Achromatic Elemental Mapping Beyond the Nanoscale in the Transmission Electron Microscope

Abstract

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.

Full text

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
[1–3]. 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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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;Þj2ja0ðÞj2d:(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 ja0ðÞj2, 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?;Þ0ðr?;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
A1(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’’ [14–17].
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
A1and varying defocus has been used. Each image has been normalized to the maximum value
for a given thickness for visualization purposes.
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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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