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Achromatic Elemental Mapping Beyond the Nanoscale in the Transmission Electron Microscope

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Newly developed achromatic electron optics allows the use of wide energy windows and makes feasible energy-filtered transmission electron microscopy (EFTEM) at atomic resolution. In this Letter we present EFTEM images formed using electrons that have undergone a silicon L_{2,3} core-shell energy loss, exhibiting a resolution in EFTEM of 1.35 Å. This permits elemental mapping beyond the nanoscale provided that quantum mechanical calculations from first principles are done in tandem with the experiment to understand the physical information encoded in the images.
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Achromatic Elemental Mapping Beyond the Nanoscale in the
Transmission Electron Microscope
K. W. Urban*
Peter Gru
¨nberg Institute and Ernst Ruska Centre for Microscopy and Spectroscopy with Electrons (ER-C),
Research Centre Ju
¨lich, D-52425 Ju
¨lich, Germany
J. Mayer
Gemeinschaftslabor fu
¨r Elektronenmikroskopie and ER-C, RWTH Aachen University, Ahornstrasse 55,
D-52074 Aachen, Germany
J. R. Jinschek
FEI Company, Achtseweg Noord 5, 5651 GG Eindhoven, Netherlands
M. J. Neish, N. R. Lugg, and L. J. Allen
School of Physics, University of Melbourne, Parkville, Victoria 3010, Australia
(Received 18 January 2013; published 2 May 2013)
Newly developed achromatic electron optics allows the use of wide energy windows and makes feasible
energy-filtered transmission electron microscopy (EFTEM) at atomic resolution. In this Letter we present
EFTEM images formed using electrons that have undergone a silicon L2;3core-shell energy loss,
exhibiting a resolution in EFTEM of 1.35 A
˚. This permits elemental mapping beyond the nanoscale
provided that quantum mechanical calculations from first principles are done in tandem with the
experiment to understand the physical information encoded in the images.
DOI: 10.1103/PhysRevLett.110.185507 PACS numbers: 61.05.jd, 68.37.Lp, 68.37.Og
Energy-filtered transmission electron microscopy
(EFTEM) is a technique that images a specimen using
inelastically scattered electrons that have undergone a
specific range of energy losses within the specimen
[13]. By selecting energy windows that cover a range of
energies pertinent to inner-shell ionization of elements
present in the sample, it is possible to obtain chemical
maps and bonding information of different atomic
species. This is possible over a large field of view, acquiring
the structural information in parallel (as opposed to serially
in scanning transmission electron microscopy, STEM).
However, up to now it was not possible to realize atomic
resolution in EFTEM. Chromatic aberration degrades the
image formed, as electrons that have lost different amounts
of energy within an energy window will be focused in
different image planes. This effect can be reduced by
decreasing the width of the energy window. However,
this also leads to a reduction of the signal to noise ratio.
Because of these competing effects, the resolution of
energy-filtered images has been limited to about 4 A
˚
[4,5]. Recently chromatic aberration (CC) correction has
been implemented [6] to supplement the now ubiquitous
spherical aberration (CS) correctors in electron optics [7,8].
We demonstrate here that this allows wide energy windows
to be used and atomic resolution to be realized. This
enables transmission electron microscopy to combine the
atomically-resolving picometer-precision interferometric
imaging with atomic-resolution chemical information.
The FEI Titan 60-300 PICO at the Ernst Ruska Centre is
a fourth-generation transmission electron microscope ca-
pable of obtaining high-resolution transmission electron
microscopy images approaching 50 pm resolution in the
CC- and CS-corrected mode at 300 keV. It is currently one
of only two microscopes in the world capable of chromatic
aberration correction. Here we present the first experimen-
tal EFTEM images using the CC- and CS-corrected optics
for a sample of crystalline silicon. Quantum mechanical
calculations from first principles were performed and are
an essential adjunct to elucidating the process of electron
propagation and image formation.
Experimental EFTEM images of silicon were obtained
using signal from the L2;3ionization edge (threshold en-
ergy for ionization 100 eV). The microscope was oper-
ated at 300 keV with a semi-convergence angle for the
incident beam of 1.7 mrad. The specimen, a wedge whose
thickness varied between 100 and 400 A
˚, was imaged
along the [110] zone axis. The three-window technique
[3] was used with the pre-edge images centered at energy
losses of 55 [Fig. 1(a)] and 75 eV [Fig. 1(b)]todoa
background subtraction on the raw post-edge data, for the
energy window centered at 120 eV [Fig. 1(c)], thus obtain-
ing the Si elemental map shown in Fig. 1(d). Energy slit
widths of 40 eV were used, which was only possible using
the achromatic objective lens (CC¼0). Overlapping win-
dows were chosen in the pre-edge region in order to avoid
positioning the first pre-edge window in the strongly
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0031-9007=13=110(18)=185507(5) 185507-1 Ó2013 American Physical Society
oscillating plasmon-loss region. The atomic ‘‘dumbbell’
structure of Si in [110] projection is resolved, where the
centers of the two atoms in each dumbbell pair are sepa-
rated by 1.35 A
˚.
To understand the complex physics and electron optics
underpinning the formation of the elemental map in
Fig. 1(d) it is necessary to model the elastic and inelastic
scattering of the incident electrons in the specimen. To do
this we supplement the approach in Ref. [9] with the use of
the quantum excitation of phonons (QEP) model [10],
which calculates the underlying elastic and thermal diffuse
scattering of the incident electrons and provides the basis
for then modeling the ionization of the silicon atoms by
both elastically and thermally scattered electrons. In the
context of the QEP model the intensity in the recording
plane (the EFTEM image) is given by
Iðr?Þ¼ZX
;n
jTðr?Þ;nðr?;t;Þj2ja0ðÞj2d:(1)
Here, Tðr?Þis the transfer function of the imaging lens
which is convolved with the auxiliary functions
;nðr?;t;Þ[10] associated with the electron at the exit
surface of a specimen of thickness t(after ionization of
atom to leave the system in a final state n). We consider
final states that are consistent with the acceptance range of
the energy filter. The integration is a quantum mechanical
average over nuclear coordinates where ja0ðÞj2, the
modulus squared of the wave function describing the nu-
clear subsystem for the set of nuclear coordinates ,is
acting as a probability distribution and accounts for the
crystal being in a superposition of phonon states. We note
that Eq. (1) is consistent with different ionization events
being incoherent with respect to each other.
If the atom is at a depth zin the specimen then
the auxiliary function at the exit surface, ;nðr?;t;Þin
Eq. (1), is obtained after channeling the auxiliary function
generated at z, immediately after ionization, through a
distance t-zto the exit surface. The generation of the
auxiliary function at zdue to an ionization event is given
by [10,11]
;nðr?;z;Þ¼ m
2ih2kn
H;n0ðr?;Þ0ðr?;z;Þ:(2)
Here, mis the relativistically corrected electron mass, his
Planck’s constant, and knis the wave number of the elec-
tron after inelastic scattering (also relativistically cor-
rected). The modulus squared of the transition potential
H;n0ðr?;Þfor an excitation of atom from the initial
(bound) state 0 to the final (continuum) state ngives the
probability of that transition occurring. The dependence
indicates that the potential moves with the atom for each
new configuration. The function 0ðr?;z;Þassociated
with the electron prior to ionization is obtained by chan-
neling the incident wave from the entrance surface for the
configuration of atoms specified by . We use an angular
momentum basis to represent the transition potentials, the
details of which are described elsewhere [12]. Although it
is convenient to think about each inelastic transition (asso-
ciated with ionization) separately, a formulation in terms of
density matrices is also possible [13].
FIG. 1. EFTEM images used to construct the Si L2;3elemental
map by means of the three-window technique in the chromatic-
and spherical-aberration corrected electron microscope. All im-
ages were taken using a 40 eV wide energy window. (a) Pre-edge
image centered at an energy loss of 55 eV. (b) Pre-edge image
centered at 75 eV. (c) Post-edge image centered at 120 eV.
(d) Resulting atomic-resolution elemental map; a standard
‘‘average background subtraction filter’’ [23] was applied.
Standard conditions for the negative-spherical aberration imag-
ing mode [19,20] were applied in all images, i.e., a (negative) CS
of 8:27 mand a defocus of þ40
A.
FIG. 2 (color online). Calculations of EFTEM images formed
using the silicon L2;3edge for a 200 A
˚thick specimen imaged at
300 keV with a beam convergence angle of 1.7 mrad.
(a) EFTEM image formed due to ionization by both elastically
and thermally scattered electrons in the QEP model [10] and
(b) an image formed by electrons which have only been elasti-
cally and thermally scattered. Line scans across the images in
(a) and (b) taken through the dumbbell pairs (as indicated by the
arrows) are shown in (c) and (d), respectively.
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Calculations were carried out to simulate the experi-
mental results in Fig. 1(d). We assumed a 200 A
˚thick
specimen, a (negative) CSof 8:27 mand a large
objective aperture size of 2
A1(consistent with experi-
ment). Assuming a defocus value of þ40
Ayields the
result shown in Fig. 2(a). It is interesting to note that
there is significant intensity between the atomic posi-
tions. This could explain the intensity between the
columns in the dumbbells in Fig. 1(d). Figure 2(b)
shows an image formed directly by electrons which
have only been elastically and thermally scattered.
Line scans across the images in Figs. 2(a) and 2(b)
were taken along the dumbbell pairs, as indicated in
Figs. 2(a) and 2(b) andareshowninFigs.2(c) and 2(d),
respectively. We see that the contrast is similar. As we
have verified, elastic scattering dominates the contrast
in Fig. 2(b), with the contribution from thermally scat-
tered electrons being small. This is an example of the
phenomenon usually termed ‘‘preservation of elastic
contrast’’ [1417].
From our transition potential approach, we can explain
why the images in Figs. 2(a) and 2(b) look qualitatively
similar. For high-energy incident electrons causing ioniza-
tion, the transition potentials become more extended
(‘‘delocalized’’) the lower the energy loss. As a conse-
quence features of the elastic and thermal scattering prior
to and after the ionization event contribute directly and
significantly to the energy-filtered image. Indeed, from
Eq. (2) we can see that, for a relatively wide transition
potential, features (amplitude and phase) in the wave func-
tion of the incident electrons
c
0away from the column
being ionized will be preserved in the inelastic wave
function
c
n[18]. This is evident in the experimental pre-
edge and post-edge images where lattice contrast is
observed in both, since the contribution to these images
is mainly due to delocalized inelastic scattering leading to
the excitation of plasmons. Figure 3(a) shows the intensity
of the elastic wave function, along a line scan in the [001]
direction, horizontally through the dumbbell structure, as it
propagates through the sample. The intensity of the elastic
FIG. 3 (color). Probe intensity within silicon. Line scans are along the [001] direction. An ionization of a Si L2;3edge [specifically
ðl¼1;m
l¼0Þ!ðl0¼0;m
l0¼0Þtransition] occurs at a depth of 80 A
˚. (a) Intensity along the [110] direction of the elastic wave as a
function of depth. (b) Intensity along the [110] direction of the inelastic wave as a function of depth. (c) Intensity of the elastic
wave function (black) and the transition probability jHn0j2(gray), at a depth of 80 A
˚. (d) Overlap of the elastic intensity and the
transition potential.
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wave is highest on the atomic columns, due to channeling
through the specimen. We now consider an ionization
event occurring at a depth of 80 A
˚from the entrance
surface. Specifically, we consider the ðl¼1;m
l¼0Þ!
ðl0¼0;m
l0¼0Þdipole transition in the angular momen-
tum basis used here. The inelastic wave function in
Fig. 3(b) for this ionization also ‘‘illuminates’’ the other
atom in the dumbbell pair, albeit with a lower intensity,
which then channels to the exit surface. The intensity of the
elastic wave function at the ionization event is presented in
Fig. 3(c). The two peaks correspond to the atomic columns
where the dumbbells sit. They are at slightly different
heights as the atoms within each column are situated at
different depths within the specimen. Overlaid is the tran-
sition probability jHn0j2for the specific ionization event.
The transition probability is substantially delocalized
and extends across the neighboring atomic columns.
Figure 3(d) shows the intensity of the inelastic wave func-
tion generated at the ionization event, which is the product
of the elastic wave function and the transition probability.
As a result of the delocalized Hn0, there is a significant
signal on nearby columns.
The effects that the post-ionization elastic channeling
has on the EFTEM image can be seen in the thickness-
defocus series of EFTEM images in Fig. 4. The series was
calculated for thicknesses between 50 and 400 A
˚, and
defocus values ranging between 0 and þ100
A. It is found
that the EFTEM images appear qualitatively similar at
varying specimen depths, with the intensity varying with
thickness due to the channeling of the incident electron
probe. The lattice contrast is most visible between defocus
values of 30 to 50 A
˚, consistent with predictions of nega-
tive spherical aberration imaging [19,20]. The similarity of
the EFTEM images over the thickness range investigated is
due to only being one element present in the specimen.
This was also observed in the experimental elemental map
as one moves away from the edge of the Si wedge.
However, one can still notice the effects of elastic contrast
being preserved. In Fig. 3(a), the pendellosung of the
elastic wave produces an intensity minimum at around
250 A
˚. Since at this thickness there is less elastic signal
on the column being ionized, we should expect a large
proportion of the ionization signal to come from points
away from the column. This is verified in Fig. 4where, for
a specimen thickness of around 250 A
˚, we see that a large
proportion of the signal forms a diffuse background, away
from the column.
In conclusion, we have demonstrated experimentally
that by using spherically and chromatically corrected elec-
tron optics the resolution of EFTEM can be improved to
atomic as proven by the 1.35 A
˚Si-dumbbell imaging. This
allows unambiguous identification of the chemical nature
of individual atom columns in the transmission electron
microscope on the basis of images produced by electrons
that have experienced a characteristic inner-shell excita-
tion energy loss. To date this has been the domain of STEM
[21,22]. From this point on it is feasible to combine the
ultrahigh precision atomic position measurements on the
basis of the interferometric imaging mode enabled by exit-
plane wave function reconstruction in the aberration cor-
rected transmission electron microscope with chemical
mapping, atom column by atom column in the same area
on the sample. Our first-principles calculations show that
the pertinent phenomena can be well described within a
quantum mechanical model for elastic and inelastic scat-
tering. The images obtained show the phenomenon of
preservation of elastic contrast.
The financial support of the German Federal Ministry
for Science and Education, the Ministry of Innovation of
the State of North-Rhine Westphalia, the German Research
FIG. 4. Thickness-defocus series of EFTEM images for the Si L2;3edge at 300 keV. An objective lens with a (negative) CSof
8:27 m, an objective aperture of 2
A1and varying defocus has been used. Each image has been normalized to the maximum value
for a given thickness for visualization purposes.
PRL 110, 185507 (2013) PHYSICAL REVIEW LETTERS week ending
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185507-4
Foundation (DFG) and the Helmholtz Association for the
PICO project is gratefully acknowledged. This research
was supported under the Discovery Projects funding
scheme of the Australian Research Council (Project
No. DP110102228). Special thanks are due to C. L. Jia
and L. Jin for providing the silicon samples and for assis-
tance with Digital Micrograph
TM
.
*k.urban@fz-juelich.de
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Studying carbon chemistry which consists of analysing various hybridizations in the carbon matrix viz., sp 1 , sp 2 or sp 3 forming π or σ bonds is routinely carried out in Energy Electron Loss spectroscopy (EELS) in a Scanning/ Transmission Electron Microscope (S/TEM) [7]. In fact, EELS is capable of discerning the type of hybridizations occurring in the carbon matrix; for example, diamond is an exclusively sp 3 hybridized carbon allotrope. On the other hand graphene, is exclusively sp 2 hybridized, while as other allotropes such as CNT or diamond like carbon, possess both, sp 2-sp 3 hybridization. The EELS edge positions and the aspects of the peaks of the Electron Loss Near Edge Structure (ELNES) signal of the C-K edge are invaluable in obtaining the electronic structure of the material. Furthermore, when these carbon allotropes are combined with nanoparticles (NP) the interface of the CNT-NP shows changes in the hybridization which are generally indicative of a change in the physical properties of the material. Even the defects in such an allotrope, be it at the interface, on the nanoparticle or in the carbon matrix, are decisive in determining the physical properties of the material as a whole. These defects are rather easily studied by modern TEM imaging and analysis employing Cs±Cc correctors, monochromators, EELS, energy dispersive x-ray spectroscopy (EDX), electron holography and electron tomography. In fact, electron tomography which allows 3D imaging of a nano-object has become a routine and versatile technique. Indeed, the selective decoration of these nanoparticles is of interest as now-a-days, researchers are looking for optimal coverage yields. Therefore, probing the atomic, chemical and electronic structure at the interface provides useful information on the propensity of the nanoparticles to adhere to certain anchorage points in order to optimize the coverage. In this regard, obtaining this information in 3D is the need of the hour. Furthermore, electron tomography that is now capable of assimilating EELS, EDX and electron holography among others, consequently provides simultaneous chemical, structural, electronic and even magnetic information in 3D. Microscopy and imaging science: practical approaches to applied research and education (A. Méndez-Vilas, Ed.) 389 ___________________________________________________________________________________________
Article
Understanding Imaging Contrast at Low Acceleration Voltages Exemplified on Two-dimensional Materials and Properties of Advanced Two-dimensional Materials by Low-voltage TEM - Ute Kaiser
Chapter
Metal Nanoparticles and Clusters are an outstanding set of nanomaterials that attract great attention due to a plethora of applications. However suitable characterization methods that can provide an atomistic picture are essential to tailor their design for exploring unique properties and novel applications. In this chapter the recent developments in advanced electron microscopic techniques that are now readily available and which can provide a complete understanding is described in detail. A brief survey of Transmission Electron Microscopy (TEM) techniques along with their principles are initially outlined, followed by specific case studies where these techniques are employed for the characterization of metallic, bimetallic, multimetallic and supported nanoparticles/clusters. The physical and chemical properties of metal NPs on various suitable supports are dependent on their unique and specific interaction between the metal and the support. Hence understanding the exact nature and atomic structure of the nanoparticle-support is essential for various important catalytic reactions. While conventional high resolution TEM (HRTEM) can enable characterization of ultra-small nanoparticles or nanoclusters, High Angle Annular Dark Field mode in STEM (HAADF-STEM) especially on an aberration-corrected instrument offers some unique advantages. In addition to catalytic nanoparticles, there is also increasing interest in few-atom nanoclusters, or indeed single atoms, as powerful catalysts and with the recent advances in aberration corrected imaging, ultrafine clusters or even isolated atoms can nowadays be characterized. Although scanning/transmission electron microscopy (STEM) is a suitable high-resolution imaging technique, in order to ascertain the complete 3D morphology of such nanoparticles, electron tomography is a viable solution. In combination with spectroscopy, it is now possible to carry out 3D–Tomography-Spectroscopy characterization; an important techniques of choice in recent times which provides the structure-morphology-chemical composition analysis in 3D. With the advent of In situ liquid cell holders it is possible to probe nucleation and growth mechanisms from the initially formed pre-nuclei. The availability of In situ gas-cell holders makes it is possible to simulate catalytic reactions very close to realistic conditions for several important reactions/transformations of industrial importance. These key advances are highlighted in the chapter with several recent examples.
Article
Elemental mapping at the atomic scale in aberration-corrected electron microscopes is becoming increasingly widely used. In this paper we describe the essential role of simulation in understanding the underlying physics and thus in correctly interpreting these maps, both qualitatively and quantitatively.
Article
The last two decades have seen dramatic advances in the resolution of the electron microscope brought about by the successful correction of lens aberrations that previously limited resolution for most of its history. We briefly review these advances, the achievement of sub-Ångstrom resolution and the ability to identify individual atoms, their bonding configurations and even their dynamics and diffusion pathways. We then present a review of the basic physics of electron scattering, lens aberrations and their correction, and an approximate imaging theory for thin crystals which provides physical insight into the various different imaging modes. Then we proceed to describe a more exact imaging theory starting from Yoshioka's formulation and covering full image simulation methods using Bloch waves, the multislice formulation and the frozen phonon/quantum excitation of phonons models. Delocalization of inelastic scattering has become an important limiting factor at atomic resolution. We therefore discuss this issue extensively, showing how the full-width-half-maximum is the appropriate measure for predicting image contrast, but the diameter containing 50% of the excitation is an important measure of the range of the interaction. These two measures can differ by a factor of 5, are not a simple function of binding energy, and full image simulations are required to match to experiment. The Z-dependence of annular dark field images is also discussed extensively, both for single atoms and for crystals, and we show that temporal incoherence must be included accurately if atomic species are to be identified through matching experimental intensities to simulations. Finally we mention a few promising directions for future investigation.
Chapter
Chromatic aberration (Cc) in the modern transmission electron microscopy (TEM) plays an important role with the advancement the resolution up to atomic level¹. Correction of Cc is especially important for high resolution energy -filtered TEM (EFTEM) with the requirement of large slit width and signal intensity to obtain an atomic resolved image, formatted from the inelastic scattered electrons in a limited time and stability constraint. As an advantage, large area and high resolution elemental map can be obtained in just tens of seconds, much faster than the traditional STEM-EELS counterpart. The short acquisition time is very crucial in the practical applications of both material science and biological science where the samples are very often sensitive to the electron beam illumination, the interesting compositions and structures are unknown, or they are the mixture of different elements and phases.
Article
The inelastic scattering of fast electrons caused by excitation of atomic electrons is considered, taking account of the Bloch wave nature of the fast electrons within the crystal. It is shown that the interference, or contrast, produced by small-angle inelastic scattering is similar to that produced by elastically scattered and plasmon scattered electrons. The result explains recent electron microscope observations of contrast in crystals obtained by energy analysis techniques.
Chapter
Electron energy-loss spectroscopy (EELS) involves analyzing the energy distribution of initially monoenergetic electrons after they have interacted with a specimen. This interaction is sometimes confined to a few atomic layers, as when a beam of low-energy (100–1000 eV) electrons is “reflected” from a solid surface. Because high voltages are not involved, the apparatus is relatively compact but the low penetration depth implies the use of ultrahigh vacuum. Otherwise information is obtained mainly from the carbonaceous or oxide layers on the specimen’s surface. At these low primary energies, a monochromator can reduce the energy spread of the primary beam to a few millielectron volts (1991) and if the spectrometer has comparable resolution, the spectrum contains features characteristic of energy exchange with the vibrational modes of surface atoms, as well as valence electron excitation in these atoms. The technique is therefore referred to as high-resolution electron energy-loss spectroscopy (HREELS) and is used to study the physics and chemistry of surfaces and of adsorbed atoms or molecules. Although it is an important tool of surface science, HREELS uses concepts that are somewhat different to those involved in electron microscope studies and will not be discussed further in the present volume. The instrumentation, theory, and applications of HREELS are described by Ibach and Mills (1982) and by Kesmodel (2006).
Article
Energy-filtered transmission electron microscopy has been applied to SiGe superlattices and layered heterostructures in order to explore detection and resolution limits of elemental distribution images obtained by electron spectroscopic imaging (ESI). A Zeiss EM 912 Omega transmission electron microscope with an integrated imaging Omega energy filter at 120 keV and the JEOL ARM equipped with a GATAN imaging filter at 1250 keV have been used. The filters selected inelastically scattered electrons corresponding to the inner-shell losses of the Si L edge. The three-window technique was applied to obtain Si distribution images. ESI was performed on cross-section TEM samples of short-period SimGen superlattices (m,n: number of monolayers in the layer sequence), ultra-thin individual layers, and Si1 − yGey alloy buffer systems with composition gradient (0 < y < 0.4). Influences of different models for background subtraction and of correlation methods for specimen drift correction were investigated.
Article
Observations of the effect of thermal diffuse scattering, single electron excitations and plasmon excitation on the quality of electron microscope images of crystals are presented and discussed. Preservation of image contrast after thermal diffuse scattering seems to be poor in practice but only a small fraction of the electrons accepted by the aperture are affected in this way. To a first approximation, contrast appears to be preserved after single electron excitation or plasmon excitation especially at small scattering angles where no evidence of interband transitions of the fast electron has been found. At larger scattering angles some loss of contrast occurs so that the size of the aperture can be important. The significance of the results is discussed with reference to electron microscopy of thick crystals, direct resolution of atomic positions and out-of-focus images.
Article
The propagation of elastic and inelastic electron waves in high-energy electron diffraction in a thin crystal foil is described in a real-space framework. Within the usual approximations of the “elastic” real-space method and applying the “single-elastic-into-inelastic” approach, a real-space slice expansion for inelastic electron waves is set up, which can be used for any type of inelastic scattering. Single-electron-excitation inelastic processes are discussed in more detail. In real space, the imaginary absorption potential for single-electron excitation can be computed for each atom individually, independent of the crystal structure and the accelerating voltage. In this work, these absorption potentials have been computed explicitly for all types of atoms and parametrized by a linear combination of four Gaussians. These parameters are tabulated.
Article
The theory of inelastic scattering is studied for the transmission of fast electrons through crystals when the fast electrons are described by Bloch waves so that Bragg reflexion is also considered. Solutions for the wave amplitudes are obtained for the case of small-angle inelastic scattering and it is shown that interband inelastic scattering transitions of the fast electron are forbidden when the interaction potential is of the long range type which might arise in the excitation of plasmons. This result would explain recent electron microscope observations of similar diffraction contrast effects obtained using elastically scattered or inelastically scattered electrons, and also shows that such inelastic scattering need not be considered in theories of diffraction contrast. The theory also predicts a Poisson distribution for the intensities of the various peaks observed in the energy spectrum of the transmitted electrons. In thick crystals, where anomalous absorption effects are important, the angular distribution of the scattered intensity round the Bragg diffraction spots is found to contain an asymmetry in qualitative agreement with the experimental observations.
Article
One of the biggest obstacles in improving the resolution of the electron microscope has always been the blurring of the image caused by lens aberrations. Here we report a solution to this problem for a medium-voltage electron microscope which gives a stunning enhancement of image quality.
Article
We propose a many-body quantum-mechanical model for multiple thermal scattering of fast electrons due to phonon excitation in condensed matter. The key approximation upon which our approach is based is in the spirit of the Born-Oppenheimer approximation. We compare the conceptual underpinnings of this model to the well-known frozen phonon model for thermal scattering. Using our model it is possible to calculate the probability distribution of both elastically and inelastically scattered electrons. The model is also extended to encompass core-shell ionization.
Article
With modern transmission electron microscopes elemental mapping with atomic resolution seems feasible. For crystalline specimens the interpretation of contrast in such energy-loss micrographs is not a simple straightforward matter, as the so-called preservation of elastic contrast can play an important role. Hence the computation of theoretical micrographs for comparison is necessary. The calculation method presented in this article is based on well-known theoretical approaches. To enable numerical evaluation we use an exciton-like representation for the excited electronic state of the crystal. The practicability of this method is demonstrated by computing lattice fringes and demonstrating the influence of the preservation of elastic contrast.