sample thickness $<10\,\text{nm}$). Without applying any post treatment, such as high temperature annealing, preliminary scanning of the samples’ PL signal were carried out by a reflective confocal microscope system (detailed in methods). Fig. 2a shows the photoluminescence (PL) intensity hyper-mapping of a typical hBN flake treated with MCI, revealing localized QEs under $532\,\text{nm}$ laser excitation. Most observed QEs can be categorized into two types: one with an emission wavelength peaking around 553 nm (colored in cyan in Fig. 2a ) and the other with an emission wavelength peaking around 590 nm (colored in red in Fig. 2a ). For the rest of the paper, these will be denoted as the 553 nm and 590 nm QEs, respectively. The spectra of $590\,\text{nm}$ QEs presented in Fig. 2a are plotted in Fig. 2b, demonstrating extraordinary consistency in their spectral profiles.

However, the QEs created in samples with thickness less than $10\,\text{nm}$ were generally unstable, with their emission lasting only hundreds of seconds under continuous illumination in ambient conditions. As illustrated in the plots of PL intensity versus illumination time for 553 nm and 590 nm QEs created in a 5 nm thick hBN sample, shown in Fig. 2c (blue triangles) and Fig. 2d (maroon diamonds), respectively, the emission rates diminished after $120\,\text{s}$ and $300\,\text{s}$ respectively. Given the small phonon side band (PSB) observed in these QEs, it is reasonable to infer that the defects are mechanically well isolated, with rigid defect structures and an intact surrounding lattice. Meanwhile, some emitters disappeared after months of storage in air. This is consistent with previous literature which has identified reactions of oxygen with carbonaceous defects in hBN as the source of optical instability in thin flakes (such as 16 monolayers) of hBN[39]. The thin samples by definition result in implantation of defects close to the hBN surface and also can result in over penetration, which may leave pores for gas transport. Therefore, the authors concluded that exposing QEs to the environment led to their instability.

To solve the stability issue, a $50\,\text{nm}$ carbon mask over a $100\,\text{nm}$ hBN flake sample was selected to achieve a $91.7\%$ stopping efficiency of the carbon ions with negligible over penetration (detailed in supplementary information). After applying MCI to the sample, QEs were created with a total QE areal density of $0.42\,\text{cts per}\,\mu\text{m}^{2}$, an order of magnitude higher than the thin samples with identical ion irradiation fluence. The spectral line profiles of the emitters found in thick films match those of the thin films, but with significantly enhanced stability. Typical PL intensity versus time for 553 nm and 590 nm QEs are shown in Fig. 2c (light blue squares) and 2d (red circles) respectively. No brightness degradation was observed for prolonged illumination with long term fluctuations attributed to the drifting of the stage. The population distribution in wavelength of the QEs created in thin and thick samples are almost identical, where $553.5\pm 2.7\,\text{nm}$ and $590.7\pm 2.5\,\text{nm}$ (Fig. 3a) were obtained from the combined data. Besides $553\,\text{nm}$ and $590\,\text{nm}$ QEs, other emitters were much less likely ($3.4\,\%$ among the created emitters) to be found in our samples, suggesting the defect creation was dominated by two ultimate processes.

As shown in Fig. 3d, the typical spectrum of a $553\,\text{nm}$ QE was slightly cut on the short wavelength side as multiple $547\,\text{nm}$ long pass filters were used to completely remove the excitation laser light ($532\,\text{nm}$ CW laser). The sharp feature was still pronounced enough for us to estimate the FWHM to be $10.5\pm 3\,\text{nm}$ ($43\,\text{meV}$, blue triangles in the insert in Fig. 3g). Besides the Raman signal of hBN, a secondary peak around $596\,\text{nm}$, $161\,\text{meV}$ from the ZPL, which is slightly lower than the optical phonon energy of hBN, about $170\,\text{meV}$[40, 41], was observed and has been attributed to the PSB. In contrast, $590\,\text{nm}$ QEs not only showed a much narrower emission profile and smaller dispersion of FWHM, with a value of $\text{FWHM}=7.1\pm 1.7\,\text{nm}$ ($25\,\text{meV}$, red diamonds in the insert in Fig. 3g). A PSB at 636 nm (151 meV from the ZPL) was not pronounced except at high excitation laser power.

Saturation behavior were observed in both types of QEs with increasing excitation laser power, and the observed maximum emission rates of $553\,\text{nm}$ and $590\,\text{nm}$ QEs were $0.43\,\text{MHz}$ (Fig. 3b) and $0.92\,\text{MHz}$ (Fig. 3e) respectively (considered as lower limits, detailed in Method). Although the maximum emission rate of $553\,\text{nm}$ QEs is much lower than the $590\,\text{nm}$ QEs, they saturate at lower excitation intensity (more than an order of magnitude smaller), suggesting the $533\,\text{nm}$ QEs have a larger absorption cross-section. It is also confirmed in the stability data, where PL intensity’s long term fluctuation of the $590\,\text{nm}$ QEs was more pronounced as its collecting efficiency is more sensitive to the drifting the stage due to the small spatial dimension responsible for absorption (confirmed below using CL).

The excitation polarization dependence information of the QEs were obtained by rotating the laser’s polarization angle, $\theta$, with a half-wave-plate. The data are shown in the inserts inside Fig. 3d and 3g for $553\,\text{nm}$ and $590\,\text{nm}$ respectively, where the QEs’ integrated PL emission intensity $I(\theta)$ can be fitted with the function,

by assuming the linear dipole response for the defects. Here the purity of the dipoles, $p$ was defined as, $p=\frac{I_{\text{A}}}{I_{\text{A}}+I_{0}}$ with a maximum value of 1, where $I_{0}$ and $I_{\text{A}}$ denote the base value and the amplitude of the fitting function. According to our data, $p$ value approaching $1$ was observed in both types of QEs (typical values of $0.962$ and $0.971$ were observed in $553\,\text{nm}$ and $590\,\text{nm}$ QEs). Such observation indicated an single in-plane transition dipole moment was formed between the defects’ ground and excited states.

Use of a Hanbury-Brown-Twiss (HBT) interferometer, the anti-bunching behavior originated from the single photon nature of the defects emission was confirmed(elaborated in the Method section). As shown in Fig. 3f and 3i, $g^{2}(0)$ values of $0.26\pm 0.22$ and $0.16\pm 0.16$ were obtained for $553\,\text{nm}$ and $590\,\text{nm}$ QEs respectively, confirming their single photon emission behavior with high single photon purity. According to the data, no profound photon bunching at time $t\neq 0$ was observed in both types, suggesting the absence of non-radiative shelving state in their electronic states[42]. Therefore the QEs’ anti-bunching data was fitted by a background corrected two-level-system model[43],

$\eta=\frac{I_{\text{e}}}{I_{\text{e}}+I_{\text{b}}}$, where $I_{\text{e}}$ and $I_{\text{b}}$ denote the integrated emission intensity and background intensity respectively. $\tau_{r}$ is the defect state’s radiative decay mean cycle life time, which is the summation of the radiative excitation and decay lifetimes (statistic of the time-resolved data were obtained by fitting the data with Eq. 2). As shown in Table 1, short radiative cycle lifetime was observed for both $553\,\text{nm}$ ($1.06\pm 0.48\,\text{ns}$) and $590\,\text{nm}$ ($0.69\pm 0.17\,\text{ns}$) QEs.

The freestanding sample also allows the characterization of the samples with the scanning transmission electron microscope-cathodoluminescence (STEM-CL) system, where the focused electron beam (e-beam) activates the defect related emission. Fig. 4 shows the CL intensity mapping data collected from an $100\,\text{nm}$ thick sample. The CL spectra was obtained by averaging over the bright pixels within the circled areas. According to the data, the CL spectra of the QEs showed identical wavelength and FWHM to their PL versions. Meanwhile, a much higher spatial resolution than the PL data was achieved, where locations of the 553 nm and 590 nm QEs were determined within 50 nm (Fig. 4a) and 4 nm (Fig. 4b) respectively. The radius of the excitation volume introduced by the e-beam, $R_{e}$, can be estimated by the empirical equation: $R_{\text{e}}=(0.0276M/\rho Z^{0.889})E_{\text{b}}^{1.67}$ in the unit of $\mu\text{m}$[44]. Where $M$ is the molar mass (24.8 g/mol), $\rho$ is the density ($2.1\,\text{g/cm}^{3}$) and $Z$ is the atomic number (mean value of N and B, 6 was applied) of the target material. $E_{\text{b}}$ denotes the energy of the e-beam in keV. For $80\,\text{keV}$ acceleration energy, which was used in our experiment, $R_{\text{e}}=99.5\,\mu\text{m}$ was estimated, which is much bigger than the thickness of the hBN flakes used in our experiment. Therefore, the excitation volume was roughly defined by the size of the e-beam[45], which was much smaller than the size of the observed emission area. So it is reasonable to consider that the interactive volume of the $590\,\text{nm}$ QEs to electron beams was more than an order of magnitude smaller than that of the $553\,\text{nm}$ QEs. This is consistent with the PL measurement, in which photon absorption cross-section of the $590\,\text{nm}$ QEs is smaller than that of the $553\,\text{nm}$ QEs by a factor of $14$, suggesting that the $590\,\text{nm}$ QEs are spatially smaller comparing to the $553\,\text{nm}$ QEs. This difference indicates $553\,\text{nm}$ and $590\,\text{nm}$ QEs originate from different sources, for example, the donor-acceptor-pair[20, 46] and single defects mechanisms respectively. This distinction can adequately explain the observed differences in ZPL linewidth and PSB strength between the two types of QEs. Besides, the CL data also confirm the low emitter density observed in the PL experiment, as no clusters of the emitters were detected, this further highlights the huge difference between the amount of carbon ions stopped by the flake and the resulting emitter density. Here we use the typical emitter density observed in a 100 nm thick hBN flake, $0.42\,\text{cts/}\mu\text{m}^{2}$ for analysis as they are stable. Compared to the carbon ions stopped by the flake, $2.5\times 10^{6}\,\text{per}\,\mu\text{m}^{2}$, an intuitive speculation is more than one carbon atom was required to form an emissive defect.

The subsequent analysis only focuses on the 590 nm QEs as they were more likely to have a single defect configuration. The identity of these single defects, however, is not immediately clear. By assuming the stopping of the carbon ions is a completely stochastic process, and the aggregation of carbon ions were negligible, the surface density of $n$ carbon ions replacing neighbouring lattice sites (forming carbon dimers, trimers or tetramers) within a monolayer of hBN, $\Gamma_{\text{n}}$ can be estimated by evaluating the possible configurations of carbon replacement. Since the concentration of carbon ions in each layer was estimated to be low ($<10^{-3}$), for each configuration, a lattice site being intact approaches $1$. Therefore, $\Gamma_{\text{n}}$ can be simply written in the form of (detailed in SI):

Here $\Gamma_{i}$ denotes the concentration of carbon ions at the $i^{\text{th}}$ layer of the hBN flake, which was obtained from the SRIM (The Stopping and Range of Ions in Matter) simulation. $V_{\text{site}}$ denotes the average volume occupied by each lattice site. $\zeta_{\text{n}}$ denote the number of possible configurations of $n$ carbon ions replacing neighbouring sites. $N$ is the total number of layers of the hBN flake. $\Gamma_{s}$ is the effective surface density measured at the implantation target. $\Gamma_{s}$ and $\Gamma_{i}$ satisfy the relationship: $\Gamma_{s}=\sum_{i=1}^{N}\Gamma_{i}=2.5\times 10^{6}\,\text{per}\,\mu\text{m}^{2}$. According to Eq. 3, the surface density of carbon dimers and trimers were estimated to be $627$ and $0.185$ per $\mu\text{m}^{2}$ respectively (detailed in SI). Considering the possible aggregation of the carbon ions inside the hBN flake and the self-repairing processes, the actual density could be higher than the estimation. Suggesting that, most likely, the emissive defects were carbon trimers or tetramers.

We utilize first principles density functional theory (DFT) calculations to further validate the proposed defect structures that might be responsible for the observed emissions at 590 nm. We consider the carbon trimer $\text{C}_{3\text{B}}$ (replacing NBN sites, left one insert in Fig. 5a) and $\text{C}_{3\text{N}}$ (replacing BNB sites, left two inset in Fig. 5a) and radial tetramer defects $\text{C}_{4\text{B}}$ (replacing $\text{BN}_{3}$ sites, left three inset in Fig. 5a) and $\text{C}_{4\text{N}}$ (replacing $\text{NB}_{3}$ sites, left four inset in Fig. 5a) and perform DFT calculations with charged defects to predict the defect transition levels within the band gap. Here we applied the charge defect calculations correction methodology [47] and calculated the charge defect formation energy ($E_{\text{f}}$) as a function of the Fermi energy ($E_{\text{Fermi}}$), and the results for $\text{C}_{4\text{B}}$, $\text{C}_{4\text{N}}$, $\text{C}_{3\text{N}}$ and $\text{C}_{3\text{B}}$ are shown in Fig. 5a in the order from left to right (details in SI). The calculated electronic states based on the $E_{\text{f}}$ analysis suggests that $\text{C}_{4\text{B}}$ has a transition energy $2.1\,\text{eV}$ corresponding to the $+2/0$ transition, which most closely agrees with the observed emission energy ($2.10\,\text{eV}$).

To corroborate the DFT prediction, atomic resolution STEM images of the samples were taken to reveal the atomic structures involved in the emission. A typical annular dark field (ADF) image of the MCI hBN sample taken over the emitter sites is shown in Fig. 5b, where the hexagonal structure of boron nitride was identified. The image was taken along the direction perpendicular to the flake plane. Here, the hBN crystals used in our experiment showed AA’ stacking, where boron and nitrogen sites were alternatively stacking on each other between layers. In such a configuration, two adjacent layers form columns of atoms with identical total $Z$ value, resulting in no contrast difference. Thus, for flakes with an even number of layers, the lattice sites exhibit identical intensity. In contrast, for flakes with an odd number of layers, the intensity difference between boron and nitrogen sites of the non-compensated monolayer is retained. Therefore, Fig. 5b were taken from an odd-layer hBN flake, where the boron (dimmer) and nitrogen (brighter) sites can be well distinguished. A statistical analysis is shown in Fig. 5c, where the histogram of the integrated intensity for each lattice site in Fig. 5b (the image shown was cropped to a quarter of the original one to match the scale) was plotted, showing unambiguous difference between the boron and nitrogen sites. Therefore, lattice sites with ADF image intensity in between the nitrogen and boron sites were attributed to carbon replacements ($Z=6$). As shown in Fig. 5d and 5e, where carbon trimer, replacing BNB sites and carbon tetramer replacing $\text{BN}_{3}$ sites (marked with yellow dashed circles) were observed respectively. The data suggested that $\text{C}_{4\text{B}}$ did form during the MCI process, supporting the emitter density analysis and DFT calculations.

MCI enables repeatable deterministic production of bright, stable and monochromatic room temperature QEs in hBN, ensuring a highly consistent yield of QEs with excellent single photon purity. The mask approach is also inherently amenable to lithography, meaning it is consistent with the ability to place QEs deterministically in space. Our research is both technological and scientific interest, as it provide consistent reproducible QE sample production, allowing reliable platform for characterization and fabrication research. According to our data, boron centered carbon teramers, $\text{C}_{4\text{B}}$ were suggested to be the origins of the 590 nm QEs, while the 553 nm QEs are attributed to the donor-acceptor pairs induced by carbon-defect clusters. The QEs produced with this method exhibiting exceptional stability, underlining the robustness of the proposed approach. Such reliability is paramount when considering the demands of any practical applications especially the industrial-scale production, where reproducibility and consistency are central to achieving standardized outputs, potentially introducing a transformative dimension to the landscape of quantum technology.