Limits of OM, SEM, SPM and XRD
NN
G.B.
core
BT
EDS
shell
NN G.B.
BT
BT-BaTiO3
0.2m NN-NaNbO3
G.B.-Grain boundary
M.G.J.-multiple grain
junction
M.G.J.
NN/BT
•Lateral resolution: ~m
•Details of microstructure:
e.g., domain structure,
chemical inhomogeneity
phase distribution, grain
boundaries, interfaces,
precipitates, dislocations,
etc.
Chemical analysis at a
nanometer scale
Why TEM?
The uniqueness of TEM is the ability to
obtain full morphological (grain size, grain
boundary and interface, secondary phase
and distribution, defects and their nature,
etc.), crystallographic, atomic structural
and microanalytical such as chemical
composition (at nm scale), bonding
(distance
and
angle),
electronic
structure, coordination number data from
the sample.
TEM is the most efficient and versatile
technique for the characterization of
materials.
An Introduction to Transmission Electron
Microscopy (TEM)/Scanning Transmission
Electron Microscopy (STEM)
• What is a TEM?
• How it works - gun, lenses, specimen stage
• Resolution
• What can a TEM do?
• Imaging and diffraction
Imaging-diffraction and phase contrast
Diffraction-Selected area electron diffraction (SAED)
and Convergent beam electron diffraction (CBED)
• Chemical analysis
EDS, Electron Energy Loss Spectroscopy (EELS)
Energy Filtered Imaging
Basic features of A Modern TEM
CM200 (200kV)
Column
Condenser
Lens
Objective Lens
SAD Aperture
Electron Gun
EDS Detector
Specimen Holder
Binocular
TV Monitor
Camera
Chamber
Magnifying
Lenses
Viewing Chamber
Cost:  $4,000,000
A simple analogue
A better comparison
Vacuum
The electron microscope is built like a series of
vessels connected by pipes and valves separate
all the vessels from each other.
The vacuum around the specimen is around 10-7
Torr.
The vacuum in the gun depends on the type of
gun, either around 10-7 Torr (the tungsten or
LaB6 gun) or 10-9 Torr (for the Field Emission
Gun).
The pressure in the projection chamber is usually
only 10-5 Torr (and often worse). This pressure is
not very good because the projection chamber
holds the negatives used to record images. Even
though we dry the negatives before putting them
in the microscope, they still will give off so many
gases that the vacuum in the projection chamber
never gets very good.
Electron Beam Source
The Lenses in TEM
Condenser lenses(two)-control how
strongly beam is focused (condensed)
onto specimen. At low Mag. spread
beam to illuminate a large area, at high
Mag. strongly condense beam.
Objective lens-focus image (image
formation) and contribute most to
the magnification and resolution of
the image.
B
Four lenses form magnification
system-determine the magnification
of the microscope. Whenever the
magnification is changed, the currents
through these lenses change.
Image Formation in TEM
Control
brightness,
convergence
Control contrast
binocular
screen
negatives
Ray Diagram for a TEM
Why Electrons?
Resolution!
In the expression for the resolution
(Rayleigh’s Criterion)
r = 0.61/nsin
-wavelength, =[1.5/(V+10-6V2)]1/2 nm
V-accelerating voltage, n-refractive index
-aperture of objective lens, very small in TEM
 sin  and so r=0.61/ ~0.1 radians
Green Light
200kV Electrons
~400nm
~0.0025nm
n~1.7 oil immersion
n~1 (vacuum)
r~150nm (0.15m)
r~0.02nm (0.2Å)
1/10th size of an atom!
UNREALISTIC! WHY?
Resolution Limited by
Lens Aberrations
Chromatic aberration is
caused by the variation of
the electron energy and
thus electrons are not
monochromatic.
point is imaged
as a disk.
Spherical
aberration
is
caused by the lens field
acting inhomogeneously on
the off-axis rays.
rmin0.91(Cs3)1/4
point is imaged
as a disk.
Practical resolution of microscope.
Cs–coefficient of spherical
aberration of lens (~mm)
Beam and Specimen Interaction
(EDS)
BF
DF
HREM
Imaging
(EELS)
SAED & CBED
diffraction
Scanning Transmission Electron Microscopy
JEOL 2000FX (STEM)
Analytical Electron Microscope
Scanning
beam
specimen
HAADF
Detector
ADF
BF
ADF
DF
BF
STEM detector
or EELS
In STEM, the
electron beam is
rastered (scan
coil) across the
surface of a
sample in a similar
manner to SEM,
however, the
sample is a thin
TEM section and
the diffraction
contrast image is
collected on a
solid-state (ADF)
detector.
HAADF-high angle
annular dark-field
Specimen Preparation-Destructive
Dispersing crystals or powders on a carbon film on a grid
3mm
Making a semiconductor specimen with a Focused Ion Beam (FIB)
1
1.
2.
3.
4.
5.
2
3
4
5
a failure is located and a strip of Pt is placed as a protective cover.
On one side of the strip a trench is milled out with the FIM.
The same is done on the other side of the strip (visible structure).
The strip is milled on both sides and then the sides connecting the
strip to the wafer are cut through.
The strip is tilted, cut at the bottom and deposited on a TEM grid.
Specimen Preparation-2
Ion-milling a ceramic
Ar (4-6keV, 1mm A)
3mm
Ultrasonic cut
Dimple center part ion-mill until a hole
grind
of disk to ~5-10m appears in disk
Jet-polishing metal
-
+
a thin stream of acid
Drill a 3mm
cylinder
A disk is mounted in a
Cut into disks
jet-polishing machine
and grind
and is electropolished
until a small hole is
made.
Ultramicrotomy-using a (diamond) knife blade
Mainly for sectioning biological materials.
To avoid ion-milling damage ultramicrotome can also be used
to prepare ceramic TEM specimens.
Specimen Holder
Rotation, tilting, heating, cooling and straining
beam
holder
a split polepiece
objective lens
Twin specimen holder
Double tilt heating
Heating and straining
Specimen Holder with Electrical
Feedthroughs
Imaging
BF and DF imaging
HREM
BF & DF Imaging – Diffraction Contrast
OA
OA
DDF
CDF
Beam
tilt
crystal
D
T-transmitted
D-diffracted
C-film
amorphous
D
Objective
aperture
T
T
BF image
C-film
Hole in OA
Objective
aperture
DF image
C-film
crystal
crystal
Diffraction + mass-thickness Contrast
Diffraction, Thickness and Mass Contrast
BF images
Weak diffraction
Strong
diffraction
2
thinner
thicker
G.B.
8
7
1
thickness
fringes
3
thickness
Disk specimen
6
5
4
8 grains are in different orientations
or different diffraction conditions
Low
mass
.
.
.
High
.
.
.
.
.
.
.
.
.
.
.
. . ..
. .... mass
T
T
S
S
Bright Dark
S
Bright Field (BF) and Dark Filed (DF) Imaging
Incident beam
allowed to pass objective aperture to
form images.
BF
specimen
diffracted
BF imaging-only transmitted beam is
beam
mass-thickness
contrast
DF imaging
only diffracted
beams are
allowed to pass
transmitted beam
the aperture to
objective aperture form images.
hole in objective
aperture(10-100m)
Particles in Al-Cu
Alloy.
thin platelets ll e
Vertical, dark
Particles e.
DF
DF
Phase Contrast Imaging
High Resolution Electron
Microscopy (HREM)
D
Si
T
BN
Objective
aperture
Electron diffraction pattern recorded
From both BN film on Si substrate.
Use a large objective
aperture.
Phases and intensities
of diffracted and
transmitted beams
are combined to form
a phase contrast
image.
Electron Diffraction
Geometry for
e-diffraction
 edhkl
Bragg’s Law:
Specimen
foil
=0.037Å (at 100kV)
=0.26o if d=4Å
 = 2d
r/L=sin2
as   0
r/L = 2
2
L
r
T
D
Reciprocal
lattice
hkl
[hkl] SAED pattern
 = 2dsin
r/L = /d or
r = Lx
1
d
L -camera length
r -distance between T and D spots
1/d -reciprocal of interplanar distance(Å-1)
SAED –selected area electron diffraction
Reciprocal Lattice
A reciprocal lattice is another way
of view a crystal lattice and is used
to understand diffraction patterns.
A dimension of 1/d is used in
reciprocal lattices.
2-D Reciprocal Lattices
For every real lattice there is an equivalent reciprocal lattice.
Real space:
Unit cell vectors: a,b
d-spacing direction
a
d10
[10]
b
d01
[01]
[01]
[10]
(10)
Reciprocal space:
Unit cell vectors: a*,b*
magnitude direction
b
a* 1/d10
a
b* 1/d01
b*
a*
(01)
01
02
10
11
A reciprocal lattice can
be built using reciprocal
12
vectors. Both the real
20
and reciprocal construc21
22
tions show the same
lattice, using different
Note: each point in the reciprocal
but equivalent
lattice represents a set of planes.
descriptions.
3-D Reciprocal Lattice
Real space:
Unit cell vectors: a,b,c
magnitude direction
a
d100
[100]
b
d010
[010]
c
d001
[001]
Orthorhombic
Reciprocal space:
Unit cell vectors: a*,b*
magnitude direction
a* 1/d100  b and c
b* 1/d010  a and c
 a and b
c* 1/d001
Note: as volume of unit cell in real space increases the
volume of unit cell in reciprocal space decreases, and
vice versa. a*,b* and c* are parallel to corresponding a,b and
c, and this is only true for the unit cells of cubic, tetragonal
and orthorhmbic crystal systems.
Lattice Vectors
Real space lattice vector
corresponds to directions
in crystal and it can be
defined as:
r=ua+vb+wc
a,b and c are unit cell vectors,
u,v and w are components of
the direction index [uvw].
A reciprocal lattice vector
can be written as:
g*=ha*+kb*+lc*
a*,b* and c* are reciprocal
unit vectors, and h,k and l
are the Miller indices of the
plane (hkl).
Effect of Spacing of planes in Real Space on
Length of Reciprocal Vector, g
-
[111]
-
(111)
d111
In a crystal of any structure, ghkl is normal to the (hkl)
plane and has a length inversely proportional to the
interplanar spacing of the planes.
Why are there so many spots?
The Ewald Sphere and Diffraction Pattern
High energy
electron case
Reciprocal lattice
k – wave vector
lkl = 1/
 – wavelength of electron
Ewald’s Sphere
Ewald’s sphere is built for interpreting diffraction
Ewald
circle
lkl=1/
C
incident
beam
2
diffracted
beam
kd
ki
g
H
G
130
0
CG-C0=0G or kd-ki=g Laue equation
Wherever a reciprocal lattice point touches the circle, e.g., at G, Bragg's
Law is obeyed and a diffracted beam will occur. At H, no diffraction.
Construction of Ewald’s Sphere
Ewald’s sphere is built for interpreting diffraction
patterns and it shows which sets of planes are at (or
close to) their Bragg angle for diffraction to occur.
•Incident wave is represented by a reciprocal vector k
(lkl=1/ and points in the direction of wave).
•Construct a circle with radius 1/ (i.e., k), which
passes through origin of reciprocal lattice, 0.
•Wherever a reciprocal point touches the circle, Bragg’s
law is obeyed and a diffracted beam will occur.
•C0–incident beam and CG–diffracted beam. The angle
between C0 and CG must be 2.
•0G is the reciprocal vector g130 and has magnitude of
1/d130.
0G/2=lklsin,  0G=2/sin,  1/d130=2/sin130
 =2d130sin130
Ewald’s Sphere Construction in 3D
SOLZ
FOLZ
In a single crystal
only a few sets of
planes are oriented
at their Bragg angle
at any one time.
ZOLZ
Polycrystalline sample
ZOLZ, FOLZ and SOLZ are zero order, first order and second order
Laue zone, respectively.
parallel beam
Virtual
aperture
specimen
Objective
lens
Diffraction
pattern
SAD
aperture
SAED
Selected Area Electron Diffraction
A TEM technique to
reduce both the area
and intensity of the
beam contributing to a
diffraction pattern by
the insertion of an
aperture into the
image plane of the
objective lens. This
Back focal produces a virtual
plane
diaphragm in the plane
of the specimen.
Focusing SAED Pattern at Fixed Screen
by changing magnetic lens strength
specimen
lens
Diffracted beam
Transmitted beam
SAED (ZOLZ) gives 2-D information
screen
Spot pattern
SAED Patterns of Single Crystal,
Polycrystalline and Amorphous Samples
a
b
c
020
110
200
r 1 r2
a. Single crystal Fe (BCC) thin film-[001]
b. Polycrystalline thin film of Pd2Si
c. Amorphous thin film of Pd2Si. The diffuse
halo is indicative of scattering from an
amorphous material.
Diffraction Spot Intensity
Spot intensity: Ihkl  lFhkll2
Fhkl - Structure Factor
N
Fhkl =  fn exp[2i(hu+kv+lw)]
n=1
fn –
atomic scattering factor
fn  Z, sin/
h,k,l are Miller indices and u,v,w fractional coordinates
Indexing Diffraction Pattern-ratio technique
Any 2-D section of a reciprocal lattice can be defined by two
vectors so only need to index 2 spots.
1.Choose one spot to be the origin and
measure r1
2.measure the spacing of a second spot r2
3.measure the angle, 
4.prepare a table giving the ratios of the
spacings of permitted diffraction planes
in the known structure
5.take measured ratio r1/r2 and locate a value close to this in
the table
6.assign more widely-spaced plane (lower indices) to the
shorter r value
7.calculate angle between pair of planes of the type you have
indexed
8.if measured  agrees with one of possible value, accept
indexing. if not, revisit the table and select another possible
pair of planes
9.finish indexing the pattern by vector addition.
Indexing Electron Diffraction Patterns
If we know the index for two diffraction spots
It is possible to index the rest of the spots by
Using vector addition as shown. Every spots
Can be reached by a combination of these two
Vectors.
Zone Axis of A SAED Pattern
Take any two g vectors, g1 (h1k1l1) and g2 (h2k2l2)
from the diffraction patter. The zone axis is given by
the vector product:
The zone axis is parallel to the electron beam direction.
_
[013]
Indexing-example
Cubic
1.Choose T as the origin, r1-7.75mm
131 (311)?
r2 
T
r1200
r=L/d r2/r1=d1/d2
2.r2-12.87mm
3.~72O
4.Get a table giving relative reciprocal
lattice spacings
5.r2/r1=1.66 gives several possible
pair of planes in the table
6.From the table of interplanar angle in cubic, ~72O gives only
one matched pair of planes, {100} (or {200}) and {311} for a
face-centered lattice. {100} diffraction is not allowed in a facecentered structure.
7.Calculating interplanar angles leads to (131) or (113) and (200)
since angle between (311) and (200) is
_ 25.2O.
8.Zone axis of pattern: r1 x r2 = [013] for (131) and (200) pair