Transmission electron microscopy in

Transmission electron microscopy in materials science A. Mogilatenko, H. Kirmse Humboldt-Universität zu Berlin, Institut für Physik, AG Kristallograph...
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Transmission electron microscopy in materials science A. Mogilatenko, H. Kirmse Humboldt-Universität zu Berlin, Institut für Physik, AG Kristallographie Newtonstrasse 15, D-12489 Berlin

Telefon 030 2093 7868, Fax 030 20937760 E-mail: [email protected] [email protected] Web: http://crysta.physik.hu-berlin.de/ag_tem/ Raum 2‘403

pdf-Dateien der Vorlesungen unter: http://crysta.physik.huberlin.de/~kirmse/ Teaching „Inorganic Materials" Vorlesungen zur Elektronenmikroskopie: Teil 1, Teil 2

Introduction and short history

First transmission electron microscope First TEM built in 1931 by Max Knoll and Ernst Ruska in Berlin

1931: magnification 17

resolution > light microscope

Nobel Prize in Physics 1986

1933: magnification 12.000 resolution < light microscope

Ray diagram in light microscopy and TEM lamp

illumination

glass lens

condensor lens

glass lens

specimen objective lens

electrons

electromagnetic lens

electromagnetic lens

first image

glass lens

electromagnetic lens

projective lens final image

ocular eye

eye fluorescent screen

Theory of image formation and resolution limit 1866 - starts working with Carl Zeiss 1873 - theoretical description of resolution limit

d Ernst Abbe: 1840-1905

: n: :

2n sin

wavelength 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

d

2n sin

!

To get a better resolution – decrease the wave length!

Light optics:

: n: :

wavelength 400 .. 800 nm refractive index of medium 1 .. 1.5 (air .. immersion system) between object and objective 70° opening angle of rays originating from object and collected by objective

=> d ~ 250 nm

Monument in Jena (Germany)

Wave-Particle Duality Louis de Broglie, 1924

h p

h 2m0eV

h 2m0eV 1

eV 2m0c 2

!

with 100 keV electrons travell at about 1/2c! V: acceleration voltage, m0: electron mass e: electron charge, c: velocity of light

Wave-Particle Duality

wave



coherent ↔ incoherent

imaging, high resolution imaging, diffraction

particle elastic ↔ inelastic

spectrometry

/ pm

Electron wavelength

V / kV 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“

TEM – multi lens system

How can I focus electron beam? electric field E electron charge e => force F

E

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 B

Magnetic electron round lens

~ 1 - 2 Tesla

Williams & Carter

Magnetic electron round lens

Wine glass with water = optical lens with huge aberrations

Electron lenses are bad lenses too!!! “if the lens in your own eyes would be as bad as electromagnetic lenses, then you would be legally blind“ Williams & Carter

Ray diagram (Strahlengang) lens object optic axis

Ray diagram

lens

back focal plane

image plane

Brennebene

Bildebene

object optic axis optische Achse

d1 d2

Ray diagram

lens

back focal plane

image plane

Brennebene

Bildebene

object optic axis

d1 d2

lens

back focal plane

image plane

object optic axis

diffraction pattern

Perfect imaging by a round lens the same focus for all rays Object marginal ray paraxial ray

Objective lens

Image plane

Spherical aberration (Öffnungsfehler) - off-axis rays are focused stronger! disk of least confusion marginal ray paraxial ray

marginal focus Objective lens

paraxial focus Image plane

A point object is imaged as a disk of finite size – limits the resolution!

Improvement in resolution

sub-Å resolution

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

Problems / disadvantages in TEM • time consuming specimen preparation is required • only small sample regions can be investigated (~ 1 nm…some µm) • electron beam damage damage dose: living objects: bio molecules: anorganic substances:

10-4 – 1 e/nm² 103 – 105 e/nm² 106 – 1011 e/nm²

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

Electron beam induced segregation effects Electron beam damage in InGaN QWs - In-clustering

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

Interaction of electrons and matter

100…400 keV

primary electrons

Energy-Dispersive X-ray Spectrometer

backscattered electrons

X-rays secondary electrons

10…200 nm

thin crystalline specimen

Electron Diffraction, Conventional imaging, High resolution imaging

diffracted beam

direct beam

elastically and inelastically scattered electrons Electron Energy Loss Spectrometer

High-Angle Annular Dark-Field Detector

Electron forward scattering from thin specimen coherent • single scattering incident beam • plural scattering (>1) • multiple scattering (>20)

thin specimen incoherent elastic coherent scattered incoherent elastic scattered electrons inelastic scattered electrons (> ~10°) electrons (1…10°) (< 1°) direct beam

Scattering of electrons Bulk material

TEM specimen

50 nm 1 nm 200 nm

50 µm

Monte-Carlo Simulation of the paths of electrons (acceleration voltage: 100 kV) trough Silicon of different thicknesses

Full width at half maximum 12 nm

TEM/STEM IMAGING

Amplitude contrast (diffraction contrast)

Electron holography

Phase contrast (highresolution imaging)

Z-contrast imaging

Lorenz microscopy

DIFFRACTION

Selected area diffraction

Convergent beam diffraction

SPECTROSCOPY

Energy dispersive X-ray spectroscopy

Micro-/ nanodiffraction

Tomography

X-ray mapping

Electron energy loss spectroscopy

Energy-filtered TEM (EFTEM)

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

Aim of investigation

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

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

Evaporation of a droplet

Dipping

TEM grids

and many more

holey carbon film

lacey carbon film

CaF2 with Pd particles (after reaction) transmission electron microscopy bright-field image Pd-CaF_HF25_slotB2; hrtem01_particel01_ovw_3kx

Humboldt-Universität zu Berlin, Institut für Physik (AG Kristallographie), Institut für Chemie (AG Festkörperchemie)

0.16 nm 0.16 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

0.24 nm 0.27 nm 0.27 nm

Matrix (after reaction) high-resolution transmission electron microscopy imaging Pd-CaF_HF25_slotB2; hrtem01_particle03_25kx

Humboldt-Universität zu Berlin, Institut für Physik (AG Kristallographie), Institut für Chemie (AG Festkörperchemie)

TEM preparation of epitaxial structures

Plan-view and cross-sectional TEM preparation Plan view (PVTEM)

Cross section (XTEM)

Initial sample

Formatting

Thinning of substrate

face-to-face gluing

Gluing in a cylinder and sawing

Mechanical thinning Cutting of a disc

Gluing of dummies Dimpling

Dimpling

Ultrasonic disc cutting Ion-beam milling

Ion-beam milling

Mechanical thinning

damage

Region 1

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

Region 2

macro-deformed layer: tilt of grains, increased dislocation density

Region 3

micro-deformed layer: weak tilt of grains, dislocation density as grown

~ 100 nm

Situation after sawing Next preparation step has to remove the damage!

Dimple grinding

Detail of a dimple grinder

Principles of dimpling technique sample Dimpler grinder of Gatan

thickness in the center ~ 20 µm

Ion-beam milling

sample

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

GaAs

Ga(Sb,As) (In,Ga)As GaAs

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

Contrast in TEM

most important for amorphous samples

most important for crystalline samples

most important in HRTEM

Amplitude contrast: mass-thickness contrast total cross section Qtot for scattering from sample (thickness t): Avogadro number total scattering cross section of an isolated atom

Q tot t

N0

tot

A

t)

! product

density atomic weight of atoms

t is called „mass thickness“

Thicker and /or higher mass (Z) areas will scatter more electrons and appear darker in the image

Amplitude contrast: diffraction contrast primary beam

Bragg’s law: n·λ = 2·d·sinθ

sample

objective lens

objective aperture

intermediate lenses projective lenses

imaging plane

Two beam conditions: Tilting the specimen unitl direct beam and one diffracted beam are strong!

Phase contrast: high resolution TEM primary beam

2-beam condition

sample

objective lens

objective aperture

intermediate lenses projective lenses

imaging plane

multiple-beam condition

Phase shift due to the inner potential of specimen Electron beam

Path through the vacuum:

 2 m e E

 m e E

– – – –

Plancks constant electron mass electron charge electron energy

Path through the specimen:

' d

 2me E V x, y, z V x, y , z – inner potential energy

Phase shift due to the inner potential of specimen Plane wave 0

 r, t

local charge energy

V x, y , z

mean inner potential

x atomic nucleus object exit wave Object

 r,t

t

projected potential: Vt (thin sample)

x, y

V x, y, z dz 0

Phase shift due to the inner potential of specimen Electron beam

Phase shift:

d

2

dz

dz 2 '

with

E

V x, y , z (interaction constant)

Total phase shift: z

d

d

V x, y, z dz

Vt x, y

! phase change depends on potential V which electrons see, as they pass through sample

HRTEM – Imaging Process y

Object

x

Diffraction pattern

gy

gx

Image

y

x

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

gr

f r' h r r' dr'

f(x,y)

point

f r

t r r' 2 points

optical system

disc

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

each point in final image has contributions from many points in specimen

HRTEM: contrast transfer function T(u)

! opposite sign of T(u) -

information limit

oposite contribution to contrast u < point resolution: -1 u, [nm ] images are directly interpretable u > point resolution: no direct interpretation is possible

point resolution

E u sin χ(u)

Eu

No simple correspondence between the image intensity and the atom column positions! Additional calculations are necessary!

u

f

u

2

1 2

Cs

3

u4

f - defocus - wave length Cs - spherical aberration u - spatial frequency

Contrast transfer

sin

Optimum for f : Scherzer

u

sin

f

u

2

1 2

Cs

Minimization of Cs

3

u4

Example: HRTEM simulation for GaAs projected potential

same thickness, only defocus change

by courtesy of Prof. Kerstin Volz

HRTEM of an isolated ZnTe nanowire

- visualization of crystal structure - analysis of defects

HRTEM of an isolated ZnTe nanowire {211}

{111}

{110}

HRTEM of an isolated ZnTe nanowire {211}

{111}

{110}

Twin formation

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