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Ultramicroscopy 174 (2017) 50–69 Contents lists available at ScienceDirect Ultramicroscopy journal homepage: www.elsevier.com/locate/ultramic Cathodoluminescence in the scanning transmission electron microscope a,⁎ M. Kociak , L.F. Zagonel a b MARK b Laboratoire de Physique des Solides, Université Paris-SudParis-Sud, CNRS-UMR 8502, Orsay 91405, France “Gleb Wataghin” Institute of Physics University of Campinas - UNICAMP, 13083-859 Campinas, São Paulo, Brazil A R T I C L E I N F O A BS T RAC T Keywords: Cathodoluminescence STEM Nano-optics Plasmonics Quantum emitters Band gap measurements Cathodoluminescence (CL) is a powerful tool for the investigation of optical properties of materials. In recent years, its combination with scanning transmission electron microscopy (STEM) has demonstrated great success in unveiling new physics in the field of plasmonics and quantum emitters. Most of these results were not imaginable even twenty years ago, due to conceptual and technical limitations. The purpose of this review is to present the recent advances that broke these limitations, and the new possibilities offered by the modern STEMCL technique. We first introduce the different STEM-CL operating modes and the technical specificities in STEM-CL instrumentation. Two main classes of optical excitations, namely the coherent one (typically plasmons) and the incoherent one (typically light emission from quantum emitters) are investigated with STEM-CL. For these two main classes, we describe both the physics of light production under electron beam irradiation and the physical basis for interpreting STEM-CL experiments. We then compare STEM-CL with its better known sister techniques: scanning electron microscope CL, photoluminescence, and electron energy-loss spectroscopy. We finish by comprehensively reviewing recent STEM-CL applications. 1. Introduction Cathodoluminescence (CL) i. e. the emission of light from a material upon interaction with an electron, is a well-known phenomenon. As a regular characterisation technique, it has been applied with great success in geological sciences and for the characterisation of semiconductors [1]. In the past fifteen years it has undergone a major rebirth related to the development of optically active nanomaterials and nanostructured materials. This rebirth is certainly linked to the fact that an electron beam can be made arbitrarily small compared to the nanometer scale at which the three main phenomena that are driving the optical behaviours of nanomaterials or nanostructured materials occur. In other words, such phenomena happen at scales that are hardly reachable with conventional far-field diffraction limited optical techniques. In contrast, modern Scanning Electron Microscope (SEM) or scanning transmission electron microscopes (STEM) can nowadays form extremely small electron probes ( < 1 nm) and benefit from optimised light detection schemes. Although such small probes can lead to very small excitation volumes, they do not lead necessarily to high spatial resolutions. However, we will see that under certain circumstances they do, which justifies in part the writing of this review. The three main phenomena under discussion (see Fig. 1) are: • Plasmon confinement (Fig. 1a): standing waves made up of a ⁎ • mixture of charge density waves and photons form at the surface of nanoparticles when their sizes become comparable to the wavelength of light [2]. These are surface plasmons (SPs). Their resonance frequency depends on the size and geometry of the nanoparticles, and can thus be tuned by changing these parameters; it also depends on the local dielectric environment of the nanoparticle. Because they are resonant, these excitations dominate the optical spectrum of small metallic nanoparticles. Finally, SPs make it possible to concentrate the electromagnetic field at the nanometer scale. These properties - size and shape resonance-energy dependance, local environment sensitivity, electromagnetic energy focusing - indicate a bright future for SP applications such as sensing or cancer therapy. Band gap variations at the nanometer scale (Fig. 1b): the energy band-gap in a semiconductor largely determines its absorption properties, and, if it is luminescent, its luminescence properties. In semiconductors or insulators, luminescence arises through the creation of charged carriers (electron-hole pairs in case of CL or photoluminescence, PL) that subsequently recombine radiatively. In the absence of deep recombination centres (see later), most of the recombinations arise close to the band gap energy. Minor differences between the emitted light and the band gap energies may be due to the presence of shallow defects close to the valence or conduction band to/from which electron-hole recombination occur Corresponding author. E-mail address: [email protected] (M. Kociak). http://dx.doi.org/10.1016/j.ultramic.2016.11.018 Received 29 July 2016; Received in revised form 16 November 2016; Accepted 18 November 2016 Available online 19 December 2016 0304-3991/ © 2016 Elsevier B.V. All rights reserved. Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel Fig. 1. Summary of the main physical properties that are efficiently investigated in STEM-CL (a–c), and how different information can be obtained by this technique (d–o), as described in detail in this review. (a). Plasmons emission arises from the deexcitation of plasmonic waves, which are essentially charge density waves. The figure shows the surface charge distribution for a triangular prism for one of the degenerate dipolar modes and for the hexapolar mode. After [3], reprinted with permission. (b). Local optical transition energy (optical band gap) variations in semiconductors. The optical property variations might arise from a local change in composition or stress, changing the “bulk” energy band gap, or from quantum confinement. In either case, electron-hole pairs will recombine where locally the energy (E) of the excited states (here schematised as the energy difference between the conduction band CB and the valence band VB) is the lowest (here along an arbitrary axis x). (c). Point defects and related atomic-like defects. Point defects or atom inclusions in a relatively high band gap material can behave as an idealised two levels system lying in the gap of the host material. (d). HAADF image of a 360 nm wide silver triangle. (e). CL polychromatic maps (see text) showing the spatio-spectral behaviour of plasmon modes; this can be directly correlated to the morphological information in (d). (f). Two typical spectra have been extracted at the tip (orange) and the side (green) of the prism. (e). (g). Angle-resolved CL spectroscopy of a plasmonic band gap material consisting in a series of silver pillars. The periodicity induces a band gap that is directly detected in STEM-CL. (h). HAADF image of a series of GaN quantum discs (QDisk) (bright contrast) embedded in a AlN (dark contrast) shell. (i). Related polychromatic map, showing individual QDisk colour variation. (j): Spectra extracted on two different QDisks. (k). Time correlation functions taken at the centre of each disc allowing to determine the QDisks lifetimes (indicated close to the corresponding peak). (l). HAADF of an h-BN flake. Because the flake is very thin, its HAADF contrast is essentially null, to be compared with the CL contrast in (m). (m). Monochromatic image filtered at the energy of an individual defect, the signature of which is shown in (n). (o). Time correlation function displaying a dip indicating single photon emission. (d-f) adapted from [4], (g) from [5], (h–k) from [6] and (l–o) from [7]. Reprinted with permission. (in the case of near band edge, NBE) and larger ones to the occurrence of excitonic recombinations or shallow defect recombinations. There are two main reasons for band gap modulation at the nanometer scale. The first reason might be a change of the material composition or characteristics - for example, a desired or undesired change of the value of x in an Inx Ga1− x N material, or a change of the stress states that modify the local energy gap. The second reason might be some quantum confinement, i. e. the fact that the electron and hole wavefunctions can be confined when a semiconductor • 51 material embedded in a higher energy gap semiconductor has at least one of its dimension smaller than a typical exciton Bohr radius, which varies from tens of nanometers to tens of ångströms. The two effects, of course, can compete to change the local emission wavelength. Such band gap monitoring and engineering is of the utmost interest in many fields: from solid state lighting (Light Emitting Diodes, LEDs), bioimaging (for example using II-VI quantum dots), photovoltaics, etc. Structural defects (Fig. 1c): Structural defects have a range of effects Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel on luminescence properties. For example, some dislocations can act as non-radiative centres, quenching the emission of the object of interest, but others can be radiative. Colour centres can be highly absorbing and/or emitting, dominating the optical properties of the host matrix in the visible range - consider for example the case of a ruby stone. Colour centres are of particular interest, as they are a solid-state realisation of a two-levels system (TLS). Among their other properties, TLSs can be used as single photon emitters (SPEs), with applications in quantum computing and quantum cryptography. Because the optical properties of nanomaterials are determined largely at the nanometer scale or below, and are intimately linked to the morphology or even the atomic structure or chemistry of the object of interest, SEM-CL and STEM-CL are clearly techniques of choice. STEM-CL has ultimately a better spatial resolution (a few nanometers proven now [8,9]) for probing optical properties of semiconducting materials, it can be less intrusive (no heating, no non-linearities), has a higher sensitivity for plasmons in very small nanoparticles [10,11], and can be easily coupled to ultra-high resolution imaging and chemical imaging techniques. STEM-CL was pioneered in the late 70's and early 80's [12–15]. However, it appears that up to the beginning of the 2000's, technological (mirror machining, optical fibres, CCD cameras…) as well as conceptual reasons (such as the difficulty of believing that CL could be employed for plasmonics or that the electron-hole diffusion could be small enough to address individual quantum-confined structures) slowed down the emergence of disruptive applications of STEM-CL. The situation changed with the first mapping of plasmons by Yamamoto [10] shown in Fig. 2 in the early 2000's and the spectral-mapping of quantum-confined GaN structures embedded in an AlN nanowire [8] (Fig. 3) ten years later. Both demonstrated that STEM-CL enables the investigation of the nanooptical properties of material at the relevant scale: that of the plasmon spatial modulation or quantum confinement lengths. The still nascent field of STEM-CL will thus be studied here; it is worth noting that the parallel revival of SEM-CL -also formerly neglected for similar reasons- has led to impressive successes in the past years [16–22]. It is by no means our goal to artificially promote STEM-CL. The two techniques are extremely similar, share many interests and concepts, and have their pros and cons defining niche applications, which will be discussed later in the paper. SEM-CL (mostly excluding plasmons and other coherent excita- Fig. 3. Mapping quantum emitters with STEM-CL. Top: HAADF image of a series of GaN quantum discs (bright) embedded in AlN (dark). Bottom: Multicolour CL image obtained on a stack of GaN quantum discs (QDisks) embedded in an AlN nanowire. This image has been obtained by colouring each wavelength-filtered image of a CL SI with the false colour corresponding to the energy (see bottom scale), and then overlapping each of them without any other data treatment. Note that despite the high contrast in the CL image, a much more thourough information extraction process must be applied to the spectral image to isolate individual QDisks' emission wavelength, see text. A rectangular area is displayed to emphasise the link between morphology (HAADF) and optical properties (CL). Accelerating voltage is 60 keV. Adapted from [8]. tions, see Section 3.1) has been covered in a reference book [1]. Applications of SEM-CL to quantum confined semiconductors can be found in a comprehensive review [23]. F. J. Garcia de Abajo has covered S(T)EM-CL theory for coherent excitations, mainly, in his excellent and dense review article on nanophotonics with electrons [24]. Tutorial papers on plasmon mapping with fast electrons (including CL) presenting simplified theories [2,25] and detailed instrumentation explanations [2] have been recently published. A more generic review describing electron-based plasmon spectromicroscopy with an emphasis on time-resolved techniques has been given [26]. Recent reviews on SEM-CL applied to coherent [27] and incoherent [20] excitations have been published. A review of the early stages of STEMCL for incoherent excitations has been published a decade ago [28]; a more recent review of applications of STEM-CL has been given [29]. The general field of STEM-CL and its applications has however not been reviewed in recent years, especially concerning incoherent excitations. Our goal is thus to present a technique which has a tremendous potential for nanooptical applications, and that has not been subject to comprehensive books, review articles or lectures over the past fifteen years, in which major steps have been made. 2. Instrumentation 2.1. The scanning transmission electron microscope, the spectral imaging and other related CL acquisition schemes 2.1.1. scanning transmission electron microscope and accessories A scheme of a modern STEM is presented in Fig. 4; a detailed discussion of all elements may be found in any textbook on STEM (the interested reader may find useful a more comprehensive description relevant to CL in [2]). An electron beam is focused onto an object of interest forming a very narrow probe. Given the high energy of the electrons (typically from 60 keV to 300 keV) and the subsequent picometer range of their wavelength, the ultimate resolution is limited mainly by the geometric aberrations of the microscope. Nowadays, an ångström-sized electron probe carrying a hundred pA is easily attainable, although many applications in STEM-CL are likely to need only a few tens of ångströms and tens of pA. Neither values are requiring aberration-corrected microscopes, but a high brightness gun is certainly necessary, see e.g. [6]. After interaction with the sample, the electron may be scattered at high angle into a high angle annular dark Fig. 2. Mapping plasmons with CL in a STEM. Left: Series of CL spectra taken at various electron beam positions on a 140 nm diameter silver nanoparticle. Right: a) Secondary electron image of a 140 nm silver nanoparticle. b) c) d) e) filtered maps of the dipolar and quadrupolar modes as seen along two different polarisation directions. Electron beam acceleration voltage is 200 keV. After [10], reprinted with permission. 52 Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel Fig. 4. (a). Scheme of a STEM fitted with CL and EELS detectors. Cond. Lens: condenser lenses; SC: scanning coils; Obj. Lens: objective lens. The light collected by the mirror can be analysed in multiple ways, described on the adjacent panels: (b). the photon beam can be directed to the entrance of a spectrometer via a collecting optics (here schematised by a convergent lens, but other means, typically optical fibres, can be used as well). A spectrum can then be acquired on a CCD camera. When the beam is scanned, one spectrum can be acquired per pixel, leading eventually to a spectrum image, the most widely discussed mode in this paper. Alternatively, a photo-multiplier (PM) can be used instead of a camera. In such a case, a slit can be used to wavelength-filter the light before hitting the PM. Upon scanning, an energy (wavelength) filtered map can be acquired. (c). Alternatively, angle-resolved emission patterns (for a given beam position) can be obtained by imaging the mirror onto a camera. The light can be optionally energy filtered and/or polarised. (d). Another possibility for angle-resolved pattern acquisition is to scan a pinhole in a plane where the light is collimated, and to send the remaining light onto a spectrometer. In this way angle-resolved spectra can be acquired. (e). Another possibility consists in sending the collected light to an intensity interferometer. It is made up of a beam splitter (BS) with one photon detector (PM or avalanche photodiodes, APD) attached to each of the two paths. The photon detection electronic signal is then sent to the required correlation electronics in charge of reconstructing a correlation function. field (HAADF) detector: the heavier the atoms under the probe are, the larger the HAADF signal. The electrons that have not been deflected can be collected by a bright field (BF) detector (not shown), giving an image which is to first order complementary to that of the HAADF. By loosing energy, the primary electrons may trigger several events. Secondary electrons (SE) can be generated and then collected. The primary electrons' energy losses can be measured by energy-dispersing the electrons in an electron spectrometer, giving information on the chemistry of the material, or its optical absorption (see Section 3.2.3). This is known as electron energy-loss spectroscopy (EELS). More importantly in the context of this review, the energy given by the electron to the material can be radiated back into the far-field. If this happens in the infra-red/visible/ultra-violet (IR/Vis/UV) range, it can be gathered by a CL collection and detection system; such a system is described at some length in [2] and its optimisation will be discussed shortly in the following sections. Finally, emission can happen in the XRay range, and Energy Dispersive X Ray spectroscopy (EDS), not shown here, can provide chemical information on the sample. sending it to a spectrometer. Getting a single spectrum at a given position is of course not sufficient for an in-depth analysis of the optical properties of nanomaterials, therefore spectral-images (SI) have to be acquired. In a STEM, HAADF, BF or SE images are acquired by scanning the beam onto the sample and acquiring the respective scalar signal at each point of the scan, so that a scalar image can be eventually recorded. Similarly, spectral-images, i.e. images with a spectrum at each pixel, can be acquired for example for CL spectra (see Fig. 4b). This gives high-precision access to the spatial variations of given spectral features. Moreover, several signals can be recorded at once (for example, HAADF, BF, EELS and CL signals), making it possible to compare, pixel-by-pixel, morphological, chemical and optical information [6]. This correlation is of prime importance in understanding the physics of optical phenomena at the nanometer scale. Note that a SI includes a huge amount of information. Extracting this information requires specific tools, from the simplest (spectra extraction or image filtering) to the more involved (multivariate analysis [30–32]) through sequential peak-fitting of the whole dataset [8,33]. In Fig. 1 (e) and (i) we have used a particular compression scheme, presented in details in [6]. Although a SI is typically acquired spectrum-by-spectrum, it can also be analysed as a stack of energyfiltered images. With this in mind, one can attribute a different colour 2.1.2. Spectrum measurement and spectral imaging Fig. 4b–e present different CL acquisition set-ups. Probably the most widely used detection scheme is the one described in Fig. 4b. It consists in simply collecting the light coming out of the CL mirror and 53 Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel 2.1.4. Intensity interferometry Very generally, the beam coming out of the CL collection system (basically, a mirror) can be analysed with any conventional optical tool, although the whole SEM-CL and almost all the STEM-CL literature concentrates on the above-mentioned modes, which only make use of the detected CL intensity. However, more complex quantities, such as the time-correlation function g(2), which reveals second order information in the CL intensity, can be measured. This function is given by: ⟨I (t ) I (t + τ )⟩ g(2) (τ ) = , and gives the probability of detecting one photon at 2 to each different energy-filtered image, following a predetermined colourscale. We note that in Fig. 1e, the colourscale roughly corresponds to the absorption colours, while in Fig. 1i it is arbitrary, the energy being above the human visible spectrum. In each energy-filtered map, the intensity of a given pixel is used to weight the red-green-blue (RGB) encoding, meaning that within each map the colour 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 SI. By no means are these representations comprehensive, but they are relatively fair in the sense that they do not rely on a specific data analysis treatment. Of course, quantitative analysis is required, as already said. Therefore, specific tools have been developed to analyse spectral-images, in particular the open-source suite Hyperspy [34]. The spectral-imaging mode will be extensively illustrated in this review. In certain occasions, a serial detector, such as a photomultiplier (PM) may be positioned after the spectrometer in place of the camera (not shown in Fig. 4b). Then, maps of the CL intensity (instead of a full SI) can be formed. These maps may be filtered, if a slit is provided after the spectrometer, or panchromatic if there is no slit. This mode, once widely used [28], is however essentially obsolete now thanks to the high sensitivity and increasing readout speed of the modern CCD or CMOS cameras. Also, it is likely that other parallel detectors will be used in the future. For example, parallel PM arrays would give the extreme speed of the PMs together with the wealth of information provided by parallel detection. Finally, a polariser might be placed in the path of the photon beam (not shown in Fig. 4b). As described in the next section, the use of a polariser together with high numerical aperture (NA) optic has to be handled with care. Indeed, a high NA optic will change the local polarisation of off-axis light rays in a complicated manner. In the general case, the original polarisation cannot be retrieved without the knowledge of the light rays intensity distribution, a knowledge which is basically integrated in the configuration described in Fig. 4b). This problem can be avoided by restricting the detection angles to a narrow range centred on the optical axis. Then both polarisations, parallel and perpendicular to the sample plane, may be roughly discerned. Doing this of course induces a loss of the detected signal. I (τ ) time τ when already one has been detected at time 0. g(2) (τ ) functions can be measured thanks to an intensity interferometer as depicted in Fig. 4e. Such an interferometer, sometimes called the “Hanbury-Brown and Twiss” (HBT) interferometer [37], is simple. The beam is sent onto a beam splitter. Each split beam is sent onto a different detector (usually a photomultiplier (PM) or a avalanche photodiode). The two signals are correlated using specifically designed electronics to produce a g(2) measurement [38]. One of the two detectors signals is usually delayed to allow for symmetric correlation measurement. Applications of g(2) (τ ) measurements will be given in Sections 3.4.1 and 3.4.2. 2.2. STEM-CL technical constraints A long discussion about the requirements for optimisation of a STEM-CL detector can be found in [2], and a more general description for CL irrespective of the type of microscope used [20] has also been given. Here, we want to recall just the essential ideas when designing or using a CL system. As we will see in Section 3, the signal can be extremely weak compared to the case of the SEM-CL, where both the interaction cross-section and the incident current can be increased dramatically. Collection and detection optimisation are thus critical here. It is more involved in STEM-CL than in SEM-CL. Indeed, besides other practical details such as higher magnetic field in the pole-piece region and higher vacuum, the main restriction is the lack of room in a STEM pole piece. This constrains the size of the mirror to around 2 mm thickness in a typical Cs-corrected STEM, while this value can easily be increased to centimetre or more in a SEM. Given these constraints, in STEM-CL, we want to gather as many photons as possible, and we want to disperse them through an optical spectrometer onto a parallel detector (a CCD typically) ideally with the highest spectral resolution and of course with the smallest loss of photons from the time they are collected to the time they hit the detector. Thus, obviously, all optical elements have to be optimised for minimising losses, which includes matching all NAs along the photon beam path. The detector should obviously also be as efficient as possible. Moreover, one can show that the condition of having the highest spectral resolution together with the highest collection angle leads to a contradiction, so that in general extreme care must be taken in design and mechanical alignment. Some trade-off between field of view, collection efficiency and spectral resolution has to be found. Due to the design of optical spectrometers, a high spectral resolution is obtained by following two rules: having the smallest spot and smallest angle (smallest numerical aperture for the spectrometer) at the entrance of the spectrometer. The spot formed on the sample appears as a magnified spot at the spectrometer entrance. So, if we want to match the numerical aperture of the collection optics (NAc) to that of the spectrometer (NAs), we need an optical system having a magnification equal to NAc / NAs . We see here the paradoxical requirement of having a high NAc and a high spectral resolution, as this leads to a large spot at the entrance of the spectrometer when a small one is required. Therefore, if a smart trade-off is not found, one is obliged to use a small slit at the spectrometer' entrance, at the price of a loss in intensity. Also, as shown in Fig. 5, this restricts the field of view attainable for a 2.1.3. Angle-resolved measurement As described in Fig. 4c and d, angular analysis can be performed on the photon beam exiting from the mirror. There is indeed a one to one correspondence between the position of a pixel in the far field image of the mirror, and the direction of propagation of the photon beam out of the sample. The emission pattern can thus be retrieved from an image of the mirror through a mathematical transformation [35]. There are two major ways of acquiring this image. The first one, depicted in Fig. 4c consists in projecting the image onto a CCD. When needed, the beam can be filtered in wavelength, to isolate mode-specific patterns [5,19]. The full angular and spectral information could then be theoretically reconstructed by using different filters sequentially. However, the second form of angular distribution measurement is more efficient if the full spectral information is to be analysed. As depicted in Fig. 4d, it consists in selecting a given photon path (thus a given direction of propagation) using a pinhole, and analysing it spectrally through a spectrometer. Then, by scanning the pinhole, a full angular and spectral mapping can be performed. An application of this mode is given in Section 3.2.3. In both modes, a polariser can be used along the beam path. The relation between the signal measured after polarisation and the polarisation of the emitted beam is not straightforward due to the high numerical aperture of the collecting optics. Nevertheless, the full polarisation information can be retrieved using dedicated schemes [36]. 54 Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel Fig. 5. Basic constraints on a spectrometer for CL spectral imaging. For the sake of simplicity, the photon beam path has been straightened and aligned with the electron beam path. The collection optic has to collect the largest signal (high numerical aperture), while at the same time the spectrometer has a small numerical aperture. This results in a large magnification of the source (O1) at the entrance plane of the spectrometer (here, the magnification has been considerably reduced for the sake of the representation). Also, the size of the light spot at the entrance of the spectrometer defines its spectral resolution. Any shift of the source (O1 to O2) with respect to the focal point of the collection optics (either due to a misalignment or a large scanned area) is magnified by the collectingpropagating optics (I1 to I2), which leads rapidly to a vanishing of signal reaching the spectrometer. Fig. 6. Coherent and incoherent excitation in CL. (a). Coherent excitation. ① An electron impinges on a nano-object (here a metallic nanorod) and ② polarises it (here, only the longitudinal dipolar plasmon mode is shown). ③ The excited mode freely oscillates which may lead to radiation in the far-field. (b). Incoherent excitation. ① An electron impinges on a thin piece of material. ② When the incoming electron is inside the material, it creates a bulk plasmon (among others but much less probable excitations), that ③ quickly de-excites in the form of a small number of electron-hole pairs. ④ the charge carriers can then drift for about a typical diffusion length distance (note that the charges are not necessarily bound together, contrary to this example), before ⑤ de-exciting either nonradiatively (black stars) or radiatively (yellow one). 3. Physical principles and applications given spectral resolution given by the entrance spot size, as a slight misalignment between the electronic and optical paths may result in a photon beam shifted away from the entrance of the spectrometer. These limitations stem from a general physical principle, namely the conservation of the etendue (see e.g. [20]), which is basically the consequence of Liouville's theorem. Applied to the present situation, it states that [20]1 FOV = d NAs 2 NAc 3.1. Coherent and incoherent excitation There exists essentially two ways of creating luminescence from a sample with a fast electron beam, as shown in Fig. 6, a coherent and an incoherent way [24]. The coherent way concerns the excitations of coherent electromagnetic waves, such as surface plasmons or guided modes within nanoobjects (it is illustrated in the case of plasmons in Fig. 6): the electromagnetic field following the electron polarises the nanoparticle and thus creates a plasmon or a polariton, that may decay in the form of a photon. This scheme is said to be coherent because the optionally emitted photon has a memory of the way it has been created; for example, an electron impinging on the same point from different angles may lead to different types of emissions. The incoherent way concerns the creation of a bulk plasmon, that very rapidly decays in the form of electron-hole (e–h) pairs. It is said to be incoherent because the e-h pairs do not have any memory of the incoming electron. Once created, the e-h pairs may diffuse into the material, and find energy minima where they can recombine either radiatively or non-radiatively. This difference is very clear in at least one case. If one considers the emission pattern, the situations prevailing in the two excitation modes are totally different. In the incoherent case, the emission pattern only depends on the object characteristics: electronic band structure details, shape of the nano-objects, etc. Whatever a particular excitation, say, an exciton, is created, the emission pattern will be the same. The situation is opposite in the case of coherent emission. For example, a plasmonic nanoantenna excited on one tip will emit light in the direction of the other tip: the light emission pattern depends both on the geometry of the object and on the interaction geometry. As a final note, one can generally say that the spectra of coherent excitations are best interpreted using the analysis of the Maxwell equations and related boundary conditions, while the spectra of incoherent excitations are best interpreted using the analysis of the Schrodinger equation and related boundary conditions. (1) where FOV is the field of view in the image plane, d is the slit width of the spectrometer or entrance spot size, whichever is the smallest. Note that the effect of a misalignment due to a shift can be accounted for by assuming that the FOV is equal to the misalignment error. Therefore, this rule must be obeyed to keep both spectral resolution and intensity. NA A slit of 100 μm and a typical NAs = 1/10 are typical values for a c reasonable spectral resolution and collection efficiency. This means that a precision at least better than 5 μm in all the three spatial directions must be realised to get both high collection and high spectral resolution without intensity loss. In practice, the alignment precision might even need to be better, as a typical mirror (parabolic or elliptical) is, in terms of imaging capability, extremely aberrated as soon as the source point is displaced from the focal point. The consequences for practical systems are that 1: alignment between the mirror and the sample has to be better than a few microns in the three dimensions and 2: the sample has to be movable independently of the mirror, otherwise only areas a few tens of microns square can be studied on each sample. Finally, for the same reason, the larger the field of view, the poorer the spectral resolution. Indeed, when scanning large regions, one expects the spot at the entrance of the spectrometer to move (and thus the spectra to shift on the camera) and possibly not to enter the spectrometer. Edwards et al. have been discussing several workarounds for this situation, the conceptually simplest one consisting in scanning the sample instead of the beam [20]; another more flexible possibility is to use a bundle of optical fibres that is optimised to conserve as much as possible intensity and spectral resolution, as discussed in [39]. 3.2. Coherent excitation 3.2.1. Transition radiation and cerenkov emission The most simple form of coherent excitations produced by an electron is probably Cerenkov emission. The light cone of Cerenkov radiation is always aligned on the electron beam path, as a clear demonstration that the Cerenkov emission is coherent. 1 A similar equation can be found in [20]. The difference here is that our expression is valid for arbitrarly large NAs. 55 Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel semi-analytically solvable systems to guide the intuition, see [2] for a discussion on this point. A general description, taking advantage of the very intuitive formalism developed for Near-Field optics has however been given in [53]. In this paper, it was shown that the signal measured in EELS, as a function of position and energy, was very close3 to a quantity known as the electromagnetic local density of states (EMLDOS), projected along the electron beam path (zEMLDOS). In a nutshell, for a given structure, the zEMLDOS is a 3D quantity that corresponds spatially to the modulation of the square of the electrical eigenfield (projected along z), and spectrally peaks at the eigenenergies of the structure. As the zEMLDOS is proportional to the square of the eigenelectrical field, it also tells directly how the density of electromagnetic energy varies locally. In the quasistatic case, i.e for objects small enough so that the Maxwell equations reduce to the Poisson equation, the interpretation can be made even simpler: the zEMLDOS gives the spatial distribution of the eigenpotential of the structure. However, the interpretation for CL is slightly more involved. Indeed, for non-dissipative modes, such as Bloch waves in a photonic band gap, all the energy lost by an electron is transformed into radiation. In these cases, EELS and CL are exactly identical, and the former interpretation applies [53]. However, in the more common case of dissipative excitations, such as plasmons, part of the energy given by the incoming electron to the medium is dissipated in the form of heat, and therefore not re-emitted. By analogy with the EELS case, and understanding that CL probes only the radiative modes, it is tempting to identify CL with a different EMLDOS [55], specifically the radiative EMLDOS (rEMLDOS), which precisely describes the density of radiative states [56]. This analogy has been made rigorous recently [57]. The EELS is still related to the zEMLDOS, while the CL is related to the zrEMLDOS. This later quantity has the same spatial properties as the full zEMLDOS. Therefore, modes are mapped spatially the same way in EELS and CL. This is demonstrated experimentally in Fig. 7a, where maps of the eigenmodes of a silver triangle are almost identical for the two first eigenmodes. However, two differences emerge between the two quantities, as well as between EELS and CL. First, of course, only radiative modes participate in the rEMLDOS. More precisely, the more radiative a mode, the higher its weight in the radiative EMLDOS. This is exemplified in the case of a gold nanoprism small enough so that only one of its modes is radiative, see Fig. 7, left. This mode, peaked at the tip of the triangle, is well known to be dipolar. Now, in the quasistatic limit, only dipolar modes are radiative. Therefore this dipolar mode is the only visible mode with CL, while all modes are seen in EELS. Second, the spectral response is slightly different between the full and the radiative zEMLDOS. Consequently, EELS and CL spectra are shifted, see Fig. 7, right. Although it might sound counterintuitive that the resonance energy value of an eigenmode depends on the technique used to measure it, it is a well-known property of damped excitations [58]. Two well-established macroscopic spectroscopic optical quantities, namely the extinction and the scattering cross-sections exhibit the same shift. The extinction cross-section quantifies the energy taken out of an incoming photon beam by absorption or scattering due to its interaction with a nanoparticle. The scattering cross-section quantifies the energy transferred through the scattering alone. It is possible to formally link the spectral properties of EELS to the extinction, and the that of the CL to scattering [11,57], explaining the close similarities in the shifts. One of the consequences of this correspondence is that the EELS intensity4 scales as the volume of the object of interest, while the In vacuum, an electron plane wave and a photon plane wave cannot exchange energy, because their momenta do not match for any energy: there is no Cerenkov emission in vacuum. However, energy and momenta matching may arise in an insulating infinite medium, and this is the reason for Cerenkov emission. For plasmons, there is also the need for the energy and momentum to be conserved. In this case, the momentum matching arises from the fact that their related electromagnetic field is evanescent and therefore contains a large distribution of plane wave momenta, see e.g. [24]. Note that in the next section, we will use a different formalism better adapted to plasmons (the electromagnetic local density of states). The emission of Cerenkov radiation depends on the electron speed and the medium's optical index, the speed of the electron needing to be larger than the speed of light in the medium for the momentum matching to be possible. If the medium possesses an interface, another type of coherent emission arises: transition radiation (TR). There are different possible interpretations for the mechanism leading to light emission in TR [24,40]. One is that when the electron traverses the surface, it experiences a sudden change of optical indices, and thus a sudden deceleration inducing then light emission. Another interpretation consists in evoking the image charge that the electron creates in the medium when it is outside. The image charge and the charge itself form a dipole of varying amplitude as the electron and its image travel towards each other and eventually collapse, and therefore produce radiation. Whatever the interpretation, the TR produces a wide band spectrum that can be analytically deduced [24], and which only depends on the dielectric constant of the medium and of the electron speed. TR was first explored in the context of CL by Yamamoto, using a STEM [41]. Recently, Brenny et al. [40] used the robustness and almost universal character of the TR radiation emission to calibrate the CL spectral acquisition chain. In most of the applications of STEM-CL, the TR are relatively weak and uniform in energy. They usually have no real influence on the detection of peaks and can be safely ignored when using SI, or corrected for by subtraction from a spectrum taken outside the region of interest. If panchromatic imaging is to be used, then TR might be an issue for weakly emitting objects [42]. Finally, it is worth noting that the frontier between Cerenkov and TR emission blurs in objects with boundaries [43], and that Cerenkov emission can be used as a probe of photonic devices [44,45]. 3.2.2. Theoretical foundations for the interpretation of coherent excitations in STEM-CL The theoretical description of the interaction of an electron beam with coherent electromagnetic modes, such as surface plasmons or guided modes is in principle relatively simple. A common and very robust assumption2 is to assume that locally the electromagnetic response of a material is well described by the dielectric constant of the corresponding bulk material. Within this so-called local continuum dielectric theory [46], the interaction of an electron and a material and therefore the EELS and CL signals, can be directly computed by solving the Maxwell equations [24]. The required boundary conditions are given by distinguishing regions of different dielectric constants, and the electron beam is supposed to be a point charge travelling at constant speed and acting as a source term in the Maxwell equations. Many numerical solutions exist to this problem, most of them now openly available, including the boundary element method (BEM [47– 49]), the discrete dipole approximation [46,50,25], the green dyadic method [51] or time domain finite difference [52]. Nevertheless, they give very little physical intuition on how to interpret STEM-CL maps in simple terms. Unfortunately, there are also only very few analytically or 3 The correspondence is not exact. There exists a Fourier transform along the electron beam direction to be done, that makes regular EELS and CL spatial variation difficult to interpret quantitatively. In the case of EELS, 3D reconstruction techniques can make the correspondence almost quantitative, see e.g. [54]. 4 Note that we are here dealing with surface excitations. Volume excitations, like bulk plasmons, will have cross-section values scaling as the thickness of the object. 2 We note that objects emitting light through coherent excitation (therefore objects of interest for CL) are all sufficiently large for the classical assumption to work perfectly. This isn't the case for very small (less than 5nm) objects, for which quantum corrections to the classical assumptions are necessary [24]. 56 Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel Fig. 8. Polarised spectrally filtered CL maps of a silver nanorods. One can see the oscillations of the plasmons waves, with different localizations for each polarisation. A typical cross-section is schematised at the top, showing the symmetry of the modes revealed by both polarisations. After [62], reprinted with permission. Fig. 7. Comparison of EELS and CL maps and spectra. Left panel: EELS (left) and CL (right) mapping of the two first plasmon modes (dipole first two lines, hexapole next lines) for a relatively small gold nanoprism (first lines of dipole and hexapole) and relatively larger silver prism (second lines). EELS and CL have almost the same spatial distributions. However, the hexapolar mode does not show up in CL for the smaller prisms, as these modes are non-radiative in small particles. Right: EELS and CL spectra acquired on two different beam positions of the larger silver prism. For both the dipolar and hexapolar modes, one sees an energy shift. Adapted from [4,11]. showing the impressive ability of electron-based spectroscopy for plasmon mapping [10], and since then demonstrated to be a well adapted tool in this respect [60–62,11,4,63]. A stereotypical case where STEM-CL has an obvious interest in understanding plasmon properties has been given in [62]. In this work, large (100 's of nanometers in length, tens of nanometers in diameters) silver nanorods were studied by spatially resolved STEM-CL, and a polariser was used in conjunction. In Fig. 8, polarised spectrally filtered maps of two silver nanorods are displayed. Both exhibit the expected spatial modulation, which reflects the modulation of the zEMLDOS. The use of a polariser helps to identify the nature of the modes, as they don't have the same symmetry along the perimeter of the nanorod: one possesses a uniform charge distribution along the cylindrical shape of the rod, therefore having an almost homogenous intensity distribution in the transverse direction, while the other has a charge sign inversion along the section, translating in a intensity distribution peaked on the sides of the cylinder. In a recent study, this kind of analysis has also been used to unravel the physics of coupled nanoholes [63]. Alternative techniques are however worth considering. SEM-CL has proved to be extremely powerful for single plasmonic particle analysis [18,64–66,52]. However, theory predicts a higher cross section at higher accelerating voltage, as confirmed already in the pioneering work of Yamamoto [10], and quite logically, the smallest nanoparticles have been measured by STEM-CL [11], see Fig. 7, rather than SEM-CL. Probably, at the moment, the advantages of SEM-CL, in particular the much higher versatility of a SEM with respect to a STEM and the increased available currents, explain the obvious practical success of the SEM-CL compared to STEM-CL for plasmonics applications. STEM-EELS is also extremely suitable for plasmon mapping, especially for very small nanoparticles, see e.g. [24,2,29,67,25]. This is because the ratio of the cross-sections of CL to EELS scales roughly as the volume of the nanoparticle [2,24], so, for particles smaller than typically a hundred nm, EELS is worth considering. One limitation, however, is the poor spectral resolution of EELS in most of the electron microscopes (at best 100 meV, even if new monochromation techniques are now providing 10 meV [68]). This is larger or of the order of a typical plasmon full width at half maximum (FWHM). In contrast, any well-made STEM-CL system can easily deliver a 10–30 meV spectral resolution without loss of intensity. Also, well-resolved EELS microscopes and spectrometers are rather expensive, and EELS SI analysis may require extensive alignments and treatments [2] whereas STEMCL is much cheaper, can fit most of the older generation microscopes and does not require extensive data treatments. CL intensity scales as the square of the volume. This is exactly what happens for the extinction cross-section, scaling as the volume, and the scattering cross-section, scaling as the volume squared. To end up this description, it is worth mentioning that combined EELS and CL experiments are quite involved, while independent EELS or CL measurements are more straightforward and give very similar information as soon as the particles are large enough. Therefore, a combined experiment should probably only be performed when trying to understand the differences between the absorption and radiative properties of modes [11,57,59], or if for example the exact shape and energy position [57] of the peaks are worth investigating. A special care has to be taken in calibrating the two different techniques' spectrometers. Indeed, the expected shifts between both (of the order of tens to one or two hundred of meV) can be rapidly smaller than a typical EELS calibration error. Also, the optical spectrometer response is usually non-uniform. In particular, it is peaked around the so-called “blazing” wavelength of the particular grating used with an asymmetric response on both sides of the peak; also, the camera used usually has a non-uniform quantum efficiency. For experiments concerned with short wavelength intervals and sharp peaks (see for example Section 3.3), these non-uniformity are causing minor effects such as small changes in the peak intensity ratios. However, in the case of plasmons or other excitations with wide peaks, this can change their shape and induce energy shifts, and if several peaks span a wide energy region, this induces large errors in the estimation of peak intensity ratios. Also, the conditions for working in EELS and CL can be quite different (acceleration voltages when working in two different microscopes [59], difference in electron beam current used for the two techniques, that can span orders of magnitude [2,11], potential local changes due to hydrocarbon or water contamination during the experiment or between different microscopes…) and care has to be taken to disentangle differences which would happen due to the different physics probed by EELS and CL or different technical details that could be different between the two spectroscopies but not related to any relevant physics. 3.2.3. Plasmons Single particles. Historically, STEM-CL was the first technique 57 Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel Fig. 6. Therefore, there is no surprise that the way CL mapping has to be interpreted is very different in the case of coherent excitations. In particular, the concept of EMLDOS mentioned in Section 3.2.2 istotally irrelevant. As briefly stated before (see Fig. 6), the processes of light emission can be decomposed into several steps that we rediscuss in a bit more details here. We first consider a very thin sample. By “very thin”, we mean that the thickness is much smaller than the mean free path λe of the electron in the material. λe depends on the material and on the accelerating voltage, with λe increasing with increasing acceleration voltage. For electrons of high energy, such as those used in a TEM, the electrons are losing energy essentially through excitations of bulk plasmons. The probability for an electron to experience n such inelastic (t / λ ) n scattering events when traversing a thickness t is Pn = n !e e−t / λe . Thus, for t / λe ⪡1, the incoming electron will experience zero inelastic event with probability P0 = 1 − t / λe and 1 inelastic event (one bulk plasmon creation) with probability P1 = t / λe . For the few electrons losing energy, the energy given by the electron to the material will be very limited and will roughly correspond to the bulk plasmon energy (typically 20– 30 eV, depending on the materials). The bulk plasmons have very short lifetimes (a few fs), and thus de-excite in the form of hot electron-hole pairs [72]. Due to energy and momentum conservation, typically only a few electron-hole pairs [73–75] can be generated.5 The hot e-h rapidly (few ps) thermalise to the local energy minimum. They then diffuse within the material before meeting a radiative or non-radiative centre in a few tens of ps. If the e-h excite a radiative centre, it will emit light with a time lapse equal to its lifetime τe. If we assume that the lifetime of the emitters is larger than any of the above-mentioned timescales, several excited states can be excited at the same time. This is the case for many emitters of interest, which have lifetimes larger than a few hundred of ps. All these excited states will then re-emit in a typical time window equal to τe. The resulting photons will then be emitted in synchronisation, as was recently demonstrated in the case of radiative point defects in nanodiamond and h-BN nanoparticles by measuring the time autocorrelation function (see Section 2.1.4) of CL emission, see Fig. 10. Note that the effect depends on the incoming electron current: at higher current, the photon bunching decreases, because the statistics of the emitted photons start to be dominated by those of the incoming electrons [75]. Applications of this physical effect to measure lifetimes at high spatial resolution will be given later, in Section 3.4.2. When the sample thickness increases, several effects arise, which are represented in Fig. 11. The simulations represented in this figure were performed using CASINO v2.4.8.1 with Rutherford cross-sections, 105 incident electrons and considering a 1 nm wide electron probe [76]. The GaN density was set to 6.15 g. cm −3. Fig. 11 shows the lateral spread of the deposited energy, which is related to the region in which carriers that will lead to CL signal are generated [77]. This does not take into account any carrier diffusion. For moderate thicknesses (t / λe < 1 ≈ 1), an increasing number of energy losses arise, each eventually responsible for additional electron-hole (e-h) pair creation. However, in this limit (t / λe ≈ 1) the beam is very weakly broadened by interaction with the sample.6 For increasingly thicker samples, or decreasing acceleration voltages, one has to rapidly take into account the deflection of the electron due to the interaction with the sample. One sees in Fig. 11a) (low energy electrons as used in a SEM) that the net result of the interaction is a spread of the electron onto a volume sometimes called the “interaction pear”. The interaction pear The EELS stability is also rather poor for obvious reasons. Indeed, a given feature at energy δE in an energy loss spectrum comes from an electron having an energy of E0 − δE , where E0 is the nominal energy of the electron. Therefore, measuring an energy loss at δE = 1 eV with an electron beam nominal energy of E0 = 10 5 eV requires a precision of 105; measuring a FWHM of 100 meV a precision of 106. These are extremely stringent conditions, partly explaining the long development time of high resolution EELS. On the other hand, CL relies on the detection of photons, whose properties do not essentially rely on the primary electron energy. Also, STEM-CL or SEM-CL can give information on the emission directionality and full polarimetric information, which is not yet available in STEM-EELS. STEM-CL is thus a very interesting alternative to STEM-EELS for quick characterisation of nanoparticles plasmonic properties. Finally, it would be tempting in this comparison to point out the fact that STEM-CL can be used for temporal investigations of SPs (lifetime measurements, measurement of autocorrelation functions…). Unfortunately, plasmon lifetimes are much too short (typically tens of fs) to be reached by STEM-CL common measurements tools and most of the PL techniques. Therefore, alternative techniques have to be found [26]. Plasmonic crystals. STEM-CL has been extensively used to study plasmonic crystals [69–71] with the set-ups shown in Fig. 4 c and d. An example is given in Fig. 9. In this paper, the authors have studied plasmonics band gap materials made up of regularly spaced silver nanorods. For a constant diameter, an energy band gap forms as seen from the dispersion relation in Fig. 9a. However, the situation changes when a defect is introduced, in this case a series of nanorods with different diameters (Fig. 9c). They induce new states in the band gap (see Fig. 9b), that can be imaged in real space as well, see Fig. 9d,e,f. 3.3. Incoherent excitation 3.3.1. Physical principle of light generation by incoherent excitations As already mentioned, there is a large difference in the way light emission is triggered for coherent and incoherent excitations, see Fig. 9. Plasmonic crystal optical properties in the reciprocal and real space. The 2D plasmonics crystal is composed of silver pillars 100 nm high and has a period of 600 nm. The nominal diameter of the pillars is 250 nm; a. Measured dispersion relation for a perfectly periodic crystal. An energy band gap is observed. b. Measured dispersion relation for an imperfect crystal where rows have been substituted with 400 nm diameters pillars, as shown on the panchromatic image in c. Two states appear in the band gap. d, e,f: real space mapping at different energies showing the localised modes at the origin of the band gap states. d, e were acquired with two different polarisation states, f is an unpolarised measurement. Reproduced from [5] with permission. 5 Note that even if the bulk plasmon would de-excite in the form of the lowest energy eh pair (i.e having an energy equal to the energy band gap Eg), the number of e-h pairs would be equal to N ≈ Eg /Ep which is typically less than ten and places an upper limit on the total number of e-h pairs created by a fast electron in a thin sample 6 Of course, using an ångström-wide electron beam, such a broadening would be already large enough to prevent atomic resolution. However, considering the nanometer spatial resolution discussed for CL applications, the broadening can be considered negligible. 58 Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel Fig. 10. Synchronised emission of photons coming from nitrogen-vacancy centres upon electron excitation. CL g(2) (τ ) measurement (continuous lines) for intensity values I ranging from 1.2 to 11 pA for an individual nanodiamond, 60 nm thick. Each measurement lasted 5–20 min. The data were fitted with the Monte Carlo simulations (dashed line). The lifetime was retrieved using an exponential fit of the bunching curves, leading to τe ≈ 26 ± 1 ns . All the parameters of the Monte Carlo simulation were kept fixed except the current, which was changed until a good agreement between the experiment and the simulation was found. The resulting fitted currents are written in parenthesis next to the measured experimental values. Inset, left: PL g(2) (τ ) measurements performed at two different laser excitation powers on another ND from the same batch. In contrast with the case of CL, the function is totally flat. After [75]. essentially dissapear for higher voltages, such as used in STEMs (Fig. 11b)). Within this volume, the electrons may interact inelastically. Excited e-h pairs may thus be generated in a volume much broader than that given by the probe size or probe geometrical broadening. Together with the further e-h diffusion, this certainly broadens the resolution one can expect from the sole consideration of the probe beam size. As a rule of thumb, the higher the electron energy and the thinner the sample (see Fig. 11c), the lower the interaction, the less the number of hot e-h pairs created, the less the energy lost by the electron, and finally the higher the spatial resolution. An important point has to be made here. In CL, we only control the electron beam, but we don't know where the emission comes from. Therefore, information extracted from CL maps will rely on assumptions about the diffusion mechanism, recombination, etc… One of the advantages of working in a STEM is to get additional information (morphology, chemistry, etc…) that can help in guiding these assumptions. Another approach is to use a near-field set-up to detect the light emitted at some place when triggered by the electrons at another [78]. Such an approach is very difficult to implement in a STEM, but would provide extremely interesting physical insights. 3.3.2. Comparison to EELS In contrast with the case of coherent excitations, where the EELS and CL signals have a very close resemblance, it turns out that in the general case STEM-CL and STEM-EELS signals are quite different and the former is much more suitable than STEM-EELS for the study of optical properties of semiconductors close to or above the band gap. There is a fundamental reason for this, aside experimental issues, especially the lack of spectral resolution of EELS, which will however sooner or later be improved [68]. In an EELS experiment on a semicondutor, one measures the whole energy transferred from the electron to the material. Therefore, EELS spectrum features close to or within the band gap will share a large resemblance with optical absorption. In particular, EELS will exhibit after the gap a large absorption band. The position of the gap is in practice difficult to define mainly because of the tail of this rather intense band. CL on the Fig. 11. Result of Monte Carlo simulations. The contour lines show the projected lateral spread of the deposited energy (which is proportional to CL signal) on a GaN film with a thickness of 50 nm hit with an electron beam with 5 keV in (a) and with 60 keV in (b). The contour lines indicate the fraction of energy deposited inside each line (the 95% contour line indicates that 95% of the energy is deposited inside this line). In (c) the deposited energy spreads up to 99% of the total value for 10, 50, 100 and 1000 nm thick GaN samples for several electron beam energies ranging from 1 to 200 keV. other hand is a two-step process. First, some energy is transferred from the electron to the material (absorption), and then converted to hot e-h pairs, which will populate excited states in the material, possibly emitting light (emission). Therefore, the cross-section for CL is proportional to that of the energy-summed EELS cross section. The energy available for the creation of e-h pairs can be extremely large, as it includes the volume plasmon. This boosts the CL cross section 59 Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel (Fig. 12) to the ca. 30 nm resolution in case of an isolated GaN QDisks 7 in Fig. 13. In the two cases, of course, the resolution is enough to get the relevant information. The same things happen for the emission of an individual nitrogen-vacancy defect in diamond, the CL intensity signature of which extends over roughly 70 nm, or in individual CdSe/CdS quantum dots for which the spatial resolution is precisely equal to their size (Fig. 13). Concerning the deleterious effect of the electron beam on the objects of interest, it is worth noting a paradoxical advantage of using a fast electron beam. Of course, such a beam can disrupt the atomic structure examined, and radiation damage is likely to kill the luminescence very quickly [87]. However, if one is able to find an appropriate acceleration voltage at which the damage is not happening rapidly, then the transfer of energy between the electron beam and the sample can be extremely weak. In a typical SEM situation (thick sample, low voltage) each electron interacts with the sample, and all the energy of each electron is transferred to the sample. This induces a large density of charge carriers, possibly leading to non-linearities. Also, this can easily heat up the sample. In a SEM, a typical number of charge carriers created per incoming electron is given by [1] N = E0 /3Eg where E0 is the incoming electron energy and Eg the energy gap of the material. Thus typically, for GaN in a SEM experiment at 30 keV, 3000 e-h pairs will be created per electron. In a STEM, for a thin sample, a large number of incoming electrons may even not interact inelastically with the sample, thus not transferring energy to the sample. For the electrons interacting inelastically, the energy transfer will be small (of the order of the bulk plasmon energy), leading to the creation of a small number (say, around 3) of e-h pairs [72,74]. This makes the STEM-CL a potentially less invasive technique. This is demonstrated in Fig. 14, where the luminescence emitted by the same CdSe/CdS Quantum dot has been recorded by STEM-CL and PL [89]. Firstly, it makes obvious from the figure that a single II-VI Quantum Dot can be measured by CL, in contradiction to early statements based on SEM-CL experiments [85]. One can see that the emission line wavelength is almost the same (the shift is due to different measurement temperatures in the PL and CL experiments). More importantly, the FWHM of the peak is larger for the PL measurement than for the STEM-CL. This surprising result points to the fact that STEM-CL can be even less disruptive than PL for measurements on sensitive luminescent nano-objects. Beyond the high spatial resolution offered by STEM-CL, the possibility of working in a linear regime even when addressing a single, atomic-like emitter and yet getting enough signal is certainly an advantage, whose exploitation is discussed in the following sections. dramatically. Moreover, schematically, the CL spectrum is very peaky possibly including a peak at the band gap energy for example. Thus, all the previously collected energy, which was spread over a large energy range in the EELS spectrum, may now be experimentally present in a peak, which significantly increases the SNR, and helps to determine precisely the optical band gap position. 3.3.3. Comparison to SEM-CL and PL SEM-CL and PL are so well adapted to the study of luminescent semiconducting materials that one may wonder why it would be attractive to switch to STEM-CL, which is burdened with all the annoyances of TEM techniques: sample preparation is difficult - for example it is absolutely impossible to study directly samples grown on a substrate and it is more costly and less versatile than the two techniques. On the other hand, it also has all the advantages of TEM techniques: in addition to the optical signal, morphology and structure can be determined with possibly atomic resolution. With respect to PL, STEM-CL has the same advantages as with SEM-CL: a spatial resolution which is not diffraction-limited (i.e sub-200 nm resolution is theoretically possible) and an easy access to the properties of deep blue or UV luminescence, which is always difficult and expensive for pure optical techniques. We note also that very high spectral resolution can be obtained with SEM-CL [79–81], although, as we will see below, not with the ultimate spatial resolution. Now, SEM-CL has two main limitations. Firstly, despite impressive sub-diffraction resolution [82,83,79,21,84], SEM-CL has not demonstrated the capacity to resolve the luminescence at the relevant scale (that of a confinement length-few ångströms or nanometers) for some of the most technologically relevant materials (such as III-V and in particular III-N). This limits its use to the study of well-separated emitters, or leads to ambiguities in the assignment of emission wavelengths. Secondly, the strong interaction of the electrons with the material, which increases very rapidly when decreasing the accelerating voltage (see Fig. 11), leads to heating of the sample and non-linearities, ultimately leading to energy shifts and broadening when trying to access individual quantum-confined objects [82,85]. STEM-CL partly addresses the two issues. The spatial resolution in CL is limited by whichever is the larger quantity between the probe size, the excitation pear radius and the diffusion length of the charge carriers. In the case of a STEM, the probe size is negligibly small. However, the main interest is that, due to the high electron speed, the excitation pear size is also extremely small for sample with thicknesses compatible with (S)TEM imaging (say a few tens to a hundred nanometers); the broadening due to the electron interaction with the sample is thus negligible at the scale of a confinement length. Thus, the diffusion length is the quantity defining the spatial resolution in STEM-CL. However, as most of the objects of interest (quantum dots, quantum wells…) are efficient charge-carrier traps, the diffusion length and thus the spatial resolution are essentially determined by the size of the object of interest, and thus it is not relevant to get a better spatial resolution. This is exemplified in Figs. 3 and 12, where the spectral imaging has been performed on a stack of GaN Quantum Discs (QDisks) embedded in AlN. The strong confinement makes the diffusion length as small as a few nanometers [9]. However, if the QDisks are separated by less than the diffusion length, emission from the nearest neighbours can overlap. In this case, as explained in Fig. 12, a rigorous analysis of the SI data allows one to assign specific emission lines to a given quantum confined structure [8]. Indeed, it is clear that the signature of each QDisk is well isolated in the combined spatial/spectral space, and can be directly correlated to the maxima in the HAADF image [8,9,29]. We note that the diffusion length is dependent both on the type of materials analysed and how they are combined into nanostructures. One can compare the resolution of a few nanometers in a stack of GaN QDisks 3.3.4. Applications of incoherent excitations Note that in the next section, we will use a different formalism better adapted to plasmons (the electromagnetic local density of states). High resolution mapping of the spatial variation of the optical transition energy and intensity. The first obvious application is the study of sets of quantumconfined objects in their environment. Fig. 12 presents the study of a set of individual GaN QDisks embedded in AlN, within a nanowire. As already explained, it is possible, through a detailed analysis of the whole SI [8,9], to assign a given emission line to a given QDisk. At the same time, it is possible to get the size of every QDisk with monolayer (ML) precision, and also to know exactly where each QDisk is within the nanowire. This makes it possible to analyse the emission wavelength as a function of the ML number, as shown in Fig. 12c. At first sight, this dispersion seems unremarkable. This is the dispersion 7 Note also that the CL intensity signal is even not symmetric with respect to the QDisk, due to the fact that the way the charge carriers are driven to the QDisk depends on the position of the electron probe with respect to the QDisk, see [86]. 60 Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel Fig. 12. Spatial and spectral identification of individual QDisks stacked in a nanowire. (a). HAADF of a nanowire containing a stack of GaN QDisks embedded in an AlN shell. GaN appears bright, AlN dark. The growth direction is from left to right. Scale bar is 20 nm. (b). 2D plot of a one-dimensional SI. Wavelength versus electron probe location is shown. On top is the HAADF profile acquired during the one-dimensional SI. Inset: magnification of part of the plot showing that individual QDisk signatures consist in well separated 2D maxima in the wavelength/position space. Note also how these maxima correspond to those in the HAADF, i.e. to the presence of GaN. (c). Dispersion relation for the QDisks of two nanowires. (d). Wavelength versus disc position for an individual nanowire (crosses are simulations). The Qdisk index increases along the growth direction. Note the redshift for a given QDisk thickness as the QDisk shell thickness decreases. After [8]. Fig. 13. Sample-dependent spatial resolution. HAADF Images of (a). A nanodiamond, (b). A set of CdSe/CdS quantum dots and (c). a GaN quantum disc within an AlN nanowire. The corresponding CL image (d). Fitted on the nitrogen vacancy emission line [88], (e). Fitted on the CdSe/CdS emission lines [89] and (f). Filtered on the GaN quantum disc [86]. Note the asymmetry of the CL intensity. can exist within III-nitrides. These fields are so strong that they can bend the bands within the QDisks; an effect called Quantum Confined Stark Effect (QCSE) [90]. If the bands are bent enough, then the difference in energy between the lowest electron state and the highest hole state can be smaller than the bulk band gap, explaining the effect seen. relation for a textbook “particle in a box”: the wavelength is proportional to the size of the box (the QDisk’ width in this case). However, confined states should naturally arise at energies larger than that of the bulk (GaN, in this case). This is not the case for some of them, see Fig. 12c. This apparent contradiction is however solved when one considers the fact that high internal (either pyro- or piezoelectric) fields 61 Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel defects [105]). Quite generally, they locally change the electronic properties of the material, creating states in the band gap, and can be detected and even quantified through CL [81]. Therefore, they are likely to quench the NBE emissions of the material because e-h pairs may be captured by these states lying at lower energy than the NBE ones. The presence of defects may thus be detected either by a quenching (darkening) of the NBE emission, or by an emission at the defects energy, if they are radiative. Its imaging resolution and different imaging modes makes STEMCL a technique of choice for studying the optical properties of 1D [102] and 2D defects [100], as there exist techniques to specifically image these defects. The case of 0D defects is more difficult, as imaging point defects requires extremely thin samples, which is generally incompatible with a high CL emission. A very good example of the potentiality of STEM-CL for 2D defect analysis has been given in [100]. In this experiment, a basal plane stacking fault (BSF) in a GaN nanocolumn (i.e wide nanowires) was studied. One can directly see in Fig. 16a the presence of the BSFs, identified as brighter lines in the image. The panchromatic image in Fig. 16b shows that there is emission almost everywhere in the nanocolumn. However, a spectrum-line clearly shows that the NBE emission at 360.6 nm is quenched when the electron probe approaches the BSF region. Indeed, at around 150 nm from the first BSF, the BSF emission (around 361.7 nm) starts showing up. This is an interesting example of correlation between conventional imaging and spectral imaging. In addition, it is worth noting that the experiments were performed at very low temperature (15 K). The use of the necessary liquid He stage is always a burden for TEM experiments. However, no emission for the BSF is expected at liquid nitrogen or room temperature, and this demonstrates the need for better Helium stages for performing meaningful spectroscopy experiments. Other defects can be obviously studied by STEM-CL. Defects in diamonds are a good example [88]. Among them, NV centres in diamond are of particular interest. Indeed, such centres are wellknown to be single photon emitters (SPE). As such, they are candidates to be used in many applications related to quantum cryptography and quantum computing. CL is a well-known tool in the study of such centres [105]. However, it is only recently that the mapping of individual NV centres has been reported [88]. The application of STEM-CL to the study of quantum-optical properties of defect centres will be presented in Section 3.4.1. Fig. 14. Comparison between PL and CL spectra of individual CdSe/CdS QDs. CL (red) and PL (blue) spectra of the same QD. The integration time is 1 min for PL and 50 ms for CL. The energy shift can be explained by a temperature difference between the measurements. Note the higher FWHM for the PL spectrum. (Inset, left) Scheme of the CL/PL experiment. (Inset, right) Scheme of the substrate used for CL/PL crosscorrelation. After [89]. The analysis also shows that, for a given QDisk thickness, known with a ML resolution, there is a wide range of emission energies. This is troubling, because the precision on both the emission wavelength and the size of the QDisks is much better than the observed differences; thus, the difference has to arise from a difference of environment. Indeed, if one plots (Fig. 12d) for a given nanowire the emission as a function of the position of the QDisks within the nanowire, one sees a systematic redshift along the growth direction. This is because the AlN shell around the nanowire generates strain which increases the bandgap, but the shell thickness decreases along the growth direction, reducing this effect, all else being equal. We thus see directly how powerful the combined use of STEM-CL and high resolution imaging can be for disentangling the physics of quantum-confined objects. Such an analysis can be nicely transposed to planar structures, such as InGaN multilayers [91]. STEM-CL finds a natural application in the III-N systems [92,8,9,93–97,86,98,99,91,100,101,97,102,103], but it is not restricted to quantum-confined systems. Indeed, STEM-CL is very useful for analysing sub-20 nm fluctuations in emission wavelength in (AlGa) N alloys [95,96], likely due to alloying modulations, or variations in exciton spectral fingerprints in h-BN [97], related to folding of this 2D material. Likewise, the very high degree of localisation in InGaN allows high resolution CL imaging [93,94,99,98,91,104]. This is interesting, because this is a material of high technological importance due to its potential tunability in the visible range, which makes it appropriate for applications such as photovoltaics or white LEDs. Fig. 15 presents two studies concerning InGaN inclusions embedded in GaN nanowires [93,98]. In such systems, the question is often to know wether all the inclusions are emitting, at which wavelength, and why. In Fig. 15 (left), one can easily see that only two inclusions are emitting, and the emission wavelength can be easily measured. The reason for one inclusion not emitting is not clear from this study [93]. However, the absence of emission may be related to threading dislocations [98]. In Fig. 15 (right), similar experiments have been performed [98]. In these experiments however, a high resolution image is available as well, demonstrating that the emitting inclusions under consideration do not include dislocations. This might explain the reason why no quenching of luminescence is observed in this case. Defect mapping. CL in general is quite well suited to studying defects in semiconductors, should they be 2 dimensional (stacking fault [100], grain boundaries [42]), 1D (dislocations [13]) or 0D (point 3.4. Advanced applications 3.4.1. Non-linear and quantum optics non-linear optics. Despite the huge interest in PL studies done with varying excitation power, the corresponding approach is much less frequent in CL. Power-dependent measurements demand the possibility of changing the excitation intensity by some orders of magnitude and can yield very rich information concerning for example the recombination routes and non-linear response of semiconductors [106–108]. In particular, for quantum-confined nanostructures, the density of carriers inside an individual quantum dot, well or disc, for instance, can have a profound effect on its emission energy and efficiency. Several effects may occur and when carrier density is sufficiently high, emitted photons can be absorbed by carriers inside the very same quantum object, an effect known as the Auger Effect8 [109]. In the case of light emitting diodes, this effect is highly undesired as it leads to a steep decrease in the external quantum efficiency, usually called “efficiency droop” [110]. Recently, STEM-CL has been used to determine the effects of varying excitation over 4 orders of magnitude on GaN QDisks embedded in AlN [111]. In this system, a strong internal electric field causes a large red shift, as discussed above, 8 This Auger effect has not to be confused with the Auger effect better known in the electron microscopy community. 62 Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel Fig. 15. Spectral-mapping of InGaN inclusions in GaN. Left: InGaN inclusions inside a GaN nanowire. After [93]. a. HAADF: inclusions appear whiter. b. Spatio-spectral mapping of the nanowire (HAADF profile is also given). Only two inclusions are emitting. They clearly emit at two different wavelengths, as seen in c. Note that the maximum of emission is shifted with respect to the centre of the inclusion, see Fig. 13 and [86]. Right: InGaN inclusions within a GaN nanowire. After [98]. a. HAADF and EDX In profile. b. Bright field image. c. d. CL filtered maps at two different energies. emitted light also does. Indeed, 3D-confined systems are best represented as TLS, see Fig. 1. Such a system can only emit one photon at a time. At first sight, the quantum behaviour of a beam coming from an SPE is not obvious. However, a beam consisting of only one photon means that the light is definitely a particle. In this case, the uncertainty on the number of photons is null, and Heisenberg principle tells us that the phase is therefore totally unknown. Single photon emission is therefore one of the (sparse) manifestations of the quantum character of light. One of the interests of having single photon states relates to their use in quantum cryptography [38]. An observer wanting to spy on a communication between two points will have to intercept single photons one by one, and read their states. However, if the incoming state is randomly generated (for example, a random possibility of being in two polarisation states), the observer will certainly project the incoming electron in generating another state by reading it, and will not be able to know in which state to re-emit the single photon, leading to the possibility for the receiver to know that the line is being spied upon. The emergence of quantum cryptography engineering has triggered numerous studies in quantum optics. Among them, the search for and characterisation of the source of single photons has been very intense. Recently, point defects in semiconductors have emerged as promising candidates, following the now famous example of nitrogen vacancy centres in diamond [37]. With the expected downscaling of quantum optics devices, analysis tools with sub-wavelength resolution which are not available with conventional PL tools, are highly desirable. CL has many potential advantages for such a role: it has been known for a long time that CL is extremely sensitive to defects [1,105], see Fig. 18 (a) and (b), and the ability for CL to measure luminescence from the infra- due to the QCSE. For QDisks sufficiently thick ( > 2 nm) and with recombination times sufficiently long ( > 100 ns) the STEM electron probe can excite individual QDisks so fast as to generate significant internal carrier densities [111,112]. In this system, the carrier density has two major effects: it blue-shifts the emission energy by partially screening the internal electric field, thus reducing the QCSE; and it induces an efficiency droop which can be attributed to the Auger effect. Fig. 17 (a) shows a collection of spectra acquired with the electron beam currents indicated in the legend when the beam was right in the middle of the QDisk (sample similar to those from Fig. 12). From 0.08 pA to about 442pA, the emission energy shifted by about 0.3 eV. Instead of observing the shift visually on the spectra, one can plot just the emission energy (peak centre) with respect to the emission intensity (peak area). The results, shown in Fig. 17 (b), correspond to 3089 spectra acquired on an individual QDisk and indicate how the energy shifts continuously as a function of emission intensity. Interestingly, in the top right of the plot, the energy increases very rapidly with the intensity. This indicates that, even if the carrier density has increased (since the emission energy has), the intensity didn't follow. Fig. 17 (c) confirms that the electron beam current has a direct effect on the emission energy, both being nearly proportional. Finally, Fig. 17(d) shows that for currents higher than 1pA emission efficiency drops rather abruptly. This behaviour, consistent with Auger effect, shows that, for this system, exciting with high currents (or at lower voltages for higher excitation cross-section) could reduce the effective light emission rate. Quantum Optics. e-h pairs can be confined in 3D, just as in the case of QDots (see e.g. [89]). In such cases, not only the object of interest presents quantum properties (like quantum confinement) but the 63 Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel red to UV in principle enables it to scan across all luminescent centres efficiently. STEM-CL presents another advantage. As explained in Section 3.3.3 and demonstrated in 3.4.1, STEM-CL has the ability to generate a very small number of e-h pairs per unit of time. SPE being two-level systems, they are already saturated when excited once. The system can be re-excited only after the TLS has gone back to its fundamental state, which happens in a typical lifetime τe timescale. Typical SPEs have lifetimes in the 1–10 ns range. Assuming an object thin enough to be in a regime where t / λe < 0.5 - a typical regime for STEM investigations-, one e-h pair will be created every two incoming electrons, leading to a rough ratio of 1 created eh pair per incoming electron. If the pairs are created directly at the SPE position and are able to excite it, this restricts the incoming current around 10–100 pA or less in order to remain in the non-saturated regime. This is easily achieved in a current STEMs - in practice, the excitation probability is even much less here, due in part to the diffusion neglected in our model, and we are not aware of any saturation measurement in SPE by STEM CL. In contrast, in the case of a low voltage and a relatively thick sample (i.e. typical SEM-CL situation), where thousands of e-h pairs can be created per incoming electrons, the saturation will be reached very rapidly. There is however an issue when characterising SPEs. Indeed, the only way to be certain that a photon beam contains only one photon is to use an intensity interferometer set-up, such as described in Section 2.1.4 and Fig. 4 e. Such a set-up allows one to measure the correlation function g(2) (τ ). Indeed, as described for few representative cases in Fig. 19, the g(2) (τ ) function provides information on the statistics of the emitted light. A purely random emission of light, such as produced by a laser, results in a flat g(2) (τ ), with a constant value of one (Fig. 19a): the probability of detecting one photon at time τ if a photon has already been detected at time 0 is the same whatever the delay τ. The photons emitted by a chaotic source of light such as a tungsten filament are bunched together, resulting in an increase of probability at small delay τ, see Fig. 19b. The width of the so-called “bunching” peak at zero delay is directly related to the typical coherence time τe of the photon beam. Fig. 16. Basal plane Stacking fault luminescence in GaN nanocolumn. (a) HAADF image of a single nanocolumn exhibiting three basal plane stacking faults in bright contrast. (b) Corresponding panchromatic imaging. (c) Spectrum-line along the nanocolumn. Reprinted with permission [100]. Fig. 17. In STEM-CL, the probe current can be changed to change the excitation power. In (a) some spectra from an individual QDisk are shown for several probe currents, from 0.08 to 442 pA. The colour of the spectra indicates the current according to the legend. The shift in peak energy can be followed in (b) as function of the spectrum intensity. In (b) whole SIs are used and the large overlap among data points shows the absence of significant damage. The spectral energy shift for several QDisks as function of the probe current is shown in (c). In this figure and in (a), we only consider the emission when the probe is exactly on top of the QDisk. The continuous shift shows that the probe current increases the carrier density across the whole range studied. Such an increase in carrier density is responsible for the drop of emission efficiency shown in (d). Emission efficiency as a function of the current. Curves are guides for the eye. 64 Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel Fig. 18. Single photon detection from point defects. a. HAADF image of a nanodiamond. b. Typical spectrum of a neutral nitrogen vacancy point defect. The shaded area represents the spectral window over which the intensity interferometric experiments have been done c. Filtered CL map of the nanodiamond shown on a. d. g2 (τ ) measurements performed on the blue and red areas indicated in a and c. After [113]. On the other hand, other possibilities exist, such as other centres in diamonds, defects in SiC… In particular, reports of SPEs emitting in the UV are very sparse [114]. One of the reasons might be the relative difficulty of performing optical measurements in the UV. There are however no particular problems with of doing them in CL. As shown in Fig. 1, STEM-CL has been successfully used to detect a new type of SPE in the UV range in hexagonal boron nitride (h-BN ) [7]. It is worth noting that this defect was already known in the literature [115]. Nevertheless, before the report in [7], there was no proof of the nature of the defect. Knowing it is an SPE indicates that the defect is a point defect, even if its structure is yet to be solved. Fig. 19. Three typical light statistics and their signatures. a. Poissonian statistics. The photons arrive randomly, so that their is an equal chance to detect a photon at any given delay τ, resulting in a flat g(2) (τ ) . This is typically the case for a laser light. b. Superpoissonian light. If the photons are emitted in the form of bunches, the correlation function presents a so-called “bunching” peak. In the case of chaotic light, the width is related to the correlation time of the light τe, of the order of few fs. In the case of bunching in cathodoluminescence [75], this is related to the lifetime of the emitters, typically in the ns range. c. Sub-poissonian light. This is the case of single photon emission. In the light emitted by a SPE, only one photon exists at a time. Therefore, the correlation function is zero at zero delay, and presents a so-called “anti-bunching” dip with width related to the lifetime τe of the emitter (see text). 3.4.2. Lifetime measurement In the preceding section, a time-dependent function (the time autocorrelation function) was used to characterise an SPE. Although the main purpose of these studies [7,113] was the detection of SPE quantum states, another benefit was the measurement of the lifetime of the emitter. However, this relied on a specific model for the emission from a very special type of emitters, and therefore intensity interferometry, as a lifetime measurement technique, seems to be of very narrow applicability. Nevertheless, we have seen in Section 3.3.1 that the way luminescence is triggered passes trough the synchronised generation of hot e-h; this eventually leads to the appearance of a bunching peak in the time correlation function. This was first demonstrated on different groups of SPEs [75], and later on quantum-confined structures [6]. Now, it can be shown [6,75] that the lifetime of the emitter can be deduced through a simple exponential fitting of the bunching peak. This opens the way for lifetime measurements at deep subwavelength. Indeed, since the spatial resolution is ultimately limited by the size of the object and/or the diffusion length, which can be extremely small [9,116], it is sensible to think that lifetime measurement could be extended to very small sizes. Lifetime measurement in a SEM-CL has undergone a constant and vigorous growth in the past few decades [117,17,22], showing amazing spatial resolution down to a few tens of nanometers. Nevertheless, this is not enough to resolve individual quantum objects. We also note that in all these works, the excitation beam was pulsed (either with blanking It is extremely short for a chaotic source of light (of the order of fs). Finally, in the case of an SPE, one expects a so-called “antibunching” dip going to zero at zero delay (Fig. 19c). An exponential fit of the antibunching dip gives a measure of the SPE lifetime [37]. Note that the use of an intensity interferometer is straightforward in the case of single photon emission. Indeed, in this case, only one photon exists at a time and therefore only one of the two detectors can be hit at a time, leading to an obvious absence of correlations between the two detectors at zero delay. The first adaptation of an intensity interferometer on a CL system is reported in [113]. In this work, the goals were: 1. to detect single photon emission with CL and 2. to evidence g 2 (τ ) spatial variations (implying changes in the quantum state of the emitted light). This was done, as exemplified in Fig. 18, where antibunching was demonstrated for a NV centre, and a change in the g 2 (τ ) function as the beam moved away from the defect centre position was observed. In these experiments, the NV centre was chosen because it is a well-known defect centre in optics, known to be photostable [37] (and also electrostable [113]), bright and easy to isolate. 65 Ultramicroscopy 174 (2017) 50–69 M. Kociak, L.F. Zagonel coatings where loaded separately. In order to understand how NDs with different coatings would internalize when loaded together, T1 NDs where coated with PAH, and T2 NDs with PEI. Therefore, by following the luminescence, one can track the type of coating. Fig. 20a shows the principle of the measurement, where both a cell ultrastructure (here shown in HAADF mode) and the luminescence can be measured at the same time. From this type of images, the content of vesicles in NDs coated with PEI (ND-PEI) and PAH (ND-PAH) can be deduced, together with structural information (like the vesicle diameter), as shown in Fig. 20b, validating STEM-CL as a promising CLEM technique. plates or a laser). With the bunching effect discussed here, however, no special gun is required. An example of the power of the technique is shown in Fig. 1. This figure shows a stack of QDisks whose widths are few tens of ångströms, and which are separated by about 15 nm. As already shown in other examples, the emission of each disc can be isolated. In addition, a correlation function can be acquired for each of these QDisks. Following an exponential fitting, the lifetime can be deduced, leading to a very high spatial resolution for lifetime determination. As is clearly seen in Fig. 1, and confirmed statistically, a decrease in lifetime corresponds to an increase in emission energy. This is explained in the following way. For such confined systems, the higher the confinement, the higher the energy on one hand, and the higher the electronhole wavefunctions overlaps leading to a shorter lifetime on the other hand. [90]. We also note that systematic comparison of lifetimes as measured in PL and in CL have been performed in the same paper, showing an excellent agreement between the two techniques thus validating CL as a nanoscale counterpart of time-resolved PL. 4. Conclusions and prospectives This review paper has focused on novel uses of STEM-CL, and its advantages and drawbacks with respect to its sister techniques (SEMCL and PL). It is clear that STEM-CL has several well-defined areas of applications where it can be very competitive, especially in high resolution investigations of plasmonics and quantum confined materials. New applications, such as time-resolved STEM-CL or bio-imaging are most likely promised to a great future. With the availability of commercial STEM-CL systems, it is clear that all these fields will be investigated. But beyond this, coupling STEM-CL with other techniques, especially those involving light injection, should lead to exciting perspectives. 3.4.3. Correlative bioimaging In the field of bio-imaging, optical and electronic microscopy each have both their own, complementary, interest. On the one hand, optical microscopy can be used in-vivo and/or to perform fast and dynamical imaging. It usually involves the use of fluorophores that can for example be functionalised to characterise a particular biological function. On the other hand, electron microscopy can image the ultrastructure of biological material. In the past year, a large effort has been made to bridge the two worlds using correlative light electron microscopy (CLEM) techniques. As the name suggests, the idea behind this technique is to combine, on the very same part of a sample, the information from both the optical and the electron microscopy by overlapping images acquired with the two techniques. Several approaches have been applied, either by taking images in different microscopes or by integrating an optical microscope into the electron microscope [118]. The success of the CLEM approaches militates for a simplification of the necessary alignment of images between techniques. It is no surprise that CL was recently seen as a potential solution to this problem. Successful proof of principle of the combined use of EM and CL imaging has been provided in SEMs [119]. Unfortunately, although the gain in spatial resolution was obvious, it did not yet lead to the cell ultrastructure resolution. Recently, the principle of integrated CLEM using STEM-CL was proven [120]. In this study, two types (T1 and T2) of luminescent nanodiamonds (NDs) were used, each having a different spectral signatures stemming from point defects. The NDs were coated with two different polymers: polyallylamine hydrochloride (PAH), and polyethyleneimine (PEI). When coating smaller (around 50 nm) NDs, PAH and PEI were indeed shown to trigger different internalization pathways [121]. In these experiments however, the two types of Acknowledgments The present paper is the result of many interactions. We started the STEM-CL project at Orsay in 2004 with Odile Stéphan and Christian Colliex, in a large part motivated by Javier Garcia de Abajo's ideas and suggestions. We have been closely working in particular on STEM-CL together since then. Their inputs have been invaluable and their imprint is obvious from the many papers cited here. Naoki Yamamoto has been an important source of inspiration and guidance, since well before we even directly interacted with him. Finally, Maria Tchernycheva and her team (Francois Julien, Lorenzo Rigutti, Gwénolé Jacopin) have early guided us in one of the most interesting field of applications for STEM-CL (III-N heterostructures). We want to thanks all of them. Our views on STEM-CL have been sharpened through constant interactions with permanent members of the team, especially Marcel Tencé, Luiz Tizei, Jean-Denis Blazit, Alberto Zobelli, Mickael Pelloux, Laura Bocher, as well as post-docs and students involved in STEM-CL: Sophie Meuret, Arthur Losquin, Zackaria Mahfoud, Hugo Lourenço-Martins, Alfredo Campos, Romain Bourrellier, Anna Tararan, Stefano Mazzucco, Jérome Schindfessel, Pabitra Das, Sounderya Nagarajan, Naoki Kawazaki, Simon Hooks. We want to thank them as well as Francois Treussart, Bruno Daudin, Bruno Gayral, Pierre Lefevbre, Julien Barjon, Brigitte Sieber, Martin Albrecht, Jurgen Christen, James Griffiths, Takumi Sannomiya, Paul Edwards, Ulrich Fig. 20. a. (left) Large field of view HAADF image of a cell where two different types of NDs with two different polymer coatings have been loaded. 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