A.E. GunnæsMENA3100 V08 Transmissions electron microscopy Basic principles Sample preparation...

A.E. Gunnæs MENA3100 V08

Transmissions electron microscopy

Basic principles

Sample preparation

Imaging

aberrations (Spherical, Chromatic, Astigmatism) contrast (Mass-thickness, Diffraction, Phase)


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.

http://ernst.ruska.de/daten_e/library/documents/999.nobellecture/lecture.html


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

Cold trap

Electron source:

●Tungsten, W

● LaB6

● FEG

Sample position


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


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.


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


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


Lens aberrations

• Lens astigmatism

Loss of axial asymmetry

y-focus

x-focusy

xThis astigmatism can not be

prevented, but it can be

corrected!


Sample preparation for TEM• Crushing

• Cutting– saw, diamond pen, ultrasonic drill, FIB

• Mechanical thinning– Grinding, dimpling

• Electrochemical thinning

• Ion milling

• Coating

• Replica methods

Plane view or cross section sample?

Is your material brittle or ductile?

Is it a conductor or insulator?

Is it a multi layered material?


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)


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


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


Apertures

Selected area aperture

Condenser aperture

Objective 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 resolutionImages (several reflections from a zone axis).


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)


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.


Bending contours

BF image

DF image

DF image

Obj. aperture

Obj. lens

sample


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


Thickness fringes, bright and dark field images

Sample Sample

DF imageBF image


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





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


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


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

http://www.maxsidorov.com/ctfexplorer/webhelp/spatial_coherency.htm

http://www.maxsidorov.com/ctfexplorer/webhelp/spatial_coherency.htm




Contrast transfer function (CTF)

http://dissertations.ub.rug.nl/FILES/faculties/science/2004/s.mogck/c2.pdf

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


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

http://www.maxsidorov.com/ctfexplorer/webhelp/effect_of_defocus.htm


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. GunnæsMENA3100 V08 Transmissions electron microscopy Basic principles Sample preparation...

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