Observation of Boron Vacancy Concentration in Hexagonal Boron Nitride at Nanometer Scale

Abstract

Negatively charged boron vacancy (V_B ) ensembles in hexagonal boron nitride (h-BN) have attracted considerable attention as a promising platform for quantum sensing. Current challenges include the experimental validation of the spatial distribution and electronic states of optically active V_B and optically inactive neutral boron vacancy (V_B ) defects. To address these issues, we employ electron energy loss spectroscopy (EELS) combined with scanning transmission electron microscopy (STEM) using monochromated 30-keV electrons, effectively reducing background interference. This approach unveils distinct spectral peaks at 2.5 and 1.9 eV, corresponding to V_B and V_B defects, respectively. Furthermore, we achieve nanometer-scale concentration mapping for V_B and V_B defects, advancing insights into spin defect configurations crucial for optimizing quantum sensor performance.

Quantum sensors hold considerable potential for measuring a wide range of physical and chemical properties, providing exceptional resolution and precision. , Ensembles of color centers (i.e., point defects caused by vacancies and impurities) in hexagonal boron nitride (h-BN) are promising platforms for next-generation quantum sensors as post negatively charged nitrogen-vacancy (NV^–) ensembles in diamond. , h-BN is a two-dimensional material with a wide bandgap at ∼ 6 eV, , and has the advantages of easy integration into quantum devices, high photon extraction efficiency, and photon wavelength diversity. , Negatively charged boron vacancies (V_B ), antisite nitrogen vacancies (N_BV_N), and carbon-based defects are color centers generating luminescence at ∼1.5, − ∼2.0, , and ∼4.1 eV, − respectively. In particular, the V_B centers exhibit spin-dependent photon emission at room temperature, a desirable property for quantum sensing. − The spatial V_B distribution uniformity, V_B concentration, and the distance between individual V_B defects are fundamental properties, in addition to the crystallinity and purity of h-BN, for determining spatial resolution and sensitivity in quantum sensors. Ion or electron irradiation on h-BN generates V_B defects, − and can simultaneously generate neutral born vacancies (V_B ) and other types of defects, − which coexist with intrinsic impurity-related defects. − , Direct observations have shown that electron and He⁺ ion irradiation preferentially generate V_B defects rather than V_N defects. − However, the distribution, concentration, and spacing of V_B and V_B defects are as yet not fully understood because of the absence of a standardized measurement method at the nanometer scale, especially for optically inactive V_B . Furthermore, despite the first-principles simulations of the electronic structures of V_B and V_B defects, ,− experimental validation remains necessary. Therefore, it is crucial to measure the arrangement and electronic states of V_B and V_B defects.

Electron energy loss spectroscopy (EELS) combined with scanning transmission electron microscopy (STEM) enables probing the subgap states of lattice defects and the chemical bonding states at defect sites. − However, measuring the detailed EELS spectral structure from point defects in bulk crystals presents a significant challenge, because of the low concentration of point defects (≲ 10³ ppm) and the weakness of EELS signals compared with other intrinsic signals. Three types of background intensity can hinder the detection of EELS signals of defect states. The first is the tail of the zero-loss peak (ZLP, i.e., elastic scattering peak), whose signal can become dominant even in several eV region in EELS. A smaller energy spread of the incident electrons evaluated with full width at half-maximum (fwhm) or more appropriately at 10^–n (n ≥ 1) of the ZLP, is required to reduce the contribution of the ZLP tail. The second is EELS signals, which can appear at around several eVs owing to the generation of Cherenkov radiation. This radiation can be reduced or ignored by lowering the energy of incident electrons or by using a thinner specimen. ,, The third is detector noise. It is very important to reduce readout noise in addition to gain noise so that weak signals are not buried in their noise.

In this study, to measure electronic states of V_B and V_B defects in h-BN by EELS, we use monochromated 30-keV electrons, reducing the fwhm of the ZLP to 40 meV, and suppressing Cherenkov radiation. ,,, To detect scattered electrons in EELS, we use a charge-coupled-device (CCD) camera with a high-sensitivity scintillator optimized for 30-keV electrons, and the readout noise reduction scheme. , EELS in combination with first-principles simulations revealed a high peak at 2.5 eV with enhanced intensity appearing at the shoulder position of 1.9 eV, which are respectively assigned to signals from V_B and V_B defects. Furthermore, we obtain the concentration maps for V_B and V_B defects at the nanometer scale.

h-BN single crystals were grown using a temperature gradient method at a high pressure, and their flakes with thicknesses of 30–200 nm were prepared using a tape-peeling method (details of the specimen preparation and experimental methods are described in Supporting Information). The h-BN flakes were dispersed on a holey carbon-film-supported copper grid and then irradiated with a 40-keV nitrogen ion (N₂ ) beam along the c-axis at a total dose of 1 × 10¹⁵ cm^–2 at room temperature, as shown in Figure a. Figure b shows the photoluminescence (PL) spectra of the pristine and irradiated h-BN flakes at room temperature with an incident photon energy of 2.33 eV. PL occurs with a peak maximum at 1.53 eV (=810 nm) only after the irradiation, indicating the formation of optically active V_B defects, as observed in previous studies. − Figure c shows the optically detected magnetic resonance (ODMR) spectrum of the irradiated h-BN flake. ODMR occurs at a microwave frequency of ∼3.5 GHz after the irradiation, corresponding to a ground state zero-field splitting between spin states m _s = 0 and m _s = ±1 for V_B in h-BN. , Figure d displays the EELS spectra of the pristine and irradiated h-BN flakes below 6.2 eV. Two characteristic EELS intensities appear in the subgap region only for the irradiated h-BN flake as indicated by the arrows (Figure d). One is an asymmetric signal centered at ∼2.5 eV and the other is a continuous intensity distribution ranging from 3.8 to 5.9 eV. These EELS intensities reflect the density of states (DOS) of the defect levels introduced by the irradiation. The asymmetric 2.5 eV signal was more clearly observed in flakes thicker than ∼100 nm. In the range of 6–30 eV, there is no marked difference in EELS profiles between the pristine and irradiated h-BN flakes (Figure S1a). In addition, no marked changes were observed at the N K edge after the irradiation; only a slightly asymmetric broadening of the peak at 191.8 eV was detected at the B K edge (Figures S1b and S1c), suggesting the formation of nitrogen vacancies (see details in Supporting Information). We also observed cathodoluminescence (CL) at approximately 4.1 eV (Figure S2), which occurred depending on the measurement position for both pristine and irradiated flakes. This indicates the presence of carbon-related defects in the original h-BN crystal. − As the energy levels associated with these defects lie outside the energy range of interest (i.e., 1.5–3.5 eV), it is appropriate to focus exclusively on the V_B and V_B defects hereafter (see details in Supporting Information).

1.

(a) Illustration of N₂ ion irradiation of h-BN flake. (b) PL spectra of pristine and irradiated h-BN flakes. (c) ODMR spectrum of irradiated h-BN flake. (d) EELS spectra of pristine and irradiated h-BN flakes. The inset optical microscopy and annular dark-field STEM images in (b) and (d) respectively show the h-BN flakes on a holey a-C film. (e) EELS spectrum after subtraction of the ZLP tail for the irradiated h-BN flake in (b), revealing four characteristic intensity peaks labeled P1–P4. Row data (solid circle) and smoothed profile (solid line).

To identify fine structures of the 2.5 eV asymmetric signal in Figure d, we conducted EELS with a high energy resolution (i.e., fwhm of the ZLP, 40 meV). By scanning the electron probe in steps of 3.6 nm in 143 nm-square areas in the irradiated h-BN flake, we obtained 1600 single EELS spectra. By summing the single spectra and subtracting the background intensity mainly due to the ZLP tail with a power-low fit (Figure S3), we found that the asymmetric 2.5 eV signal is composed of four characteristic intensities, as shown in Figure e. The high intensity peak P2 locates at 2.5 eV, overlapping with relatively low intensity peaks labeled P1 at 1.9 eV, P3 at 2.9 eV, and P4 at 3.45 eV. The appearance of the intense signal at 2.5 eV in EELS is consistent with the maximum absorption at ∼2.6 eV in PL excitation measurements for V_B defects in h-BN. Note that the asymmetric 2.5 eV signal is weaker than intrinsic bulk signals. For instance, the EELS intensity of the 2.5 eV signal (i.e., integrated intensity in the range of 1.34–3.34 eV) is approximately 10^–1 of that of optical phonons (i.e., integrated intensity in the range of 0.13–0.28 eV), despite the 13-fold difference in integration range (Figure S4).

To understand the fine structures of the 2.5 eV asymmetric signal in Figure e, we conducted first-principles simulations (details of the calculation methods are described in Supporting Information). Figures a–c show the electronic DOS values of h-BN crystals without defects, with a V_B defect, and with a V_B defect, respectively (see Figure S5 for a wider energy range). Occupied and unoccupied states are filled and blank, while up- and down-spin states are displayed in the upper and lower side, respectively. The three DOS diagrams are aligned with the 2s levels (Figure S5). The positions of VBM and CBM in Figures b and c denote those for the perfect crystal (Figure a). As shown in Figures b and c, subgap states between VBM and CBM differ largely depending on whether the charge of V_B is – 1 or zero. The diagonal components of the dielectric tensor perpendicular and parallel to the c-axis are written as ε _xx = ε_1,xx + iε_2,xx (=ε _yy ) and ε _zz = ε _1,zz + iε_2,zz , respectively. Figures e–g show the imaginary parts ε_2,xx and ε_2,zz for the perfect crystal, the V_B defect, and the V_B defect, respectively (see Figure S6 for a wider energy range and real parts). The imaginary parts represent absorption. Note that ε _2,xx for the V_B defect is intense with fine structures denoted as A–F in the 2.0–4.0 eV range (Figure f). This indicates that electronic excitations at 2.0–4.0 eV in the ab-plane direction are dominant compared with those along the c -axis. For the V_B defect, ε _2,xx has a relatively low intensity and fine structures denoted as G–J in the 0.5–2.5 eV range (Figure g), whereas there is no characteristic intensity in ε _2,xx and ε _2,zz for the perfect crystal because of the absence of subgap states (Figure e). The A–F peaks in Figure f and the G–J peaks in Figure g originate from the electron excitations between subgap states, A–F in Figure b and G–J in Figure c. The loss function L when the electron incident direction is parallel to the c-axis and the convergence angle α = 0 is calculated as

$$L=\mathrm{-I}\mathrm{m}\left[\frac{1}{2{\mathit{\epsilon }}_{zz}}\ln (1+\frac{{\mathit{\epsilon }}_{zz}{\beta }^2}{{\mathit{\epsilon }}_{xx}{{\theta }_E}^2})\right]$$

θ_E = ΔE/2E ₀ in nonrelativistic form, where E ₀ (=30 keV) and ΔE respectively represent the incident energy and energy loss of the primary electron: θ_E = 4.2 × 10^–2 mrad for ΔE = 2.5 eV. Considering that the electron probe used in STEM–EELS has α (≠0), β is approximately replaced with β* = $\sqrt{{\alpha }^2+{\beta }^2}$ to calculate L (details are described in Supporting Information). Figures h–j show L for the perfect crystal, the V_B defect, and the V_B defect, respectively. The profile of L mainly reflects that of ε_2,xx . The A′–F′ peaks in Figure i and the G′–J′ peaks in Figure j reflect the A–F peaks in Figure f and the G–J peaks in Figure g, respectively. This is because ε_2,xx in L becomes dominant when θ_E ≪ β and also because ε_2,zz is originally small. Reflecting the intensities of ε_2,xx in L for the V_B and V_B defects (Figures f and g), the intensity of L for the V_B defect [L (V_B )] in the range including the A′–F′ peaks (Figure i) is higher than that L for the V_B defect [L (V_B )] in the range including the G′–J′ peaks (Figure j). Figures i and j also suggest that the EELS intensity in the 4–6 eV range in Figure d originates from other types of defects and partly from the V_B defects. Figure shows plots of L (V_B ) and L (V_B ) with coefficients of 0.16 and 0.84, respectively, and their linear combination, 0.16 L (V_B ) + 0.84 L (V_B ), where L was plotted so that the linear combination profile matched the smoothed EELS spectrum (Figure e) (see Figure S8 for the method of determining the coefficients). The good agreement between the linear combination and the EELS spectrum enables the assignment of the origin of the P1–P4 peaks in EELS and reveals the concentration ratio of the V_B defects to the V_B defects, V_B /V_B is 5.3 as the average value within the measured 143 nm-square area. The intense P2 peak in EELS corresponds to the A′ and B′ peaks in L (V_B ), and, thus, the electron excitations A and B in Figure b. The P3 and P4 peaks correspond to the C′ and E′ peaks in L (V_B ), whereas the P1 peaks correspond to the I’ peak in L (V_B ). The finding that the optically inactive V_B coexists with the optically active V_B implies that adjusting the charge state from 0 to – 1 can increase the V_B concentration through electron injection. , Figure shows a schematic unifying our understanding from the results of PL, EELS, and first-principles simulations in this study and PL excitation in a previous study for V_B . As illustrated in the DOS schematics of the ground state for V_B (Figure ), the 1.53 eV PL occurs as an electronic relaxation process after the 2.5 eV excitation (i.e., absorption in EELS and PL excitation) between the occupied and unoccupied defect states. The remaining energy of approximately 1 eV is attributed to nonradiative relaxation.

2.

First-principles simulations. [(a)–(c)] DOS values of h-BN crystals without defects, with a V_B defect, and with a V_B defect, respectively. The filled and blank areas are the occupied and unoccupied states, respectively. The upper and lower sides are the up- and down-spin states, respectively. [(e)–(g)] Imaginary parts of dielectric function, ε_2,xx (solid line) and ε_2,zz (dashed line) for perfect crystal in (e), V_B in (f), and V_B in (g). Intensities in ε _2,xx denoted by A–F in (f) and G–J in (g) originate from electron excitations indicated by A–F in (b) and G–J in (c), respectively. [(h)–(j)] Loss functions (L) for perfect crystal in (h), V_B in (i), and V_B in (j). Intensities in L denoted by A′–F′ in (i) and G′–J′ in (j) predominantly reflect the intensities in ε_2,xx denoted by A–F in (f) and G–J in (g).

3.

Plots of the loss function L for V_B (blue) and V_B (green) in Figure with factors of 0.16 and 0.84, respectively, their linear combination (magenta), and smoothed EELS spectrum (black) in Figure e.

4.

Schematic of the 2.5 eV electron excitation (i.e., absorption) and 1.5 eV luminescence accompanied by nonradiative decay at the V_B defect in h-BN, illustrated in the DOS schematic of the ground states.

To evaluate the absolute concentrations of V_B and V_B by EELS, we utilize the vacancy concentration in the supercell for first-principles simulations, which is 13889 ppm for both V_B and V_B . Using the integrated intensities for V_B and V_B (i.e., V_B + V_B ) in the range of 1.0–3.0 eV and the π-plasmon in the loss functions and those in the EELS spectrum, we estimated the average concentration of V_B + V_B as approximately 2000 ppm (details are given in Figure S9). We assumed that the intensity ratio of V_B to the π plasmon in EELS is proportional to the V_B concentration. Then, the average V_B and V_B concentrations are approximately estimated as 300 and 1700 ppm, using the coefficients 0.16 and 0.84 (Figure ), respectively. The average V_B concentration can be evaluated directly using the integrated intensities for V_B in the range of 2.3–3.0 eV, resulting in 300 ppm as well (details are given in Figure S10). By implementing this method for the original 1600 single spectra from the 143 nm-square area (i.e., 40 × 40 pixels), we obtained the concentration map of V_B and its histogram, as shown in Figures a and b, respectively. The V_B concentration is nearly uniform without significant segregation (Figure a). The Gaussian fit in Figure b provides the center and standard deviation of 330 ± 33 ppm, which is close to the average value of 300 ppm estimated above. Figures c and d respectively show the map of the concentration ratio of V_B to V_B (i.e., V_B /V_B ) and its histogram, where the V_B /V_B ratio at each pixel was obtained using the integrated intensities in the ranges of 1.7–2.0 eV for V_B and 2.3–2.6 eV for V_B (Figure S8a). The V_B /V_B map represents the distribution of the charge state ratio (i.e., 0 to – 1). The negative values of the V_B /V_B ratio for several pixels are due to the excess removal of ZLP tail signals and the low signal-to-nose ratio. The Gaussian fit in Figure d gives V_B /V_B =5.0 ± 1.7, which closely matches the average V_B /V_B =5.3 obtained after integrating the 1600 single spectra described above. By multiplying the V_B map (Figure a) and the V_B /V_B map (Figure c), we also obtained the concentration map of V_B and its histogram as shown in Figures e and f, respectively. The Gaussian fit in Figure f provides the center and standard deviation of 1647 ± 648 ppm, which is close to the average value of 1700 ppm estimated above. Figures g–i show plots of typical single EELS spectra at 1 pixel (3.6 nm-square areas) in Figure c with the V_B /V_B values of 1.4, 5.0, and 7.1, respectively. The smoothed line profiles certainly reveal the increase in P1 intensity at ∼ 1.9 eV from Figures g to i. Regarding the spatial resolution of the maps (Figure ), the diameter and scan step of the electron probe we used were 0.6–0.7 and 3.6 nm, respectively, whereas the effective diameter considering the delocalization of EELS around 2.5 eV was estimated to be 8 nm. Thus, the maps in Figure are blurred by approximately 2 × 2 pixels compared with the actual intensity distribution.

5.

Concentration maps of vacancies in the irradiated h-BN flake. The V_B map in (a) and its histogram in (b). The V_B /V_B ratio map in (c) and its histogram in (d). The V_B map in (e) and its histogram in (f). All maps have the same area. The centers and standard deviations for Gaussian fits in the histogram are 300 ± 33 ppm, 5.0 ± 1.7, and 1647 ± 648 ppm in (b), (d), and (f), respectively. [g–h] Typical single EELS spectra at 1 pixel (3.6 nm-square areas) with the V_B /V_B ratios of 1.4, 5.0, and 7.1 in (g), (h), and (i), respectively.

Finally, we briefly discuss the quantitative aspects of the concentration maps in Figure . The primary concern lies in the comparison between the electron arrival time interval Δt at the electron probe position in STEM–EELS and the lifetime τ from the excited state back to the ground state for V_B and V_B . In this study, Δt was 1.3 ns (i.e., the probe current of ∼120 pA) and the exposure time at each pixel was 0.6 s in Figure . The excited state for V_B returns to the ground state predominantly via a singlet metastable state. , The lifetime of this metastable state is approximately 10–30 ns at room temperature, making τ longer than this, − whereas the lifetime of V_B remains unknown. This suggests the potential for underestimating the V_B concentration during EELS measurement at each pixel. The measurement was probably performed with a certain fraction of V_B in the metastable state, specifically with a reduced concentration of V_B . Reducing the probe current to below 1 pA and increasing the exposure time would resolve this issue, although it is expected to result in a lower signal-to-noise ratio of the spectrum, making measurements more challenging. Alternatively, when the τ of V_B is comparable to that of V_B , the V_B /V_B ratio can be considered quantitative despite the underestimation of the respective absolute densities. In any case, the optimization of EELS conditions and a more precise quantitative evaluation of both relative and absolute densities remain future challenges.

In summary, in this study, we investigated the intricate characteristics of optically active V_B and optically inactive V_B defects in nitrogen-ion irradiated h-BN by STEM–EELS with monochromated 30-keV electrons and first-principles simulations. EELS played a pivotal role in identifying the subgap states resulting from the irradiation, distinguishing distinct spectral peaks at 2.5 and 1.9 eV corresponding to V_B and V_B defects, respectively. The concentrations of V_B and V_B defects were estimated as approximately 300 and 1700 ppm on average, respectively. We also accomplished the concentration mapping of these defects at the nanometer scale, which revealed their near-uniform distribution without significant segregations. As a future challenge, it is necessary to optimize EELS conditions by considering the lifetime τ to avoid the underestimation of defect concentration. Such optimization is imperative for precise quantitative assessments, as it provides indispensable insights that are vital for the future application of h-BN in quantum technology sectors.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.5c02988.

• Details of experimental method, first-principles simulations, other possible defects, loss function calculation, and additional figures (PDF)

J.K. and T. Teraji conceived and directed the project. T. Taniguchi made the h-BN crystal. Y.M. and Y.Y. conducted the nitrogen-ion irradiation. J.K. conducted EELS experiments and analyses. C.S., Y.Y., and J.C. measured PL, ODMR, and CL spectra, respectively. T.M. conducted first-principles simulations. All authors have discussed the experimental and simulated results. J.K. wrote the manuscript with the support of all the authors.

The authors declare no competing financial interest.