1. Diffraction of “low energy” electrons from free-standing transmission gratings Ben McMorran and Alex Cronin University of Arizona

2. free-standing silicon nitride gratings note the cross section

3. SEM basics objective lens sample ~3mm to 42mm 100 µm aperture SE I +10V detector PMT phosphor ~ +500V

4. SEM basics sample SE I +10V detector PMT phosphor ~ +500V objective lens ~3mm to 40mm 100 µm aperture

5. basic setup to observe diffraction objective lens diffraction grating 4 µm diameter tungsten wire ~30 mm SE I ~40 mm 100 µm aperture

6. images of 4 micron wire through diffraction grating 4 keV beam twist = -10±2° 1.5 keV beam twist = 5±3°

7. images of 4 micron wire through diffraction grating 4 keV beam twist = -10±2° 1.5 keV beam twist = 5±3°

8. images of 4 micron wire through diffraction grating 1.5 keV beam twist = 5±3° 4 keV beam twist = -10±2°

9. images of 4 micron wire through diffraction grating spacing between orders Δs  E -1/2 why is there asymmetry? 160 140 120 100 80 60 40 20 0 -40-2002040 200 150 100 50 0 -60-40-200204060 4 keV beam twist = -10±2° 1.5 keV beam twist = 5±3°

10. grating geometry   w l gold coating grating bar grating k vector

11. grating geometry  ( ,z) z

12. grating geometry z  ( ,z)

13. grating geometry  ( ,z) z

14. grating geometry  ( ,z) z

15. grating geometry  ( ,z) z

16. grating geometry  ( ,z) z

17. grating geometry  ( ,z) z

18. grating geometry  ( ,z) z

19. calculation of phase due to image charge o{o{ z  ( ,z) r1r1 r2r2

20. calculation of phase due to image charge o{o{ z  ( ,z) r1r1 r2r2

21. calculation of phase due to image charge o{o{ z  ( ,z) r1r1 r2r2

22. calculation of phase due to image charge o{o{ z  ( ,z) r1r1 r2r2 where

23. calculation of phase due to image charge o{o{ z  ( ,z) r1r1 r2r2 where

24. calculation of phase due to image charge o{o{ z  ( ,z) r1r1 r2r2 where E = 1 keV  v ~ 10 7 m/s  τ ~ 10 -14 sec

25. target twist axis Electron beam So, if we measure diffraction at different twist angles…

26. …we ought to see something like this:

27. grating 1 st aperture target (4 µm wire) sliding platform 3 rd aperture description of apparatus

28. grounding strap twist lever tilt stage

29. diffraction profiles - comparison 10±2°: 5±2°: 0±2°: -10±2°: 500 eV 1.5 keV 4 keV

30. data refining 160 140 120 100 80 60 40 20 0 -40-2002040 200 150 100 50 0 -60-40-200204060 4 keV beam twist = -10±2° 1.5 keV beam twist = 5±3°

31. 4 keV beam twist = -10±2° 160 140 120 100 80 60 40 20 0 -40-2002040 200 150 100 50 0 -60-40-200204060 1.5 keV beam twist = 5±3° data refining

32. 1.5 keV beam twist = 5±3° boil images down to I n data – compare to theory 160 140 120 100 80 60 40 20 0 -40-2002040 200 150 100 50 0 -60-40-200204060 4 keV beam twist = -10±2° data refining

33. conclusion have seen diffraction of electrons with energies down to 500 eV through a transmission grating have seen asymmetry in diffraction pattern due to interaction with grating a simple model using image charges seems to explain asymmetry

34. goals more angles with better precision more energies include detector capable of measuring absolute intensity of diffraction orders (not just relative intensity) search for energy-dependent permittivity