Letter pubs.acs.org/journal/apchd5
Lifetime Measurements Well below the Optical Diffraction Limit Sophie Meuret,† Luiz H. G. Tizei,† Thomas Auzelle,‡,§ Rudee Songmuang,‡,⊥ Bruno Daudin,‡,§ Bruno Gayral,‡,§ and Mathieu Kociak*,† †
Laboratoire de Physique des Solides, Université Paris-Sud, CNRS-UMR 8502, Orsay 91405, France Université Grenoble Alpes, F-38000 Grenoble, France § CEA, INAC-PHELIQS, “Nanophysique et semiconducteurs group”, F-38000 Grenoble, France ⊥ CNRS, Institut Néel, F-38000 Grenoble, France ‡
S Supporting Information *
ABSTRACT: The dependence of excited electron−hole state properties on the size of their host semiconducting nanostructures is the seed for a plethora of applications such as light-emitting diodes (LEDs) and photovoltaic cells. However, the inability of state-of-the art, diffractionlimited optical techniques to probe lifetime variations at the scale of individual quantum emitters precludes the full understanding of the nanostructures’ optical properties. Here, we demonstrate the measurement of the individual lifetimes of quantum emitters a few angströms thick separated by only a few nanometers, lifting the ambiguities usually faced by diffraction-limited techniques. This relies on the ability to monitor with subnanometer precision a fast electron beam that triggers extremely localized cathodoluminescence signals further analyzed through intensity interferometry (spatially resolved time-correlated cathodoluminescence, SRTC-CL). We demonstrate SRTC-CL to be a true nanometer counterpart of time-resolved photoluminescence, opening the way for a deeper understanding of suboptical wavelength objects such as biomarkers, quantum heterostructures, active parts of LEDs, or quantum optics devices. KEYWORDS: lifetime measurement, cathodoluminescence, STEM, intensity interferometry, time-resolved cathodoluminescence, III−V, quantum wells
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discovered, is that the very tip used for the near-field measurement influences strongly the value of the lifetime.6 Such a near-field effect, at the heart of nano-optics, can be usefully exploited in many situations, such as for mapping the local density of electromagnetic states.7 Another approach is to use electrons, rather than photons, to excite the objects of interest. Indeed, cathodoluminescence (CL), in particular in the scanning transmission electron microscope (STEM), has proved to be a relevant tool for the study of various emitters in semiconductors with an ultimate resolution of ca. 5 nm.5,8−10 Therefore, it showed that despite its weaknesses, such as vacuum requirements, relative lack of flexibility, potential electron beam damages, or increased costliness to name a few, CL has clear advantages over PL in terms of spatial resolution. When it comes to the measurement of lifetimes, the gain in spatial resolution in using time-resolved CL (TR-CL) rather than time-resolved PL (TR-PL) is less obvious. The main problem in using TR-CL lies in the difficulty in providing a high-brightness electron gun that can be pulsed in order to reproduce with electrons what is commonly done
he electron−hole (eh) excited-state deexcitation governs the optical properties of semiconductors. The physical properties of these eh states, specifically their emission energy and lifetime, depend on various parameters. These can be the size of the confining potential in the case of quantum wells (QW) or quantum dots (QDots),1,2 the presence of an electrical field in the case of the quantum-confined Stark effect (QCSE) or spectral diffusion,2,3 the type of defects in singlephoton emitters, or the presence of surface states in the vicinity of a particular emitter, to name a few. Whichever the parameters, a very small variation can lead to dramatic changes; see, for example, the atomic-scale dependence of GaN QDots or QW emission energy on their thickness.4,5 Therefore, all applications, from LEDs to quantum optics or biomarkers, rely on the understanding and monitoring of structures that can be as small as an atom and separated by only a few nanometers. Characterization techniques providing lifetime measurements at the nanometer scale and furnishing structural and morphological information on the same object are thus required. An optical technique combining the performances of photoluminescence (PL) in terms of spectral and temporal resolutions and near-field techniques in terms of spatial resolution would be ideal. One of the main disadvantages of such a near-field time-resolved approach, as was quickly © XXXX American Chemical Society
Received: March 25, 2016
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Figure 1. Combined lifetime, spectral, and structural measurement. (a) Sketch of the experiment illustrated here on an AlN nanowire (hexagonal cylinder in the sketch) embedding GaN QDiscs (red and white sections in the sketch). An electron probe (e−) passes through the sample. Background-subtracted EEL spectra (bottom) containing chemical information can be obtained by measuring inelastic scattered electrons. Emitted photons are collected by a mirror (M) and sent to either an intensity interferometer or an optical spectrometer (not shown). The intensity interferometer (see Methods) is essentially made up of a beam splitter (BS) splitting the beam along two paths ending with two photomultipliers (PM). The signals from the two PMs are time-correlated to produce the g(2)(τ) function. τe is quantified by fitting g(2)(τ) with an exponential (right inset). (b) Alternatively, an optical spectrum can be measured from the same area, and spectral images can be obtained by scanning the probe (not shown). (c) Energy-filtered CL image of the AlN NW containing GaN QDiscs from which the g(2)(τ) and the spectrum in (a) and (b) have been measured. (d) HAADF image of the same AlN NW acquired with a higher spatial resolution microscope. GaN base and QDiscs appear white; AlN appears dark. (e) High-resolution HAADF image of the area from which the g(2)(τ) and the spectrum in (a) and (b) have been measured. Such highresolution imaging allows one to access structural parameters of the sample. Scale bars are 20 nm in (c) and (d) and 1 nm in (e). (d), (e) and (c) were acquired on the same NW in two different microscopes.
with photons in TR-PL. The gun brightness is defined as the current per unit of area and solid angle, and it is a quantity that is conserved in an S(T)EM for angles small enough to avoid geometric aberrations and consequent beam broadening. Thus, it basically determines the maximum available current density for achievable probe sizes. It is therefore difficult to reduce the size of the beam without compromising signal-to-noise ratio. Nevertheless, TR-CL has proved to be a very useful technique when trying to access time-dependent information at high spatial resolution scales. In their pioneering work,11 using a beam-blanking system, Grundmann et al. demonstrated the possibility of mapping the excitonic lifetime changes around dislocations in GaAs/InGaAs/GaAs heterostructures. Later, Merano et al.12 used a laser-pulsed electron gun to study the charge carrier recombination dynamics of InGaAs/AlGaAs quantum structures. In this work, not only lifetimes but also the full dynamics of charge carrier recombination is tracked with high spatial resolution. However, despite remarkable advances in the design of pulsed guns,13 demonstrating that relevant physics such as local band gap variations under strain gradients and related exciton diffusion can be tracked using TR-CL,14 the goal of lifetime measurement at the scale of individual quantum emitters has remained elusive. In this Letter, we use a completely different approach to measure lifetimes of quantum emitters with sub-15 nm spatial
resolution. This approach exploits the measurement of time correlations in the CL signal15,16 as a function of the position of the electron beam of an STEM (spatially resolved timecorrelated CL, SRTC-CL). We demonstrate the combined measurement of the structure, emission energy, and lifetimes of atomically thin GaN quantum discs separated by less than 15 nm in an AlN nanowire matrix. We show that lifetimes measured in SRTC-CL are identical to those measured in TRPL, based on a statistical study of the same samples with the two different techniques. We then apply SRTC-CL to a specific example of distorted quantum emitter for which all the information (structure, morphology, emission energy, lifetime) is used to lift ambiguities that would have arisen from the use of state-of-the-art optical techniques. Fast electrons (accelerated typically to more than 60 keV) traversing thin samples typically create only a few excitations and in most cases zero or one. Most of these excitations are volume plasmons, which decay in the form of eh pairs on a femtosecond time scale. These eh pairs may diffuse and excite lower energy states, such as those associated with localized defects or QWs, on a time scale of tens of picoseconds. These lower energy states may then decay to the ground states by emitting photons. The photon emission arises in a time window on the order of their lifetime τe.16 The typical lifetimes we are dealing with here are in the nanosecond range, much larger B
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than the volume plasmon to eh pair decay and diffusion times. Therefore, from the point of view of the lowest energy states, their excitation happens almost instantaneously. Thus, as several eh pairs are created upon electron excitation, several of these lowest energy states are excited almost at the same time. Therefore, the photons they emit are created in a typical time window that is equal to the lifetime τe (Figure 1a), forming photon bunches. This bunching behavior manifests itself as a peak of high amplitude in the second-order correlation function g(2)(τ). It can be shown that g(2)(τ) decays exponentially with a time constant equal to the emitters’ lifetime.16 The lifetime can thus be directly measured from a g(2)(τ) through a simple exponential fit. In order to benefit from such information at the nanometer scale, we have designed a dedicated scanning transmission electron microscope experimental setup (see Figure 1 and Methods). In our setup, a free-electron beam is sent onto an object, which under excitation emits light (CL). The light is collected by a parabolic mirror and sent to an optical spectrometer (not shown) or a light intensity interferometer (right side of sketch in Figure 1a). In these modes we acquire optical spectra (Figure 1b) or g(2)(τ) functions (inset of Figure 1a), from which τe is extracted by exponential fitting. By scanning the beam we form spectrum images (in which each pixel contains one spectrum,5 not shown) or total CL intensity images (Figure 1c). Finally, electrons scattered at high angles allow the formation of high-angle annular dark-field (HAADF) images (Figure 1d,e) containing structural information down to the atomic scale. When relevant, electron energy-loss (EEL) spectra containing chemical information can be acquired by measuring inelastically scattered electron energies. We illustrate such an ensemble of readily correlated measurements in Figure 2 for a sample whose properties are inaccessible to optical techniques due to spatial resolution constraints. This sample is composed of nanowires (NWs, see Methods) including a set of eight GaN quantum discs (QDiscs), a few angströms thick, separated by 15 nm AlN barriers (Figure 2a). The wires are grown along the polar direction. A color-coded compression of the spectral image of a NW is shown in Figure 2b, where each energy layer was encoded with a different color.8 Despite their proximity, the emission of each QDisc (in the 3.8 to 4.7 eV range) is clearly distinguishable. Comparison to QDisc positions obtained from HAADF images (Figure 2a) allows the deduction of the exact emission energy of each QDisc (see ref 5 and Supplementary Figures 2 and 3). The emission energy distribution along the NWs is not uniform among different NWs due to QDisc thickness variations and strain effects5 (Supplementary Figures 2 and 3). Each QDisc lifetime is determined using SRTC-CL (Figure 2c); they range from 0.5 to 2.3 ns. Longer lifetimes are correlated to lower emission energies, as confirmed over 38 QDiscs (Supplementary Figure 3). This behavior is expected because of the QCSE. In the presence of the strong spontaneous electrical field in these polar materials, the electrons and holes tend to spatially localize on different sides of the QDiscs. The separation increases with the increasing width (and therefore decreasing emission energy) of the QDiscs.3 Therefore, a smaller energy corresponds to a reduced eh spatial overlap, in other words an increased radiative lifetime.3 The width of the g2(τ) peak is determined by the emitters’ lifetimes under electron excitation.16 In the preceding example, we have implicitly assumed that the measured lifetimes were
Figure 2. Nanometer-scale lifetime measurement. (a) HAADF image of a NW containing 8 GaN QDiscs. Scale bar is 20 nm. (b) Compression of a spectral image acquired on an AlN nanowire containing 8 GaN QDiscs and (c) series of g2(τ) measured at each QDisc position. These have been shifted on the abscissa to align with the corresponding QDisc for clarity. For each peak the time scale goes from −20 to 20 ns. The deduced lifetime is printed close to each bunching peak.
coinciding with lifetimes that would be deduced from wellestablished techniques, e.g., time-resolved microphotoluminescence (TR-μPL). In order to validate this assumption, spectrally filtered TR-μPL (see Methods and Figure S4 of the Supporting Information) was used to measure the lifetimes of isolated GaN QDiscs in individual AlN NWs, which have been statistically compared to SRTC-CL measurements (Figure 3). In contrast to the previous cases presented so far in this work, NWs containing only a single QDisc were used, as μPL cannot distinguish closely packed QDiscs. CL and PL lifetime distributions (Figure 3) are consistent, demonstrating that
Figure 3. Lifetime measurement on individual GaN/AlN nanowires containing a unique QDisc. Comparison of lifetime vs energy retrieved via both techniques. C
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(top and bottom in Figure 4c), while that at 3.7 eV is also very localized at the thinnest part of the QCS (right side of Figure 4c). Each of the three spots is expected to originate from locations where the local energy of a radiative excited eh states is minimum. The spatial extension of the signal results from the charge carrier diffusion. In contrast with the case of the stack of QDiscs, where each successive QDisc acts as a very efficient trap and therefore the diffusion is lower, here the eh pairs may diffuse on a longer scale (see, for example, ref 19 for an extensive discussion on the apparent spread of CL signals). It is thus tempting to attribute each emission to the recombination of a different eh excited state in the QCS, although the QCS appears as a continuous GaN layer. This is confirmed by retrieving associated lifetimes through combined spatial and spectral filtering of g(2)(τ). The excited states localized at the top and bottom of the QCS have lifetimes of 8 and 9 ns. The excited state localized at the thinnest part (right side of the image) of the QCS has a lifetime of 1 ns. The high-energy emission state is thus localized at the thinnest part of the QCS and possesses the shortest lifetime. The two other excitations are localized on thicker parts of the QCS, where confinement is much weaker, leading, as expected, to longer lifetimes. The difference in lifetimes, despite similar emission energy, may point to slight differences in thickness accross the QCS or to the presence of defects. Despite very similar growth conditions and the fact that they are both made up of a continuous layer of GaN, the physics of the QCSs and the QDiscs are totally different. The low-energy eh states seem spatially homogeneous over a whole QDisc, while three different, although spatially and/or spectrally very close, eh states tend to localize within a QCS. This deduction could not have been made by state-of-the art techniques such as TR-μPL or TR-CL.12,20,21 Previous attempts to measure lifetimes using CL relied on pulsed guns (TR-CL) with relatively low brightness. They unambiguously demonstrated that the use of CL to obtain time-dependent information is a disruptive approach.12,14,20,22 Nevertheless, even if in these seminal works the diffraction limit was exceeded, the spatial resolution was limited to the size of the electron probe (50−100 nm), still too large to probe individual quantum-confined structures separated by the short distances relevant to actual devices.5,10 Here, the continuous and much brighter gun used furnishes both an increased electron current and a probe size sufficiently reduced (around 1 nm) so that the spatial resolution is limited by the charge carrier diffusion length, which, in nanostructures, can be shown to give access in several cases to the relevant information about the quantum emitters of interest.8 Given the fact that we were aiming to achieve such a small beam size, we need to stress several constraints. We have used here a current intensity value between 5 and 25 pA for the g2(τ) measurements. This range of electron currents has been optimized following two prescriptions. First, it has to be small enough to avoid the incident random electron statistics swamping the synchronized emission.16 In other words, the bunching peak drastically diminishes when the current is sufficiently high for two successive electrons to create excitations in the medium on a time scale smaller than the lifetime. For the given thickness of the wires and mean free path of the electrons in GaN, this corresponds roughly to one inelastic event per incoming electron.18 Therefore, as soon as more than one electron per lifetime impinges on a wire, the bunching peak drastically decreases. This happens typically for a current of one electron per nanosecond, namely, for a current intensity value larger
they are the same physical quantity. As already discussed, lifetime increases for decreasing emission energy.4 We also note that for QDiscs thick enough (typically larger than 3 nm; see ref 17) for the QCSE to induce large red-shifts (typically larger than 1 eV; see ref 17) with respect to the emission energy of the bulk GaN, the radiative decay may not be monoexponential17 due to a lifetime dependence on the eh density. Indeed, such large red-shifts are correlated with long lifetimes (up to milliseconds4). During such a long lifetime duration, the QWs are likely to be excited several times, leading to a charge carrier accumulation screening the internal field, thus reducing the lifetime.18 Several lifetimes can thus be observed, leading to a non-monoexponential decay. Because of the small thicknesses of the QWs explored here,18 a few angströms, the QCSE effect is too weak to induce such large lifetimes, as is obvious in Figure 3 and confirmed by the fact that the emission energies are always larger than or only slightly below the GaN bulk band gap energy. Nevertheless, such extreme cases are usually handled in the case of TR-μPL measurements through multiexponential fitting procedures. Similarly, a multiexponential fitting procedure could be envisaged in the case of SRTCCL to retrieve sets of lifetimes; see Supporting Information for an example with two components. SRTC-CL’s high spatial resolution can be exploited to address more complicated questions, such as the emission origin in objects separated by only a few nanometers with superimposed spectral features. As an example, we show a single GaN quantum confined structure (QCS) embedded in an AlN nanowire (Figure 4). Such QCSs are complex 3D structures formed by bent, thin GaN layers of varying thickness (Figure 4a,b). The QCS in Figure 4c−e shows two main emission peaks (3.2 and 3.7 eV). From the spectrum image (Figure 4c), one further deduces that the 3.2 eV emission originates from two very localized (about 50 nm full width at half-maximum) regions separated by around 100 nm at the limits of the QCS
Figure 4. Lifetime measurement of light emission sources overlapping both spectrally and spatially at the subwavelength scale. (a) HAADF image and (b) Ga (orange) and Al (purple) EELS maps of a GaN quantum QCS in an AlN NW. (c) Color-coded spectrum-image compression of a QCS. (d and e) CL intensity images filtered on energy values indicated at the bottom. The boxes indicate the areas scanned during lifetime measurements, the value of which is indicated next to each box. (a)/(b) and (c)−(e) have been acquired from different NWs. Scale bars are (a, b) 20 nm and (c−e) 50 nm. D
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Spectrum Image Color-Coded Compression. Spectrum images encode the spatial and spectral variations in the CL signal. They are usually difficult to present globally. One possibility, used here, is to perform a color-coded compression of the spectrum image. The principle is the following.8 Although a spectrum image is acquired spectrum-by-spectrum, it can also be analyzed as a stack of energy-filtered images. One can then attribute a different color to each different energyfiltered image, following a predetermined color scale (see the color scales of Figure 2b and Figure 4c). In this paper, we have chosen a rainbow-like false color scale: the lowest energy is red and the highest is violet. Each color has a given red-green-blue (RGB) encoding. In each energy-filtered map, the intensity of a given pixel is used to weight the RGB encoding, meaning that within each map the color is preserved but is more or less intense. Each energy-filtered map therefore results in an RGB image. All the RGB images corresponding to all the filtered images are finally summed to provide a final, compressed, RGB representation of the spectrum image. Such a representation is arbitrary and cannot replace a systematic spectrum analysis (see for example Supporting Information S2 and S3), but it gives a useful overview of the main spatiospectral features.8,18 Time-Resolved μ-PL Measurements. The experiment was optimized to work in the UV range. We used a titanium sapphire (Coherent Mira 900) pulsed laser emitting at 750 nm with a repetition rate of 82 MHz. The average output power is about 100 mW. The wavelength is then tripled with a nonlinear crystal to obtain an excitation wavelength of 250 nm, which lowers the power to about 10 mW. An attenuator is then added to choose the excitation power, from 10 to 100 μW. The objective lens used to focus the beam on the sample has a numerical aperture of 0.4 with a magnification of 20, resulting in a spot of about 2 μm. The sample is cooled to liquid helium temperature (T = 4 K). The emitted photons are transmitted to a spectrometer that can either send the signal to a CCD camera giving an emission spectrum or select a given wavelength to be sent to a photomultiplier (PMT) detector for time-resolved measurements. For the TR-PL experiments, we studied AlN/GaN nanowires with only one QDisc of GaN per nanowire. The QDiscs were thick, and their emission wavelength was typically between 3.1 and 3.9 eV. Some defects in the AlN matrix can also be observed between 3.5 and 5.0 eV. Due to the restricted spatial resolution of the experiment, more than one nanowire was excited at a time. Spectral selection before the PMT usually allows the selection of only one emission. However, in most of the 30 measurements, the fit was the sum of two lifetimes, a shorter lifetime between 60 and 600 ps and a longer lifetime between 0.7 and 5 ns. The first contribution is associated with a secondary emission, coming either from the overlap with the GaN bases of the nanowire or from some defects in the AlN matrices.25 Even if the intensity of this secondary signal is small, its short lifetime makes a visible contribution in the TR-μPL experiment. The second lifetime is associated with the luminescence coming from the GaN QDiscs. Intensity Interferometry Setup. The setup for intensity interferometry is similar to that described in refs 15 and 16 with only a few modifications. Briefly, the CL photon beam collimated by a parabolic mirror is focused onto a 600 μm optical fiber (OF) with a convergent lens. The other end of the OF is placed at the focal point of a convergent lens that further collimates the beam, which is directed toward a 50/50 beam
than 200 pA. Although this sounds like a small value, a highbrightness gun is still required to achieve such a current in a 1 nm probe size. Second, we kept the current sufficiently high to avoid lengthy acquisition times, even at the price of some bunching-peak reduction. Indeed, the typical exposure time for a lifetime or a CL spectrum image measurement is tens of seconds (depending on emission intensity and lifetime value). Therefore, acquiring statistically relevant information from heterogeneous samples (including most nano-objects) is straightforward. However, when two eh excited states are separated by a distance smaller than the diffusion length, the determination of the lifetime spatial distribution remains challenging. A strategy to cope with this situation, considering the demonstrated relatively low correlation function acquisition times, could be to acquire g2(τ,x,y), i.e., a data set consisting of correlation functions acquired systematically as a function of the two spatial coordinates. Multiple lifetimes can be theoretically extracted from g2(τ) through fitting with multiple exponentials (see Supporting Information for a double-lifetime determination). Determination of the lifetime spatial distribution would thus be possible with a precision much better than the diffusion length using spatial oversampling and postprocessing of g2(τ,x,y), much in the spirit of routine procedures applied for spectrum imaging,5,8 or in a similar spirit for stochastic optical reconstruction microscopy.23 SRTC-CL is applicable to any luminescent material not suffering from electron damage, and regular CL setups have already proved the high spatial localization of emission centers (point defects16 or excitons in insulators, III−N materials including InGaN10,24 or AlGaN25 alloys or heterostructures, II−VI quantum dots,9 rare earths in a matrix,26 extended defects such as dislocations27−29 or stacking faults,21 etc.). Also, simulations at lower voltages (see Supporting Information) show that SRTC-CL is not restricted to the STEM and can be performed in the scanning electron microscope (SEM). The simple adaptation of an intensity interferometer to any regular SEM would thus allow lifetime measurements without relying on costly pulsed-gun technologies.
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METHODS Electron Microscopy Experiments. Electron microscopy experiments were performed in scanning transmission electron microscopes. All cathodoluminescence experiments were performed in a VG HB501 operated at 60 keV. Light was collected with an in-house-made system.5 For these experiments, the sample was kept at around 150 K. Atomically resolved HAADF images and EEL data have been acquired using an NION USTEM200 operating at 200 keV. Samples. The samples were grown by molecular beam epitaxy. Nanowires with a single GaN insertion were grown using the method described in ref 30. For multiple GaN insertions, the same route was used, but in addition the last steps including the GaN QDisc growth and the AlN capping were repeated eight times. For the nonflat GaN insertions (QCSs), the AlN section underneath the GaN insertion was grown by inclining the N and Al cell toward grazing incidence. As described in ref 31, this implies an increase in the diameter of the nanowire and the appearance of semipolar facets on top of the NW. Apart from this step, the growth of the GaN insertion was performed in conditions similar to the growth conditions of the other samples. E
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Songmuang, R.; Kociak, M. Nanometer Scale Spectral Imaging of Quantum Emitters in Nanowires and Its Correlation to Their Atomically Resolved Structure. Nano Lett. 2011, 11, 568−573. (6) Ambrose, W. P.; Goodwin, P. M.; Keller, R. A.; Martin, J. C. Alterations of Single Molecule Fluorescence Lifetimes in Near-Field Optical Microscopy. Science 1994, 265, 364−367. (7) Carminati, R.; Cazé, A.; Cao, D.; Peragut, F.; Krachmalnicoff, V.; Pierrat, R.; De Wilde, Y. Electromagnetic density of states in complex plasmonic systems. Surf. Sci. Rep. 2015, 70, 1−41. (8) Kociak, M.; Stephan, O.; Gloter, A.; Zagonel, L. F.; Tizei, L. H. G.; Tence, M.; March, K.; Blazit, J. D.; Mahfoud, Z.; Losquin, A.; Meuret, S.; Colliex, C. Seeing and measuring in colours: Electron microscopy and spectroscopies applied to nano-optics. C. R. Phys. 2014, 15, 158−175. (9) Mahfoud, Z.; Dijksman, A. T.; Javaux, C.; Bassoul, P.; Baudrion, A.-L.; Plain, J.; Dubertret, B.; Kociak, M. Cathodoluminescence in a Scanning Transmission Electron Microscope: A Nanometer-Scale Counterpart of Photoluminescence for the Study of II-VI Quantum Dots. J. Phys. Chem. Lett. 2013, 4, 4090−4094. (10) Griffiths, J. T.; Zhang, S.; Rouet-Leduc, B.; Fu, W. Y.; Bao, A.; Zhu, D.; Wallis, D. J.; Howkins, A.; Boyd, I.; Stowe, D.; Kappers, M. J.; Humphreys, C. J.; Oliver, R. A. Nanocathodoluminescence Reveals Mitigation of the Stark Shift in InGaN Quantum Wells by Si Doping. Nano Lett. 2015, 15, 7639−7643. (11) Grundmann, M.; Christen, J.; Bimberg, D.; Fischer-Colbrie, A.; Hull, R. Misfit dislocations in pseudomorphic In0.23Ga0.77As/GaAs quantum wells: Influence on lifetime and diffusion of excess excitons. J. Appl. Phys. 1989, 66, 2214. (12) Merano, M.; Sonderegger, S.; Crottini, A.; Collin, S.; Renucci, P.; Pelucchi, E.; Malko, A.; Baier, M. H.; Kapon, E.; Deveaud, B.; Ganiere, J. D. Probing carrier dynamics in nanostructures by picosecond cathodoluminescence. Nature 2005, 438, 479−482. (13) Feist, A.; Echternkamp, K. E.; Schauss, J.; Yalunin, S. V.; Schaefer, S.; Ropers, C. Quantum coherent optical phase modulation in an ultrafast transmission electron microscope. Nature 2015, 521, 200−203. (14) Fu, X.; Jacopin, G.; Shahmohammadi, M.; Liu, R.; Benameur, M.; Ganiere, J.-D.; Feng, J.; Guo, W.; Liao, Z.-M.; Deveaud, B.; Yu, D. Exciton Drift in Semiconductors under Uniform Strain Gradients: Application to Bent ZnO Microwires. ACS Nano 2014, 8, 3412−3420. (15) Tizei, L. H. G.; Kociak, M. Spatially Resolved Quantum NanoOptics of Single Photons Using an Electron Microscope. Phys. Rev. Lett. 2013, 110, 153604. (16) Meuret, S.; Tizei, L. H. G.; Cazimajou, T.; Bourrellier, R.; Chang, H. C.; Treussart, F.; Kociak, M. Photon Bunching in Cathodoluminescence. Phys. Rev. Lett. 2015, 114, 197401. (17) Bretagnon, T.; Lefebvre, P.; Valvin, P.; Bardoux, R.; Guillet, T.; Taliercio, T.; Gil, B.; Grandjean, N.; Semond, F.; Damilano, B.; Dussaigne, A.; Massies, J. Radiative lifetime of a single electron-hole pair in GaN/AlN quantum dots. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 113304. (18) Zagonel, L. F.; Tizei, L. H. G.; Vitiello, G. Z.; Jacopin, G.; Rigutti, L.; Tchernycheva, M.; Julien, F. H.; Songmuang, R.; Ostasevicius, T.; de la Peña, F.; Ducati, C.; Midgley, P. A.; Kociak, M. Nanometer-scale monitoring of quantum-confined Stark effect and emission efficiency droop in multiple GaN/AlN quantum disks in nanowires. Phys. Rev. B: Condens. Matter Mater. Phys. 2016, 93, 205410. (19) Zagonel, L. F.; Rigutti, L.; Tchernycheva, M.; Jacopin, G.; Songmuang, R.; Kociak, M. Visualizing highly localized luminescence in GaN/AlN heterostructures in nanowires. Nanotechnology 2012, 23, 455205. (20) Herman, M. A.; Bimberg, D.; Christen, J. Heterointerfaces In Quantum-wells and Epitaxial-growth Processes - Evaluation By Luminescence Techniques. J. Appl. Phys. 1991, 70, R1−R52. (21) Corfdir, P.; Lefebvre, P.; Balet, L.; Sonderegger, S.; Dussaigne, A.; Zhu, T.; Martin, D.; Ganiere, J. D.; Grandjean, N.; DeveaudPledran, B. Exciton recombination dynamics in a-plane (Al,Ga)N/
splitter (BS). The BS splits the beam in two paths that are directed toward two photomultipliers (PM), optimized in the blue optical range (Hamamatsu H10682-210). The signals from the two PMs are sent onto a time-correlator (PicoHarp300), enabling the construction of the g2(τ). All optical elements’ numerical apertures are optimized to work with the OF. Time Resolution of SRTC-CL. The time resolution of SRTC-CL experiments is determined by photon arrival discretization and correlation electronics, being here on the order of 130 ps. The exposure time of the SRTC-CL measurements varied between 25 and 80 s. Monte Carlo simulations following the methodology of ref 16 show that the precision in lifetime measurements is on the order of 0.05 ns for the signal-to-noise ratio observed experimentally. As an example, we show in Supplementary Figure 5 simulated measurements with two emitters with lifetimes of 1 and 0.5 ns. Repeated simulations demonstrate that these values can be systematically retrieved.
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ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsphotonics.6b00212. Methods and Figures S1−S5 (PDF)
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We express all our thanks to M. Walls for his careful reading of the manuscript. This work has received support from the National Agency for Research under the program of future investment TEMPOS-CHROMATEM with the reference ANR-10-EQPX-50. The authors acknowledge financial support from the European Union under the Framework 7 program under a contract for an Integrated Infrastructure Initiative. The research leading to these results has received funding from the European Union Seventh Framework Programme [FP7/2007− 2013] under Grant Agreement No. 312483 (ESTEEM2). S.M. acknowledges the financial support from the French Ministry of Defense through a grant from the Direction Generale de l’Armement (DGA). The work has been partly supported by the EMOUVAN project, ANR-15-CE24-0006.
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