Transcript Transmisjons-elektron

Transmissions electron microscopy
Basic principles
Sample preparation
Imaging
aberrations (Spherical, Chromatic, Astigmatism)
contrast (Mass-thickness, Diffraction, Phase)
A.E. Gunnæs
MENA3100 V08
Basic principles, first TEM
Electrons are deflected by both
electrostatic and magnetic fields
Force from an electrostatic field (in the gun)
F= -e E
Force from a magnetic field (in the lenses)
F= -e (v x B)
Wave length:
λ= h/(2meV)0.5 (NB non rel. expr.)
λ= h/(2m0eV(1+eV)/2m0c2)0.5 (relativistic expression)
200kV: λ= 0.00251 nm (v/c= 0.6953, m/m0= 1.3914)
a) The first electron microscope built by Knoll
and Ruska in 1933, b) The first commercial
electron Microscope built by Siemens in 1939.
Nobel prize lecture: http://ernst.ruska.de/daten_e/library/documents/999.nobellecture/lecture.html
A.E. Gunnæs
MENA3100 V08
Basic TEM
Electron gun
Electron source:
●Tungsten, W
● LaB6
● FEG
Cold trap
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
A.E. Gunnæs
MENA3100 V08
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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MENA3100 V08
-Spherical
- Chromatic
-Astigmatism
Spherical aberrations
•
Cs corrected TEMs are now available
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
The diffraction and the spherical aberration limits on resolution
have an opposite dependence on the angular aperture of the objective.
A.E. Gunnæs
MENA3100 V08
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/eV
2000FX: Cc= 2.2 mm
2010F: Cc= 1.0 mm
Force from a magnetic field:
F= -e (v x B)
A.E. Gunnæs
MENA3100 V08
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
A.E. Gunnæs
MENA3100 V08
Lens aberrations
•
Lens astigmatism
Loss of axial asymmetry
x
This astigmatism can not be
prevented, but it can be
corrected!
y-focus
y
A.E. Gunnæs
x-focus
MENA3100 V08
Sample preparation for TEM
•
Crushing
Plane view or cross section sample?
•
Cutting
–
•
saw, diamond pen, ultrasonic drill, FIB
Is your material brittle or ductile?
Is it a conductor or insulator?
Mechanical thinning
–
Grinding, dimpling
•
Electrochemical thinning
•
Ion milling
•
Coating
•
Replica methods
A.E. Gunnæs
Is it a multi layered material?
MENA3100 V08
TEM sample preparation: Thin films
Cut out cylinder
•
Top view
Cut out a cylinder
and glue it in a Cu-tube
Cut out slices
•
Cross section
•
Grind down/
dimple
Glue the interface
of interest face to
face together with
support material
Focused Ion Beam
(FIB)
Ione 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
Ione beam thinning
A.E. Gunnæs
MENA3100 V08
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)
Si
200 nm
GIF
- Energy filtering
Holography
A.E. Gunnæs
MENA3100 V08
Glue
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
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MENA3100 V08
Selected area
aperture
Apertures
Condenser aperture
Objective aperture
Selected area aperture
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MENA3100 V08
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).
A.E. Gunnæs
MENA3100 V08
Objective aperture: Contrast enhancement
Si
Ag and Pb
hole
glue
(light elements)
All electrons contributes 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
(Amplitude contrast)
Mass-thickness contrast
One grain seen along a
50 nm low index zone axis.
A.E. Gunnæs
MENA3100 V08
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.
A.E. Gunnæs
MENA3100 V08
Bending contours
sample
Obj. lens
Obj. aperture
BF image
DF image
DF image
A.E. Gunnæs
MENA3100 V08
Thickness fringes/contours
e
In the two-beam situation the intensity
of the diffracted and direct beam
is periodic with thickness (Ig=1- Io)
000
g
Ig=1- Io
Sample (side view)
t
Hole
Sample (top view)
Ig=(πt/ξg)2(sin2(πtseff)/(πtseff)2))
t = distance ”traveled” by the diffracted beam.
ξg = extinction distance
Positions with max
Intensity in Ig
A.E. Gunnæs
MENA3100 V08
Thickness fringes, bright and dark field images
Sample
Sample
BF image
A.E. Gunnæs
DF image
MENA3100 V08
Phase contrast: HREM and Moire’ fringes
Long-Wei Yin et al., Materials Letters, 52, p.187-191
HREM image
2 nm
Interference pattern
http://www.mathematik.com/Moire/
200-400 kV TEMs are most
commonly used for HREM
A.E. Gunnæs
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).
MENA3100 V08
Moire’ fringe spacing
Parallel Moire’ spacing
dmoire’= 1 / IΔgI = 1 / Ig1-g2I = d1d2/Id1-d2I
g2
g1
Rotational Moire’ spacing
dmoire’= 1 / IΔgI = 1 / Ig1-g2I ~1/gβ = d/β
β
g2
Parallel and rotational Moire’ spacing
dmoire’= d1d2/((d1-d2)2 + d1d2β2)0.5
A.E. Gunnæs
g1
MENA3100 V08
Δg
Δg
Simulating HREM images
Contrast transfer function (CTF)
CTF (Contrast Transfer Function) is the function which
modulates the amplitudes and phases of the electron
diffraction pattern formed in the back focal plane of the
objective lens. It can be represented as:
In order to take into account the effect of the
objective lens when calculating HREM images, the
wave function Ψ(u) in reciprocal space has to be
multiplied by a transfer function T(u).
In general we have:
Ψ(r)= Σ Ψ(u) T(u) exp (2πiu.r)
T(u)= A(u) exp(iχ),
k=u
The curve depend on:
•Cs (the quality of objective lens)
l (wave-length defined by accelerating voltage)
Df (the defocus value)
u (spatial frequency)
A(u): aperture function 1 or 0
Χ(u)= πΔfλu2+1/2πCsλ3u4 : coherent transfer function
A.E. Gunnæs
MENA3100 V08
Simulating HREM images
Contrast transfer function (CTF)
Effect of the envelope functions can be represented as:
where Ec is the temporal coherency envelope (caused by
chromatic aberrations, focal and energy spread,instabilities in the
high tension and objective lens current), and Ea is spatial
coherency envelope (caused by the finite incident beam
convergence).
http://www.maxsidorov.com/ctfexplorer/webhelp/background.htm
A.E. Gunnæs
MENA3100 V08
Contrast transfer function (CTF)
Contrast transfer functions and damping
envelopes of the JEOL 2010F at optimum
defocus (analytical model).
The highly coherent electron source used
in the 2010F, a FEG, is apparent from the
many oscillations in the CTF of the 2010F
http://dissertations.ub.rug.nl/FILES/faculties/science/2004/s.mogck/c2.pdf
A.E. Gunnæs
MENA3100 V08
Scherzer defocus
Δ f = - (Csλ)1/2
Δ f = -1.2(Csλ)1/2
Scherzer condition
Extended Scherzer condition
http://www.maxsidorov.com/ctfexplorer/webhelp/effect_of_defocus.htm
A.E. Gunnæs
MENA3100 V08
HREM simulations
One possible model for which the simulated HREM images match rectangular region I
HREM simulation along [0 0 1] based on the above structures. The numbers before and after the slash
symbol “/” represent the defocus and thickness (nm), respectively
”The assessment of GPB2/S′′ structures in Al–Cu–Mg alloys ”
Wang and Starink, Mater. Sci. and Eng. A, 386, p 156-163, 2004.
A.E. Gunnæs
MENA3100 V08