From Exit Wave to Structure: Is the Phase Object Approximation Useless?

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

5. Advantages of electrons: • 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] • less radiation damage than X-rays[2] • sensitive to ionization of atoms[3]. [1] M. Brown [2] R. Henderson [3] J. Spence

6. Radiation Source Brightness Elastic Mean-Free Absorption Length Minimum Probe Size (particles/cm2 / Path (nm) (nm) (nm) eV/steradian) Neutrons 1024 107 108 106 X rays 1026 103 105 102 Electrons 1029 101 102 10-1 1 Source: NTEAM Project

7. Electron microscope

8. Electron microscope = coherentimaging Image wave = object wave * impuls response YIM = YOB*P IIM = |YIM|2 Deblurring (deconvolution) of the electron microscope 1) retrieve image phase: holography 2) deconvolute the impulse response function 3) reconstruct exit (object) wave

10. Focus variation method

12. transport of intensity equation

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

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

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 light atoms heavy atoms heavy atoms

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

21. Expansion in eigenfunctions of the Hamiltonian: with

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

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

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

25. [001] [110]

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

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

28. 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)

29. Im () 0 0 Re ()

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

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

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

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

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

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

36. Transfer functions Ultimate resolution = atom

37. Resolving atoms = new situation Model based fitting (quantitative) resolution precision resolving refining 1 Å 0.01 Å precision resolution

38. resolution ρ = 1 ÅN= 10000σCR= 0.01 Å ρ dose Å σCR resolution versus precision Precision (error bar)

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

42. Amorphous structures never resolvable in 2D 3D HR Electron Tomography (HRET) data parameters N/a3 < 1.5/r3 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 y-1 should be used instead

45. Current technology: • HAADF-image Focused e-beam • Local energy spectrum Scanning coils Sample HAADF Detector • 0.2 nm • Dislocation core in GaN [0001] Image Filter Scanning Electron Microscopy & HREM & Spectroscopy A STEM / HRTEM : Tecnai G2 • 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 N. Browning, C. Kisielowski, LDRD, 2002-2003

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

47. 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 no image contrast  we need a strategy

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