Diffraction of “low energy” electrons from free-standing transmission gratings Ben McMorran and Alex Cronin University of Arizona
free-standing silicon nitride gratings note the cross section
SEM basics objective lens sample ~3mm to 42mm 100 µm aperture SE I +10V detector PMT phosphor ~ +500V
SEM basics sample SE I +10V detector PMT phosphor ~ +500V objective lens ~3mm to 40mm 100 µm aperture
basic setup to observe diffraction objective lens diffraction grating 4 µm diameter tungsten wire ~30 mm SE I ~40 mm 100 µm aperture
images of 4 micron wire through diffraction grating 4 keV beam twist = -10±2° 1.5 keV beam twist = 5±3°
images of 4 micron wire through diffraction grating 4 keV beam twist = -10±2° 1.5 keV beam twist = 5±3°
images of 4 micron wire through diffraction grating 1.5 keV beam twist = 5±3° 4 keV beam twist = -10±2°
images of 4 micron wire through diffraction grating spacing between orders Δs E -1/2 why is there asymmetry? keV beam twist = -10±2° 1.5 keV beam twist = 5±3°
grating geometry w l gold coating grating bar grating k vector
grating geometry ( ,z) z
grating geometry z ( ,z)
grating geometry ( ,z) z
grating geometry ( ,z) z
grating geometry ( ,z) z
grating geometry ( ,z) z
grating geometry ( ,z) z
grating geometry ( ,z) z
calculation of phase due to image charge o{o{ z ( ,z) r1r1 r2r2
calculation of phase due to image charge o{o{ z ( ,z) r1r1 r2r2
calculation of phase due to image charge o{o{ z ( ,z) r1r1 r2r2
calculation of phase due to image charge o{o{ z ( ,z) r1r1 r2r2 where
calculation of phase due to image charge o{o{ z ( ,z) r1r1 r2r2 where
calculation of phase due to image charge o{o{ z ( ,z) r1r1 r2r2 where E = 1 keV v ~ 10 7 m/s τ ~ sec
target twist axis Electron beam So, if we measure diffraction at different twist angles…
…we ought to see something like this:
grating 1 st aperture target (4 µm wire) sliding platform 3 rd aperture description of apparatus
grounding strap twist lever tilt stage
diffraction profiles - comparison 10±2°: 5±2°: 0±2°: -10±2°: 500 eV 1.5 keV 4 keV
data refining keV beam twist = -10±2° 1.5 keV beam twist = 5±3°
4 keV beam twist = -10±2° keV beam twist = 5±3° data refining
1.5 keV beam twist = 5±3° boil images down to I n data – compare to theory keV beam twist = -10±2° data refining
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
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