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Ultramicroscopy 174 (2017) 50–69
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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
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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.
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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
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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].
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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.
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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].
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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
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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.
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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
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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].
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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
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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.
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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
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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.
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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.
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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. (right) magnification of a vesicle,
together with energy-filtered CL maps showing the existence of two differently emitting NDs inside the same vesicle. b. Cytometric plots of internalization vesicles labeled with polymer
coated fluorescent NDs. The diameter of the circular markers is proportional to the vesicle size (refer to the scale bar). Different vesicles with the same number of ND-PAH and ND-PEI
but different diameters appear as concentric circles. The occurrence (i.e. the number of vesicles encompassing the same number of NDs whatever its coating is) is given by the colour.
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Hohenester, Franz Schmidt, Cleva Ow-Yang and the Attolight team
(especially Samuel Sonderegger and Jean Berney) for fruitful and
stimulating interactions that powered the writing of this review.
Finally, we want to thank C. Colliex and M. Walls for their in-depth
and sharp reading of this manuscript that helped making it clearer.
This work has received support from the National Agency for Research
under the program of future investment TEMPOSCHROMATEM with
the Reference No. ANR-10-EQPX-50 and the french CNRS METSA
Research Federation FR CNRS 3507. This work has received support
from CNPq and from projects 2014/23399-9 and 2012/10127-5, Sao
Paulo Research Foundation (FAPESP).
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