Transcript Slide 1 - Nanosggswu Nanosggswu

Properties of Electrons, their Interactions with Matter and
Applications in Electron Microscopy
The electron e is an elementary particle that carries a negative charge. the electron was by J.
J. Thompson in 1897 (Nobel Prize 1906). While studying so-called cathode rays, which in fact
are electron beams, he discovered that these rays are negatively charged particles. In fact,
the mass of the electron is approximately 1/1836 of that of a proton.
Wave properties
In 1924, the wave-particle dualism was postulated by de Broglie (Nobel Prize 1929). All
moving matter has wave properties (Figure 1), with the wavelength  being related to the
momentum p by
h/mv=h/p
(h : Planck constant; m : mass; v : velocity)
This equation is of fundamental
importance for electron microscopy
because
this
means
that
accelerated electrons act not only
as particles but as waves too.
An electron accelerated in an electric field V gains an energy E = eV which further
corresponds to a kinetic energy Ekin = mv2/2. Thus:
E = eV = m0v2 / 2
From this, the velocity v of the electron can be derived:
v = (2eV/m)1/2
(V : acceleration voltage; e : electron charge = -1.602 176 487 × 10-19 C; m0 : rest mass of
the electron = 9.109 x 10-31 kg).
It follows for the momentum p of the electron:
p(2meV)1/2
Now, the wavelength  can be calculated from the de Broglie equation according to
h/(2meV)1/2
The values calculated for acceleration potentials commonly used in TEM are listed in Table 1.
It is important to note that these electrons move rather fast, and their speed approaches light
velocity. As a result, a term considering relativistic effects must be added:
(c : light velocity in vacuum = 2.998 x 108 m/s).
It thus is evident that
relativistic effects
cannot be neglected
for electrons with an
energy E ≥ 100 kV.
Characteristics of the electron wave
Waves in beams of any kind can be either coherent or incoherent. Waves that have
the same wavelength and are in phase with each other are designated as coherent.
In phase with each other means that the wave maxima appear at the same site
(Figure 2). The analogue in light optics is a Laser beam. On contrast, beams
comprising waves that have different wavelengths like sun rays or are not in phase
are called incoherent (Figure 2).
Electrons accelerated to a selected energy have the
same wavelength. Depending on the electron gun,
the energy spread and as a result the wave length
as well varies. Furthermore, the electron waves are
only nearly in phase with each other in a
thermoionic electron gun while the coherency is
much higher if a field emitter is the electron source.
The generation of a highly monochromatic and
coherent electron beam is an important challenge
in the design of modern electron microscopes.
However, it is a good and valid approximation to
regard the electron beam as a bundle of coherent
waves before hitting a specimen. After interacting
with a specimen, electron waves can form either
incoherent or coherent beams.
Waves do interact with each other. By linear superposition, the amplitudes of the two waves
are added up to form a new one. The interference of two waves with the same wavelength
can result in two extreme cases (Figure 3):
(i) Constructive interference: If the
waves are completely in phase with
each other, meaning that the maxima
(and minima) are at the same position
and have the same amplitude, then
the amplitude of the resulting wave is
twice that of the original ones.
(ii) Destructive interference: If two
waves with the same amplitude are
exactly out of phase, meaning that
the maximum of one wave is at the
position of the minimum of the
other, they are extinguished.
An electron passing through a solid may be scattered
not at all
once (single scattering)
several times (plural scattering ), or
very many times (multiple scattering )
Each scattering event might be elastic or inelastic.
The scattered electron is most likely to be forward
scattered but there is a small chance that it will be
backscattered.
Electron-Matter Interactions
Electron microscopy is not just a single technique but a diversity of different ones that offer
unique possibilities to gain insights into structure, topology, morphology, and composition of
a material.
Various imaging and spectroscopic methods represent indispensable tools for the
characterization of all kinds of specimens on an increasingly smaller size scale with the
ultimate limit of a single atom.
The wealth of very different information that is obtainable by various methods is
caused by the multitude of signals that arise when an electron interacts with a
specimen. Gaining a basic understanding of these interactions is an essential
prerequisite before a comprehensive introduction into the electron microscopy
methods can follow.
A certain interaction of the incident electron with the sample is obviously necessary since
without the generation of a signal no sample properties are measurable.
The different types of electron scattering are of
course the basis of most electron microscopy
methods and will be introduced in the following.
When an electron hits onto a material,
different interactions can occur, as
summarized in Figure 4. For a systemization,
the interactions can be classified into two
different types, namely elastic and inelastic
interactions.
(i) Elastic Interactions
In this case, no energy is transferred from
the electron to the sample. As a result, the
electron leaving the sample still has its
original energy E0:
Eel = E0
Of course, no energy is transferred if the
electron passes the sample without any
interaction at all. Such electrons contribute
to the direct beam which contains the
electrons that passes the sample in direction
of the incident beam (Figure 4).
Furthermore, elastic scattering happens if the electron is deflected from its path by Coulomb
interaction with the positive potential inside the electron cloud. By this, the primary electron
loses no energy or – to be accurate – only a negligible amount of energy.
These signals are mainly exploited in TEM and electron diffraction
methods.
(ii) Inelastic Interactions
If energy is transferred from the incident electrons to the sample, then the electron energy of
the electron after interaction with the sample is consequently reduced:
Eel < E0
The energy transferred to the specimen can cause different signals such as X-rays, Auger or
secondary electrons, plasmons, phonons, UV quanta or cathodoluminescence. Signals
caused by inelastic electron-matter interactions are predominantly utilized in the methods
of analytical electron microscopy.
Elastic Interactions
Incoherent Scattering of Electrons at an Atom
For the basic description of the elastic scattering of a single
electron by an atom, it is sufficient to regard it as a negatively
charged particle and neglect its wave properties.
An electron penetrating into the electron cloud of an atom is
attracted by the positive potential of the nucleus (electrostatic
or Coulombic interaction), and its path is deflected towards the
core as a result (Figure
5).
The Coulombic force F is defined as: F = Q1Q2 / 4π εo r2
Smaller r, larger is F and consequently the scattering angle. In rare cases, even complete
backscattering can occur, generating so-called back-scattered electrons (BSE). These
electrostatic electron matter interactions can be treated as elastic, which means that no
energy is transferred from the scattered electron to the atom. In general, the Coulombic
interaction is quite strong, e.g. compared to that of X-rays with materials.
Because of its dependence on the charge, the force F with which an atom attracts an electron
is stronger for atoms containing more positives charges, i.e. more protons. Thus, the
Coulomb force increases with increasing atomic number Z of the respective element.
Interaction cross-section and mean free path
A cross section is the effective area which governs the probability of some scattering or
absorption event
The probability of scattering is described in terms of either an "interaction cross-section" or
a mean free path.
The concept of the interaction cross-section is based on the simple model of an effective
area. If an electron passes within this area, an interaction will certainly occur. If the cross
section of an atom is divided by the actual area, then a probability for an interaction event
is obtained. Consequently, the likelihood for a definite interaction increases with increasing
cross-section.
Each scattering event might occur as elastic or as inelastic interaction. Consequently the
total interaction cross section T is the sum of all elastic and inelastic terms:
T = elastic + inelastic
For every interaction, the cross section can be defined depending on the effective radius
r:
For the case of elastic scattering, this radius relast is
(Z : atomic number; e : elementary charge; V : electron potential;  : scattering angle).
This equation is important for understanding some fundamentals about image formation
in several electron microscopy techniques.
Since the cross-section and thus the likelihood of scattering events as well increases for
larger radii, scattering is stronger for heavier atoms (with high) Z than for light elements.
Moreover, it indicates that electrons scatter less at high voltage V and that scattering into
high angles  is rather unlikely.
By considering that a sample contains a number of N atoms in a unit volume, a total
scattering interaction cross section QT is given as
Introducing the sample thickness t results in
This gives the likelihood of a scattering event. The term t is designated as mass-thickness.
Inspite of being rather coarse approximations, these expressions for the interaction cross
section describe basic properties of the interaction between electrons and matter
reasonably well.
Another important possibility to describe interactions is the mean free path ,
which unfortunately has usually the same symbol as the wavelength. Thus, we call
it mfp here for clarity.
For a scattering process, this is the average distance that is traveled by an electron
between two scattering events. This means, for instance, that an electron in
average interacts two times within the distance of 2mfp. The mean free path is
related to the scattering cross section by:
For scattering events in the TEM, typical mean free paths are in the range of some
tens of nm.
For the probability p of scattering in a specimen of thickness t follows then:
TEMs are patterned after Transmission Light Microscopes and will
yield similar information.
Morphology
The size, shape and arrangement of the particles which make up the specimen as well as their
relationship to each other on the scale of atomic diameters.
Crystallographic Information
The arrangement of atoms in the specimen and their degree of order, detection of atomic-scale
defects in areas a few nanometers in diameter.
Compositional Information (if so equipped)
The elements and compounds the sample is composed of and their relative ratios, in areas a few
nanometers in diameter.
In brief, a EM utilizes energetic electrons to provide
morphologic,
compositional
and
crystallographic
information on samples.
The purpose of the C-lens is to focus the light onto the specimen.
The condenser aperture controls the fraction
of the beam which is allowed to hit the
specimen.
1. The "Virtual Source" at the top represents the electron gun, producing a stream of
monochromatic electrons.
This stream is focused to a small, thin, coherent beam by the use of condenser lenses 1 and
2. The first lens (usually controlled by the "spot size knob") largely determines the "spot
size"; the general size range of the final spot that strikes the sample. The second lens(usually
controlled by the "intensity or brightness knob" actually changes the size of the spot on the
sample; changing it from a wide dispersed spot to a pinpoint beam.
3. The beam is restricted by the condenser aperture (usually user selectable), knocking out
high angle electrons (those far from the optic axis, the dotted line down the center).
The beam strikes the specimen and parts of it are transmitted
4. This transmitted portion is focused by the objective lens into an image. Optional
Objective and Selected Area metal apertures can restrict the beam; the Objective aperture
enhancing contrast by blocking out high-angle diffracted electrons, the Selected Area
aperture enabling the user to examine the periodic diffraction of electrons by ordered
arrangements of atoms in the sample.
5. The image is passed down the column through the intermediate and projector lenses,
being enlarged all the way.
6. The image strikes the phosphor image screen and light is generated, allowing the user to
see the image. The darker areas of the image represent those areas of the sample that
fewer electrons were transmitted through (they are thicker or denser). The lighter areas of
the image represent those areas of the sample that more electrons were transmitted
through (they are thinner or less dense).
TEM can be compared with a slide projector.
In a slide projector light from a light source is made
into
a parallel beam by the condenser lens; this passes
through the slide (object) and is then focused as an
enlarged image onto the screen by the objective lens.
In the electron microscope, the light source is
replaced by an electron source, the glass lenses are
replaced by magnetic lenses, and the projection
screen is replaced by a fluorescent
screen, which emits light when struck by electrons,
or, more
frequently in modern instruments, an electronic
imaging device such as a CCD (charge-coupled device)
camera.
The whole trajectory from source to screen is under
vacuum and the specimen (object) has to be very thin
to allow the electrons to travel through it
Basic principle of Transmission Electron Microscope
After having little knowledge that an
accelerated electron beam can have a very
high resolving power, we then move on to
see how one can use this electron beam in
imaging technology.
There are 3 types of electron microscopes,
namely
the
transmission
electron
microscope (TEM), scanning electron
microscope (SEM), and scanning tunneling
microscope (STM).
In this Lecture we will introduce the basic
principle of TEM.
Fig. shows a schematic outline of a TEM.
A TEM contains four parts: electron source,
electromagnetic lens system, sample holder,
and imaging system.
A TEM functions under the same basic principles as an optical microscope.
Electron Gun….
At the top of the TEM column is the electron gun, which is the
source of electrons. The electrons are accelerated to high
energies (typically 100-400 keV) and then focused towards the
sample by a set of condenser lenses and apertures.
The electron beam comes from a filament, made of
various types of materials.
The most common is the Tungsten hairpin gun.
This filament is a loop of tungsten which functions as
the cathode.
A voltage is applied to the loop, causing it to heat up.
The anode, which is positive with respect to the
filament, forms powerful attractive forces for
electrons.
This causes electrons to accelerate toward the anode.
Some accelerate right by the anode and on down the
column, to the sample.
Other examples of filaments are Lanthanum
Hexaboride filaments and field emission guns.
Electron source of a
TEM.
Selection of a Electron source or electron gun
The source is chosen so that the rates of electrons incident on the sample per unit area and
leaving the source per unit solid angle (brightness) are maximized. This is so that the
maximum amount of information can be extracted from each feature of the sample.
As I mentioned before there are two major types of electron source. Guns are more cheaper
and more common of the to generate electrons by thermionic emission. If enough thermal
energy is added to a material its electrons may overcome the energy barrier of the work
function and escape.
Unfortunately, to avoid the source melting, the material used must either have a very high
melting point (such as W) or an exceptionally low work function (certain rare-earth boride
crystals such as LaB6 are widely used).
Another way of extracting electrons from a material is by applying a very large electric field. By
drawing tungsten wire to a very fine point (<0.1 μm), application of a potential of 1 kV gives an
electric field of 1010 A m-1 which is large enough to allow electrons to tunnel out of the sample.
This is called field emission.
Field emission guns are around twice as expensive as thermionic electron guns, and must be
used under ultra-high vacuum conditions. They are favorable for applications in which a high
brightness and low energy-spread of incident electrons is needed. (e.g. HRTEM, FEG.)
.......................Electron Guns
•Two main types of gun – Thermionic and Field Emission.
•Thermionic sources produce electrons when heated.
•Field emission sources produce electrons when exposed to an intense
electric field.
•FEG’s give much more brightness than thermionic systems.
•FEG’s give a more monochromatic
electron source and finer probe (i.e. better
resolution).
Comparison of the three types of source operating at 100kV
A thermionic electron gun is operated as follows:
Select the accelerating potential ( kV ).
Increase the current passing through the filament until the knee of the emission
curve is reached (saturation), giving the best compromise between the beam
current emitted (as high as possible) and the filament lifetime (as long as
possible).
Adjust the bias to give the desired combination of source size and beam current.
J =AGT2 e-w/kT
where J is the emission current density, T is the temperature of the metal, W is the work
function of the metal, k is the Boltzmann constant, and AG is a parameter which is materials
specific
Electron Source (Thermionic gun, Field emission)…….
Schottky and cold field-emission guns comparing in electron microscopes
A field emission gun is based on a release of electrons from surface of sharply pointed
tungsten tip as a result of application of a strong electric field (>107 Vm-1).
The field emission is caused by applying a voltage between the tip and an aperture metal
anode.
There are two types of field emission gun differ mainly by their tips:
CFE - cold field emitter is the base type. Application of the very strong electric field causes the
surface energy barrier to deform to such an extent that it becomes physically very narrow.
There becomes a finite probability of electrons from the Fermi level penetrating the barrier
even at ambient temperature. Usually made of single crystal tungsten sharpened tip with
radius of about 100 nm, the needle is so sharp that electrons are extracted directly from the
tip.
SE – Schottky emitter. The Schottky emitter combines the high brightness and low energy
spread of the cold field emitter with the high stability and low beam noise of thermal emitters.
A commercial Schottky emitting cathode is less sharp than the others; there a monatomic layer
of ZrO is formed on the tungsten surface. This coating reduces the work function of the
tungsten from 4.54 to 2.8 eV. At an operating temperature of about 1800 K, this emitter may
not be as bright as the cold field emitter but it delivers stable high currents and is less
demanding in operation.
The follow table summarizes the properties of common sources:
Source Brightne Source
type ss[A/cm size
2/sr]
[nm]
Energy
spread
(eV)
Vacuum
requiremen
t (Torr)
SE
~108
20
0.9
10-9
CFE
~109
5
0.22
10-10
Electromagnetic lens system
After leaving the electron source, the electron
beam is tightly focused using electromagnetic lens
and metal apertures.
The system only allows electrons within a small
energy range to pass through, so the electrons in
the electron beam will have a well-defined energy.
Sample Holder, Vacuum
Chamber
The sample holder is a platform equipped with a
mechanical arm for holding the specimen and
controlling its position.
Imaging System
The imaging system consists of
another electromagnetic lens system
and a screen.
The electromagnetic lens system
contains two lens systems, one for
refocusing the electrons after they
pass through the specimen, and the
other for enlarging the image and
projecting it onto the screen.
The screen has a phosphorescent
plate which glows when being hit by
electrons.
Image forms in a way similar to
photography.
Important point to remember
TEM, the transmission of electron beam is highly
dependent on the properties of material being examined.
Such properties include density, composition, etc. For
example, porous material will allow more electrons to
pass through while dense material will allow less. As a
result, a specimen with a non-uniform density can be
examined by this technique.
Whatever part is transmitted is projected onto a phosphor
screen for the user to see.
Advantages
A Transmission Electron Microscope is an impressive instrument with a number of
advantages such as:
1. TEMs offer the most powerful magnification, potentially over one million times
or more
2. TEMs have a wide-range of applications and can be utilized in a variety of
different scientific, educational and industrial fields
3. TEMs provide information on element and compound structure Images are highquality and detailed TEMs are able to yield information of surface features, shape,
size and structure
4. They are easy to operate with proper training
Disadvantages
1. TEMs are large and very expensive
2. Laborious sample preparation
3. Potential artifacts from sample preparation
4. Operation and analysis requires special training
5. Samples are limited to those that are electron transparent, able to tolerate the
vacuum chamber and small enough to fit in the chamber
6. TEMs require special housing and maintenance
7. Images are black and white
Electron microscopes are sensitive to vibration and electromagnetic fields and must
be housed in an area that isolates them from possible exposure.
A Transmission Electron Microscope requires constant upkeep including maintaining
voltage, currents to the electromagnetic coils and cooling water.
First and second condenser lens
C1- Create a demagnified image of
the gun crossover and Control the
minimum spot size obtainable in the
rest of the condenser system.
C2-The convergence of the beam at the
specimen. Diameter of the illuminated area of
the specimen.