The Basic of Transmission
Electron Microscope
Text book: Transmission electron microscopy by David B
Williams & C. Barry Carter. 2009, Springer
Background survey
• http://presemo.aalto.fi/tem1
Microscopy and the Concept of Resolution
Rayleigh criterion for visible light microscopy
: point resolution
: wavelength
: refractive index
: semi-angle of the lens
sin  1,   0.61
For TEM the approximate:
 1.22/
Interaction of Electrons with Matter
XEDS
EELS
DF
BF
Depth of field: a measure of how much of the object
that we are looking at remains in focus at the same time.
Depth of focus: the distance over which of the image
can move relative to the object and still remains in focus
Condenser lens apertures (C2) are inserted to narrow
the beam and to increase the depth of field of the
specimen and depth of focus of the images.
In the TEM, the specimen is usually in focus from the
top to the bottom surfaces at the same time,
independent of its topography, so long as it’s electron
transparent. The TEM image is 2D projection of 3D
specimen!
Why use TEM?
Atomic level images; information about specimen’s chemistry
and crystallography.
Limitation: Sampling; interpreting transmission images;
electron beam damage and safety; specimen preparation
TEM should used together with low magnification OM, SEM
and XRD to fully solve a materials problem!
Thinner is better! Specimen
below 100 nm should be used
wherever possible, and in
HRTEM or electron
spectrometry, specimen
thickness less than 50 nm or
10 nm are essential.
Some fundamental properties of electrons
 1.22/
Scattering and
Diffraction
Basic TEM operation
Different kinds of electron scattering from
a thin specimen and a bulk specimen
TEM
SEM
• Elastic/inelastic -> energy
• Coherent/incoherent-> in
phase
• Elastic scattering:
coherent at low angles
(<10°); incoherent (>10°)
• Inelastic scattering:
incoherent (<1°)
Scattering and the cross section of scattering
Assumption: Single scattering
Plural scattering : electron scattering more than once
Multiple scattering: scattered > 20 times.
total the number of scattering events per
unit distance that the electron travels
through the specimen.
The mean free path:
The average distance that the electron travels between scattering events.
Comparison of X-rays diffraction and
electron diffraction
X-rays are scattered by the electrons in a material through
an interaction between the negatively charged electrons
and the electronagnetic field of the incoming X-rays.
Electrons are scattered by both the electrons and nuclei in
a materials; the incoming negatively charged electron
interact with the local eelctromagnetic fields of the
specimen. The incoming electrons are therefore directly
scattered by the specimen; it is not a field-to-field
exchanges as occurs for the case of X-rays.
Fraunhofer diffraction and Fresnel diffraction
Fraunhofer diffraction occurs when a flat wavefront
interacts with an object. Since a wave emitted by a point
becomes planar at large distaces, this is known as farfield diffraction. (Young’s slits) – electron diffraction
patterns
Fresnel diffraction occurs when it’s not Fraunhofer. This
case is also known as near-field diffraction. - images
A word about angles•
We can control the angle of incidence of
electrons on the specimen and we will
define the angle of incidence as .
•
In the TEM we use aperture or detector
to collect a certain fraction of the
scattered electrons and we will define
any angle of collection as .
•
We will define all scattering angles
controlled by the specimen as . This
maybe a specific angle, such as twice
the Bragg angle (where  = 2B) or a
general scattering angle . So  is the
scattering semi-angle for diffraction even
though it is 2B.
Elastic Scattering
Particles and Waves
Electron particls have a scattering
cross section and differential
scttering cross section.
Electron particles can be scattered
through particular angles.
(remember our angles are semiangles).
The Electrons interact with the
nucleus and the electron cloud
throuhg Coulomb forces.
We can relate this process to
scattering of other particles such
as  particles, so lots of analysis
can carry over from other systems.
Wave are diffracted by atoms or
”scattering centers”
How strongly a wave is scattered
by an atom is determined by the
atomic-scattering amplitude.
When we gather atoms together
into a solid, the diffraction
process gets much more
complicated but it is central to
TEM.
We can relate the process to the
diffraction of X-rays, so lots of
analysis already exists.
When we discuss X-ray and electron spectrometry you’ll
see that we have to use a particle discription. When we
discuss imaging, HRTEM and DPs you’ll see that we use
a wave description.
Electron scattering from single, isolated atoms
An isolated atom can scatter a
high-energy electron by two
mechanism. Coulombic
interaction within the electron
cloud results in low-angle
scattering; coulombic attraction
by the nucleus causes higherangle scattering (and perhaps
complete backscatter when  >
90).
So Z, V, and  all affect image contrast and are the three major reasons why you cannot
avoid having to study the physics of electron scattering.
Collective scattering from many atoms
together within the specimen
The Rutherford cross section
(V, Z, )
Thinner
is
better!
High-angle Rutherford-scattered
electron are incoherent
1. The high-angle, forward scattering can be used to form
exceptionally high-resolution images of a crystalline
specimen in which the image contrast is due solely to the
value of Z (Z-contrast), not the orientation of the
specimen (as in the case for low-angle coherent
diffraction.
2. Second (but much less important), the high-angle
backscattered electrons (BSEs) can be used to form
images of the beam-entrance surface of the specimen, in
which the contrast is not only due to differences in Z, but
also to changes in surface topography of the specimen
(such as SEM-BSE). BSE images are rarely used in the
TEM because the BSE signal is small.
The atomic-scattering factor
The scattering-factor approach is complementary to the
Rutherford differential cross section analysis, becasue it is
most useful for describing the low-angle (i.e., <3) elastic
scattering where the Rutherford model is inappropriate.
The Structure factor F()
Diffraction equations
n = 2d sinB
Bragg’s Law
Laue equations
Assignment
• Reading and summary (in presentation): deadline
is 16.9. 2016
Summary should be made as a teaching
presentation, so your peer can learn the topic
from your presentation (you may use note for
description of content in the slides if needed).
• Evaluation: everyone get two summaries for
evaluation, deadline 19.9.2016, before lecture.
• Home work (not this week)