Download - Chapter 4 - TEM
Intensive SEM/TEM training: TEM Aïcha Hessler-Wyser 1
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
Intensive SEM/TEM training: TEM Aïcha Hessler-Wyser 2
Outline
a. TEM principle b. A little about diffraction c. TEM contrasts d. Examples e. Structure analysis
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EPFL: Philips CM300
300’000V
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EPFL: Philips CM300
300’000V
Canon
Illumination
Projection
Echantillon
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a. TEM principle
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plan
foca
l im
age
Fi
Fi’
fi
a. TEM principle
Lenses, general principle of optical geometry First approximation: thin lens…
plan
foca
l ob
jet
Fo
Fo’ 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
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b. a little about diffraction
Interaction of electrons with the sample
Specimen
Inc
ide
nt
be
am
Auger electrons
Backscattered electrons BSE
secondary electrons SE Characteristic
X-rays
visible light
“absorbed” electrons electron-hole pairs
elastically scattered electrons
dire
ct
be
am
inelastically scattered electrons
Bremsstrahlung X-rays
1-100 nm
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b. a little about diffraction
Specimen
Inc
ide
nt
be
am
Auger electrons
Backscattered electrons BSE
secondary electrons SE Characteristic
X-rays
visible light
“absorbed” electrons electron-hole pairs
elastically scattered electrons
dire
ct
be
am
inelastically scattered electrons
Bremsstrahlung X-rays
1-100 nm
How about diffraction
???
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b. a little about diffraction
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, the probability 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 the Avogadro's number (atoms/mole), A the atomic weight (g/mole) and ! the atomic density
!
" =1QT
=A
N0#T$
!
"T =" él +" inél
!
QT = N"T =N0"T#A
!
QT t =N0"T (#t)
A
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b. a little about diffraction
The atomic scattering factor 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 a scattering centre, a spherical scattered wave is created, which has amplitude "sc but the same phase: 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.
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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
– f(#) is a measure of the amplitude of an electron wave scattered from an isolated atom.
– $f(#)$2 is proportional to the scattered intensity.
– f(#) can be calculated from Schrödinger's equations, and we obtain the following description:
f(#) depends on %, # and Z
!
f (" ) 2 =d#d$
f (! ) =1+ E0
m0c2
!
"#
$
%&
8! 2a0!
sin"2
!
"
###
$
%
&&&
2
Z ' fX( )
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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, are a function of scattering angle and wave length % [Å].
Tiré de L.H. Schwartz and J.B. Cohen, Diffraction from Materials fn : fé fX = 1 : 104 : 10
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b. a little about diffraction
[ ]!=
"=
mailleatomesi
iimaille ifirrA rK#$# 2exp)(]2exp[/1
with ri th position of an atom i: ri = xi a + yi b + zi c
and K = g: K = h a* + k b* + l c*
[ ]!=
++=
mailleatomesi
iiiih lzkyhxif )(2expF kl "
The structure factor The amplitude (intensity) of a diffracted beam depends on the lattice structure and its atom positions: The structure factor is given by the sum of all scattering centres (the atoms) of the crystal that can scatter the incident wave:
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b. a little about diffraction
objet
transmis
diffusé
rétr
o-
diff
usé
If wavelets are coherent (phase relation well defined), resulting wave is the sum of the wavelets (interference) and the observed intensity Ic is the squared resulting wave modulus (usually called "diffraction").
( ) ( ) ( )i i2 i a 2 i a
' 'c i i
i i
e eI * A A! " + # ! " +$ %$ %
= && = ' (' (' (' () *) *+ +
k r k r
r r rr r
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").
( ) ( ) ( ) ( )! " + # ! " +$ %
= && = =' (' () *
+ + +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 diffraction Each point of the object re-emits a spherical wavelet. When all combined together, they are doing the resulting wave (transmitted, scattered or backscattered)
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b. a little about diffraction
Diffraction: Coherent elastic scattering
intensity
only if
n! !!!
plane wave
sample: random atoms? lattice?
spherical wavelets
Fresnel
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 " Diffraction patterns complex to interpret
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b. a little about diffraction
b) Irregular fringes, astigmatism.
c) Underfocussed, uniform fringes
d) Focussed, min of contrast, no fringes
e) Overfocussed, uniform fringes
Fresnel fringes can also be used to correct the astigmatism in the objective lens.
Diffraction and Fresnel 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
A "#
C
B
"#
"# "#
d
Faisceau incident
Faisceau diffracté
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#'
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b. a little about diffraction
2 sin" dhkl = n !#
distance
entre
plan atomiques d
" !
" différence de chemin parcouru
dhkl = n !/2 sin"#
k k’
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
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c. TEM contrasts
Imaging mode
Echantillon
Lentille objectif
Plan image
Plan focal
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c. TEM contrasts
Diffraction mode
Echantillon
Lentille objectif
Plan image
Plan focal
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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: Each family of crystalline plane generates diffract in a single direction. This corresponds to a single spot the the focal plane.
pict
ure
from
Mor
niro
li
hu+kv+lw=0
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c. TEM contrasts
Diffraction patterns for fcc
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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
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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.
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Bright field Dark field 100 nm
P.-A. Buffat!
c. TEM contrasts
Bright field (BF), dark field (DF)
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Nickel based superalloys
Contrast $/$’!
c. TEM contrasts
Bright field (BF), dark field (DF)
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0.5
0.6
0.7
0.8
0.9
1
1.1
0 50 100 150 200 250 300 350
c(Ga)normalized
distance/nm
A
I/1
II/1 II/2
I/2
B
III
Can vertical quantum wells emit light? We need local concentrations to model the electronic properties
Segregation of chemical species in OMCVD AlGaAs structures on patterned substrates
c. TEM contrasts
Bright field (BF), dark field (DF)
Because of the Z dependence of the structure factor, we can observe a chemical contrast in dark field mode!
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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 clair Champ sombre
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c. TEM contrasts
Exctinction distance This intensity depends on the extinction distance: 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 [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
!
t < tmax " #$g%"$g10
!
"g =#Ve cos$ B
%Fg
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Fast assessment of thicknesses of complex multilayer structures by TEM, 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
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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
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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. (tiré de J.V. Edington, Practical Electron
Microscopy in Materials science)
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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
tg(2#hkl) = R/CL
dhklR= %CL (=cte)
2dhklsin#hkl=n%
R
CL
dhkl
2#hkl
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. For small angles, # ! sin# ! tg# and with the Bragg's law we have:
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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
FIB lamella of ! 50 nm thickness, GJS600 treated
Bright Field micrograph, 2750x (Philips CM20)
Simulated diffraction on JEMS software
Hexagonal %-(AlFeSi)
Monoclinic Al3Fe
40-3
0-20
[304]
[831]
0-13 1-2-2
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d. Structure analysis
Powder diagram
111
200
220
311 222
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.
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c. TEM contrasts
High resolution contrast (HRTEM)
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High Angle Annular Dark Field =HAADF
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
HRTEM HAADF-STEM
c. TEM contrasts
Scanning transmission (STEM)
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