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Lecture 9: Electron microscopy
instrumentation
Contents
1 Electron sources
1.1 Thermionic source . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Field emission source . . . . . . . . . . . . . . . . . . . . . . .
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2 Electron beam characteristics
2.1 Brightness . . . . . . . . . .
2.2 Temporal coherency . . . . .
2.3 Spatial coherence and source
2.4 Thermionic gun assembly . .
2.5 Field gun assembly . . . . .
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3 Electron lenses
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4 Lens defects
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1
Electron sources
The first part of any TEM is the production of the electron beam. There
are two main types of sources, which differ in the physics of electron beam
production.
1. Thermionic sources
2. Field emission sources
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1.1
Thermionic source
A thermionic source is a heated source. If sufficient energy is provided to an
electron in a solid to overcome the barrier that prevents the electron from
escaping (work function, φ) then the electron can be emitted. In thermionic
emission, this energy is provided by heating the source. The relation between
the current density (J), the source temperature (T ), and the work function
(φ) is given by Richardson’s law.
J = AT 2 exp(−
φ
)
kB T
(1)
where A is the Richardson’s constant (units Am−2 K −2 ) and is constant for
a given source material. To increase the current density either temperature
should be increased or a material with a lower work function should be chosen.
Usually, refractory materials like Tungsten are used as thermionic sources. W
has a high melting point of 3600 K and a work function of 4.5 eV . Lathanum
hexaborate (LaB6 ) is another good thermionic source material with a melting
point of 2500 K but with a lower work function of 2.4 eV . The disadvantage
of LaB6 is that is a ceramic material and hence susceptible to thermal shocks.
The source has to heated slowly to the operating temperature and similarly
cooled slowly during turn off.
Consider a W thermionic source with the Richardson’s constant of 6 × 105
Am−2 K −2 . The operating temperature is 2700 K. The current flux, using
equation 1, is 1.78 × 104 Am−2 . Figure 1 shows a picture of a LaB6 crystal
used as thermionic source in TEM.
1.2
Field emission source
In field emission an applied voltage is used to generate a large electric field
at a sharp tip. This large electric field is used to the extract the electrons
from the source to generate the beam. The electron beam is generated due to
tunneling from within the solid to vacuum. The sharp tip is used to generate
the large electric field since field (E) is equal to Vr .
The schematic of how field emission works in shown in figure 2. Consider
a metal with a work function φ. An electron removed from the metal, at a
distance x from the surface, is attracted to the now positively charged metal
with a potential called image potential. The image potential is given by
P E(x) = −
e2
16π0 x2
(2)
This equation is valid only for x much larger than the atomic spacing so that
we can ignore the atomic arrangement in the metal. According to figure 2
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Figure 1: LaB6 crystal used as a thermionic source in TEM. Taken from
Transmission Electron microscopy - Williams and Carter.
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Figure 2: (a)Potential energy of an electron near the surface of a metal,
(b) applied external field, and (c) total potential. Taken from Principles of
Electronic Materials and Devices - S.O. Kasap.
the total energy also includes the Fermi energy (EF ) and the work function
(φ). When an external potential is applied with the metal being the cathode
an electric field is generated. If E is the external field, then the potential at
a distance x due to this field is −eEx. Hence the total potential energy of
the electron is given by
P E(x) = (EF + φ) −
e2
− eEx
16π0 x
(3)
Thus, the potential energy for the electron to escape the metal is lowered
due to the application of the external field. When the external field is large
(either by increasing the potential or making a sharp tip) the barrier becomes
narrow so that electrons can tunnel through this barrier. This constitutes
field emission. The process is shown schematically in figure 3.
Tungsten is the materials commonly used for field emission in the TEM.
A sharp tungsten needle is used for field emission, shown in figure 4. The
field emission source can either be at room temperature (cold source) or
heated. Heating lowers the required electric field for emission. Typically,
ultra high vacuum is needed for field emission sources. This is because any
contamination at the the tip would affect the field emission. Field emission
sources are more stable than thermionic sources and they also produce a
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MM3030: Materials Characterisation
Figure 3: (a)Potential energy of an electron under an applied field, (b) electron tunneling at large external fields, and (c) field emission. Taken from
Principles of Electronic Materials and Devices - S.O. Kasap.
Figure 4: W tip used as a field emission source in TEM. Taken from Transmission Electron microscopy - Williams and Carter.
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Figure 5: Comparison of various electron sources. Taken from Transmission
Electron microscopy - Williams and Carter.
higher current flux. The various electron sources are compared in figure 5.
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Electron beam characteristics
The electron beam in the TEM has certain characteristics which are defined
by the source that is used and also by the electron gun assembly. The beam
characteristics can be defined by a few parameters
2.1
Brightness
Brightness is related to the intensity of the electron source. Current from
the source is measured in Am−2 , called the emission current (ie ). The beam
also has a finite diameter (d0 ) and a certain angular spread (α0 ). This is
related to the semi-angle of the electron divergence from the source. These
are defined in figure 6. The brightness (β) of a TEM beam is given by
β =
4ie
(πd0 α0 )2
(4)
Brightness increases linearly with accelerating voltage in the case of thermionic
sources. Higher the value of β, more electrons will be available to form the
image from the sample. But this would also cause an increase in sample
damage from the beam.
2.2
Temporal coherency
An ideal electron beam for the TEM should be monochromatic but there
will be always be an energy spread of the beam. Also the beam should be in
phase especially for electron diffraction. For the electron beam it is possible
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MM3030: Materials Characterisation
Figure 6: Electron gun arrangement and beam characteristics from a
thermionic source. Taken from Transmission Electron microscopy - Williams
and Carter.
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to define a coherence length (λc ). This is related to the electron velocity (v)
and the energy spread (∆E) by
λc =
vh
∆E
(5)
Smaller the energy spread larger will the coherence length. Need stable
sources for this. Typically, in a TEM ∆E ∼ 3 eV (for a 100 kV source).
2.3
Spatial coherence and source size
This is related to the source size. Ideally, we want a point source but all
sources are finite in size and there is a spatial spread in the region from where
electrons are emitted. We can define an effective source size for coherent
illumination (dc ) to be given by
dc =
λ
2α
(6)
where α is angle subtended by the source at the specimen. We can have a
larger effective source size, by limiting the angle. This can be done by using
an aperture.
2.4
Thermionic gun assembly
The electron beam assembly is shown in figure 6. The figure defines the
beam diameter at cross-over, the semi-angle of the beam (controlled by the
aperture), and the beam current. The electron source is the cathode. Electrons from the source pass through a grid called the Wenhnelt cylinder. The
grid give energy to the electron beam and also focuses the beam to the gun
cross-over point. The beam diameter and semi-angle is defined at the crossover point, as shown in figure 6. Electron past the cross-over move towards
the anode plate. The parts of the thermionic TEM gun is shown in 7. To
reduce thermal shock in these systems the electron gun has to heated slowly
to the operating conditions and turned off slowly as well. This is especially
true for a LaB6 source. In a Philips CM 12 (operating at 120 kV) the beam
is usually turned on in steps of 20 kV, with a minute of hold time at each
step.
2.5
Field gun assembly
The assembly of the field emission gun is shown in figure 8. There are
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Figure 7: Parts of a thermionic electron gun. Taken from Transmission
Electron microscopy - Williams and Carter.
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Figure 8: Assembly of a field emission gun. Taken from Transmission Electron microscopy - Williams and Carter.
2 anodes in the assembly. The first anode supplies the extraction voltage
to pull the electrons from the source. The source can be cold (cold field
emission) or heated. The second anode supplies the voltage that is needed to
accelerate the electrons. Field emission sources are better than thermionic
sources in terms of beam brightness. The comparison is shown in figure 5.
The cost of the field emission sources is greater and also vacuum levels in
the TEM is more stringent. This is because field emission sources are more
susceptible to contamination. Typically, differential pumping is used in the
field emission gun to obtain greater vacuum.
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Electron lenses
The electrons emitted from the source (thermal of field emission) have to be
focused on the specimen and the beam from the specimen has to be magnified for imaging. Electron lenses work in a similar fashion to conventional
optical lens used in microscopy. The difference is that the beam that is being
manipulated is electrical than electro magnetic. Also, the strength of the
lenses (focus point) can be varied (even though the lens position is fixed) unlike lenses in an optical microscope which have fixed focal length but whose
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MM3030: Materials Characterisation
Figure 9: Assembly of an electron lens. Taken from Transmission Electron
microscopy - Williams and Carter.
position can be varied.
Electron lenses are magnetic in nature. A schematic diagram of the lens
is showed in figure 9. The lens consists of a cylindrical core made of soft
iron with holes in it. Soft iron pole pieces are used with a hole (bore) for
the electrons to pass through. Usually, there are 2 pole pieces, the upper
and lower, with a gap separating them. Copper coils are surround each pole
piece. When current is passed through these coils it generates a magnetic
field in the soft iron cores. The field lines extend into the bore and serve to
deflect the electron beam. The strength of the field determines the power of
the lens. A picture of an electron lens is shown in figure 10.
Electrons in a magnetic field are subjected to a Lorentz force. The general
equation for the Lorentz force
→
−
→
−
→
−
→
−
−
−
F = q (E + →
v × B ) = −e (→
v × B ) = −evBsinθ
(7)
For an electron, the charge (q) is −e and in an electron gun the electric field
is zero. θ is the angle between the electron velocity and the magnetic field
and the arrangement in an electron gun is shown schematically in figure 11.
In an electron lens, as seen from figure 11, the magnetic field is acting along
−
the z-axis. Electrons have velocity, →
v , making an angle θ with the magnetic
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Figure 10: Picture of an electron lens. Taken from Transmission Electron
microscopy - Williams and Carter.
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Figure 11: Electron path in a lens. Taken from Transmission Electron microscopy - Williams and Carter.
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field. This can be resolved into two components, v1 and v2 , parallel and
perpendicular to the field. Component v1 is not affected by the magnetic
field but v2 is. v2 lies in the plane of the electron lens and the effect of the
magnetic field is to deflect it perpendicular in the same plane. This is continuously happening to the electron so that it traces a spiral path (if v1 is
zero, the trace will be a circle) in the lens. The trajectory is helical,similar
to what happens in a cyclotron.
The radius of the spiral path traced by the electron in the lens can be calculated using equation 7.
me v 2
r
me v
r =
eB sin θ
F = evB sin θ =
(8)
The period of rotation gives rise to the cyclotron frequency (ω)
ω =
eB
me
(9)
where me is the mass of the electron. Lenses in the TEM are dynamic.
When the current through the soft iron core is changed the magnetic field is
changed, which changes the value of r. Similarly, increasing the voltage in
the source changes the velocity of the electrons which affects r.
Apertures in the TEM are used to limit the collection angle of the lens. This
also allows us to increase the depth of field/focus and control the resolution
and image contrast. Depth of focus is defined as the depth of sharpness in
the image while the depth of field defines the depth of the sharpness in the
sample. This defines how much of the sample is in focus. This is similar to
a conventional camera operation. By using a aperture the amount of light
or electrons entering the lens is limited. This increases the depth of field. A
schematic of an aperture is shown in figure 12. Some pictures of apertures
in the TEM are shown in figure 13. In the TEM the depth of field/focus
is usually much larger than the thickness of the sample. So that the whole
depth of the sample is under focus. Similarly, a SEM also has a high depth
of focus much higher than a conventional optical microscope. The use of
apertures in an Electron microscope helps in achieving the high depth of
focus.
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Lens defects
Electron lenses are highly imperfect and lens defects affect the resolution.
While the electron wavelength in the TEM is of the order of pm (10−12 m)
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Figure 12: Electron aperture below the specimen that limits the beam passing through the specimen. Taken from Transmission Electron microscopy Williams and Carter.
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Figure 13: Typical apertures in the TEM. Taken from Transmission Electron
microscopy - Williams and Carter.
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Figure 14: Spherical aberration in a lens causes a point to be focused as a
disk. Taken from Transmission Electron microscopy - Williams and Carter.
the lens defects limit the resolution to Å (10−10 m).
1. Spherical aberration Spherical aberration occurs when the lens field
acts in homogeneously for off axis rays. These off axis electrons do not
get focused to the same point as the near axis rays so that a point from
the specimen gets focused as a disk, as shown in figure 14. This affects
the resolution of the instrument. Referring to figure 14, the Gaussian
image plan is where the image is formed and where the detector is
placed for imaging (either a fluorescent screen or a CCD). But the
minimum diameter occurs closer to the lens in a plane called the plane
of least confusion. Sometimes this is used to define the resolution of
the instrument but the actual resolution at the imaging plane will be
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MM3030: Materials Characterisation
Figure 15: Chromatic aberration in the TEM. Taken from Transmission
Electron microscopy - Williams and Carter.
poorer.
2. Chromatic aberration Electrons in the TEM are not completely monochromatic. There could be an energy spread of electrons coming from
the source, though this is usually small. But when the electrons pass
through the specimen, some of the electrons undergo inelastic collisions,
so that there is a energy spread in the beam transmitted through the
specimen. If these electrons are not filtered (done in Electron Energy
Loss spectroscopy) then the electrons with different energies are focused at different spots by the lens, as shown in figure 15. This again
causes a point to spread into a disk, similar to spherical aberration.
3. Astigmatism Astigmatism occurs when the magnetic field within the
lens is non uniform. This could occur due to problems in lens manufacturing (e.g. improper machining). This again affects the focusing.
The above three lens defects are the main factors limiting the resolution in
the TEM. Spherical aberration has the maximum effect on the resolution.
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This is usually written as
1
rmin = 0.91 (Cs λ3 ) 4
(10)
where rmin is the radius of the disk in the imaging place and Cs is called the
spherical aberration coefficient. This is lens dependent parameter and defines
how much a point object gets spread out as a disk. For an electron beam of
energy 100 keV the wavelength is around 3.7 pm. For a Cs of 3 mm (typical
in a TEM) rmin calculated using equation 10 is 0.3 nm, much higher than
the theoretical resolution given by the wavelength. One way to increase the
resolution is to increase electron energy (decreasing wavelength) but this will
lead to increased beam damage.
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