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Part of Topical Section on Fundamentals and Applications of Diamond and Nanocarbons

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Phys. Status Solidi A, 1–6 (2013) / DOI 10.1002/pssa.201300044

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Spatially and spectrally resolved cathodoluminescence with fast electrons: A tool for background subtraction in luminescence intensity second-order correlation measurements applied to subwavelength inhomogeneous diamond nanocrystals Luiz Henrique Galvão Tizei*,1, Sophie Meuret1, Sounderya Nagarajan1, François Treussart2,3, Chia-Yi Fang4, Huan-Cheng Chang4, and Mathieu Kociak*,1 1

Laboratoire de Physique des Solides, Université Paris-Sud, CNRS-UMR 8502, Orsay 91405, France Laboratoire Aimé Cotton, CNRS UPR 3321, Université Paris Sud, Orsay 91405, France 3 Ecole Normale Supérieure de Cachan, Cachan 94235, France 4 Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 106, Taiwan 2

Received 1 April 2013, revised 18 May 2013, accepted 23 May 2013 Published online 5 August 2013 Keywords cathodoluminescence, diamond, electron microscopy, fast electrons, quantum optics * Corresponding

authors: e-mail [email protected], [email protected], Phone: þ33 169155361, Fax:þ33 169158004

Measurements of the photon second-order correlation function, g(2)(t), is a common tool for the characterization of single photon emitters, like nitrogen-vacancy color centers in diamond. Such measurement requires background photoluminescence correction, which is easy when this background is homogeneous on a few wavelengths scale. However, if the sample contains emitting centers separated by a distance smaller than the optical diffraction limit, and having different and overlapping emission, these background correction techniques cannot be applied. We have recently shown that

cathodoluminescence (CL) can be used to measure g(2)(t) at the subwavelength scale. Here we propose a method, based on spatially and spectrally resolved CL, to subtract the background taking into account the nanometer spatial distribution of the emitted light. To this end, a nanometer-resolved spectrum image is acquired on the same region where the g(2)(t) is measured. As an example, we show the use of this method to the subtraction of the H3 background signal from a g(2)(t) measurement done on NV0 color centers.

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1 Introduction Color centers, such as the H3, a defect consisting in two nitrogen atoms in substitution and one vacancy, or the nitrogen-vacancy (NV) center – a substitutional nitrogen near a carbon vacancy – dominate the visible range optical properties of diamond. Some, of them – in particular the two charge states of NV centers, namely, the neutral (NV0) and negatively charged (NV) – are attracting a large attention. Indeed, among other properties, they are also perfectly stable single photon emitters, a property that finds applications in the domain of quantum information. Second order correlation function, g(2)(t), measurements are routinely used to demonstrate non-classical properties of

light. These measurements are mostly done with photoluminescence (PL) in a confocal microscope [1], or in some cases electroluminescence [2, 3]. More recently, we have demonstrated the possibility of measuring g(2)(t) using cathodoluminescence (CL, [4]) in a scanning transmission electron microscope (STEM). For example, g(2)(t) measurements allow the detection of single photon emission [1] or the presence of macroscopic correlation in bosonic systems [5]. The g(2)(t) function is defined by gð2Þ ðtÞ ¼

hIðtÞIðt þ tÞi hIðtÞi2

;

ð1Þ

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where I(t) is the light intensity at time t. In practice we measure the histogram of the delay t between two consecutively detected photons, which represents the numerator of (1), and we normalize it with the mean intensity to obtain g(2)(t). With respect to first order measurement (like integrated intensity or spectrum measurements), g(2)(t) measurements have a specific drawback when dealing with low intensity light source, such as the single photon emitters: (1) the acquisition time of the histogram of delays decreases with the square of the intensity and (2) the background degrades the signal faster than in a linear system. To reduce the acquisition time we need a high collection and detection efficiencies. This depends of course on the experimental setup and can, in principle, be optimized to allow sufficiently fast experiments. However, the stability of the emitter has also to be considered. The high photostability and thus the possibility of long counting time experiments is a reason for the success of diamond NV color centers. On the other hand, the second point is fundamentally linked to the object being probed in a well-designed experimental setup, where all other sources of light are suppressed, and the detector dark and readout noises are made vanishingly small. In such conditions, any background light detected will come from the sample. The background signal is produced by other emitting centers, unwanted fluorescent pollution in the vicinity of the single photon emitters, or the substrate. Evidently, knowledge of the background count rate, Ic(t), would allow to subtract its uncorrelated contribution from the total signal, leading to a quantitative correction of g(2)(t) [6]. The problem is reduced to the measurement of Ic(t). In an optical confocal microscopy experiment, this is usually achieved by measuring the count rate on the same sample at different locations, separated by at least a few times the laser spot diameter. The hypothesis here is that Ic(t) is homogeneous on the sample, ruling out the possibility of correcting background effects in inhomogeneous samples. Particularly, in samples that are intrinsically smaller than a diffraction limited laser spot, such as nanoparticles, a quantitative subtraction without hypothesis is difficult. For example, a nanoparticle may contain other luminescence centers in addition to the one of interest. Here we propose a different approach to circumvent this issue based on the recently demonstrated use of CL for subwavelength measurement of g(2)(t) [7]. In this experiment, we use a 1 nm wide focused fast electron beam (i.e., electrons with high energy, usually on the 60–100 keV range), to excite the material instead of a laser beam. The main idea is to take advantage of the high spatial resolution allowed by this technique to measure on the same nanoobject the g(2)(t) function (at one or more positions) and the spatial distribution of the spectral signature of the emitted light, and to use this information to correct the signal for the background. In addition, nanometer-resolved TEM images of the sample can be acquired, allowing the precise positioning of the electron beam to excite, for example, a small region where the signal of interest is maximal even in a highly heterogeneous object. ß 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

As a proof of principle, we have analyzed the influence of a H3 background emission on the measurement of g(2)(t) for NV0 in diamond nanoparticles and the efficiency of our method. In itself, this particular background signal (H3) appears because of the broadband excitation nature of an electron. However, it is also the broadband characteristics and the spatial resolution intrinsic to electrons that allow this background subtraction afterwards. 2 Experimental setup The experiments described here have been performed on a VG HB 501 scanning transmission electron microscope (STEM) that can be operated between 40 and 100 keV. The results shown here were acquired at 60 keV unless otherwise stated. Routinely, a 1 nm electron beam can be formed on this system having typical current ranging from 0.1 pA up to 1 nA. This focused probe of fast electrons has been used to excite diamond nanoparticles containing different color centers (blue band, H3, NV0, 1.40 eV centers [8]). The sample was kept at a temperature of approximately 150 K during experiments. The light emitted from the nanoparticles has been collected using a cathodoluminescence system (nanoCL, Fig. 1, [9]) build in-house. This system has been optimized to have maximum throughput [9], allowing the detection of single photon emitters in diamond [7, 10]. g(2)(t) measurements have been performed using a standard Hanbury Brown and Twiss (HBT) intensity interferometer fitted to the output of the nanoCL system. The light sent to the interferometer was filtered by a band pass filter in the wavelength range 570–720 nm. Two diamond samples have been used. The first sample used was micrometer size diamond crystals (Sigma–Aldrich, USA) which have been crushed by a mortar and pestle to reduce their size (down to the 100 nm range). Sample #1 contains different color centers, in particular H3 and NV0, and has been used for the g(2)(t) measurements. Sample #2 consists of diamond nanocrystals specifically prepared from type 1b diamond to contain mostly NV color centers [11]. Similarly, sample #3 is prepared from type Ia diamond nanocrystals to contain mostly H3 color centers [12]. Both samples were produced by 40-keV Heþ irradiation of diamond powders (Microdiamant) followed by thermal annealing at 800 8C. Sample #3 was used as a H3 CL emission reference to validate our model of the H3 emission to be used for background subtraction in sample #1. All sample powders were suspended in water and dispersed on a lacey carbon film held on top of a copper grid. For the spectrum measurements we have used an optical spectrometer equipped with diffraction gratings that allow a wavelength dispersion of 0.34 nm pixel1. Spectra have been acquired using a high quantum efficiency charge coupled device array detector. Spatially resolved spectral information is acquired as spectrum images. That is, the electron beam is scanned over a given sample area in a 2D array of pixels. At each pixel the electron beam is maintained fixed for an exposure time of a few hundred milliseconds, during which a spectrum is acquired. The end result is a 3D www.pss-a.com

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Figure 1 Sketches showing the electron microscope, the cathodoluminescence collection system (a) and the HBT interferometer (b). (c) Annular Dark Field (ADF) image of a diamond nanocrystal from sample #1, which allows the precise positioning of the electron beam within the nanoparticle.

data cube, or otherwise speaking, a 2D image in which each pixel contains a spectrum [13]. Finally, the spatial resolution achievable with a 1 nm wide focused fast electron probe is a key advantage, allowing for the detection of the light emitted by single particles, even if they are in close proximity. In Fig. 2, we show a color coded image of a mixture of samples #2 and #3 containing particles with either NV0 (red) or H3 (green) defects (spectrum c and d, respectively). The intensity of each color is proportional to the intensity of the luminescence at that pixel. Clearly, approximately 100 nm sized particles in close proximity can be discriminated based on their spectral signature. This possibility is crucial for the background subtraction method proposed.

3 Typical spectroscopic results Cathodoluminescence is a versatile broadband technique which allows the excitation of emitters with CL emission from the near ultraviolet (UV) to near infrared range. In the case of diamond, this allows one to obtain precise information on the near-band edge (NBE) emission although it lies in the UV range [14]. Another interesting advantage is that different color center species in diamond can be detected in the same experiment depending on the detection apparatus [10, 15, 16]. Specifically for this experiment, we are interested in H3 and NV0 emissions as observed in Fig. 3a. One can see that the H3 emission tail acts as a background to the NV0 signal in the spectral window collected for the g(2)(t) measurements (between dotted vertical lines). Such background impacts the g(2)(t) measurement. In particular, it limits the antibunching at zero delay for single photon emitters. However, within certain limits, if the background can be properly quantified, its effect can be subtracted from the g(2)(t) curves. We define the signal to background ratio (SBR) by SBR ¼

Figure 2 Mixture of sample #2 and sample #3 containing diamond nanoparticles with either NV0 or H3 centers. (a) ADF image of this mixture. (b) Color coded intensity map of the NV0 (red) and H3 (green) nanoparticles. Note that even in close proximity, the particles origin (sample #2 or #3) can be unambiguously assessed. (c) and (d) Typical spectra for particles containing NV0 or H3 centers, respectively. www.pss-a.com

I NV0 ; I NV0 þ I H3

ð2Þ

where I NV0 and IH3 are the integrated intensities in the g(2)(t) measurements spectral window of the NV0 and the H3 signals, respectively. We have used an exponential function as a model of H3 emission background tail (Fig. 3b). To ensure the reproducibility of the fit, we have measured it on seven nanoparticles containing only H3 emission. Although not supported by any theoretical statement, Fig. 3b demonstrates that the exponential fit is a good model for H3 emission background. Despite the fact that background removal techniques are not widely applied in CL, they are widespread and mature in a related spectroscopy technique using fast electrons, namely the electron energy loss spectrum, where they are used routinely to treat spectral images often relying on ad hoc background functions [17]. ß 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

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Figure 3 (a) H3 and NV0 signal from a sample #1 single diamond nanoparticle (inset shows the NV0 signal after background subtraction). The dotted lines indicate the wavelength range, 570–720 nm, defined by filters and used for the HBT experiments. The different colored curves show the fit to the background (red) and the range of confidence of the fit (blue and green). The signal to background ratio is 0.74 for this spectrum, with a one sigma confidence interval between 0.69 and 0.78. (b) H3 signal from a different diamond nanoparticle used to validate the exponential model used for the background subtraction.

Figure 4 displays an analysis of the signal to background ratio of the emitted light from a single nanoparticle. Figure 4b shows the intensity of the NV0 intensity as a function of the position (after H3 background subtraction). This intensity is extracted from a multiple linear square fit analysis. The square in Fig. 4b indicates the position of the electron beam where the g(2)(t) curve displayed in Fig. 5 was measured. This position was optimized to correspond to NV0 maximal intensity. Figure 4c shows the SBR map inferred from Eq. (2). This analysis allows us to use the SBR at the precise position where the g(2)(t) measurement is performed, so that g(2)(t) can be background corrected following Brouri et al. [6] procedure: ð2Þ gcorr ðtÞ ¼ ½C N ðtÞ  ð1  SBR2 Þ=SBR2 , where CN(t) is the number of coincidence counts at delay t, after its normalization to 1 at long delays (longer than 300 ns) and SBR is the signal to background ratio defined in Eq. (2). Note that the analysis relies on the fact that the H3 center photons come from multiple centers and their time distribution follows a poissonian statistics [6]. The g(2)(t) was measured in a single diamond nanoparticle of size 370 nm  180 nm. During the

With this information we have returned to the spectra containing H3 and NV0 emission to estimate the contribution of H3 emission to the total detected intensity. Considering the fit parameters obtained from an interpolation of the H3 signal (between the decay between 520 and 550 nm and the flat region above 750 nm). We have estimated the contribution of the H3 emission to be 26% of the total intensity I NV0 þ I H3 , thus a SBR ¼ 0.74. Considering the error on the fit coefficients of H3 emission tail, this contribution is between 21% (SBR ¼ 0.79) and 31% (SBR ¼ 0.69), validating this fitting procedure as a good tool to estimate the background for this system in particular. 4 Background subtraction using spectrum images One of the great advantages of spectroscopy techniques that use nanometer focused fast electron probes is the possibility to acquire spectrum images [13, 17, 18], as the desired signal can be recorded with nanometric spatial resolution. The availability of correlated spatial and spectral information allows the comprehension and discrimination of effects which would be hardly deciphered with only point spectra coupled to images. This same benefit can be used in cathodoluminescence with fast electrons [9, 10] and, particularly, to determine the spectral signature at the position where the g(2)(t) is measured. ß 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Figure 4 (a) Annular dark field image of the diamond particle where the g(2)(t) measurement of Fig. 5 was performed. The electron beam is continuously raster scan within the drawn square. The contour of the particle is also sketched in white and reproduced in the other panel for comparison. (b) Weight of the NV0 signal to the overall spectrum (retrieved from a multiple linear square fit). (c) Map of the SBR ratio as defined by Eq. (2). www.pss-a.com

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Finally, recent experiments with our setup show that depending on experimental conditions the antibunching dip may not depend only on the number of centers and may change, depending on electron beam current, density of centers and sample thickness [20]. For this reason we do not link the depth of the antibunching dip to the number of centers. The discussion of this effect is beyond the scope of the article and will be presented elsewhere [20].

Figure 5 Second order correlation function g (t) measurement. The black curve corresponds to the fit of the non-processed g(2)(t) (data not shown) by the exponential function (3) leading to a zero delay antibunching dip g(2)(0) ¼ 0.90. The red curve is a fit to the background subtracted data inferred from the spectrum image of Fig. 4b, and shown as a dotted gray curve, having a zero delay dip g(2)(0) ¼ 0.81. The green and blue curves show the confidence interval. (2)

acquisition, the electron beam was kept scanning a region 42 nm  48 nm wide (rectangle in Fig. 4). The total acquisition time was 260 s. The background subtracted experimental data is shown in gray in Fig. 5. To measure the depth of the antibunching dip we have fit the curve with an exponential model: ( 1  g eðtt0 Þ=trad if t  0; ð2Þ ð3Þ g ðtÞ ¼ 1  g eþðtt0 Þ=trad if t < 0; where g is the antibunching dip, t is the time delay, t0 is the zero time reference and is the radiative lifetime (we used the simplest model to the g(2)(t) function, as the available data does not allows us to discriminate between it and others, such as the one proposed in Ref. [3]). A fit by this function of the non processed data results in g(2)(0) ¼ 0.9 (which is shown in black in Fig. 5). For this curve trad ¼ 34  4 ns, which is consistent with previous measurements in nanodiamond [19]. However, the emission spectrum of Fig. 3a shows that in the wavelength integration window used for the intensity correlation measurement we have a nonnegligible contribution of H3 color centers emission. Using the exponential model described in Section 4 we have estimated this H3 emission background to represent 26  5% of the total intensity. Considering this background estimate, we can subtract its contribution from the measurement. This subtraction, along with the confidence limits, is shown in Fig. 5 (red, green, and blue curves, respectively). The background subtracted data fit gives g(2)(0) ¼ 0.81. The confidence interval of this fit to the treated data is represented by the blue and green curves in Fig. 5, which result in g(2)(0) ¼ 0.78 and g(2)(0) ¼ 0.83, respectively (calculated based on the uncertainty on the H3 background fit).

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5 Conclusions Here we have described an alternative method to estimate the contribution of different spectral emission to g(2)(t) measurements using combined CL and spectrum imaging. The main idea is to take advantage of the high spatial resolution provided by 1 nm wide focused electron beam excitation to properly estimate this contribution. Moreover, high spatial resolution allows the excitation of a subwavelength region where the emission of the signal of interest is maximal, even in a highly heterogeneous sample (Fig. 4). As an example, we have described the case of H3 centers acting as a background to NV0 emission in single diamond nanocrystals. A well adapted model to the H3 center emission allowed us to estimate the contribution of its emission at the position of the g(2)(t) measurement, allowing a justified subtraction. The extension to other types of background light and single photon centers in diamond should be straightforward, as well as the use of this background removal technique in other systems. Acknowledgements This work has received support from the National Agency of Research under the program of future investment TEMPOS/CHROMATEM with the Reference No. ANR-10-EQPX-50. This work has received support from the French “Investment for the Future” program under the project NanoSaclay Laboratory of Excellence. The research leading to these results has received funding from the European Union Seventh Framework Programme [No. FP7/2007-2013] under Grant Agreement No. N312483 (ESTEEM2). S. M. acknowledges the financial support from the French Ministry of Defense through a grant from the Direction Générale de l’Armement (DGA).

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