Chapter 4 - Tem Basics.pdf

5. Transmission Electron Microscopy

Dr Aïcha Hessler-Wyser Bat. MXC 134, Station 12, EPFL+41.21.693.48.30.

Centre Interdisciplinaire de Microscopie Electronique CIME

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Outline a.
b.
c.
d.
e.


TEM principle A little about diffraction TEM contrasts Examples Structure analysis

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Intensive SEM/TEM training: TEM

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Canon

Illumination Echantillon Projection

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a. TEM principle

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a. TEM principle Lenses, general principle of optical geometry

Fi

plan focal objet

plan focal image

First approximation: thin lens…

F o

Fi’

Fo ’

fi

fo

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

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a. TEM principle Parallel or converging illumination

A third lens is needed to make sure to have a parallel illumination Intensive SEM/TEM training: TEM

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b. a little about diffraction

Backscattered electrons BSE

Auger electrons

elastically scattered electrons

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Specimen

direct beam

“absorbed” electrons

Incident beam

Interaction of electrons with the sample

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secondary electrons SE Characteristic X-rays visible light

electron-hole pairs

Bremsstrahlung X-rays inelastically scattered electrons

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b. a little about diffraction

Backscattered electrons BSE

Auger electrons

visible light

electron-hole pairs

Specimen

elastically scattered electrons

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secondary electrons SE Characteristic X-rays

direct beam

“absorbed” electrons

Incident beam

How about diffraction ???

Bremsstrahlung X-rays inelastically scattered electrons

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b. a little about diffraction Mean free path –
It is the distance an electron travels between interactions with atoms:
=

Differential cross section

1 A = QT N 0 T 

–
This term describes the angular distribution of scattering from an atom, and is written d/d
. The electrons are scattered through an angle  into a solid angle
and both angles are linked by a simple geometrical relation:  = 2
(1 cos  ) –
therefore

d d 1 = d 2
sin  d

d = 2
sin d

–
We can calculate  for scattering into all angles which are greater than : 2
2
 =

d

 d = 2
 d sind



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The values of  can vary form 0 to
, depending on the specific type of scattering.

Aïcha Hessler-Wyser

b. a little about diffraction Scatter from isolated atoms –
The interaction cross section represents the chance of a particular electron to under any kind of interaction with an atom. –
The total scattering cross section is the sum of all elastic and inelastic scattering cross sections:


T =
él +
inél

 =
r 2 Ze

rél = where r depends on the scattering mechanisms. E.g. V
–
If a specimen contains N atoms/vol, it has then a thickness t, the probability of scattering from the specimen is givent by QTt: QT = N T =

N 0 T
A

QT t =

N 0 T (
t) A

with QT the total cross section for scattering from the specimen in units of cm-1, N0 the Avogadro's number (atoms/mole), A the atomic weight (g/mole) and
the atomic density. Intensive SEM/TEM training: TEM

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b. a little about diffraction The atomic scattering factor An incident electron plane wave is given by:




 ( r ) =  0 e 2
ik  r

When it is scattered by a scattering centre, a spherical scattered wave is created, which has amplitude sc but the same

phase:
e 2
ik  r  sc ( r ) =  0 f ( )
r where f(
) is the atomic scattering factor, k the wave vectors of the incident or scattered wave, and r the distance that the wave has propagated. Intensive SEM/TEM training: TEM

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b. a little about diffraction The atomic scattering factor The incident electrons wave has a uniform intensity. Scattering within the specimen changes both the spatial and angular distribution of the emerging electrons. The spatial distribution (A) is indicated by the wavy line. The change in angular distribution (B) is shown by an incident beam of electrons being transformed into several forward-scattered beams.

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b. a little about diffraction The atomic scattering factor The atomic scattering factor is related to the differential elastic scattering cross section by d 2 f ( ) =

d


–
f(
) is a measure of the amplitude of an electron wave scattered from an isolated atom. –
f(
)2 is proportional to the scattered intensity. –
f(
) can be calculated from Schrödinger's equations, and we obtain the following description:  E0   1 +

m 0c 2    f ( ) = 8
2 a0 sin   2

2

(Z  f X )



f(
) depends on ,
and Z Intensive SEM/TEM training: TEM

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b. a little about diffraction The atomic scattering factor 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 !), electrons and X rays, as a function of scattering angle and wave length  [Å].

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

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b. a little about diffraction The structure factor The amplitude (intensity) of a diffracted beam depends on the lattice structure and its atom positions:

with ri th position of an atom i: and K = g:

ri = xi a + yi b + zi c

K = h a * + k b* + l c *

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

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b. a little about diffraction

rétr o d iffu sé

Interaction: diffusion and diffraction

objet

Each point of the object re-emits a spherical wavelet. When all combined together, they are doing the resulting wave (transmitted, scattered or backscattered) 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 resulting wave modulus (usually called "diffraction").

 e2 ikr +ai Ic (r ) =  * =
A i' (r )

i r 

 e2 ikr +ai ' A r ( ) 

i 
r  i

 

If wavelet phases are not correlated (uncoherent), they cannot interfere and the observed intensity Iinc is the sum of the intensity of each wavelet (usually called "diffusion").

sé

diffu

transmis Intensive SEM/TEM training: TEM

 ' e2 ikr +ai ' e2 ikr +ai Iinc (r ) =
ii * =
A i (r ) A i (r )

r r i i  January 2009

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 2  =
Ii (r ) i

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b. a little about diffraction Diffraction: Coherent elastic scattering

plane wave

sample: random atoms? lattice?

nel

Fres

spherical wavelets

ity intens f only i n
!!!

me<<matom<<msample



The energy transfer (loss) from the electron to the sample is usually negligible.

If electrons go through a thick sample: 
Multiple interaction occur: dynamical effects 
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b. a little about diffraction Diffraction and Fresnel fringes Fresnel fringes are a practical way of measuring the coherency: On the edge of a hole in a specimen, when the image is out of focus, alternating dark and bright fringes appear, they are called Fresnel fringes. They are a phase-contrast effect.

W crystals

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

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b. a little about diffraction Diffraction and Fresnel fringes

Fresnel fringes can also be used to correct the astigmatism in the objective lens. b)
Irregular fringes, astigmatism. c)
Underfocussed, uniform fringes d)
Focussed, min of contrast, no fringes e)
Overfocussed, uniform fringes

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b. a little about diffraction Fraunhofer diffraction Parallel illumination Electrons arriving all parallel onto the objective lens are focussed in a single point: a transmitted spot or a diffracted spot a radiation a sample (crystal?)

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b. a little about diffraction The Bragg's law Considering an electron wave incident onto a crystal, Bragg's low shos that waves reflected off adjacent scattering centres must have a path difference equal to an integral number of wavelengths if they have to remain in phase (constructive interference) In a TEM, the to total path difference is 2dsin if the reflecting hkl planes are spaced a distance d apart and the wave is incident and reflected at an angle B. n=2dsin


Faisceau incident

Faisceau diffracté 







A

C B

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d

b. a little about diffraction The Bragg's law 2 sin dhkl = n 
dhkl = n /2 sin
différence de  chemin parcouru



 distance

d

entre plan atomiques

Elastic diffraction k

|k| = |k’|

k’

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

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g = k-k’

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c. TEM contrasts Imaging mode

Echantillon

Lentille objectif

Plan focal

Plan image

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c. TEM contrasts Diffraction mode

Echantillon

Lentille objectif

Plan focal

Plan image

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c. TEM contrasts Diffraction mode Direct correlation between the back focal plane (first diffraction pattern formed in the microscope) of the objective lens and the screen

Imaging mode Direct correlation between the image plane (first image formed in the microscope) of the objective lens and the screen

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c. TEM contrasts Diffraction: Zone axis Several (hi ki li) planes intersect with a common direction [u v w] (zone axis) of the crystal. If electron beam is along [u v w ] direction, they all will be in Bragg condition. They satisfy the zone equation: hu+kv+lw=0

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c. TEM contrasts Diffraction patterns for fcc

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picture from Morniroli

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

c. TEM contrasts Different type of contrasts Thickness contrast

HAADF

Z contrast

(D)STEM

Diffraction contrast => BF and DF

Obj. ap.
SA ap.


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 Intensive SEM/TEM training: TEM

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c. TEM contrasts Bright field (BF), dark field (DF) Bright fied (BF) : the image is formed with the transmitted beam only
0
Dark field (DF): the image is formed with one selected diffracted beam
hkl It gives information on regions from the sample that diffract in that particular direction. Note the particular case ot the DF mode: the incident beam is tilted. Intensive SEM/TEM training: TEM

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c. TEM contrasts Bright field (BF), dark field (DF) 100 nm

Bright field

Dark field

P.-A. Buffat
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c. TEM contrasts Bright field (BF), dark field (DF)

Nickel based superalloys Contrast
/
’


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c. TEM contrasts Bright field (BF), dark field (DF) Segregation of chemical species in OMCVD AlGaAs structures on patterned substrates 1.1 A

B

c(Ga)normalized

1 III

0.9

Can vertical quantum wells emit light? We need local

concentrations to model the electronic properties

0.8

0.7

0.6

II/2

II/1

I/1

I/2

0.5 0

50

100

150

200

250

300

350

distance/nm

Because of the Z dependence of the structure factor, we can observe a chemical contrast in dark field mode! Intensive SEM/TEM training: TEM

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c. TEM contrasts Bright field (BF), dark field (DF) Bright filed image. The arrows point on stressed parts of the interface and induced strain in the substrate. The film has a columnar structure

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Polysilicon on Si wafer

HRTEM image A disorganized layer is present between the substrate (left) and the polysilicon right. The polysilicon is polycristalline and contains stacking faults or twins

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c. TEM contrasts Thickness fringes If we admit at this stage that a transmitted beam and a diffracted beam can interact in the material, we can calculate the intensity of each one. It varies periodically with the thickness t, resulting in equal thickness fringes.

Champ sombre

Champ clair Intensive SEM/TEM training: TEM

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c. TEM contrasts Exctinction distance This intensity depends on the extinction distance:
Ve cos B g =

Fg

and thus on the crystal orientation and the atomic number of the sample atoms. We usually admit that kinematic theory is valid as long as the diffracted beam intensity/incident beam intensity is lower than 10%. Thus, the thickness limit is g g t < t max  

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g [nm]

Al

Ag

Au

(111)

72

29

23

(200)

87

33

25

(220)

143

46

35

(400)

237

75

55


g calculated for metals at 300 kV

10 36

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c. TEM contrasts Thickness fringes and chemical contrast

TEM dark field image g=(200)dyn


HRTEM zone axis [001]
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HRTEM zone axis [001]
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TEM: contrastes Thickness fringes and chemical contrast

Quanum wires InP/GaInAs. Cleaved wedge method The bending of the fringes indicates clearly the presence of a chemical concentration gradient close to the interfaces.

P.-A. Buffat Intensive SEM/TEM training: TEM

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TEM: contrastes Bended samples When a sample is deformed, the diffraction conditions are not the same in two different regions. In bright field, the diffracting area appears in dark. It is then possible to observe lines with a different contrast: they are called bend contour.

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TEM: contrastes Bended samples When a sample is deformed, the diffraction conditions are not the same in two different regions. In bright field, the diffracting area appear in dark. It is then possible to observe lines with a different contrast: they are called bend contour. Each line can be associated with a family of diffracting planes.

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(tiré de J.V. Edington, Practical Electron Microscopy in Materials science) 40

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c. TEM contrasts High resolution contrast (HRTEM)

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c. TEM contrasts Source specimen

FEG

project. pot.

atom pos.

phase of exit wave

Illumination coherent

projected potential specimen

exit wave objective lens

Transfer Function thickness

Spherical aberration Cs

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

image image of “projected potential”

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defocus

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c. TEM contrasts

High Angle Annular Dark Field =HAADF

Scanning transmission (STEM) High angle thermal diffuse scattering ~z2 = z-contrast incoherent imaging: no interference effects dedicated STEM: beam size ~0.1-0.2nm Limitation: beam formation by magnetic lens: Cs !!!

Analytical EM: probe-size ~1nm for EDX and EELS analysis Intensive SEM/TEM training: TEM

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HRTEM

HAADF-STEM

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d. Structure analysis Zone axis Each diffraction spot corresponds to a well defined familly of atomic planes. On a diffraction pattern, the distances between the diffracted spots depend on the lattice parameter, but their ratio is constant for each Bravais lattice. Quick structure identification, manual or computer assisted.

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d. Structure analysis Diffraction pattern indexing Simulation: Software JEMS (P. Stadelmann) If we propose possible crystal, it calulates its electron diffraction for all orientations and compares with experimental diffraction pattern.

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d. Structure analysis Camera length Diffraction spots are supposed to converge at infinity. The projective lenses allow us to get this focal plane into our microscope: The magnification of the diffraction pattern is represented by the camera length CL.

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d. Structure analysis Camera length

dhkl

Diffraction spots are supposed to converge at infinity. The projective lenses allow us to get this focal plane into our microscope:

2
hkl

The magnification of the diffraction pattern is represented by the camera length CL. tg(2
hkl) = R/CL

CL

For small angles,

sin

tg
and with the Bragg's law 2dhklsin
hkl=n we have:

R

dhklR= CL (=cte) Intensive SEM/TEM training: TEM

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d. Structure analysis Phase identification The detailed analysis of the diffrated spots gives us the crystalline structure of the sample. If the microscope is perfectly calibrated, it is then possible to get the crystal interplanar distance, and thus its lattice parameter. However, usually, we have possible strucures and diffraction allows us to choose between the candidates.

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d. Structure analysis Phase identification 0-13 1-2-2

[831]

Hexagonal
-(AlFeSi)

40-3

0-20

FIB lamella of
50 nm thickness, GJS600 treated Bright Field micrograph, 2750x (Philips CM20)

[304]

Simulated diffraction on JEMS software Intensive SEM/TEM training: TEM

Monoclinic Al3Fe

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d. Structure analysis Powder diagram Polycrystaline TiCl •
All reflexions (i.e. all atomic planes

222 311

with structure facteur) are present

220 200

•
They are also called "ring pattern" •
Angular

relations

between

111

the

atomic planes are lost.

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