Atomic resolution electron microscopy

1. Atomic resolution electron microscopy Dirk Van Dyck (Antwerp, Belgium) Nato summer school Erice 10 june 2011

2. 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

3. Future of nanoscience understanding • Characterization • structure • properties Theory Modelling Design Fabrication Language: numbers (3D atomic positions (+/- 0.01 Angstrom))

4. Bandgap engineering

5. Quantitative experiment • Detection of individual particles • Model based fitting • Ultimate precision determined by the counting statistics • Image is only an experimental dataset source object detectors instrumental parameters

6. Electrons are the best particles to investigate (aperiodic) nanostructures • 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.

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. Quantitative refinement Resolving (direct method) experiments atomic structure Refining

10. EM: resolvingatoms = new situation Model based fitting (quantitative) resolution precision resolving refining 1 Å 0.01 Å precision resolution

11. ρ Å σCR resolution versus precision Precision = resolution/ sqrt (dose) Resolution = 1 Å Dose = 10000 electrons Precision =0.01Å

12. Quantitative refinement in EM Step 1: resolving (direct step) • 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)

13. Direct stepInverting the imaging (Exit wave reconstruction)Inverting the electron-object interaction (electron channelling)

14. 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

15. image deconvolution (deblurring)

16. Electron microscope: coherent imaging • image wave = object wave * point spread function

17. Electron interference Merli,Missiroli,Pozzi (Bologna1976) Physics World (Poll 2002) : The most beautiful experiment in physics.

19. Point spread function and transfer function of the EM point spread function(real space) microscope’s transfer function(reciprocal space)

20. Measurement of the aberrations Diffractogram Forweakobjects Amorphous: (Random): White noise object

21. 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

23. Image interpretation at optimum focus Schematic representation of the unit cell of Ti2 Nb10O25

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

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

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

27. Inverting the imaging: from image to exit wave Image wave = object wave * impuls response YIM = YOB*P IIM = |YIM|2 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

28. From HREM images to exit wave

30. 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)

31. zone axis orientationelectron channelling light atoms light atoms heavy atoms heavy atoms

32. 1s-state model (for one column) Mass focus reference wave background position width DW-factor residual aberrations

33. 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)

35. S 5 Al + Cu Amplitude of Phase of total exit wave S 5 Al: Cu Phase of Phase of Courtesy C. Kisielowski, J.R. Jinschek (NCEM, Berkeley)

38. Data mining the object wave • Position of the atom columns (2D,3D) • Weigth of the columns • Single atom sensitivity • Local Tilt • Residual aberrations • .....

39. Argand Plot 1s-state model) Defocus circle mass circle reference wave background position width DW-factor residual aberrations

40. Argand plot of Au (100) (simulations) Single atom sensitivity exit wave - vacuum  = vacuum Courtesy C. Kisielowski, J.R. Jinschek (NCEM, Berkeley)

42. Graphene

44. Atomaire structuur in 3 dimensies 2D beelden van een zilver nanodeeltje in een aluminium matrix [101] [100] Number of Ag atoms from 2 projections S. Van Aert, K.J. Batenburg, M.D. Rossell, R. Erni, G. Van Tendeloo. Nature 470 (2011) 374-377.

45. Atomaire structuur in 3 dimensies Discrete electron tomography 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)

47. Conclusions • 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

48. In-situ heating experimentsSublimation of PbSeMarijn Van Huis (TU Delft)

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