5. transmission electron microscopy - cime | epfl · pdf file ·...

Intensive SEM/TEM training: TEM Aïcha Hessler-Wyser1April 2010

5. Transmission ElectronMicroscopy

Dr Aïcha Hessler-Wyser

Bat. MXC 134, Station 12, EPFL+41.21.693.48.30.

Centre Interdisciplinaire de Microscopie Electronique

CIME


Outline

a. TEM principleb. A little about diffractionc. TEM contrastsd. Examplese. Structure analysis


EPFL: Philips CM300EPFL: Philips CM300

300300’’000V000V


EPFL: Philips CM300EPFL: Philips CM300

300300’’000V000VCanon

Illumination

Projection

Echantillon


a. TEM principle


plan

foca

lim

age

Fi

Fi’

fi

a. TEM principle

Lenses, general principle of optical geometryFirst approximation: thin lens…

plan

foca

lob

jet

Fo

Fo’

fo

In particular, an image of the source placed at the object focal point F0 of thecondensor 2 will give a parallel illumination onto the sample


a. TEM principle

Parallel or converging illumination

A third lens is needed to make sure to have a parallel illumination


b. a little about diffraction

Interaction of electrons with the sample

Specimen

Inc

ide

nt

be

am

Auger electrons

Backscattered electronsBSE

secondary electronsSE Characteristic

X-rays

visible light

“absorbed” electrons electron-hole pairs

elastically scatteredelectrons

inelasticallyscattered electrons

BremsstrahlungX-rays

1-1-100 nm100 nm



Specimen

Inc

ide

nt

be

am

Auger electrons

Backscattered electronsBSE

secondary electronsSE Characteristic

X-rays

visible light

“absorbed” electrons electron-hole pairs

elastically scatteredelectrons

inelasticallyscattered electrons

BremsstrahlungX-rays

1-1-100 nm100 nm

How aboutdiffraction

???



Mean free path– It is the distance an electron travels between interactions with

atoms:

Scatter from isolated atoms– The interaction cross section represents the chance of a particular

electron to have any kind of interaction with an atom.– The total scattering cross section is the sum of all elastic and

inelastic scattering cross sections:

– If a specimen contains N atoms/vol, it has then a thickness t, theprobability of scattering from the specimen is given by QTt:

with QT the total cross section for scattering from the specimen in units of cm-1, N0 theAvogadro's number (atoms/mole), A the atomic weight (g/mole) and ! the atomicdensity

!

" =1QT

=A

N0#T$

!

"T =" él +" inél

!

QT = N"T =N0"T#A

!

QT t =N0"T (#t)

A



The atomic scattering factor

The incident electrons wave has auniform intensity.

Scattering within the specimenchanges both the spatial andangular distribution of the emergingelectrons.

The spatial distribution (A) isindicated by the wavy line.

The change in angular distribution(B) is shown by an incident beam ofelectrons being transformed intoseveral forward-scattered beams.




An incident electron plane wave is given by:

!

"(! r ) ="0 e2#i! k $! r

!

!

"sc (! r ) ="0 f (# ) e

2$i! k %! r

! r

When it is scattered by ascattering centre, a sphericalscattered wave is created, whichhas amplitude "sc but the samephase:

where f(#) is the atomic scatteringfactor, k the wave vectors of theincident or scattered wave, and rthe distance that the wave haspropagated.



The atomic scattering factorThe atomic scattering factor is related to the differential elasticscattering cross section by

–f(#) is a measure of the amplitude of an electron wave scatteredfrom an isolated atom.–$f(#)$2 is proportional to the scattered intensity.

–f(#) can be calculated from Schrödinger's equations, and weobtain the following description:

f(#) depends on %, # and Z

!

f (" ) 2 =d#d$

!

f (" ) =

1+E0

m0c2

#

$ %

&

' (

8) 2a0*

sin"2

#

$

% % %

&

'

( ( (

2

Z + fX( )




fn = 10+14 m fé 10+14 m fX 10+14 m

(sin#)/% 0.1 0.5 0.1 0.5 0.1 0.5

1H -0.378 -0.378 4'530 890 0.23 0.02

63Cu 0.67 0.67 51'100 14'700 7.65 3.85

W 0.466 0.466 118'000 29'900 19.4 12

Atomic scattering factors for neutrons (independent of #!), electronsand X rays, are a function of scattering angle and wave length % [Å].

Tiré de L.H. Schwartz and J.B. Cohen, Diffraction from Materialsfn : fé fX = 1 : 104 : 10



[ ]!=

"=

mailleatomesi

iimaille ifirrA rK#$# 2exp)(]2exp[/1

with ri th position of an atom i: ri = xi a + yi b + zi c

and K = g: K = h a* + k b* + l c*

[ ]!=

++=

mailleatomesi

iiiih lzkyhxif )(2expF kl "

The structure factorThe amplitude (intensity) of a diffracted beam depends on the latticestructure and its atom positions:

The structure factor is given by the sum of all scattering centres (theatoms) of the crystal that can scatter the incident wave:



objet

transmis

diffusé

rétr

o-di

ffus

é

If wavelets are coherent (phase relation well defined),resulting wave is the sum of the wavelets (interference)and the observed intensity Ic is the squared resultingwave modulus (usually called "diffraction").

( ) ( ) ( )i i2 i a 2 i a

' 'c i i

i i

e eI * A A! " + # ! " +$ %$ %

= && = ' (' (' (' () *) *+ +

k r k r

r r rr r

( ) ( ) ( ) ( )! " + # ! " +$ %

= && = =' (' () *

+ + +i i2 i a 2 i a

' ' 2inc i i i i i

i i i

e eI * A A Ik r k r

r r r rr r

Interaction: diffusion and diffractionEach point of the object re-emits a spherical wavelet.When all combined together, they are doing the resultingwave (transmitted, scattered or backscattered)



Diffraction:Coherent elastic scattering

intensity

only if n! !!!

plane wave

sample:random atoms?lattice?

sphericalwavelets

Fresnel

Fraunhoferme<<matom<<msample

!The energy transfer (loss) from the electron to the sample isusually negligible.

! If electrons go through a thick sample:" Multiple interaction occur: dynamical effects" Diffraction patterns complex to interpret


Fresnel fringes are a practical way ofmeasuring the coherency:

On the edge of a hole in a specimen, whenthe image is out of focus, alternating dark andbright fringes appear, they are called Fresnelfringes. They are a phase-contrast effect.

hole in a carbon film, 200 kV field emission gun... up to 150 fringes visible: very high coherence

W crystals


Diffraction and Fresnel fringes



b) Irregular fringes,astigmatism.

c) Underfocussed,uniform fringes

d) Focussed, min ofcontrast, nofringes

e) Overfocussed,uniform fringes

Fresnel fringes canalso be used tocorrect theastigmatism in theobjective lens.

Diffraction and Fresnel fringes



Fraunhofer diffractionParallel illuminationElectrons arriving all parallel onto the objective lens are focussed in asingle point: a transmitted spot or a diffracted spot

a radiation

a sample (crystal?)



A"

C

B

"

" "

d

Faisceauincident

Faisceaudiffracté

The Bragg's lawConsidering an electron wave incident onto a crystal, Bragg'slow shos that waves reflected off adjacent scattering centresmust have a path difference equal to an integral number ofwavelengths if they have to remain in phase (constructiveinterference)

In a TEM, the to total path difference is 2dsin# if the reflecting hklplanes are spaced a distance d apart and the wave is incidentand reflected at an angle #B.

n%=2dsin#&



2 sin" dhkl = n !

distance

entre

plan atomiquesd

onde entrante

onde sortante

"!

"différence dechemin parcouru

“1”

“2”

“1”

“2”

dhkl = n !/2 sin"

kk’

g = k-k’

Elastic diffraction

|k| = |k’|

Periodic arrangement of atoms in the real space:g : vector in the reciprocal space

The Bragg's law


c. TEM contrasts

Imaging mode

Echantillon

Lentille objectif

Plan image

Plan focal


c. TEM contrasts

Diffraction mode

Echantillon

Lentille objectif

Plan image

Plan focal


c. TEM contrasts

Diffraction modeDirect correlation betweenthe back focal plane (firstdiffraction pattern formed inthe microscope) of theobjective lens and thescreen

Imaging modeDirect correlation betweenthe image plane (first imageformed in the microscope) ofthe objective lens and thescreen


c. TEM contrasts

Diffraction: Zone axisSeveral (hi ki li) planes intersect with a commondirection [u v w] (zone axis) of the crystal.If electron beam is along [u v w ] direction, they allwill be in Bragg condition. They satisfy the zoneequation:

Each family of crystalline plane generates diffract ina single direction. This corresponds to a single spotthe the focal plane.

pict

ure

from

Mor

niro

li

hu+kv+lw=0


c. TEM contrasts

Diffraction patterns for fcc


Thickness contrast

Z contrast

Diffraction contrast => BF and DF

Phase contrast

The objective aperture allows to

select a transmitted spot to increase

the contrast in image mode

The selected area aperture allows to

select a region from which the

diffraction pattern is considered

HAADF

(D)STEM

Obj. ap.

SA ap.

c. TEM contrasts

Different type of contrasts


c. TEM contrasts

Bright field (BF), dark field (DF)Bright fied (BF) : theimage is formed withthe transmitted beamonly '0

Dark field (DF): theimage is formed withone selecteddiffracted beam 'hkl

It gives information onregions from thesample that diffract inthat particulardirection.

Note the particularcase ot the DF mode:the incident beam istilted.


Bright field Dark field100 nm

P.-A. Buffat

c. TEM contrasts

Bright field (BF), dark field (DF)


Nickel basedsuperalloys

Contrast #/#’

c. TEM contrasts



Can verticalquantum wells emitlight?We need localconcentrations tomodel theelectronicproperties

Segregation of chemical species in OMCVD AlGaAs structures onpatterned substrates

c. TEM contrasts


Because of the Z dependence of the structure factor, we can observe achemical contrast in dark field mode!


Polysilicon on Si wafer

Bright filed image.The arrows point on stressed parts of theinterface and induced strain in the substrate.The film has a columnar structure

HRTEM imageA disorganized layer is presentbetween the substrate (left) andthe polysilicon right. The polysiliconis polycristalline and containsstacking faults or twins

c. TEM contrasts



c. TEM contrasts

Thickness fringes

If we admit at this stage that a transmittedbeam and a diffracted beam can interactin the material, we can calculate theintensity of each one. It varies periodicallywith the thickness t, resulting in equalthickness fringes.

Champ clair Champ sombre


c. TEM contrasts

Exctinction distance

This intensity depends on theextinction distance:

and thus on the crystal orientationand the atomic number of thesample atoms.

We usually admit that kinematictheory is valid as long as thediffracted beam intensity/incidentbeam intensity is lower than 10%.Thus, the thickness limit is

(g [nm] Al Ag Au

(111) 72 29 23

(200) 87 33 25

(220) 143 46 35

(400) 237 75 55

(g calculated formetals at 300 kV

!

t < tmax " #$g%"$g10

!

"g =#Ve cos$ B

%Fg


Fast assessment of thicknesses of complex multilayer structures by Fast assessment of thicknesses of complex multilayer structures by TEMTEM, in collaboration with Dr. E. Gini, IQE-ETHZ, Prof.K.Melchior

TEM dark field image g=(200)dyn

HRTEM zone axis [001] HRTEM zone axis [001]

c. TEM contrasts

Thickness fringes and chemical contrast


TEM: contrastes

Thickness fringes and chemical contrast

Quanum wires InP/GaInAs.

Cleaved wedge method

The bending of the fringesindicates clearly thepresence of a chemicalconcentration gradientclose to the interfaces.

P.-A. Buffat


TEM: contrastes

Bended samples

When a sample is deformed, thediffraction conditions are not thesame in two different regions.

In bright field, the diffracting areaappears in dark.

It is then possible to observe lineswith a different contrast: they arecalled bend contour.


TEM: contrastes

Bended samples

When a sample is deformed, thediffraction conditions are not thesame in two different regions.

In bright field, the diffracting areaappear in dark.

It is then possible to observe lineswith a different contrast: they arecalled bend contour.

Each line can be associated witha family of diffracting planes. (tiré de J.V. Edington, Practical Electron

Microscopy in Materials science)


c. TEM contrasts

High resolution contrast (HRTEM)


SourceFEG

Illuminationcoherent

specimen

exit wave

objective lensSpherical aberration

Cs

image

projectedpotential

TransferFunction

image of “projectedpotential”

Problems:defocusing for contrast: delocalization of information, information limit not used

specimen project. pot. atom pos. phase of exit wave

defocus

thic

knes

s

c. TEM contrasts


High Angle Annular Dark Field =HAADF

High anglethermal diffuse

scattering~z2

= z-contrast

incoherent imaging:no interference effects

dedicated STEM:beam size ~0.1-0.2nm

Limitation: beamformation by magnetic

lens: Cs !!!

Analytical EM: probe-size ~1nmfor EDX and EELS analysis

HRTEM HAADF-STEM

c. TEM contrasts

Scanning transmission (STEM)


d. Structure analysis

Zone axisEach diffraction spot corresponds to a well defined familly of atomicplanes.On a diffraction pattern, the distances between the diffracted spotsdepend on the lattice parameter, but their ratio is constant for eachBravais lattice.Quick structure identification, manual or computer assisted.



Diffraction pattern indexing

Simulation: Software JEMS (P. Stadelmann)If we propose possible crystal, it calulates itselectron diffraction for all orientations andcompares with experimental diffractionpattern.



Camera length

Diffraction spots are supposed toconverge at infinity.

The projective lenses allow us to get thisfocal plane into our microscope:

The magnification of the diffractionpattern is represented by the cameralength CL.



tg(2#hkl) = R/CL

dhklR= %CL (=cte)

2dhklsin#hkl=n%

R

CL

dhkl

2#hkl

Camera length

Diffraction spots are supposed toconverge at infinity.

The projective lenses allow us to get thisfocal plane into our microscope:

The magnification of the diffractionpattern is represented by the cameralength CL.

For small angles, # ! sin# ! tg#and with the Bragg's lawwe have:



Phase identification

The detailed analysis of the diffrated spots gives us the crystallinestructure of the sample.

If the microscope is perfectly calibrated, it is then possible to getthe crystal interplanar distance, and thus its lattice parameter.

However, usually, we have possible strucures and diffractionallows us to choose between the candidates.



Phase identification

FIB lamella of ! 50 nm thickness, GJS600treated

Bright Field micrograph, 2750x (PhilipsCM20)

Simulated diffraction on JEMS software

Hexagonal $-(AlFeSi)

Monoclinic Al3Fe

40-3

0-20

[304]

[831]

0-131-2-2



Powder diagram

111

200

220

311222

Polycrystaline TiCl

• All reflexions (i.e. all atomic planes

with structure facteur) are present

• They are also called "ring pattern"

• Angular relations between the

atomic planes are lost.


5. transmission electron microscopy - cime | epfl · pdf file ·...

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