Optical Signatures of Quantum Emitters in Suspended Hexagonal Boron Nitride Annemarie L. Exarhos,† David A. Hopper,†,‡ Richard R. Grote,† Audrius Alkauskas,§,⊥ and Lee C. Bassett*,† †
Quantum Engineering Laboratory, Department of Electrical and Systems Engineering, and ‡Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States § Center for Physical Sciences and Technology, Vilnius LT-10257, Lithuania ⊥ Department of Physics, Kaunas University of Technology, Kaunas LT-51368, Lithuania S Supporting Information *
ABSTRACT: Hexagonal boron nitride (h-BN) is rapidly emerging as an attractive material for solid-state quantum engineering. Analogously to three-dimensional wide-bandgap semiconductors such as diamond, h-BN hosts isolated defects exhibiting visible fluorescence at room temperature, and the ability to position such quantum emitters within a two-dimensional material promises breakthrough advances in quantum sensing, photonics, and other quantum technologies. Critical to such applications is an understanding of the physics underlying h-BN’s quantum emission. We report the creation and characterization of visible single-photon sources in suspended, single-crystal, h-BN films. With substrate interactions eliminated, we study the spectral, temporal, and spatial characteristics of the defects’ optical emission. Theoretical analysis of the defects’ spectra reveals similarities in vibronic coupling to h-BN phonon modes despite widely varying fluorescence wavelengths, and a statistical analysis of the polarized emission from many emitters throughout the same single-crystal flake uncovers a weak correlation between the optical dipole orientations of some defects and h-BN’s primitive crystallographic axes, despite a clear misalignment for other dipoles. These measurements constrain possible defect models and, moreover, suggest that several classes of emitters can exist simultaneously throughout free-standing h-BN, whether they be different defects, different charge states of the same defect, or the result of strong local perturbations. KEYWORDS: hexagonal boron nitride, single-photon source, fluorescent defect, single crystal, dipole−lattice coupling, Huang−Rhys factor structure responsible for its visible fluorescence remains unknown. Here, we describe the creation and optical characterization of single-photon sources in suspended, single-crystal h-BN membranes under ambient conditions. Marked differences between the photoluminescence (PL) response of regions freely suspended or supported on Si/SiO2 substrates as well as those near extended defects or edges point to strong interfacedependent effects in the defects’ formation and optical properties. To eliminate this bias, we concentrate on a set of individual emitters hosted within a freely suspended region of a single-crystal h-BN membrane. A comprehensive study of the emitters’ PL spectra, polarization properties, brightness, and photon emission statistics reveals some qualitative similarities
D
efect engineering in solid-state materials is a rapidly progressing field with applications in quantum information science,1,2 nanophotonics,3 and nanoscale sensing in biology and chemistry.4 Inspired by the success of the archetypal nitrogen-vacancy center in diamond,5 recent efforts have uncovered analogous systems in other wide-bandgap semiconductors such as silicon carbide,6,7 which offer exciting opportunities for defect engineering on the wafer scale.2 Meanwhile, optically active impurities in low-dimensional materials can provide additional functionalities due to intrinsic spatial confinement and the ability to create multifunctional layered materials.8,9 Within the class of van der Waals materials, hexagonal boron nitride (h-BN) is an ideal candidate for exploring optically active defects due to its large (5.955 eV) band gap10 and its unique optical,11 electrical,12,13 and vibronic properties14 that may influence the defects’ underlying physics. Despite a recent surge of attention to hBN’s defects,15−21 the underlying electronic and chemical © 2017 American Chemical Society
Received: January 30, 2017 Accepted: March 7, 2017 Published: March 7, 2017 3328
DOI: 10.1021/acsnano.7b00665 ACS Nano 2017, 11, 3328−3336
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ACS Nano but many quantitative differences in their optical signatures. The defects’ absorptive and emissive dipoles are generally not aligned to h-BN’s crystallographic basis vectors, although a statistical analysis of many emitters throughout the same flake hints at a weak correlation. Together, these measurements support the presence of multiple defect species within h-BN, clarifying conflicting earlier reports and providing a framework for further theoretical and experimental investigations of their properties. Due to h-BN’s crucial role as a two-dimensional (2D) dielectric constituent in layered materials, its defects have received a surge of attention in recent years. Scanningtunneling microscopy of graphene/h-BN heterostructures revealed charged impurities attributed to native defects in hBN possibly involving carbon.22 Carbon impurities have also been implicated in ultraviolet PL23 and cathodoluminescence24 from h-BN, even at the single-defect level.25 Recently, singlephoton sources at visible wavelengths have been reported from monolayer, multilayer, and bulk h-BN.15−21 Fluorescence from these emitters can be excited at room temperature using subband-gap light (typically at 532 nm), and their resulting PL exhibits zero-phonon-line (ZPL) energies ranging over at least 600 meV between 1.6 and 2.2 eV (560−775 nm).16,19 Other basic emitter properties (e.g., optical lifetime, spectral line shape, brightness) also vary widely. These disparate observations have given rise to several proposed physical models, including the point defect NBVN (an antisite complex consisting of a nitrogen atom occupying the site of a boron vacancy)15 and a broader family of extended Stone−Wales defects occurring along grain boundaries.20 Some variation in emission properties can be attributed to the heterogeneity of local environments for defects confined in a low-dimensional material, but sample preparation also plays a major role. Previous studies have used h-BN samples ranging from submicrometer flakes15,16,19 to bulk crystals,17 and defects have been created using various approaches including annealing, electron irradiation, ion implantation, laser exposure, and chemical etching.15,16,20,21 Our goal in this work is to eliminate most of these external sources of variation. By characterizing multiple defects observed within suspended regions of large-area, single-crystal h-BN flakes, we eliminate sample-to-sample variations and substrate interactions that are observed to play an important role in the material’s visible emission characteristics. We further describe a general framework for analyzing the defects’ spectral, temporal, and spatial emission characteristics, including a quantitative theoretical analysis of vibronic coupling in the room-temperature phonon sideband. Fascinatingly, even under these controlled conditions, the measurements reveal a rich phenomenology, with evidence for multilevel electronic structures, metastable states, photoswitching, and complex chemistries.
Figure 1. Visible fluorescence from exfoliated h-BN. (a) White light optical micrograph of exfoliated h-BN on a patterned Si/SiO2 substrate. (b) Tilted SEM image of the same flake. (c) PL image of the exfoliated flake under 532 nm excitation. (d) PL image of the partially suspended film denoted by the square in (c). The dashed line shows the edge of the suspended h-BN flake that hangs over the center of the etched hole.
and bare Si/SiO2 substrate. A higher-resolution image (Figure 1d) of the partially covered hole denoted in Figure 1c reveals bright spots within the free-standing h-BN membrane that we characterize as single- and few-photon emitters. Figure 1c,d show a significant difference between the brightness of supported versus suspended regions. This difference in brightness appears to reflect substrate-dependent defect formation, with a higher defect density observed on supported regions, but the apparent brightness of individual emitters seems to depend on the substrate as well. We note that there is some evidence of a broad spectral background on supported regions, but it does not appear to be entirely responsible for the change in overall PL brightness between supported and suspended regions. More details can be found in the Substrate Interactions section of the Supporting Information. The brightest emitters in the suspended region approach the average brightness of those on the supported region, while the vast majority of suspended emitters are dimmer than their supported counterparts (see Figures S6 and S7 in the Supporting Information). Additionally, the PL intensity from supported h-BN varies as a function of the substrate conditions, with the brightest regions occurring where h-BN overlays a released SiO2 membrane at the edge of a hole, rather than the full Si/SiO2 heterostructure. These puzzling effects are visible in Figure 1c and much more apparent in Figure S6.26 Proximity to a substrate can modulate an emitter’s radiative and nonradiative decay rates,27 but substrate-induced brightening of individual emitters is surprising, since substrate interactions frequently quench PL rather than enhance it.28,29 These substratedependent effects are interesting topics for further study, but for the remainder of this work we focus on emitters contained in the suspended region highlighted by Figure 1d. Single-Photon Sources in Suspended h-BN. The PL characteristics for four single-photon sources in the freely suspended h-BN membrane are summarized in Figure 2. Single-photon emission is established by the presence of an antibunching dip near zero delay in the photon autocorrelation function, g(2)(t), that drops below the threshold indicated by a
RESULTS AND DISCUSSION Figure 1 shows an exfoliated, single-crystal h-BN flake on a patterned Si/SiO2 substrate under various imaging modalities. The defects are created via electron irradiation and annealing in an argon atmosphere (see Materials and Methods).21 Brightfield optical microscopy (Figure 1a) shows the holes etched into the substrate beneath the flake, and scanning electron microscopy (SEM) (Figure 1b) confirms that the flake suspends the holes. Spatial PL images (Figure 1c,d) recorded with 532 nm excitation at ∼150 μW exhibit strong PL from the supported h-BN as compared to both the suspended regions 3329
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Figure 2. Single emitters in free-standing h-BN. Panels from left to right: PL spectra, photon autocorrelation measurements over short (30 ns) and long (1 μs) time scales, and PL excitation and emission polarization dependences. Each row corresponds to a different single-photon emitter. Dotted lines in the short-time autocorrelation plots indicate the single-emitter threshold. Gaps in the long time scale autocorrelation data correspond to regions where detector crosstalk afterflashes interfere with data collection.
Figure 3. Vibronic analysis of single-emitter spectra. (a) Emission line shape for SE1 (points), as a function of the change in lattice energy during optical relaxation (ΔE = EZPL − E, where E is the observed photon energy). The data are binned to produce approximately uniform uncertainty, as indicated by the representative error bar. Curves show the results of a fit using the model described in the text (thick red curve), along with the ZPL and PSB components (thin curves) as indicated by the legend. (b−d) Best-fit one-phonon probability distribution functions for emitters SE1, SE2, and SE5.
emitter (SE5) in the suspended h-BN region with broadly similar characteristics to SE1 and SE2 are provided in the Supporting Information.26 Electron−Phonon Coupling. The shape of a defect’s emission spectrum depends on the vibronic coupling between optical dipole transitions and phonons in the host material. In general, this coupling can be a complicated function that depends on the symmetry and shape of the defect wave functions and vibrational resonances due to both bulk and quasi-localized phonon modes.30 Still, the general theory of such coupling in three-dimensional crystals is well established.31,32 For the emitters whose PL spectra exhibit a clearly discernible ZPL (SE1, SE2, and SE5), we apply this theory in a
dotted line in each panel of the second column in Figure 2. The room-temperature emission spectra of single defects (leftmost column of Figure 2) exhibit striking differences in both shape and spectral weight, with features extending 550−700 nm (1.77−2.25 eV). Some spectra, such as for SE1 and SE2, include a clear ZPL and phonon sideband (PSB) and are similar in shape to those reported from experiments with supported hBN samples.15,17−21 Other spectra, such as SE3 and SE4, display spectral features distinct from what has been thus far reported. The emission of SE4, in particular, is characterized by a much broader spectral distribution than for SE1 and SE2, with a comparatively high-energy ZPL that appears to be outside our detection bandwidth. Measurements of a fifth single 3330
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ACS Nano Table 1. Properties of Single Emitters in Suspended h-BN emitter
EZPL (eV)
SHR
ΓZPL (meV)
SE1 SE2 SE3 SE4 SE5a
2.0405 ± 0.0003 1.9269 ± 0.0003
1.0 ± 0.1 1.2 ± 0.1
30 ± 1 31 ± 2
2.0812 ± 0.0003
1.7 ± 0.1
31 ± 1
τ1 (ns) 3.33 4.7 2.72 0.94 1.7
± ± ± ± ±
0.05 0.4 0.04 0.04b 0.2
τ2 (ns) 710 1100 89.1 335
± ± ± ±
10 700 0.6 8
Δθ (deg) 79 86 31 42 71
± ± ± ± ±
Vexc
4 6c 1 2 10c
0.22 0.76 0.38 0.84 0.6
± ± ± ± ±
0.03 0.08d 0.01 0.05 0.1d
a
Spectral, temporal, and polarization data in this row might not originate from the same emitter.26 bLifetime likely limited by detector timing jitter. c θexc determined using the minimum measured intensity (θexc = θmin + 90°). dVexc determined using the maximum and minimum measured intensities.
general way to extract the vibronic coupling as a function of phonon energy by fitting the measured emission line shapes. Figure 3a presents a fit of this model to the emission line shape of SE1, which is derived from the corresponding spectrum in Figure 2 by converting the spectral density to energy units and accounting for the E3 dependence of spontaneous emission, where E is the photon energy. Free parameters in the fit include the ZPL energy, EZPL, the full width at half-maximum of the Lorentzian ZPL line shape, ΓZPL, and the Huang−Rhys factor, SHR. The best-fit values for these parameters are presented along with other data in Table 1. The fit also returns the functional form of the n-phonon contributions to the PSB, In(ΔE), which are probability distribution functions describing the change in lattice vibrational energy, ΔE, due to the emission (ΔE > 0) or absorption (ΔE < 0) of n phonons during optical relaxation. I1(ΔE) is the underlying distribution describing the vibronic coupling, and In = I1 ⊗ In−1 for n > 1. Figure 3a shows the contributions from n = 1, 2, and 3 phonons to the SE1 line shape, and the best-fit distributions I1(ΔE) for SE1, SE2, and SE5 are plotted in Figure 3b−d, respectively. Further details of the line shape analysis and fitting procedure can be found in the Materials and Methods as well as the Supporting Information.26 While we caution that the theory and fitting procedure relies on several approximations, we can draw useful information from qualitative comparisons of the results. In particular, SHR quantifies the strength of electron−phonon interactions for a given defect and I1(ΔE) highlights the energies of dominant phonon modes. Interestingly, despite ZPL energies differing by over 100 meV, SE1 and SE2 exhibit similar Huang−Rhys factors (SHR ≈ 1) and PSB structure, with clear peaks around ΔE = 30, 75, and 175 meV, albeit with differences between 100 and 150 meV. In contrast, SE5 exhibits a larger SHR and qualitatively different PSB. All emitters have room-temperature ZPL line widths of ∼30 meV, several times larger than comparable observations from diamond nitrogen-vacancy centers.33,34 Compared to the usual case in three-dimensional (3D) semiconductors, the existence of low-energy phonon modes in h-BN associated with out-of-plane vibrations (≲15 meV) might contribute to the ZPL broadening, in which case SHR ≫ 1 and all optical transitions (both in the PSB and near the ZPL) generally involve many such phonons. Our analysis cannot rule out this possibility, but we believe it to be unlikely based on theoretical expectations for the low-energy scaling of electron− phonon interactions, which we constrain in our analysis to remove the covariance between SHR, ΓZPL, and the low-energy components of I1(ΔE).26 At higher phonon energies, we find no evidence for coupling to quasi-localized phonon modes with energies in excess of the 200 meV bulk phonon cutoff energy in h-BN,35 in contrast to the case for some color centers in diamond.36
An additional consideration concerns the potential influence of piezoelectric coupling, which could dominate over the usual deformation−potential coupling in centrosymmetric crystals. Such a theory was recently used to describe the temperaturedependent shifts of ZPL width and position for defects in multilayer h-BN nanoflakes.19 Our model does not include piezoelectric coupling since the 150-nm-thick sample in this work is well within the bulk three-dimensional limit in which hBN possesses inversion symmetry and is not piezoelectric. This reasoning justifies our use of the theory typically applied to 3D materials in the case where the low-energy coupling is dominated by deformation−potential coupling. In the case of SE3 and SE4, spectral fits are poorly constrained since EZPL cannot be identified unambiguously, although the broad spectrum of SE4 suggests a much larger value for SHR. SE3 was observed to blink during measurements, and we believe the two peaks visible in its spectrum around 568 and 595 nm in Figure 2 may represent the distinct ZPLs of two configurations of the same defect. If that is the case, the individual spectral configurations seem broadly similar to SE1 and SE2. Temporal Emission Statistics. A defect’s photon emission statistics can also provide insight into the number and relaxation lifetimes of individual electronic levels involved in its optical cycle. The central columns of Figure 2 show g(2)(τ) for each emitter over both short (|τ| < 30 ns) and long (|τ| < 1 μs) time scales where the entire emission spectrum for λ > 550 nm was collected. Significant bunching (g(2)(t) > 1) is observed for some emitters at intermediate delay times, indicating the participation of at least three electronic levels with different lifetimes.37 We adopt a fitting function that accounts for three levels as well as experimental nonidealities that lift the observed g(2)(0) slightly above zero: g(2)(t ) = 1 − ρ2 [(1 + a)e−|t | / τ1 − ae−|t | / τ2]
(1)
where t is the delay time, a is the photon bunching amplitude, τ1 and τ2 correspond to the lifetimes of excited states within the electronic structure of the defect at the effective pump rate determined by the excitation laser, and ρ < 1 accounts for a Poissonian background (see Materials and Methods).38 The 1 criterion to identify single emitters is g(2)(0) < 2 (1 + ρ2 a), as denoted by the dotted line in the second column of Figure 2. That criterion is independent of any background and is satisfied by at least 6 standard deviations for SE1−SE5. Best-fit values for τ1 and τ2 are given in Table 1. The short lifetimes (τ1) vary from ∼1 ns (SE4) to several nanoseconds (SE1 and SE2) and appear to roughly correlate with differences in the spectral shapes. The variation of long lifetimes (τ2) is probably influenced by a dependence on the excitation rate, but the obvious presence of metastable states with lifetimes approach3331
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Figure 4. Polarization dependence of visible emitters in suspended h-BN. (a) Color-coded image indicating the direction (color) and degree (saturation) of PL excitation polarization dependence. Arrows indicate the orientation of the excitation dipole extracted from fits to the polarization-dependent PL intensity for each spot. The h-BN crystal orientation is noted. The dotted line corresponds to the edge of the h-BN film over the suspended region. Emitters without arrows correspond to those for which excitation polarization dependence was unable to be obtained (e.g., due to rapid blinking). (b−d) Excitation dipole visibility (b), brightness (c), and orientation (d, filled circles) for the spots identified in (a). Confirmed single-photon sources are colored red, and open circles (triangles) in (d) denote their excitation (emission) dipole orientations. Separate measurements for SE1, SE3, and SE5 are included in (b) and (d). The dashed line in (b) indicates the PL background visibility. Dotted (dashed) lines in (d) denote angles parallel (perpendicular) to the h-BN ⟨112̅0⟩ axes. Inset to (d): p-value test statistic for a model of dipole alignment to h-BN crystal directions, as a function of the crystal rotation angle, θ. The dotted line and greenshaded region indicate the EBSD measurement and corresponding uncertainty of θ.
ing 1 μs indicates a potential role for spin physics and intersystem crossings in the defects’ optical dynamics. Optical Dipole Orientation. All five single emitters display polarization dependence for both the excitation absorption (black points) and emission (colored triangles), as shown in the rightmost column of Figure 2. Solid curves indicate normalized fits using the function Idip(θ) = b + A cos2 θ, where θ corresponds to either the excitation or emission polarization angle, b is the offset, and A is the amplitude. For SE2, the excitation polarization dependence differs dramatically from the usual emission pattern expected for a single dipole. Instead, it exhibits relatively little polarization contrast except in a narrow range of angles where the emission is essentially extinguished. The dotted line for the excitation polarization dependence of SE2 in Figure 2 is not a fit. Rather, it serves as a guide to the eye emphasizing this unusual behavior. SE5 exhibits similar features.26 The angle between the excitation and emission dipoles, Δθ, as determined by fits to Idip(θ), is listed in Table 1 along with the excitation visibility, Vexc = A/(2b + A). While the excitation visibilities range widely from 20% to over 80%, the polarization visibility in emission appears to be ideal for all five single emitters, within the resolution and bandwidth of our measurements.26 Unity visibility suggests that emission occurs via a single in-plane electric dipole transition. However, all emitters exhibit severely misaligned excitation and emission angles, with Δθ ranging from 30° to nearly 90°. The variations in excitation visibility and strong misalignment between absorptive and emissive dipoles could have multiple explanations. Reorientation between different atomic configurations is possible, particularly for flexible molecular structures with multiple conformations, although it seems less likely for point defects composed of a few atoms in the crystalline host to exhibit large dipole orientation shifts due to atomic reconfiguration. On the other hand, if a dipole possesses
a significant out-of-plane component, relatively small deviations could produce large apparent angular shifts in the in-plane projections we measure in this study. The presence of such canted dipoles might also explain the large variation in brightness we observe between emitters. If any such atomic reconfigurations occur, however, they must be highly reproducible in order to explain the stable, high-visibility, polarized emission from all defects we have observed. Alternatively, the presence of multiple excited states with different symmetries can mean that absorption probes a transition associated with the higher-lying state, while emission occurs only from the lower-energy state at a different polarization.39 This occurs, for example, in the case of the diamond silicon-vacancy center.40 Multiple electronic levels are also indicated by the bunching observed in photon autocorrelation measurements, discussed above, suggesting these defects exhibit a relatively complex level structure. For all confirmed single emitters, we observe that the full defect spectrum varies uniformly with excitation polarization. However, since the emission polarization dependence is measured only for a relatively narrow PL band (λPL ∈ [600 nm, 650 nm]), it may not capture energy-dependent variations in the PL polarization. Future photoluminescence excitation measurements as a function of excitation and emission energy are needed to clarify this issue. Dipole−Lattice Coupling. While only five spots in the present suspended film were sufficiently isolated and bright to confirm as single emitters via autocorrelation measurements, all spots for which g(2)(t) was recorded show evidence of antibunching. The polarization and spectral signatures of other features in Figure 1d also suggest that most spots are single emitters. Figure 4a is a composite image created from multiple spatial PL maps of a region of the suspended flake, recorded at various linear excitation polarizations between 0° and 180°. The individual images are color filtered and summed 3332
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relatively large value of p > 0.1 for some alignment angles indicates that we cannot statistically exclude lattice locking based on these observations. Moreover, the close agreement between the best-fit angle, θFit = (9. 5+2.6 −1.0)°, and the EBSDdetermined orientation, θEBSD = (7 ± 4)°, suggests that lattice locking might indeed play a role; that is, the observed alignment of some dipoles to the crystal axes might not be coincidental. This statistical analysis includes the polarization dependence of all five confirmed single emitters, since we do not have a clear justification for excluding any of them. However, their disparate spectral and temporal characteristics (Figure 2) suggest that h-BN’s visible emission might result from several different defect structures. The varied dipole orientations and (mis)alignment with the underlying lattice (Figure 4d) further support this idea. For example, SE4 and SE5 (spots 16 and 8, respectively, in Figure 2) have well-defined emission dipoles that are clearly not aligned with the crystallographic axes. This observation seems to be inconsistent with simple point-defect models such as NBVN,15 suggesting instead a role for more complex chemistries or strong structural deformations. Future studies regarding the orientation statistics of similar defects, ideally classified by their spectral and temporal emission properties, should help ascertain the nature of dipole−lattice coupling. Finally, we observe that Figure 4a hints at possible correlations between dipole orientation and defect position on the suspended h-BN membrane. Emitters near the edge of the membrane (dashed curve in Figure 4a) appear to have similar excitation dipole orientations that are generally different from emitters elsewhere in the region. These correlations might be influenced by strain variations across the suspended sample. Strain near edges has been suggested to play a role by previous reports,19−21 although we emphasize that, in contrast to some prior reports, defects in our h-BN sample are not restricted to grain boundaries or edges of the flake, but rather are distributed throughout the suspended region. In fact, all of the emitters in the suspended region of the present sample are spatially well resolved from the physical edge of the membrane, although we have also observed bright fluorescence localized along extended folds or dislocations in agreement with earlier reports (see, for example, Figure 1c).
such that the resulting color, value, and saturation correspond to excitation dipole orientation, visibility, and PL brightness, respectively.41 Such images are helpful in identifying candidate single emitters based on their visibility and brightness. To quantify the polarization measurements in Figure 4a, we fit each PL image to a set of 2D Gaussian peaks to extract the amplitude of each identifiable spot and then fit each spot’s intensity variation to the dipole formula Idip(θ). The best-fit visibility, peak brightness, and excitation dipole angle for 19 isolated spots in Figure 4a are plotted in Figure 4b−d, and the excitation dipole angles are superimposed as arrows in Figure 4a. SE1, SE3, and SE5 do not appear in Figure 4a, but separate measurements of visibility and dipole orientation are included in Figure 4b,d (the brightness is not comparable since these measurements were acquired under different illumination conditions). Figure 4b,c highlight the significant variation in both the visibility and brightness of emitters in free-standing hBN. Notably, this variation extends to the confirmed singlephoton emitters (red bars) as well. All emitters in Figure 4 originate from the same suspended flake of single-crystal h-BN, which presents an opportunity to look for correlations between the observed dipole orientations and the host’s crystallographic axes. Such alignments are generally expected for simple native defects (e.g., vacancies, substitutional atoms, and their binary complexes) based on group theory considerations. The in-plane orientation of the flake’s crystallographic axes, determined using electron backscatter diffraction (EBSD),26 is plotted in Figure 4a. The vectors {a1, a2, a3} are parallel to the equivalent ⟨112̅0⟩ hexagonal lattice vectors, corresponding to bonds connecting in-plane B and N atoms in h-BN. By symmetry, undistorted mono- or diatomic defects can give rise to electric dipole matrix elements parallel or perpendicular to these crystallographic axes. Furthermore, the typical AA′ stacking of multilayer hBN42 entails a 60° rotation between alternate layers. This means that the allowed orientations for in-plane dipoles of simple defects in single-crystal h-BN should be spaced at 30° increments. Those possible orientations are indicated in Figure 4d by dashed and dotted lines. A cursory examination of the data does not reveal any obvious correlation between the observed dipole angles and primitive crystallographic vectors. Rather, the dipoles appear to be nearly uniformly distributed at random angles, and those of some confirmed single emitters are clearly not aligned to the lattice vectors. Nonetheless, a statistical analysis of these data does provide tentative evidence for dipole−lattice alignment, at least for a subset of the observations. The inset to Figure 4d plots the p-value test statistic corresponding to a lattice-locking model in which each dipole is assumed to align along or orthogonal to the nearest allowed lattice vector (spaced with a 30° period), as a function of the crystal rotation angle, θ. In calculating the χ2 fit statistic, we retain the excitation and emission dipoles of all confirmed single emitters, but for each crystal orientation we exclude from the 15 observations of unconfirmed spots a subset that exhibit the worst alignment (five are excluded in the case of Figure 4d), on the basis that they could be overlapping defects. Further details on the model and statistical analysis are provided in the Supporting Information.26 The p-value calculated from χ2 is interpreted as the probability that a random sample of observations derived from our model would exhibit misalignment angles equal to or worse than the data. The fact that the p-value rises to a
CONCLUSION H-BN offers a rich assortment of single-photon sources whose physics can be explored and harnessed. Electron irradiation and annealing of thin films exfoliated from bulk single-crystal h-BN result in bright and stable visible single-photon emission. However, even within a single-crystal membrane free from substrate interactions, the emitters exhibit marked variation in their optical signatures. Taken together, the absence of a clear lattice−dipole correlation as well as strong qualitative variations in spectral, temporal, and spatial emission characteristics indicates that h-BN’s visible single-photon emission results from a heterogeneous class of defect structures. We hope this work will serve as a framework for future measurements, analyses, and theoretical predictions regarding this fascinating class of quantum emitters. As a key building block in functional van der Waals materials, the availability of stable, highly localized, optically addressable electronic states in h-BN offers exciting opportunities for quantum science and engineering, where the integration of single-photon sources in 2D materials can enable additional functionalities. 3333
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where In = I1 ⊗ In−1 are the normalized n-phonon probability distributions. At finite temperatures, the 1-phonon distribution is defined in terms of an underlying distribution function describing the electron−phonon coupling for phonon energy E, S(E), and the Bose− Einstein phonon distribution function, n(E, T) = 1/(eE/kT − 1), in a piecewise fashion as
MATERIALS AND METHODS Sample Preparation and Characterization. Our samples consist of single-crystal h-BN (HQ Graphene) that is mechanically exfoliated43 onto patterned Si substrates capped with a 90 nm layer of thermal oxide chosen for optimal contrast in bright-field optical microscopy.44 Holes are created in the support wafer by optical lithography followed by dry etching. The process results in three distinct regions of the patterned substrate: Si/SiO2, free-standing SiO2, and etched holes several micrometers wide and ∼5 μm deep. Exfoliated h-BN flakes are typically ∼1000 μm2 in area and extend over all three regions. We confirm that the exfoliated h-BN maintains the single-crystallinity of its parent crystal45 using EBSD imaging, which additionally determines the in-plane crystallographic orientation of exfoliated flakes. Film thickness is determined using atomic force microscopy; the flake studied here is 150 nm thick in the vicinity of the suspended region. Raman spectroscopy confirms that this flake exhibits bulk behavior, as expected for a membrane containing several hundred atomic layers.46 Exfoliated samples are cleaned using an O2 plasma treatment, exposed to electron irradiation in a scanning electron microscope, and annealed in an argon atmosphere. Additional details regarding the sample treatment and characterization can be found in the Supporting Information.26 Experimental Design. A home-built confocal scanning fluorescence microscope is used to acquire PL images, spectra, and photon emission statistics, where the collected PL is directed either to a pair of silicon single-photon avalanche diodes or to a spectrometer. Finite-Temperature Phonon Sideband Analysis. Measured PL spectra as a function of wavelength are corrected for the photon detection efficiency of our confocal setup (determined by observing a calibrated light source in place of the sample) and binned to obtain the spectral distribution function (S(λ)). Next, we calculate the distributions S(E) and L(E), where
S(E) = S(λ)(hc /E2) accounts for
dλ dE
=
hc E2
⎧ for E > 0 ⎪ I1(E) = A[n(E , T ) + 1]S(E) ⎨ ⎪ ⎩ I1(E) = An(− E , T )S(− E) for E < 0
where A is a normalization constant. S(E) is defined for energies E ∈ [0, Emax], where Emax is typically the maximum phonon energy, which, in h-BN, is ∼200 meV.35 We use a Lorentzian line shape to model the room-temperature ZPL since weak intralayer coupling in h-BN means that thermal broadening effects should dominate.32,35,47 We apply the model to analyze the spectra for SE1, SE2, and SE5, for which the ZPL can be clearly identified. Fits have the following free parameters: SHR, the FWHM of the Lorentzian line shape for the ZPL (ΓZPL), the ZPL energy (EZPL), and the phonon spectral function S(E), which is parametrized by discrete values at energies
{
dE 3dE , 2 , 2
..., Emax −
dE 2
},
for some energy resolution, dE. Fits in
this work are performed with dE = 5 meV. Note that S(0) = 0 is required in order to yield a finite value for I1(0), and S(E) is constrained to be linear with E for E < 25 meV. Additional details regarding the necessity and choice of constraints for fitting and full emission line shapes for SE1, SE2, and SE5 can be found in the Supporting Information.26 Autocorrelation Analysis. The second-order autocorrelation function is given by (2) (τ ) = g ideal
(2)
⟨I(t ) I(t + τ )⟩ ⟨I(t )⟩2
(7)
A single-photon source is characterized by the limiting cases g(2)(0) = 0 (only one detector can observe a single photon at the same time) and g(2)(∞) = 1 (uncorrelated Poissonian counts). However, the presence of a Poissonian background (e.g., laser scatter or diffuse PL) results in a measured value of g(2)(0) > 0 even for a single emitter. Assuming a steady-state count rate, S, from the emitter on top of a Poissonian background, B, the measured autocorrelation function is38
and corresponds to the underlying spectral
probability distribution function of emitting phonons with energy E and L(E) = S(E)/E3
(6)
(3) 3
is the spectral line shape which accounts for the E energy dependence due to spontaneous emission. Only the function L(E) can be directly compared with the predictions of the Huang−Rhys theory, developed below. In the conversions between different spectral functions, we propagate experimental uncertainties associated with photon shot noise, background noise in the CCD detector, and long-time fluctuations observed in the spectral shape between exposures. The combined effects of applying calibration corrections for the wavelength-dependent quantum efficiency of our setup together with the line shape conversions tend to amplify the noise at longer wavelengths. To compensate for this, we adjust the binning as a function of wavelength to yield approximately uniform uncertainty for each data point. Following the theory developed by Maradudin31 and applied extensively to diamond defects by Davies,32 the predicted spectral line shape as a function of lattice energy, E, is modeled by
L(E) = e−SHR I0(E) + I0(E) ⊗ IPSB(E)
(2) (2) gmeasured (t ) = 1 − ρ2 + ρ2 g ideal (t )
where ρ = S/(S + B) and the limiting cases are g (0) = 1 − ρ and g(2)(∞) = 1. Note that, as defined, this expression does not take into account the instrument response of the single-photon counters, which can also increase the observed value of g(2)(0). For a two-level system, the ideal autocorrelation function is (2) g ideal (t ) = 1 − e−|t | / τ
∑ e−SHR n
n SHR In(E) n!
2
(9)
where τ = 1/(Γ + Wp), Γ is the spontaneous decay rate, and Wp is the effective pump rate.48 In the limit that Γ ≫ Wp, τ corresponds to the excited-state lifetime. The autocorrelation measurements taken for the single emitters presented here are performed at the same power. However, because τ is pump-power-dependent, the decay times determined through fits to the autocorrelation data may not correspond exactly to the excited-state lifetimes. Two-level fits to measured autocorrelation data are performed using the following fit function:
(4)
where SHR is the Huang−Rhys factor, I0(E) is the normalized ZPL line shape, and IPSB is the predicted PSB when the broadening of the ZPL is neglected. The convolution with I0(E) accounts approximately for both of these effects.32 The PSB can be divided into contributions involving integer numbers of phonons:
IPSB(E) =
(8) (2)
(2) gmeasured (t ) = A(1 − ρ2 e−|t − t0| / τ )
(10)
where t0 is the zero delay offset and A is the uncorrelated amplitude, i.e., the steady-state number of counts as t → ∞. Normalizing the data by A gives the same limiting cases as in eq 8. Data for which bunching is observed is fit using a three-level model: (2) gmeasured (t ) = A{1 − ρ2 [(1 + a)e−|t − t0| / τ1 − ae−|t − t0| / τ2]}
(5) 3334
(11)
DOI: 10.1021/acsnano.7b00665 ACS Nano 2017, 11, 3328−3336
Article
ACS Nano where τ1 and τ2 are the short and long decay times and a is the associated population weight. Again, the measured time scales depend on both intrinsic lifetimes of the participating electronic states and the optical pumping rate. The oft-quoted criterion for a single emitter in a two-level system is g(2)(0) < 0.5, but this is insufficient proof for a system exhibiting bunching (e.g., for a three-level system), where the normalized amplitude at short delays can be >1. In that case, the g(2)(0) threshold for a single emitter is half of the maximum bunched amplitude, which is given by the limit of eq 11 as τ1 → 0 and t → 0: (2) gmaximum = 1 + ρ2 a bunching
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(12)
For a three-level system therefore, the generalized requirement is that 1 g(2)(0) < 2 (1 + ρ2 a). In the case of an autocorrelation measurement fit to a two-level function, a = 0 and the expression reduces to the usual limit of 0.5.
ASSOCIATED CONTENT S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.7b00665. Details on the experimental layout, sample processing, defect creation, sample characterization, substrate interactions, additional single-emitter characterization, singleemitter locations, emitter stability, statistical analysis of the dipole orientation, and finite-temperature phonon sideband analysis (PDF)
AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. ORCID
Annemarie L. Exarhos: 0000-0003-3026-7737 David A. Hopper: 0000-0003-1965-690X Audrius Alkauskas: 0000-0002-4228-6612 Lee C. Bassett: 0000-0001-8729-1530 Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS The authors thank K. Oser for assistance in sample preparation, J. Ford for help with EBSD measurements, and M. Mackoit and M. W. Doherty for useful discussions. This work was supported by the Army Research Office (W911NF-15-1-0589) and NSF MRSEC (DMR-1120901). A.A. acknowledges a grant (No. MERA.NET-1/2015) from the Research Council of Lithuania. REFERENCES (1) Awschalom, D. D.; Bassett, L. C.; Dzurak, A. S.; Hu, E. L.; Petta, J. R. Quantum Spintronics: Engineering and Manipulating Atom-Like Spins in Semiconductors. Science 2013, 339, 1174−1179. (2) Heremans, F. J.; Yale, C. G.; Awschalom, D. D. Control of Spin Defects in Wide-Bandgap Semiconductors for Quantum Technologies. Proc. IEEE 2016, 104, 1−15. (3) Gao, W. B.; Imamoglu, A.; Bernien, H.; Hanson, R. Coherent Manipulation, Measurement and Entanglement of Individual SolidState Spins Using Optical Fields. Nat. Photonics 2015, 9, 363−373. (4) Schirhagl, R.; Chang, K.; Loretz, M.; Degen, C. L. NitrogenVacancy Centers in Diamond: Nanoscale Sensors for Physics and Biology. Annu. Rev. Phys. Chem. 2014, 65, 83−105. (5) Doherty, M. W.; Manson, N. B.; Delaney, P.; Jelezko, F.; Wrachtrup, J.; Hollenberg, L. C. The Nitrogen-Vacancy Colour Centre in Diamond. Phys. Rep. 2013, 528, 1−45. 3335
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