Atomic resolution electron microscopy

Dirk Van Dyck (Antwerp, Belgium)

Nato summer school Erice10 june 2011

Richard Feynman’s dream (1959)There’s plenty of room a the bottom:

an invitation to enter a new field of physics

It would be very easy to make an analysis of any complicated chemical substance; all one would have to do would be to look at it and see where the atoms are. The only trouble is that the electron microscope is one

hundred times too poor. I put this out as a challenge: Is there no way to make the electron microscope more

powerful?The sentence with the most information is: nature

consists of atoms

Characterization• structure• properties

TheoryModelling

DesignFabrication

understanding

Language: numbers (3D atomic positions (+/- 0.01 Angstrom))

Future of nanoscience

Bandgap engineering

Detection of individual particles Model based fitting Ultimate precision determined by the counting statistics Image is only an experimental dataset

Quantitative experiment

source object detectors

instrumental parameters

strong interaction

sub surface information

easy to detect

use of lenses (real space Fourier space)

electron beam brighter than synchrotron

less radiation damage than X-rays

larger scattering factor than X-rays

sensitive to charge of atoms.

Electrons are the best particles to Electrons are the best particles to investigate (aperiodic) nanostructuresinvestigate (aperiodic) nanostructures

7

Ultimate goal

•Quantitative model based fitting in 2D and 3D.

•Atoms are the ultimate alfabet.

•Extracting all information from HREM images

•Only limited by the statistical counting errors

8

Problem

•Model parameters (atom positions) scrambled in the experimental data

•Model based fitting : search for global fitness optimum in huge dimensional space

•Need to „resolve“ an approximate starting structure close to the global optimum: direct method

•Refinement : convergence and uniqueness guaranteed

04/19/23

Quantitative refinement

Resolving (direct method)

experiments atomic structure

Refining

EM: resolving atoms = new situation

Model based fitting (quantitative)

resolution precision

resolving refining

resolution precision

1 Å 0.01 Å

Å

ρ

σCR

resolution versus precision

Precision = resolution/ sqrt (dose)

Resolution = 1 Å

Dose = 10000 electrons

Precision =0.01Å

•Inverting the imaging: from image to exit wave

•Inverting the scattering:from exit wave to atomic structure

Step 2: refining (iterative)

•Model based fitting with experimental data

•Model for the imaging (image transfer theory)

•Model for the scattering (multislice, channelling)

Quantitative refinement in EM

Step 1: resolving (direct step)

Direct step

Inverting the imaging (Exit wave reconstruction)

Inverting the electron-object interaction (electron channelling)

Transfer in the microscopePrinciples of linear imaging

I(r) = O(r)*P(r) : convolution

O(r) = object function

P(r) = point spread function

Fourier space

I(g) = O(g).P(r) : multiplication

image deconvolution (deblurring)

Electron microscope: coherent imaging

image wave = object wave * point spread function

Electron interferenceMerli,Missiroli,Pozzi (Bologna1976)

Physics World (Poll 2002) : The most beautiful experiment in physics.

Point spread function and transfer function of the EM

point spread function(real space)

microscope’s transfer function(reciprocal space)

Measurement of the aberrations

Diffractogram

For weak objects

Amorphous: (Random):

White noise object

Measurement and (semi) automatic correction of the aberrations: Zemlin tableau

22

Intuitive image interpretation

• Phase transfer at optimum focus = pi/4

•Cfr phase plate in optics (Zernike)

•Phase contrast microscopy

•Weak phase object: phase proportional to projected potential

• Image contrast : projected potential

Image interpretation at optimum focus

Schematic representation of the unit cell of Ti2 Nb10O25

Comparison of experimental images (top row) (Iijima 1972) and computer-simulated images (bottom row) for Ti2 Nb10O25

N slices

Δz

NNn ppppqqqqr ]]]][[[[)( 22110012 Exit Wave functionExit Wave function

Ref: J. M. Cowley and A. F. Moodie, Acta Cryst. 10 (1957) 609

]),,(exp[ zzyxViq nn

]/)(exp[),( 22 zyxkiyxp

phase gratingphase grating

propagatorpropagator

Image simulation: the Multislice method

Best EM: resolution 0.5 Angstrom: resolving individual atoms

Ultimate resolution = atom

Transfer functions of TEM

0 1 20,0

0,5

1,0

1/A

1/A

1/A

1/A

detector

0 1 2-1

0

1electron microscope

0 1 20,0

0,5

1,0

thermal motion

0 1 20,0

0,5

1,0

Si atom

Image wave = object wave * impuls response

Deblurring (deconvolution) of the electron microscope

1) retrieve image phase: holography , focal series reconstruction2) deconvolute the (complex) point spread function3) reconstruct the (complex) exit wave of the object

OB*P

IIM = |IM|2

Inverting the imaging: from image to exit wave

From HREM images to exit wave

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From exit wave to structureZone axis orientation

• Atoms superimpose along beam direction

• Electrons are captured in the columns

• Strong interaction: no plane waves

• Very sensitive to structure

• Atom column as a new basis

• Strong thermal diffuse scattering (absorption)

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light atoms heavy atoms light atoms heavy atoms

zone axis orientation electron channelling

1s-state model (for one column)

)1)(1)(()0,(),( /1

iiEts eerrzr

reference wavebackground

Mass focus

positionwidth

DW-factorresidual aberrations

Diffraction pattern

Fourier transform of exit wave

Kinematic expression, with dynamical (thickness dependent) scattering factors of columns.

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Channelling based crystallography

• Dynamical but local (symmetry is kept)

• Simple theory and insight

• Dynamical extinction

• Sensitive to light elements

• Exit wave more peaked than atoms

• Patterson (Dorset), direct methods (Kolb)

Phase of total exit wave 5 Al: Cu

Amplitude of

Phase of

Courtesy C. Kisielowski, J.R. Jinschek (NCEM, Berkeley)

5 Al + Cu

Phase of

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Data mining the object wave

• Position of the atom columns (2D,3D)

• Weigth of the columns

• Single atom sensitivity

• Local Tilt

• Residual aberrations

•.....

1s-state model)

)1)(1)(()0,(),( /1

iiEts eerrzr

reference wavebackground

mass circle Defocus circle

positionwidth

DW-factorresidual aberrations

Argand Plot

exit wave - vacuum

vacuum

=

Courtesy C. Kisielowski, J.R. Jinschek (NCEM, Berkeley)

Argand plot of Au (100) (simulations)Single atom sensitivity

Graphene

Atomaire structuur in 3 dimensies

S. Van Aert, K.J. Batenburg, M.D. Rossell, R. Erni, G. Van Tendeloo.Nature 470 (2011) 374-377.

Number of Ag atoms from 2 projections

2D beelden van een zilver nanodeeltje in een aluminium matrix

[101] [100]

Discrete electron tomography

Atomaire structuur in 3 dimensies

S. Van Aert, K.J. Batenburg, M.D. Rossell, R. Erni, G. Van Tendeloo.Nature 470 (2011) 374-377.

46

Future

• Resolution gap imaging-diffraction is closing

• Exit wave same information as diffraction wave

• Quantitative precision only limited by dose

• Experiment design

• In situ experiments

• Femtosecond (4D) microscopy (Zewail)

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• Resolution close to physical limits (atom)

• Resolution of imaging same as diffraction

• Applicable to non-periodic objects

• 3D atom positions with pm precision

• Precision only limited by dose

Conclusions

In-situ heating experimentsSublimation of PbSe

Marijn Van Huis (TU Delft)

Experiment design

Intuition is misleading

“Ideal” HREM: Cs = 0f = 0

“Ideal object”:phase object

we need a strategy

no image contrast

50 Å thick silicon [100] crystal at 300 kV

0.0 0.2 0.4 0.6 0.8 1.00.00

0.01

0.02

without correction for chromatic aberration with chromatic aberration corrector with monochromator

stan

dar

d d

evia

tio

n o

f p

osi

tio

n c

oo

rdin

ates

(Å

)

spherical aberration constant (mm)

0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4 without monochromator, without Cc-corrector

with monochromator with C

c-corrector

Lower bound on standard deviation of the positionC

s (mm)

Precision of a Si atom position as a function of CsAccelerating voltage = 50 keV

Resolution limits of HREM (Courtesy C Kisielowski)

Non-corrected HREM

Au

Cs-corrected HREM

HREM approaches the physical limits by interaction processThus the same limits as electron diffraction