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Structural Analysis of Nanostructures with Electron Microscopy
1
Structural Analysis of Nanostructures with Electron
Microscopy
1
Introduction
1.1 The Limitation of Light Microscopy
Light Microscopy is a often used technique in many dierent elds. It's resolution
d is given by(1)
λ
λ
d=
≈
,
(1)
2n sin α
2nNA
with the index of refraction n, the wavelength of the used radiation (usually light)
λ and the opening angle of the used aperture. NA is the numerical aperture of the
used objective. Objectives with high numerical apertures are already developed
and techniques like oil immersion that change the refractive index between
objective and specimen lead to a maximum resolution for visible light which is
around 0.2 µm(2) . Therefore the greatest potential for improvement lays in the
wavelength which can be changed by using a dierent kind of radiation. This is
achieved by using UV-light instead of visible light which leads to an improvement
of the resolution by a factor of two, giving the maximum resolution of
UV-microscopy around 0.1 µm(2) . Nevertheless this is not enough to resolve very
tiny structures e.g viruses or pollen. So for further improvement much shorter
wavelength had to be considered.
1.2 The Electron as Wave
X-rays and γ -rays may seem to be a good choice for improving the resolution due
to their small wavelength (in the Angstrom to pico-metre range). The problem in
their case is that there are only a few materials with an index of refraction
signicantly diering from 1, therefore they are very dicult to manipulate.
Electrons are very easy to manipulate because they are charged particles and
therefore interact with electric and magnetic elds. Louis De Broglie postulated in
1924 that one can allocate a certain wavelength to a particle. This so called
De-Broglie wavelength is for fast electrons given by(3)
λDB
v
u
u
=t
h2
2m0 eU0 1 +
eU0
2m0 c2
.
(2)
Here h represents Planck's constant, m0 the rest mass of the electron, c the speed
of light and eU0 the kinetic energy of an electron accelerated in an electric eld
depending from the voltage U0 and the electrons charge e. For voltages from
around 100 kV up to a few MV you obtain wavelength in the range of γ - or X-rays.
Electrons can therefore be used to obtain far higher resolutions than it is possible
with light microscopy, opening the eld of electron microscopy.
Fultz, Howe, Transmission Electron Microscopy and Diractometry of Materials
J. Picht and J. Heydenreich, Einfuhrung in die Elektronenmikroskopie
(3)
L. Reimer, Transmission Electron Microscopy
(1)
(2)
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Structural Analysis of Nanostructures with Electron Microscopy
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2
The interaction between Electrons and Matter
The interaction between electrons and matter is fundamental for electron
microscopy because information about the specimen is obtained by examining an
electron beam that travelled through a specimen (TEM) or by using the
interaction of an electron beam with the specimen to generate secondary signals
providing information about the specimen (SEM).
2.1 Elastic Scattering
Elastic scattering is scattering at the nuclei in the specimen due to the
Coulomb-force. Momenta and kinetic energy are conserved and usually the energy
exchange between the electrons and the material is low enough to be neglected
(especially for low scattering angles). Nevertheless at higher scattering angles atom
displacement can occur, when the energy exchange overcomes a certain threshold.
If the electrons are described as electron wave it is very important that the
potential of a nucleus is able to shift the phase of the incoming electron wave. This
eect can be used to produce contrast for high-resolution-imaging (HRTEM).
2.2 Inelastic Scattering
For this process total energy and momenta are conserved but the energy exchange
between the electrons and the material is much higher than in the case of elastic
scattering and can therefore no longer be neglected. Inelastic scattering can be
considered as a electron-electron-interaction because the shell electrons are able to
screen out the nucleus' potential. Inelastic scattering can lead to ionization
processes, plasmon excitations (longitudinal waves in an electron plasma), the
generation of phonons and heat and to the excitation of electron-hole-pairs.
2.3 Bragg Diraction
At periodic structures electrons can be scattered following Bragg's law which was
originally formulated for X-rays. Since the De-Broglie-wavelength of electrons and
neutrons is in the range of X-rays for certain velocities Bragg's law is also
applicable for them. it is given by(4)
2d sin Θ = nλ.
(3)
With d the distance between lattice layers, Θ the incident angle of the wave, n the
order of diraction and λ the wavelength of the wave. This law is only applicable
for very thin materials (e.g. foils), for diraction phenomena in thick crystals a
theoretical description based on Schrödinger's equation has to be used.
2.4 Secondary Radiation
The dierent interaction processes treated in 2.1-2.3 lead to the emission of
secondary radiation by the specimen. The occurring radiations are:
• Secondary electrons generated by ionization and the Auger-eect
(4)
L. Reimer, Transmission Electron Microscopy
Hauptseminar Nanooptik
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Structural Analysis of Nanostructures with Electron Microscopy
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• X-rays generated by the drop-back of outer shell electrons
• Visible light generated by recombination of electron-hole-pairs
• Backscattered primary electrons
3
The Transmission Electron Microscope (TEM)
In Figure 1 a schematic drawing of a Transmission electron microscope is shown.
The whole microscope has to be evacuated to reduce the collision frequency of the
Figure 1: Schematic drawing of a TEM, source: wikimedia.org, 31.03.2016
used electrons with gas molecules to increase the mean free path of the electrons.
The basic parts of this type of microscope shall be explained in the following
sections.
3.1 Electron Gun and Electron Lenses
The electron gun provides the electron beam which is used for examining the
specimen. The electron beam is generated by a cathode were electrons emerge
from. There are three types of cathodes. Thermionic cathodes are usually made of
Tungsten and have to be heated to high temperatures around 2500◦ C to 2800◦ C to
overcome the electrons workfunction. The shape of the cathode has inuence on
the width of the electron beam. Alternative to thermionic cathodes LaB6 or CeB6
cathodes can be used. Those materials have a very low electron workfunction,
therefore such cathodes only have to be heated up to around 1500◦ C. The last type
of cathode is the so called eld emission cathode, were the electrons are sucked o
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Structural Analysis of Nanostructures with Electron Microscopy
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a very small tip by a huge electric eld. This type of cathode provides a very thin
electron beam but only a low electron current in comparison to the other two types.
Before using the electron lenses the rst focusing of the electron beam is done
while it is generated. This is achieved by using the so called Wehnelt cylinder. The
Wehnelt cylinder is a cylinder with a small hole, where electrons can emerge,
which is put around the cathode and set on the most negative potential in
comparison to cathode and anode. Electrons are sucked o the cathode through
the hole in the Wehnelt cylinder to the anode which has also a hole in itself. The
electrons are opposed by the negative potential of the Wehnelt cylinder while
ying by and therefore focused. Also the Wehnelt cylinder decreases the needed
acceleration voltage at the anode. Further focusing and beam shaping is done by
electron lenses. Those use electric and magnetic elds to manipulate the electron
beam, since electrons are refracted at bent equipotential lines. In electrostatic
lenses dierent beam paths are possible, since electric elds are able to decelerate
or accelerate an electron. Today usually magnetic lenses are used consisting of
several coils to achieve the required eld geometry. Most important is an linear
increase of the refraction of the beam with increasing distance to the optical axis
and rotational symmetry of the elds.
3.2 Specimen, Specimen Stage and Detection/Recording
System
In a transmission electron microscope the electron beam is transmitted through
the specimen . The interaction of the electrons with the specimen can then be used
for producing contrast (see: 3.3 Imaging Modes). The specimen is placed on a very
thin grid which is positioned on the specimen holder. There are high mechanical
requirements for the specimen holder which has to be movable relatively fast
(several microns per minute) with very high repositioning accuracy and has to be
extremely resistible against mechanical drifts in the range of nanometres per
minute. Also only very thin specimens are needed. Usually with a thickness in the
range of a few hundreds or tens of nanometres. This of course requires careful
preparation. There are several techniques for producing such specimens like for
example mechanical milling, chemical etching, ion etching, etc. For detection
several dierent detectors can be used, measuring for example scattering angle and
energy of the transmitted electrons. Often used are detectors like scintillators and
ampliers like photomultipliers. For imaging a simple uorescent screen can be
used. In other imaging modes the picture has to be calculated via a computer. For
saving the image older systems use photographic lm while today often CCDs or
even TV cameras are used.
3.3 Imaging Modes
A transmission electron microscope can use several dierent modes for image
formation which use dierent signals and techniques and therefore provide dierent
resolutions and information about the specimen. Which mode is most useful
depends on the specimen and the information you want to focus on. The following
sections give a brief overview about the dierent imaging modes. Pleased note that
there are even more sub modes not covered in this overview. In general the
resolution of the TEM is limited by the lenses and lens aberrations of the system.
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Structural Analysis of Nanostructures with Electron Microscopy
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Bright- and Dark-Field-Imaging
Bright and dark eld imaging are the standard modes of the TEM. They are based
on Electron scattering in the specimen. In bright eld mode only unscattered
electrons are used for imaging. This is achieved by only detecting the primary
beam which went through the specimen without any deection. In a bright eld
image objects that scatter or absorb electrons appear dark because there are no
electrons detected for such objects. In the dark eld mode it is just vice versa.
Here only the scattered electrons are detected and used for imaging. Objects that
scatter electrons then appear bright. Figure 2 shows schematically at which
position the detectors are placed to collect the dierent signals. The term annular
dark eld imaging is used because the dark eld signal is measured by using an
annulus around the beam of scattered electrons as it is also the case for high angle
annular dark eld imaging. Bright- and dark eld imaging can be performed
Figure 2: Schematic drawing of the dierent detector positions for bright-, dark- and
high angle annular dark eld imaging, source wikimedia.org, 31.03.2016
perfectly simultaneous. Often it is helpful to compare the pictures obtained with
both techniques to get more information about the specimen. The resolutions
achievable with these techniques are between 0.2 and 0.5 nm(5) .
High Angle Annular Dark Field Mode (HAADF)
In the high angle annular dark eld mode only strongly scattered electrons are
used for image formation. This is done by positioning the detector beside the axis
of the primary electron beam as it is shown in Figure 2. Detection is performed
with an annulus around the electron beam, this increases the collection eciency
and therefore the signal to noise ratio. HAADF is often performed in a scanning
transmission electron microscope (STEM). A STEM is equipped with a scanning
apparatus which scans the electron beam over the specimen. HAADF provides
very high resolutions down to the sub-nanometre regime. The particular advantage
of this technique is that the contrast strongly depends on the atomic number Z of
the atoms in the specimen. So the technique is also referred as Z-contrast imaging.
The Z-contrast is so high because heavy atoms scatter electrons much stronger
than lighter atoms, so the scattering angle is strongly depending on the atomic
number Z of the specimen atoms, therefore the contrast is especially good, when
only highly scattered electrons are taken into account for image formation.
(5)
L. Reimer, Transmission Electron Microscopy
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Structural Analysis of Nanostructures with Electron Microscopy
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High resolution Transmission Electron Microscopy (HRTEM)
HRTEM uses the change in the electron wave's phase due to inelastic scattering to
generate pictures of the specimen. This technique is extremely dicult and time
consuming, since the electron wave's phase can not be measured directly. The
electron microscope therfore has to be tuned very carefully to convert the
information of the electron wave's phase into the amplitude which can be
measured. So that later the phase information can be calculated out of the
measured amplitude. It is very important to have aberration corrected lenses
because also lens aberrations can change the electron wave's phase and therefore
falsify the data. Usually the lens system and it's aberrations are mathematically
treated to take it's inuence into account when calculating the images. Therefore
the so called contrast transfer function is used. Usually computer simulations are
done to see what kind of images are to be expected for the specimen. this means
that a lot of information about the specimen has to be known already before doing
the measurement.
Because of simulations and careful tuning of the microscope this technique is very
expensive and time consuming but allows even resolving single atoms. Resolution
down to 0.5 Å(6) are possible today.
3.4 Analytical Modes
Electron Energy Loss Spectroscopy(EELS)
Electron energy loss spectroscopy is a TEM mode which allows it to obtain
information about electronic and atomic properties of the specimen. Even
information about the dispersion relation of the specimen can be obtained if the
scattering angle of the electrons is additionally measured(7) . The information is
obtained by measuring the energy of the electrons after they travelled through the
specimen. By comparing the measured energy with the energy the electrons had
before they hit the specimen the energy loss can be calculated. Sorting the electron
energies with a multi channel analyser then provides a characteristic spectrum
giving information about plasmon excitations, the band gap in semiconductors and
even the ne structure of the atoms in the material. Because all these processes
need a characteristic amount of energy which the electrons may loose by travelling
through the specimen. EELS combines an energy resolution of around 0.1 eV(8)
with spatial resolutions down to 0.1 nm(9) .
Dierential Phase Contrast (DPC)
This technique is able to measure electric or magnetic elds inside the specimen by
measuring the electrons beams deection. Electrons are charged particles and
therefore inuenced by even small magnetic or electric elds, so an electron beam
travelling through such a eld inside a specimen will be deected. This deection
can be measured by using a detector as it is shown in Figure 3. The detector
consists of an annulus which is divided into four segments. Between two opposing
(6)
Kisielowski et. al. Detection of single atoms buried defects in three dimensions by aberration
corrected electron microscopy with 0.5 Å information limit
(7)
Egerton Electron energy-loss spectroscopy in the TEM
(8)
Rose Optics of high-performance electron microscopes
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Structural Analysis of Nanostructures with Electron Microscopy
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Figure 3: Schematic of a detector for dierential phase contrast measurement, source:
Lohr et. al
segments the dierential signal is measured and as long a the electron beam, which
is shown in green, illuminates the annulus evenly the dierential signal between
the opposing segments will be zero. If the electron beam is shifted by an inner
electric or magnetic eld of the specimen the dierential signal will be no longer
zero and one can obtain information about the inner strength and direction of the
examined inner electric or magnetic eld. This technique allows nanometre and
sub-nanometre resolutions(9) only depending on the used electron microscope and
is usually performed in an STEM.
4
The Scanning Electron Microscope (SEM)
The Scanning Electron Microscope generates the electron beam also with an
electron gun and uses lenses similar to the TEM. Important for the SEM is that
the specimen is only hit by the electron beam which than generates dierent
secondary signals via interaction with the specimen. Those secondary signals are
then used for imaging and analysis. The whole system has to be evacuated as well
as the TEM. Since the electron beam don't has to travel through the specimen
usually lower electron energies are used and bulk specimens can be examined. This
is a great advantage of the SEM in comparison to the TEM. A schematic drawing
of a SEM is displayed in Figure 4. The following sections give information about
dierent modes of imaging and analysis used in the SEM.
4.1 Secondary Electron and Backscattered Electron Mode
The detection of secondary electrons is the standard mode of the SEM. The
secondary electrons are generated by the primary electron beam as it was
(9)
Lohr et al. Dierential phase contrast 2.0-Opening new elds for an established technique
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Structural Analysis of Nanostructures with Electron Microscopy
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Figure 4: Schematic of a scanning electron microscope (SEM), source: scixchange.missouri.edu, 02.04.2016
explained in (2.4). Those secondary electrons can only leave the specimen, when
they are generated close to the surface because otherwise they will be absorbed
inside the specimen due to their low energy. So this method of measurement gives
a high surface contrast because the amount of electrons leaving the specimen
depends on the surface properties. For surfaces where the beam enters
perpendicular, so for at surfaces most of the secondary electrons escape within
the specimen and are therefore not available for detection while at steep surfaces
and especially at edges most of the electrons emerge from the specimen. Thus
edges and steep surfaces of the specimen appear bright in the picture because
many electrons are detected while at surfaces have a darker appearance. The
detection of secondary electrons is made with an Everhart-Thornley-Detector
which is positioned sideways to the specimen. The Everhart-Thornley-Detector
attracts the slow secondary electrons with an applied voltage around +400 V. The
Electrons are then further accelerated through a scintillator using voltage around
+2000 V. afterwards the signal of the scintillator is coupled via light pipe to a
photomultiplier which amplies the signal and is coupled to a screen and the image
recording system forming a two dimensional image of the specimens surface. Due
to the contrast depending on the surface properties SEM picture have usually a
high depth of focus and appear almost three dimensional. Before image formation
the whole specimen has to be scanned by the primary electron beam. By using
eld emission cathodes which provide a very thin electron beam, resolutions down
to 0.4 nm(10) , which is currently the world's highest resolution of a SEM, are
possible. In a SEM the resolution is not limited by the used electron lenses, the
limiting component is the scanning pattern for the electron beam and the scanning
pattern of the imaging device.
Similar to the secondary electron mode also the backscattered electron mode uses
electrons for imaging. Here electrons are detected that were elastically
backscattered from the atoms of the specimen. Backscattered electrons are very
fast and therefore dicult to attract with voltage. The backscattered electron
(10)
Hitachi Launches World's highest FE-SEM Nanotech Now, 31.05.2011
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Structural Analysis of Nanostructures with Electron Microscopy
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detector is positioned above the specimen and uses an annulus for detection. The
interaction volume of the electron beam with the specimen has a teardrop-shape as
it is shown in Figure 5. The backscattered electrons emerge from deeper within the
Figure 5: Interaction volume and dierent signals in a SEM, source: linode.com,
14.04.2016
specimen than the secondary electrons. Also heavier elements backscatter more
electrons than lighter elements therefore they appear brighter than lighter
elements. The backscattered electron mode gives more material contrast. It's
resolution is lower than the one of the secondary electron mode because there are
less backscattered electrons than secondary electrons for detection what limits the
resolution. Nevertheless the backscattered electron mode is very important because
of it's material contrast and can provide many information about the specimen
especially when pictures of the backscattered electron mode and the secondary
electron mode are compared to each other.
4.2 Cathodoluminescence and
Electron-Beam-Induced-Current
Cathodoluminescence is a technique especially useful to examine semiconductors.
It uses the generation of electron-hole-pairs in the specimen. Those
electron-hole-pairs recombine and emit photons which can be in the visible part of
the spectrum. As you can see in Figure 6 the light emitted by the specimen can be
collected with a parabolic mirror around the specimen and lead to a detection
device. Using a monochromator allows it to take a look at light of a certain
wavelength. Another possibility is using a CCD-Chip to collect a whole spectrum
for every scanning point on the specimen. It is so possible to map the optical
activity of the specimen by scanning it completley. Since the primary electron
beam is actually to energetic to excite electron hole pairs this is usually done by
secondary or tertiary electrons, so there is no energetic limit to this technique
which means that also isolators can be examined with cathodoluminescence. The
technique is limited by the photon yield and especially by the diusion length of
electrons and holes in the specimen. If the diusion length of those charge carriers
is large they will drift through the specimen before recombining which means that
you collect light from dierent parts of the specimen and not only from the
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Structural Analysis of Nanostructures with Electron Microscopy
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Figure 6: Schematic of the experimental setup for cathodoluminescence, source: intechopen.com, 02.04.2016
scanning point you are hitting momentarily with the electron beam. So the
spectrum is blurred in case of high diusion length. Very low diusion length of
the charge carriers in the specimen can provide high resolutions in the range of
tens on nanometre or nanometres.(11)(12)
Simultaneaously to cathodoluminescence it is possible to measure the so called
electron-beam induced current (E-BIC) therefore an inner electric eld is required
which separates the generated electron-hole-pairs in the specimen by drift. This for
example is given at a pn-junction. If the p and n side of such a junction are
connected to each other a low current (in the range of nanoamperes) between them
can be measured which is due to the electron-hole-pairs generated by the primary
beam. This technique so allows one to map the electronic activity of the specimen
and obtain information about the minority carriers and the diusion length of the
charge carriers inside the specimen.
5
Chemical Analysis
For chemical analysis there are many methods. Two of those are in a way very
similar to electron microscopy and therefore covered by this overview. The
technique of X-ray uorescence (XRF) uses X-rays to bombard the specimen and
generate characteristic secondary X-rays. Those secondary X-rays have a much
lower energy than the primary beam but can be detected using an X-ray detector
giving a characteristic spectrum for the specimen. The dierent X-ray energies in
the spectrum give information about the elements inside the specimen. The
electron microprobe (EMP) uses an electron beam to generate those secondary
X-rays which give the characteristic spectrum. In comparison to XRF EMP has
the advantage that the electron beam can be scanned over the specimen which
gives information about the chemical composition related to the spatial position of
the beam on the specimen. State of the art EMP systems can give information
about chemical composition with an accuracy of around 10 ppm.
Lähnemann et. al. Localization and defects in axial (In,Ga)N/GaN nanowire heterostructures
investigated by spatially resolved luminescence spectroscopy
(12)
Zagonel et. al. Nanometer Scale Spectral Imaging of Quantum Emitters in Nanowires and Its
Correlation to Their Atomically Resolved Structure
(11)
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Structural Analysis of Nanostructures with Electron Microscopy
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11
Sources
[1] Fultz, Howe, Transmission Electron Microscopy and Diractometry of
Materials, 3rd Edition, Springer 2008
[2] J. Picht and J. Heydenreich, Einführung in die Elektronenmikroskopie, Verlag
Technik, Berlin 1966
[3] L. Reimer, Transmission Electron Microscopy, 3rd Edition, Springer 1993
[4] Kisielowski et al. Detection of single atoms buried defects and in three
dimensions by aberration corrected electron microscopy with 0.5 Å information
limit. Microscopy and Microanalysis 14 2008
[5] R.F. Egerton. Electron energy-loss spectroscopy in the TEM. Reports on
Progress in Physics 72:0160502 (2009)
[6] M. Lohr, R. Schregle, M.Jetter, C. Wachter, T. Wunderer, F. Scholz, J. Zweck.
Dierential phase contrast 2.0-Opening new elds for an established technique.
Ultramicroscopy 117 (2012)
[7] http://www.nanotech-now.com/news.cgi?story id=42612, retrieved 02.04.2016
[8] J.Lähnemann, C. Hauswald, M. Wölz, U. Jahn, M. Hanke, L. Geelhaar,
O.Brandt. Localization and defects in axial (In,Ga)N/GaN nanowire
heterostructures investigated by spatially resolved luminescence spectroscopy. J.
Phys. D: Appl. Phys. 47O:394010 (2014)
[9] Zagonel et. al. Nanometer Scale Spectral Imaging of Quantum Emitters in
Nanowires and Its Correlation to Their Atomically Resolved Structure. Nano
Letters 11:568 (2011)
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und Nanophotonik
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