Transmissions electron microscopy
Basic principles
Sample preparation
Imaging
aberrations (Spherical, Chromatic, Astigmatism)
contrast (Mass-thickness, Diffraction, Phase)
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Project report
• Report due Monday May 11, 14.00
• Project presentation and oral ”exam” Friday May 15
• Possible report outline:
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Introduction about the material and motivation
Experimental methods used
Results and discussion
Conlusions
References
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Basic principles, first TEM
Wave length of electrons:
200kV: λ= 0.00251 nm
(v/c= 0.6953, m/m0= 1.3914)
Electrons are deflected by both
electrostatic and magnetic fields
Force from an electrostatic field
F= -e E
Force from a magnetic field
F= -e (v x B)
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Ernst Ruska: Nobel Prize in physics 1986
a) The first electron microscope built by Knoll
and Ruska in 1933, b) The first commercial
electron microscope built by Siemens in 1939.
Basic TEM
Electron gun
Electron source:
●Tungsten, W
● LaB6
Cold trap
● FEG
Sample position
Vacuum requirements:
- Avoid scattering from residual gas in
the column.
- Thermal and chemical stability of the
gun during operation.
- Reduce beam-induced contamination
of the sample.
LaB6: 10-7 torr
FEG: 10-10 torr
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The lenses in a TEM
Filament
Anode
The diffraction limit on resolution
is given by the Raleigh criterion:
1. and 2. condenser lenses
δd=0.61λ/μsinα, μ=1, sinα~ α
Sample
Objective lens
Compared to the lenses in an
optical microscope they are very
poor!
Intermediate lenses
The point resolution in a TEM is
limited by the aberrations of the
lenses.
Projector lens
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- Spherical
- Chromatic
- Astigmatism
Spherical aberrations
r2
α
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r1
Spherical aberration coefficient
ds = 0.5MCsα3
M: magnification
Cs :Spherical aberration coefficient
α: angular aperture/
angular deviation from optical axis
r2
α
r1
2000FX: Cs= 2.3 mm
2010F: Cs= 0.5 nm
Disk of least confusion
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Chromatic aberration
Disk of least confusion
Chromatic aberration coefficient:
v - Δv
dc = Cc α ((ΔU/U)2+ (2ΔI/I)2 + (ΔE/E)2)0.5
Cc: Chromatic aberration coefficient
α: angular divergence of the beam
U: acceleration voltage
I: Current in the windings of the objective lens
E: Energy of the electrons
v
Thermally emitted electrons:
ΔE/E=kT/eU
2000FX: Cc= 2.2 mm
2010F: Cc= 1.0 mm
Force from a magnetic field:
F= -e (v x B)
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Lens astigmatism
x
•
Lens astigmatism
Loss of axial asymmetry
This astigmatism can not be
prevented, but it can be
corrected!
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y-focus
y
x-focus
Resolution limit
Year
Resolution
1940s
~10nm
1950s
~0.5-2nm
1960s
0.3nm (transmission)
~15-20nm (scanning)
1970s
0.2nm (transmission)
7nm (standard scanning)
1980s
0.15nm (transmission)
5nm (scanning at 1kV)
1990s
0.1nm (transmission)
3nm (scanning at 1kV)
2000s
<0.1 nm (Cs correctors)
http://www.sfc.fr/Material/hrst.mit.edu/hrs/materials/public/ElecMicr.htm
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Technical data of different sources
Tungsten
LaB6
Cold
FEG
Schottky
Heated
FEG
Brightness
(A/m2/sr)
(0.3-2)109
(0.3-2)109
1011-1014
1011-1014
1011-1014
Temperature
(K)
2500-3000
1400-2000
300
1800
1800
Work function
(eV)
4.6
2.7
4.6
2.8
4.6
Source size
(μm)
20-50
10-20
<0.01
<0.01
<0.01
Energy spread
(eV)
3.0
1.5
0.3
0.8
0.5
http://dissertations.ub.rug.nl/FILES/faculties/science/1999/h.b.groen/c1.pdf
H.B. Groen et al., Phil. Mag. A, 79, p 2083, 1999
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Sample preparation for TEM
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Samples need to be ~100 nm thick. How?
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Crushing
Cutting
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saw, diamond pen, ultrasonic drill, FIB
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Mechanical thinning
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Is your material brittle or ductile?
Is it a conductor or insulator?
Grinding, dimpling
Electrochemical thinning
Ion milling
Coating
Replica methods
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Plane view or cross section sample?
Is it a multi layered material?
TEM sample preparation: Thin films
Cut out cylinder
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Top view
Cut out a cylinder
and glue it in a Cu-tube
Cut out slices
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Cross section
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Grind down/
dimple
Glue the interface
of interest face to
face together with
support material
Focused Ion Beam
(FIB)
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Ion beam thinning
Grind down and
glue on Cu-rings
or
Cut a slice of the
cylinder and grind
it down / dimple
Cut off excess
material
Ion beam thinning
Imaging / microscopy
TEM
- High resolution (HREM)
- Bright field (BF)
- Dark field (DF)
- Shadow imaging
(SAD+DF+BF)
BiFeO3
Pt
TiO2
SiO2
STEM
- Z-contrast (HAADF)
- Elemental mapping
(EDS and EELS)
GIF
- Energy filtering
Holography
– Map magnetic domains
– Map electrostatic potential
– Enhance resolution
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Si
200 nm
Glue
Apertures
Condenser aperture
Objective aperture
Selected area aperture
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c
Simplified ray diagram
b
a
Parallel incoming electron beam
3,8 Å
Si
Sample
1,1 nm
PowderCell 2.0
Objective lense
Diffraction plane Objective aperture
(back focal plane)
Image plane
MENA3100 V08
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Selected area
aperture
Use of apertures
Condenser aperture:
Limits the number of electrons hitting the sample (reducing the intensity),
Reducing the diameter of the discs in the convergent electron diffraction pattern.
Selected area aperture:
Allows only electrons going through an area on the sample that is limited by the SAD aperture
to contribute to the diffraction pattern (SAD pattern).
Objective aperture:
Allows certain reflections to contribute to the image. Increases the contrast in the image.
Bright field imaging (central beam, 000), Dark field imaging (one reflection, g), High resolution
Images (several reflections from a zone axis).
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Objective aperture: Contrast enhancement
Si
Ag and Pb
hole
glue
(light elements)
All electrons contribute to the image.
Intensity: Thickness and density
dependence
A small aperture allows only electrons in the
central spot in the back focal plane to contribute
to the image.
Diffraction contrast
Mass-thickness contrast
(Amplitude contrast)
One grain seen along a
50 nm low index zone axis.
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Diffraction contrast: Bright field (BF),
dark field (DF) and weak-beam (WB)
Objective
aperture
BF image
DF image
Weak-beam
Dissociation of pure screw dislocation
In Ni3Al, Meng and Preston, J.
Mater. Scicence, 35, p. 821-828, 2000.
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Bending contours
sample
Obj. lens
Obj. aperture
BF image
DF image
DF image
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Thickness fringes, bright and dark field images
Sample
Sample
BF image
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DF image
Phase contrast: HREM and Moiré fringes
Long-Wei Yin et al., Materials Letters, 52, p.187-191
HREM image
Interference pattern
2 nm
A Moiré pattern is an interference
pattern created, for example, when
two grids are overlaid at an angle, or
when they have slightly different mesh
sizes (rotational and parallel Moire’
patterns).
http://www.mathematik.com/Moire/
200-400 kV TEMs are most
commonly used for HREM
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Moire’ fringe spacing
Parallel Moire’ spacing
dmoire’= 1 / IΔgI = 1 / Ig1-g2I = d1d2/Id1-d2I
Rotational Moire’ spacing
dmoire’= 1 / IΔgI = 1 / Ig1-g2I ~1/gβ = d/β
g2
g1
β
g2
Parallel and rotational Moire’ spacing
dmoire’= d1d2/((d1-d2)2 + d1d2β2)0.5
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g1
Δg
Δg
HREM of boundaries
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