Atomic resolution electron microscopy Dirk Van Dyck ( Antwerp, Belgium ) Nato summer school Erice 10 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 Theory Modelling Design Fabrication understanding Language: numbers (3D atomic positions (+/ 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 sourceobjectdetectors 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 investigate (aperiodic) nanostructures Electrons are the best particles to investigate (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

9/3/2015 Quantitative refinement Resolving (direct method) experiments atomic structure Refining

EM: resolving atoms = new situation Model based fitting (quantitative) resolutionprecision resolving refining resolution precision 1 Å0.01 Å

Å ρ σ CR resolution versus precision Precision = resolution/ sqrt (dose) Resolution = 1 Å Dose = 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 microscope Principles 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 interference Merli,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 Ti 2 Nb 10 O 25

Comparison of experimental images (top row) (Iijima 1972) and computer-simulated images (bottom row) for Ti 2 Nb 10 O 25

N slices ΔzΔz Exit Wave function Ref: J. M. Cowley and A. F. Moodie, Acta Cryst. 10 (1957) 609 phase grating propagator Image simulation: the Multislice method

Best EM: resolution 0.5 Angstrom: resolving individual atoms Ultimate resolution = atom Transfer functions of TEM

Image wave = object wave * impuls response Deblurring (deconvolution) of the electron microscope 1) retrieve image phase: holography, focal series reconstruction 2) deconvolute the (complex) point spread function 3) reconstruct the (complex) exit wave of the object    OB *P I IM = |  IM | 2 Inverting the imaging: from image to exit wave

From HREM images to exit wave

30 From exit wave to structure Zone 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)

31 light atoms heavy atoms light atoms heavy atoms zone axis orientation electron channelling

1s-state model (for one column) reference wave background Massfocus position width DW-factor residual aberrations

Diffraction pattern Fourier transform of exit wave Kinematic expression, with dynamical (thickness dependent) scattering factors of columns.

34 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

38 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) reference wave background mass circle Defocus circle position width DW-factor residual 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) 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)

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)

47 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 experiments Sublimation of PbSe Marijn Van Huis (TU Delft)

Experiment design Intuition is misleading “Ideal” HREM:Cs = 0  f = 0 “Ideal object”:phase object  we need a strategy no image contrast

50 Å thick silicon [100] crystal at 300 kV

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

Resolution limits of HREM (Courtesy C Kisielowski) Non-corrected HREM Au Cs-corrected HREM HREM approaches the physical limits by interaction process Thus the same limits as electron diffraction