Chapter 14 High Resolution TEM

(1)

Spring 2013 MSE-603 High-resolution TEM Marco Cantoni

Chapter 14 High Resolution TEM

Pb

Ti _O

Pb

Ti

• K. Ishizuka (1980) “Contrast Transfer of Crystal Images in TEM”, Ultramicroscopy 5,pages 55-65.

• L. Reimer (1993) “Transmission Electron Microscopy”, Springer Verlag, Berlin. • J.C.H. Spence (1988), “Experimental High Resolution Electron Microscopy”, Oxford

University Press, New York.

Bright Field Imaging

(2)

High resolution….?!

electron at 300keV:

•

v = 2.33 10

-8

m/s (0.78 c)



= 0.00197nm

•



_diff

= 10

-3

rad

Precipitate in a ceramic: PbTiO

₃

Pb

Ti

Atomic resolution…?

(3)

CuO

2

Hg

“White-atom” contrast

High-resolution

• The image should ressemble the

atomic structure !

• Atomes…?

Thin samples: atom columns:

orientation of the sample

(incident beam // atom

columns)

• The observed contrast varies

with thickness and

defocalisation…!

• Need to compare with

simulations !

(4)

the TEM in “high-resolution” mode

A high-resolution

image is an

interference image of

the transmitted and

the diffracted beams!

Diffracted electrons:

coherent elastic

scattering

(the electrons have

seen the crystal

lattice )

The quality of the

image depends on the

optical system that

makes the beams

interfere

Bright Field High-Resolution

The objective lens

•

Field with rotational symmetry

•

Lorenz Force : F = -e v

^

B

e on optical axis: F = 0

e not on optical axis : deviated

optical axis: symmetry axis

•

Scherzer 1936:

•

Magnetic lens with rotational

symmetry:

Aberration coefficients:

C

_s

: spherical

C

_c

: chromatical

–

Always positive !!

4

/

1

4

/

3

66

.

0

s

res

C

D





Example:



= 0.00197nm, C

_s

= 1 mm

D

_res

= 1.8 10

-10

= 1.8Å

Resolution limit:

(5)

Image formation

• Source:

coherent and

monochromatic

• Illumination:

parallel

• Sample: thin

, nicely prepared

(no amorphization), orientation

(zone axis)

• objective lens:

aberrations,

focus, stability !

• projection lens system

(magnification)

Source

FEG

Illumination

coherent specimen

exit wave

objective lens Spherical aberration Cs

image

• Illumination:

parallel beam

• Sample:

weak phase object:

weak phase object aproximation (WPOA)

• Objective lens:

Abbé’s principle

transfert function

coherent transfer function (CTF)

• Image contrast (intensity)

Image formation

r k

r











2i 0

exp

)

(

Source

FEG

Illumination

coherente specimen

exit wave

image

)

(

)

(

)

(

x



o

x



T

x



i









)

(

)

(

)

(

I

_i

x







_i

x





_i*

x



(6)

sample = phase objet

2

)

(

2

h

E

me

k



2

))

(

2

h

r

V

E

me

k







E

z

x

V

_p

















(

,

)

2



Wave vector in vacuum:

Wave vector in a potential

:

Phase shift



due to the cristal potential V

_p

:

Exit wave function:

Plane wave

Cristal potential

Exit wave



(

;

)



)

(

exp

i

V

p

z

o

x











WPOA

• Weak phase object approximation:



(

;

)



1

(

;

)

(

exp

i

V

p

z

i

V

p

z

o

x

















Multi-slice calculation:

Calculation of the exit wave function for complex

structures:

No absorbtion,effect of the object on the outgoing wave: only phase shift



0



V

₁p1



’

₁



₂

V

p2



’

₂



3

V

_p3

The sample is cut into thin slices

(7)

Abbé’s principle

Transfer Function

•

The optical system (lenses) can be described by a convolution with a

function T(x):

Point spread function (PSF): describes how a point on the object side is

transformed into the image.

T(x)

•

Transfer Fonction

:

Décrit comment une fonction d’onde “objet” est

transformé dans une fonction d’onde “image”

• The image INTENSITY observed on a

screen (or a camera / negative plate etc.)

(8)

Transfer Function

• Phase factors:

– Spherical Aberration

– Defocus

• Amplitude factors:

– (objective) apertures

– spatial coherence enveloppe (non-parallel, convergent

beam)

– Temporal coherence envelope (non monochromatic

beam, instabilities of the gun and lenses)



2

(

)



(

)

(

)

exp

)

(

)

(

h



a

h



i

h



E

s

h



E

t

h



T







Transfer Function





2

4

3

5

.

0

25

.

0

)

(

)

(

2

exp

)

(

h

z

h

C

i

T

s













h



Object plane

image plane



z

(9)

• Illumination

• Sample

• objective lens

• Image, contrast

Image formation

r k

r













2i 0

exp

)

(

Source

FEG

Illumination

coherent specimen

exit wave

image

)

(

)

(

)

(

x



o

x



T

x



i









)

(

)

(

)

(

I

_i

x







_i

x





_i*

x





(

;

)



1

(

;

)

(

exp

i

V

p

z

i

V

p

z

o

x





















3 4 2

5

.

0

25

.

0

)

(

)

(

2

exp

)

(

i

avec

C

h

z

h

T

h









h





h





_s









The « magic » of image contrast

Espace

Fourier

(10)

but….

For a direct and simple interpretation of the image contrast:

the imaginary part (sin) of the transfer function exp[2pi



(h)] should be ~1

The only free parameter in the microscope is: the defocus



z

CTF

• CTF: contrast transfer function

(« useful » = V

p

)

















3

4

2

sin

)

(

k

C

k

z

k

CTF



s







(11)

Scherzer Defocus



s

C

z





4

3



4

/

1

4

/

3

66

.

0

s

scherzer

C

D





With



z

_scherzer

The CTF has a wide

pass band

The first zero crossing of the CTF defines the « point-to-point » resolution of

an electron microscope

The atom columns appear as dark areas on a bright background

Spatial and temporal coherence



2

(

)



(

)

(

)

exp

)

(

)

(

h



a

h



i

h



E

_s

h



E

_t

h



T







CM300UT FEG

Field emission

C

_s

: 0.7mm



z= 44nm

Resolution (point to point): 1.7Å

Information limite : ~1.2Å

Information

limit

Resolution

(Scherzer)

(12)

A good microscope

CM300UT FEG

Emmission à éffet de champs

C

_s

: 0.7mm

z= 44nm

Résolution (point à point): 1.7Å

Limite d’information: ~1.2Å

CM30ST LaB6

Emmission thermionique

C

_s

: 2mm

z= 76nm

Résolution (point à point): 2.1Å

Limite d’information: ~1.9Å

Pass bands



z=44nm



z=67nm



z=84nm



z=98nm

directe

(13)

Defocus

proj. pot.

Wave funct.

Au [100], thickness 20nm

scherzer

defocus

1. p.b.

2. p.b.

3. p.b.

HRTEM image formation

Source

FEG

Illumination

coherent specimen

exit wave

image

projected

potential

Transfer

Function

image of “projected potential”

Problems:

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

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

(14)

Variation of the contrast with: thickness, defocus

Au, face centered cubic

(15)

Comparaison: experiment and simulation

104 ºC

135 ºC

cubic

rhombohedral

direct observation of the B-site cationic order in the ferroelectric relaxor

Pb(Mg

_1/3

Ta

_2/3

)O

₃

by high-resolution Transmission Electron Microscopy

excellent dielectric, electrostrictive, and

pyroelectric properties for

high performance sensors and

actuators

nanoscale chemical inhomogeneity in

the

B

-site sublattice

(16)

Mg and Ta randomly distributed

on the different B-sites

„disordered“

Mg and Ta occupy

alternatively the different B-sites

„ordered“

1:1-type superstructure

Pb Ti _O [110] zone axis

perovskite

The cation ordering on the B-site of Pb(Mg

1/3

,Ta

2/3

)O

3

Chemical ordered regions in Pb(Mg1/3,Ta2/3)O3, two different models

Space-charge model:

perfect 1:1 ratio in ordered regions

Mg : Ta = 1:1

Mg

Ta

Random-site model

(also called random layer)

Perfect overall stochiometry

Mg : Ta = 1:2

Mg/Ta

Ta

[110] direction

1:1

1:2+

1:2

B. P. Burton and E. Cockayne, Ferroelectrics 270, 1359 (2002). B. P. Burton

J. Phys. Chem. Solids 61, 327 (2000).

first-principles total energy calculations:

random-layer model is an energetically stable ground state structure

(17)

Different zone axes

HRTEM image simulation with JEMS

Space Charge

Random layer

(18)

Image contrast simulation [211] zone axis

Space charge

model

Random layer

model

defocus

thickness

experimental image compared to simulations

Space-charge

Random-site

Ta

Mg

Pb Pb

Cantoni, M; Bharadwaja, S; Gentil, S; Setter, N. 2004.

Direct observation of the B-site cationic order in the ferroelectric relaxor Pb(Mg1/3Ta2/3)O-3. JOURNAL OF APPLIED PHYSICS 96 (7): 3870-3875.

(19)

Maximilian Haider, Stephan Uhlemann,

Eugen Schwan, Harald Rose, Bernd Kabius, Knut Urban

NATURE, VOL 392, 1998

f=68 nm f=96 nm

hexapole

transfer doublet

JEOL: JEM-2010F

the aberration-corrected transmission electron microscope

(Rose, 1990; Haider et al., 1998)

• Cs-corrector

Super microscopes…..

Cs=0.2mm

(20)

Cs correctors 2008: FEI Titan

Sharp interfaces

No delocalisation at interfaces anymore

(21)

Gold crystal

•

direct imaging of heavy and light atoms in a sinlge

image

•

No delocalisation: atoms are seen at their real

position

Atomic-Resolution Imaging of Oxy gen in SrT iO 3 C. L. Jia, M. Lentzen, K. Urban SCI E NCE V O L 299 (2003)

Chun-Lin Jia, Markus Lentzen, and Knut Urban Microsc. Microanal. 10, 174–184, 2004

simulation

Experimental image

200kV, cs corrected TEM

Oxygen vacancies in YBa

₂

Cu

₃

O

_x

Cs-corrected imaging