1. From Exit Wave to Structure: Is the Phase Object Approximation Useless? ° University of Antwerp, Department of Physics, B-2020 Antwerp, Belgium °°NCEM, Lawrence Berkeley Laboratory, U.S.A. D. Van Dyck°, P. Geuens°, C. Kisielowski°°, J.R. Jinschek°° Cairns, Australia July 2, 2003

2. Evolution in Science describe  understand  design macro  micro  nano

4. Evolution in theory Prediction of properties (materials, molecules from “first principles” Ingredients: atom positions with high precision (0.01 Å) experimenttheory

5.  strong interaction  nanostructures  sub surface information  easy to detect  use of lenses (real space  Fourier space)  bright sources “A synchrotron in the electron microscope”[1][1]  less radiation damage than X-rays[2][2]  sensitive to ionization of atoms[3].[3] [1][1] M. Brown [2][2] R. Henderson [3][3] J. Spence Advantages of electrons:

6. RadiationSource BrightnessElastic Mean-Free Absorption Length Minimum Probe Size (particles/cm2 / Path (nm) (nm)(nm) eV/steradian) Neutrons10 24 10 7 10 8 10 6 X rays10 26 10 3 10 5 10 2 Electrons10 29 10 1 10 2 10 -1 1 Source: NTEAM Project

7. Electron microscope

8. Electron microscope = coherentimaging Image wave = object wave * impuls response Deblurring (deconvolution) of the electron microscope 1) retrieve image phase: holography 2) deconvolute the impulse response function 3) reconstruct exit (object) wave    OB *P I IM = |  IM | 2

10. Focus variation method

12. transport of intensity equation

13. Phase of total exit wave  5 Al: Cu Courtesy C. Kisielowski (NCEM,Berkeley) Phase of total exit wave Au [110] wedge

15. Meyer R.R. et al., Science 289 (2000), 1324-1326.

16. The phase object approximation Wavelength of the electron Wavelenght inside the object Relative phase shift

17. Total phase shift Transmission function:  ( x,y) = exp  i  V p (x,y)  Weak object With

18. Zone axis orientation: channelling Atoms superimpose along beam direction Strong scattering Plane wave methods not appropriate Atom column as a new basis

19. From exit wave to structure: channelling theory light atoms heavy atoms light atoms heavy atoms

20. High energy equation: e - feels the mean potential of the atom column:

21. Expansion in eigenfunctions of the Hamiltonian: with

22. Energy Delocalized states Localized 1s state U(x,y) < 0.1 nm S-state model S-state

23. parameterization of the analytic expression of the wave function: fast calculation analytic derivatives

24. S-state model multislice phase amplitude GaN [110] thickness 8 nm 300 keV

25. [001] [110]

26. Exit wave of column Amplitude peaked at the atom column position Phase constant over the atom column

27. Van Dyck D., Op de Beeck M., UM 64 (1996), 99-107. Amplitude ofPhase of Cu Au

28. 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

29. Im (  ) Re (  ) 0 0

30. Au [110] – Vacuum wave Courtesy C. Kisielowski, J.R. Jinschek (NCEM, Berkeley)

31. Re (  )  =  exit wave Im (  )  exit wave -  vacuum  vacuum  = Re (  ) Im (  ) layer 1 layer 2 layer 10 layer 9 Courtesy C. Kisielowski, J.R. Jinschek (NCEM, Berkeley)

32. Au [110] – Vacuum wave Courtesy C. Kisielowski, J.R. Jinschek (NCEM, Berkeley)

33. EW phase image EW amplitude image  exit wave -  vacuum  vacuum  = “vacuum” measured in hole Courtesy C. Kisielowski, J.R. Jinschek (NCEM, Berkeley) Au [110] hole (300 keV)

34.  exit wave -  vacuum  vacuum  = Im (  ) Re (  ) Courtesy C. Kisielowski, J.R. Jinschek (NCEM, Berkeley)

35. counts phase  [rad] Im (  ) Re (  )  amplitude Gauss fitting: sigma  0.1 rad Radial data distribution Averaged amplitude Courtesy C. Kisielowski, J.R. Jinschek (NCEM, Berkeley)

36. Ultimate resolution = atom Transfer functions

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

38. resolution dose ρ = 1 Å N= 10000 σ CR = 0.01 Å Å ρ σ CR resolution versus precision Precision (error bar)

41. Is HREM able to resolve amorphous structures? Requirement: or parametersdata

42. 3D HR Electron Tomography (HRET) parameters data Amorphous structures never resolvable in 2D N/a 3 < 1.5/   2 Ångstrom resolution sufficient in 3D

43. Conclusions All object information can be obtained from the exit wave Single atom sensitivity The phase object approximation is not appropriate The channelling wave  should be used instead

45. Scanning Electron Microscopy & HREM & Spectroscopy A STEM / HRTEM : Tecnai G 2 Scanning coils Sample Focused e-beam HAADF Detector Image Filter Upgrade to HRTEM/STEM @ NCEM in 2002 First instrument of this kind in the US Probe size 0.13 nm (currently at NCEM: ~1 nm) Energy resolution: 200 - 300 meV (currently: ~1eV) Information Limit : < 0.1 nm @ 200 kV Phase Contrast & Z-Contrast & Spectroscopy on identical areas Current technology: HAADF-image Local energy spectrum Dislocation core in GaN [0001] 0.2 nm N. Browning, C. Kisielowski, LDRD, 2002-2003

46. Courtesy: L.M. Brown, Inst. Phys. Conf. Ser. 153 (1997), p. 17-22.

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

49. Spherical aberration corrector? improves the point resolution Chromatic aberration corrector? improves the information limit Monochromator? improves the information limit reduction of electrons Ultramicroscopy 89(2001), 275-290 Do these correctors improve the precision as well?

51. The electron microscope of the future Quantitative 3D structure determination on atomic scale Spectroscopy on atomic scale Flexibility, experiment design Nanolab The ideal instrument for the characterisation of nanostructures