Transmission electron microscopy in

materials science

Humboldt-Universität zu Berlin,

Institut für Physik, AG Kristallographie

Newtonstrasse 15, D-12489 Berlin

Telefon 030 2093 7868, Fax 030 20937760

E-mail: anmog@physik.hu-berlin.de

holm.kirmse@physik.hu-berlin.de

Web: http://crysta.physik.hu-berlin.de/ag_tem/

Raum 2‘403

A. Mogilatenko, H. Kirmse

pdf-Dateien der Vorlesungen unter:

http://crysta.physik.hu-

berlin.de/~kirmse/

Teaching

„Inorganic Materials"

Vorlesungen zur

Elektronenmikroskopie:

Teil 1, Teil 2

Introduction and short history

First TEM built in 1931 by

Max Knoll and Ernst Ruska

in Berlin

Nobel Prize in Physics 1986

First transmission electron microscope

1931: magnification 17

resolution > light microscope

1933: magnification 12.000

resolution < light microscope

Ray diagram in light microscopy and

TEM

lamp electrons

glass lens

glass lens

glass lens

eye

ocular

illumination

condensor lens

specimen

objective lens

projective lens

final image

first image

electromagnetic

lens

electromagnetic

lens

electromagnetic

lens

eye

fluorescent

screen

Ernst Abbe:

1840-1905

1866 - starts working with Carl Zeiss

1873 - theoretical description of

resolution limit

Theory of image formation and resolution

limit

sin2nd

: wavelength

n : refractive index of medium

between object and objective

: opening angle of rays originating

from object and collected by objective

„… it is poor comfort to hope that human ingenuity will find ways and

means of overcoming this limit.“

Resolution: Light Microscopy

no lens imperfections =>

resolution is limited by diffraction at edges of lens system

: wavelength

n: refractive index of medium

between object and objective

: opening angle of rays originating from object

and collected by objective

Light optics:

400 .. 800 nm

1 .. 1.5 (air .. immersion system)

70°

=> d ~ 250 nm

! To get a better resolution –

decrease the wave length! sin2n

d

Monument in Jena (Germany)

Wave-Particle Duality Louis de Broglie, 1924

2

0

0

0

212

2

cm

eVeVm

h

eVm

h

p

h

V: acceleration voltage, m0: electron mass

e: electron charge, c: velocity of light

with 100 keV electrons travell

at about 1/2c!

!

Wave-Particle Duality

wave particle

imaging,

high resolution imaging,

diffraction

spectrometry

elastic ↔ inelastic coherent ↔ incoherent

Electron wavelength

V = 300kV => = 1.97 pm => resolution only ~ 0.1 nm ?

„magnetic lenses of TEMs have similar quality as

bottom of bottle of champagne would have for light microscope“

V / kV

/ p

m

TEM – multi lens system

How can I focus electron beam?

electric field E

electron charge e => force F

F = -e*E

force in opposite direction of electric field

magnetic induction B

electron velocity v => Lorentz force

F = -e(v x B)

force perpendicular to magnetic field and electron

velocity direction

E

B

Magnetic electron round lens

Williams & Carter

~ 1 - 2 Tesla

Williams & Carter

Wine glass

with water =

optical lens with

huge aberrations

“if the lens in your own eyes would be as bad as

electromagnetic lenses, then you would be legally blind“

Electron lenses are

bad lenses too!!!

Magnetic electron round lens

Ray diagram

(Strahlengang)

optic

axis

lens

object

optic

axis

lens

object

back focal

plane

image

plane

d1

d2

Brennebene Bildebene

optische

Achse

Ray diagram

optic

axis

lens

object

back focal

plane

image

plane

d1

d2

Ray diagram

Brennebene Bildebene

optic

axis

lens

object

image

plane

back focal

plane

diffraction

pattern

Perfect imaging by a round lens

Objective lens Image plane

the same focus for all rays

Object

marginal ray

paraxial ray

Spherical aberration (Öffnungsfehler) - off-axis rays

are focused stronger!

Objective lens Image plane

marginal ray

paraxial ray

A point object is imaged as a disk of finite size –

limits the resolution!

marginal focus

paraxial focus

disk of least

confusion

Improvement in resolution

H. Rose, Journal of Electron Microscopy: 1-9 (2009)

sub-Å

resolution

Problems / disadvantages in TEM

damage dose:

living objects: 10-4 – 1 e/nm²

bio molecules: 103 – 105 e/nm²

anorganic substances: 106 – 1011 e/nm²

• time consuming specimen preparation is required

• only small sample regions can be investigated

(~ 1 nm…some µm)

• electron beam damage

Rose equation: links resolution d and contrast c c * d > 5/n0.5

n: number of electrons per unit area

example: c = 5 %; d = 0.3 nm => n > 105 e/nm²

Smeeton et al., Appl. Phys. Lett. 83 (2003) 5419

Electron beam induced segregation effects

Electron beam damage in InGaN QWs - In-clustering

Interaction of electrons and matter

thin crystalline specimen

primary electrons

elastically and inelastically scattered electrons

backscattered electrons

secondary electrons

X-rays

Electron Energy Loss Spectrometer

High-Angle Annular Dark-Field

Detector

Energy-Dispersive X-ray

Spectrometer

Electron Diffraction, Conventional imaging,

High resolution imaging

direct

beam

diffracted

beam

10…200 nm

100…400 keV

Electron forward scattering from thin specimen

thin specimen

coherent

incident beam

direct beam

coherent

elastic scattered

electrons

(1…10°)

incoherent

inelastic scattered

electrons

(< 1°)

incoherent

elastic

scattered

electrons

(> ~10°)

• single scattering

• plural scattering (>1)

• multiple scattering (>20)

Full width at

half maximum

Scattering of electrons

1 nm

Bulk material

12 nm

200 nm

50 nm

TEM specimen

Monte-Carlo Simulation of the paths

of electrons (acceleration voltage: 100 kV)

trough Silicon of different thicknesses

50 µm

Full width at

half maximum

IMAGING DIFFRACTION SPECTROSCOPY

Amplitude

contrast (diffraction

contrast)

Phase

contrast (high-

resolution

imaging)

Selected

area

diffraction

Energy

dispersive

X-ray

spectroscopy

Electron

energy loss

spectroscopy

Electron

holography

Z-contrast

imaging

Convergent

beam

diffraction

Micro-/

nano-

diffraction

Energy-filtered

TEM (EFTEM)

X-ray

mapping

TEM/STEM

Lorenz

microscopy Tomography

TEM specimen preparation

Why sample preparation for Transmission Electron

Microscopy

• Electrons with properties of particles and waves

• Strong interaction between electrons of the

beam and atoms of the samples scattering

• Sufficient intensity/number of transmitted

electrons only for small thickness (about 100 nm)

• Essential thickness depends on, e.g.,

materials properties, acceleration voltage, and

requirements of individual investigation method

Demands on sample preparation

• No change of materials properties including:

– Structure (amorphous, polycrystalline,

crystalline)

– Chemistry (composition of the bulk material,

of surfaces, and of interfaces)

• But:

Artifacts inherent in every preparation

method!

• Criterion of appropriate preparation technique:

Influence on structural and chemical

properties as small as possible!

Shape of the sample

• TEM sample holders

• Limits of sample size:

– Diameter: 3 mm

due to the furnace

of the TEM sample

holder

– Maximum

thickness of

sample edge: ca.

100 µm

Type of sample

• Structural properties

– size distribution of

entities

– area density

– structural defects

• Chemical properties

– composition

– modification

– interface sharpness

• Electronic properties

• Magnetic properties

• Particles

• Bulk material

• Epitaxial structures

Materials properties

• Hardness

• Sensitivity for

chemical solutions

Preparation strategy

Aim of investigation

TEM preparation of small particles

• Dispersion in a non

dissolving liquid (e.g.:

methanol, water, etc.) in an

ultrasonic bath

• Transfer to a carbon film

supported by a copper grid

Dipping Evaporation of a droplet

TEM grids

holey carbon film lacey carbon film

and many

more

CaF2 with Pd particles (after reaction)

transmission electron microscopy bright-field image

Humboldt-Universität zu Berlin,

Institut für Physik (AG Kristallographie), Institut für Chemie (AG Festkörperchemie)

Pd-CaF_HF25_slotB2; hrtem01_particel01_ovw_3kx

Matrix (after reaction)

high-resolution transmission electron microscopy imaging

Humboldt-Universität zu Berlin,

Institut für Physik (AG Kristallographie), Institut für Chemie (AG Festkörperchemie)

Pd-CaF_HF25_slotB2; hrtem01_particle03_25kx

0.24 nm

Lattice plane distances d (nm)

CaF2 Pd PdF2 PdO

0.31541 0.22458 0.30756 0.30431

0.27315 0.19451 0.26868 0.26680

0.19314 0.13754 0.23832 0.26430

0.16472 0.11730 0.21748 0.21521

0.15770 0.11230 0.18834 0.20060

0.13657 0.09725 0.17757 0.16751

0.12533 0.08925 0.16061 0.15358

0.12216 0.08699 0.15378 0.15215

0.16 nm

0.27 nm

0.27 nm

0.16 nm

TEM preparation of epitaxial structures

Plan-view and cross-sectional TEM

preparation

Ultrasonic disc cutting

Gluing of dummies

Mechanical thinning

Ion-beam milling

Dimpling

Gluing in a cylinder and sawing

face-to-face gluing

Formatting

Cross section (XTEM)

Thinning of substrate

Cutting of a disc

Dimpling

Ion-beam milling

Initial sample

Plan view (PVTEM)

Region 1

Region 2

Region 3

Beilby layer: change of chemical composition, strong deformation, amorphisation

~ 100 nm

macro-deformed layer:

tilt of grains,

increased dislocation density

micro-deformed layer:

weak tilt of grains,

dislocation density as grown

Situation after sawing

Next preparation step has to remove the damage!

Mechanical thinning damage

Principles of dimpling technique

Dimple grinding

Dimpler grinder of Gatan

sample

Detail of a dimple grinder

thickness in the

center ~ 20 µm

Ion-beam milling

Ion gun arrangement for milling of

both sides of the sample;

possible ions: Ar+, Xe+, I+, ...

acceleration voltage: 1...5 kV

usual angle : < 10°

Layout of a vacuum

chamber with two ion guns

sample

HRTEM of Ga(Sb,As) QD on (In,Ga)As seed QD TU#5294cs/2, links: qdot4_012c.jpg, rechts: qdot5_012c.jpg

Humboldt-Universität zu Berlin, Institut für Physik, AG Kristallographie

Forschungszentrum Jülich GmbH, Institut für Festkörperforschung

TEM Philips CM200 FEG cS, GaAs spacer thickness: 4.5 nm

Ga(Sb,As)

GaAs

GaAs

GaAs

(In,Ga)As

most important in

HRTEM most

important for

amorphous samples

most important

for crystalline samples

Contrast in TEM

Amplitude contrast: mass-thickness contrast total cross section Qtot for scattering from sample (thickness t):

Thicker and /or higher mass (Z) areas

will scatter more electrons and appear

darker in the image

! product is called „mass thickness“ t A

N Q tot

tot

t) 0 t

Avogadro number density

atomic weight of atoms total scattering cross section

of an isolated atom

Amplitude contrast: diffraction contrast

Bragg’s law: n·λ = 2·d·sinθ

Two beam conditions:

Tilting the specimen unitl direct

beam and one diffracted beam are

strong!

primary beam

sample

objective aperture

imaging plane

intermediate lenses projective lenses

objective lens

Phase contrast: high resolution TEM

multiple-beam

condition

2-beam

condition primary beam

sample

objective aperture

imaging plane

intermediate lenses projective lenses

objective lens

Phase shift due to the inner potential of

specimen

Path through the vacuum:

Eem2

Eem – Plancks constant

– electron mass

– electron charge

– electron energy

zyxVEme ,,2'

zyxV ,, – inner potential

energy

Path through the specimen:

d

Electron beam

Phase shift due to the inner potential of

specimen

x

local charge energy

atomic nucleus

mean inner potential

Plane wave

tr ,0

trObject ,

object exit wave

Plane wave

zyxV ,,

t

t dzzyxVyxV0

,,,projected potential:

(thin sample)

Phase shift due to the inner potential of

specimen

Phase shift:

zyxVdzdz

d ,,'

22

Ewith (interaction constant)

Total phase shift:

yxVdzzyxVd t ,,,

d

Electron beam

z

! phase change depends on potential V

which electrons see, as they pass

through sample

x

y

gx

gy

x

y

Object

Image

Diffraction pattern

HRTEM – Imaging Process

Role of optical system

transfer of each point in specimen into region in final image

f(x,y): specimen (transmission) function describes specimen

g(x,y): extended region of point x,y in image

h(r-r`): weighting term: point spread function

'''' rrtrfdrrrhrfrg

optical system

image g(x,y)=g(r)

f(x,y) point

disc

2 points

each point in final image has contributions

from many points in specimen

point

resolution

information

limit

u, [nm-1]

χ(u)uE sinuE

HRTEM: contrast transfer function

! opposite sign of T(u) - oposite contribution to

contrast

u < point resolution:

images are directly

interpretable

u > point resolution: no

direct interpretation is

possible

T(u)

No simple correspondence between the image

intensity and the atom column positions!

Additional calculations are necessary!

f - defocus

- wave length

Cs - spherical aberration

u - spatial frequency

432

2

1uCufu s

Contrast transfer

Minimization of Cs Optimum for f : Scherzer

432

2

1sinsin uCufu s

Example: HRTEM simulation for GaAs

projected

potential

by courtesy of Prof. Kerstin Volz

same thickness,

only defocus

change

HRTEM of an isolated ZnTe nanowire

- visualization of crystal structure

- analysis of defects

{110}

{211}

{111}

HRTEM of an isolated ZnTe nanowire

Twin formation

{110}

{211}

{111}

HRTEM of an isolated ZnTe nanowire