a.e. gunnæsmena3100 v10 transmissions electron microscopy sample preparation basic principles...
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A.E. Gunnæs MENA3100 V10
Transmissions electron microscopy
Sample preparation
Basic principles
Imaging
aberrations (Spherical, Chromatic, Astigmatism) contrast (Mass-thickness, Diffraction, Phase)
A.E. Gunnæs MENA3100 V10
Sample preparation for TEM• Crushing
• Cutting– saw, diamond pen, ultrasonic drill, FIB
• Mechanical thinning– Grinding, dimpling
• Electrochemical thinning
• Ion milling
• Coating
• Replica methods
• FIB
Plane view or cross section sample?
Is your material brittle or ductile?
Is it a conductor or insulator?
Is it a multi layered material?
A.E. Gunnæs MENA3100 V10
Grind down/dimple
TEM sample preparation: Thin films
• Top view
• Cross section or
Cut out a cylinderand glue it in a Cu-tube
Grind down andglue on Cu-rings
Cut a slice of thecylinder and grindit down / dimple
Ione beam thinning
Cut out cylinder
Ione beam thinning
Cut out slices
Glue the interface of interest face to face together withsupport material
Cut off excessmaterial
• Focused Ion Beam (FIB)
A.E. Gunnæs MENA3100 V10
Basic principles, first TEM
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)
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)
Nobel prize lecture: http://ernst.ruska.de/daten_e/library/documents/999.nobellecture/lecture.html
a) The first electron microscope built by Knoll and Ruska in 1933, b) The first commercial electron Microscope built by Siemens in 1939.
A.E. Gunnæs MENA3100 V10
Basic TEM
Electron source:
●Tungsten, W
● LaB6
● FEG
Electron gun
A.E. Gunnæs MENA3100 V10
Electron gunsThermionic gun Field emission gun (FEG)
A.E. Gunnæs MENA3100 V10
Technical data of different sourcesTungsten LaB6 Cold
FEGSchottky 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
H.B. Groen et al., Phil. Mag. A, 79, p 2083, 1999http://dissertations.ub.rug.nl/FILES/faculties/science/1999/h.b.groen/c1.pdf
Monochromator:Energy spread lessthan 0.15 ev
A.E. Gunnæs MENA3100 V10
Basic TEM
Electron gun
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 torrFEG: 10-10 torr
Electron source:
●Tungsten, W
● LaB6
● FEGCold trap
Sample position
A.E. Gunnæs MENA3100 V10
The lenses in a TEM
Sample
Filament
Anode
1. and 2. condenser lenses
Objective lens
Intermediate lenses
Projector lens
Compared to the lenses in an optical microscope they are very poor!
The point resolution in a TEM is limited by the aberrations of the lenses.
The diffraction limit on resolution is given by the Raleigh criterion:
δd=0.61λ/μsinα, μ=1, sinα~ α
-Spherical - Chromatic-Astigmatism
A.E. Gunnæs MENA3100 V10
Spherical aberrations
• Spherical aberration coefficient
ds = 0.5MCsα3
M: magnificationCs :Spherical aberration coefficientα: angular aperture/ angular deviation from optical axis
2000FX: Cs= 2.3 mm2010F: Cs= 0.5 nm
r1
r2
Disk of least confusion
α
Cs corrected TEMs are now available
The diffraction and the spherical aberration limits on resolution have an opposite dependence on the angular aperture of the objective.
A.E. Gunnæs MENA3100 V10
Aberrations in a nutshell
Core of the M100 galaxy seen through Hubble (source: NASA)
Before Cs correction
After Cs correction
Q.M. Ramasse
A.E. Gunnæs MENA3100 V10
Resolution limit
Year Resolution
1940s ~10nm
1950s ~0.5-2nm
1960s0.3nm (transmission)~15-20nm (scanning)
1970s0.2nm (transmission)7nm (standard scanning)
1980s0.15nm (transmission)5nm (scanning at 1kV)
1990s0.1nm (transmission)3nm (scanning at 1kV)
2000s <0.1 nm (Cs correctors)
http://www.sfc.fr/Material/hrst.mit.edu/hrs/materials/public/ElecMicr.htm
A.E. Gunnæs MENA3100 V10
Chromatic aberration
v
v - Δvdc = Cc α ((ΔU/U)2+ (2ΔI/I)2 + (ΔE/E)2)0.5
Cc: Chromatic aberration coefficientα: angular divergence of the beamU: acceleration voltageI: Current in the windings of the objective lensE: Energy of the electrons
2000FX: Cc= 2.2 mm2010F: Cc= 1.0 mm
Chromatic aberration coefficient:
Thermally emitted electrons:ΔE/E=KT/eV
Force from a magnetic field:F= -e (v x B)
Disk of least confusion
A.E. Gunnæs MENA3100 V10
Lens aberrations
• Lens astigmatism
Loss of axial asymmetry
y-focus
x-focusy
xThis astigmatism can not be
prevented, but it can be
corrected!
A.E. Gunnæs MENA3100 V10
Operating modes
Convergent beam Parallel beam
Can be scanned (STEM mode)
Specimen
Imaging modeor Diffraction mode
Spectroscopy and mapping(EDS and EELS)
A.E. Gunnæs MENA3100 V10
Image or diffraction mode
1. and 2. condenser lenses
Objective lens
Intermediate lenses
Projector lens
Spesimen
Filament
Anode
Diffraction plane
Image plane
Objective aperture
Selected area aperture
Image or diffraction patternSTEM detectors (BF and HAADF)
Bi-prism
Viewing screen
A.E. Gunnæs MENA3100 V10
Advanced nanotool
JEOL 2010F FEGTEM Ultra high resolution version with analytical possibilities
A.E. Gunnæs MENA3100 V10
Imaging / microscopy
200 nm
Si
SiO2
TiO2
Pt
BiFeO3
Glue
TEM - High resolution (HREM) - Bright field (BF) - Dark field (DF) - Shadow imaging (SAD+DF+BF)
STEM - Z-contrast (HAADF) - Elemental mapping (EDS and EELS)
GIF - Energy filtering
Holography
A.E. Gunnæs MENA3100 V10
Simplified ray diagram
Objective lense
Diffraction plane(back focal plane)
Image plane
Sample
Parallel incoming electron beamSi
a
b
cPow
derCell 2.0
1,1 nm
3,8
Å
Objective aperture
Selected area aperture
A.E. Gunnæs MENA3100 V10
Apertures
Selected area aperture
Condenser aperture
Objective aperture
A.E. Gunnæs MENA3100 V10
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 resolutionImages (several reflections from a zone axis).
A.E. Gunnæs MENA3100 V10
Objective aperture: Contrast enhancement
All electrons contributes to the image. A small aperture allows only electrons in the central spot in the back focal plane to contribute to the image.Intensity: Thickness and density
dependence
Mass-thickness contrast
Si Ag and Pb
glue(light elements)
hole
50 nmOne grain seen along a low index zone axis.
Diffraction contrast(Amplitude contrast)
A.E. Gunnæs MENA3100 V10
Diffraction contrast: Bright field (BF), dark field (DF) and weak-beam (WB)
BF image
Objectiveaperture
DF image Weak-beam
Dissociation of pure screw dislocationIn Ni3Al, Meng and Preston, J.Mater. Scicence, 35, p. 821-828, 2000.
A.E. Gunnæs MENA3100 V10
Bending contours
BF image
DF image
DF image
Obj. aperture
Obj. lens
sample
A.E. Gunnæs MENA3100 V10
Thickness fringes/contours
Sample (side view)
e
000 g
t
Ig=1- Io
In the two-beam situation the intensityof the diffracted and direct beamis periodic with thickness (Ig=1- Io)
Ig=(πt/ξg)2(sin2(πtseff)/(πtseff)2))
t = distance ”traveled” by the diffracted beam.ξg = extinction distance
Sample (top view)Hole
Positions with max Intensity in Ig
A.E. Gunnæs MENA3100 V10
Thickness fringes, bright and dark field images
Sample Sample
DF imageBF image
A.E. Gunnæs MENA3100 V10
Phase contrast: HREM and Moire’ fringes
2 nm
http://www.mathematik.com/Moire/
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).HREM image
Long-Wei Yin et al., Materials Letters, 52, p.187-191
200-400 kV TEMs are most commonly used for HREM
Interference pattern
A.E. Gunnæs MENA3100 V10
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
Parallel and rotational Moire’ spacingdmoire’= d1d2/((d1-d2)2 + d1d2β2)0.5
β
g1
g2
Δg
g1g2 Δg
A.E. Gunnæs MENA3100 V10
Simulating HREM imagesContrast 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:
k = u
The curve depend on:•Cs (the quality of objective lens) (wave-length defined by accelerating voltage)f (the defocus value)u (spatial frequency)
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), A(u): aperture function 1 or 0
Χ(u)= πΔfλu2+1/2πCsλ3u4 : coherent transfer function
A.E. Gunnæs MENA3100 V10
Simulating HREM imagesContrast 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 V10
Scherzer defocus
http://www.maxsidorov.com/ctfexplorer/webhelp/effect_of_defocus.htm
Δ f = - (Csλ)1/2Δ f = -1.2(Csλ)1/2
Scherzer condition Extended Scherzer condition
A.E. Gunnæs MENA3100 V10
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 V10
HAADF image of an icosahedral FePt particle (false colors): thanks to the small probe size, it is possible to probe precisely the chemical structure of samples at the atomic level, revealing here a small crystalline layer of iron oxide surrounding the outermost shell of the particle.
Combined HAADF and EELS
A.E. Gunnæs MENA3100 V10
Energy filtering
A. Thøgersen et al., Collaboration with Prof. T. Finnstad, UiO, S. Diplas, SINTEF and UniS, UK and NIMS, Japan