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

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

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Diffraction of “low energy” electrons from free-standing transmission gratings

Ben McMorran and Alex CroninUniversity of Arizona

200 nm

free-standing silicon nitride gratings

note the cross section

SEM basics

objective lens

sample

~3mm to 42mm

100 µm aperture

SEI

+10V

detector

PMT

phosphor

~ +500V

SEM basics

sample

SEI

+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

SEI

~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?

160

140

120

100

80

60

40

20

0

-40 -20 0 20 40

200

150

100

50

0

-60 -40 -20 0 20 40 60

4 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

21

11

2),,,(

rr

qezU o

o{ z

(,z)

r1

r2

calculation of phase due to image charge

21

11

2),,,(

rr

qezU o

path

Ldt1

o{ z

(,z)

r1

r2

calculation of phase due to image charge

2/

2/

),;,(1

,;l

l

ooimage dzzUv

21

11

2),,,(

rr

qezU o

path

Ldt1

o{ z

(,z)

r1

r2

calculation of phase due to image charge

2/

2/

),;,(1

,;l

l

ooimage dzzUv

21

11

2),,,(

rr

qezU o

path

Ldt1

o{ z

(,z)

r1

r2

2/

2/

w

w

oi

n de nimage

no

n

2where

calculation of phase due to image charge

2/

2/

),;,(1

,;l

l

ooimage dzzUv

21

11

2),,,(

rr

qezU o

path

Ldt1

o{ z

(,z)

r1

r2

2/

2/

w

w

oi

n de nimage

no

n

2where

,,,,,* lwEII nnnn

calculation of phase due to image charge

2/

2/

),;,(1

,;l

l

ooimage dzzUv

21

11

2),,,(

rr

qezU o

path

Ldt1

o{ z

(,z)

r1

r2

2/

2/

w

w

oi

n de nimage

no

n

2where

,,,,,* lwEII nnnn

?)(E E = 1 keV v ~ 107 m/s τ ~ 10-14 sec

target

twist axis

Electron beam

So, if we measure diffraction at different twist angles…

…we ought to see something like this:

40

30

20

10

0

x106

-40 -20 0 20 40

0 order

30

20

10

0

x106

-40 -20 0 20 40

+1 order-1 order

20

15

10

5

0

x106

-40 -20 0 20 40

+2 order-2 order

-0.10

-0.05

0.00

0.05

0.10

-40 -20 0 20 40

(I1 - I-1)/(I1 + I-1)

-0.2

-0.1

0.0

0.1

0.2

-40 -20 0 20 40

(I2 - I-2)/(I2 + I-2)

500 eV

grating

1st aperture

target (4 µm wire)

sliding platform

3rd aperture

description of apparatus

description of apparatus

grounding strap

twist lever

tilt stage

diffraction profiles - comparison

120

100

80

60

40

20

0

-60 -40 -20 0 20 40 60

twist = 5±3°, 500 eV

100

80

60

40

20

0

-60 -40 -20 0 20 40 60

twist = 10±2°, 500 eV

60

40

20

0

-60 -40 -20 0 20 40 60

twist = -10±2°, 500 eV

140

120

100

80

60

40

20

0

-60 -40 -20 0 20 40 60

twist = 0±2°, 500 eV

200

150

100

50

0

-60 -40 -20 0 20 40 60

twist = 5±3°, 1.5 keV

140

120

100

80

60

40

20

0

-60 -40 -20 0 20 40 60

twist = 10±2°, 1.5 keV

100

80

60

40

20

0

-60 -40 -20 0 20 40 60

twist = -10±2°, 1.5 keV

150

100

50

0

-60 -40 -20 0 20 40 60

twist = 0±2°, 1.5 keV

140

120

100

80

60

40

20

0

-40 -20 0 20 40

twist = 10±2°, 4 keV

150

100

50

0

-40 -20 0 20 40

twist = 5±3°, 4 keV

160

140

120

100

80

60

40

20

0

-40 -20 0 20 40

twist = -10±2°, 4 keV

160

140

120

100

80

60

40

20

0

-40 -20 0 20 40

twist = 0±2°, 4 keV

10±2°:

5±2°:

0±2°:

-10±2°:

500 eV 1.5 keV 4 keV

data refining

160

140

120

100

80

60

40

20

0

-40 -20 0 20 40

200

150

100

50

0

-60 -40 -20 0 20 40 60

4 keV beam

twist = -10±2°

1.5 keV beam

twist = 5±3°

4 keV beam

twist = -10±2°

160

140

120

100

80

60

40

20

0

-40 -20 0 20 40

200

150

100

50

0

-60 -40 -20 0 20 40 60

1.5 keV beam

twist = 5±3°

data refining

1.5 keV beam

twist = 5±3°

• boil images down to In data – compare to theory

160

140

120

100

80

60

40

20

0

-40 -20 0 20 40

200

150

100

50

0

-60 -40 -20 0 20 40 60

4 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