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


Outline

a.  TEM principle b.  A little about diffraction c.  TEM contrasts d.  Examples e.  Structure analysis


EPFL: Philips CM300

300’000V


EPFL: Philips CM300

300’000V

Canon

Illumination

Projection

Echantillon


a. TEM principle


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


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 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



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

???



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



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.



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.



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( )



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



[ ]!=

"=

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:



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)



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



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



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?)



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#'



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


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 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


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


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) : 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.


Bright field Dark field 100 nm

P.-A. Buffat!

c. TEM contrasts

Bright field (BF), dark field (DF)


Nickel based superalloys

Contrast $/$’!

c. TEM contrasts



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


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


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


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


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


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


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.


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)


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.



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.



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.



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:



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.



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



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.


c. TEM contrasts

High resolution contrast (HRTEM)


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)

Chapter 4 - TEM

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