Use of gratings in neutron instrumentation
description
Transcript of Use of gratings in neutron instrumentation
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Use of gratings in neutron instrumentation
F. Ott, A. Menelle, P. Humbert and C. Fermon Laboratoire Léon Brillouin CEA/CNRS Saclay
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Objective
Study of the neutron diffraction on periodical gratings.(produced by lithographic techniques).
Theoretical calculation of the diffraction intensities:– Born / DWBA approximation (fails for large diffraction
intensities)– matrix formalism : full dynamical calculation.
Application of gratings in neutron optics.– Example: energy analyser for time of flight neutron reflectometer
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Outline
Theoretical background
Fabrication of gratings
Energy analysis on a reflectometer using gratings
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Off-specular diffraction geometry
r
kikr
qz
qx
q
i r
q
q
zi r i r
xi r i r
42 2
42 2
sin cos
sin sin
Diffraction condition
q mdx 2
Thin film plane+ grating
Side view
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Modelisation of the grating
Medium - stratified along (Oz)- periodical of period d along (Ox)
it is possible to divide the grating in sub-layers in which the optical index varies as a rectangle function of period d
medium 2, vacuum
medium 1, grating
medium 0, substrate
specular reflexion
diffracted mode +1
diffracted mode -1
n2
n2n1
n0
indices
n0
periodicity d
x
z
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Dynamical calculation : matrix formalism
( , ) ( )x z z enn
i ndx
2
k x c en
i ndx
n
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( )
Continuity conditions at the interfaces
k x02 0 k k n
dn/ / / / 0
2
k V2 N N... ...0
D
u
dD
u
di
i
ii
i
i
1
1
1
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Fabrication of gratings.
Fabrication of periodical gratings by optical U.V. lithography.– Periodicities from 2 to 50 µm, resolution of 1 µm – aspect ratio of the order of 1
développement de la résine
gravure de la couche mince
dissolution de la résine résiduelle
résinecouche mincesubstrat
masque Cr (déposé sur le verre) plaqué sur l'échantillon
verreU.V.
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Etching techniques Dry argon etching: not element specific
– 8 inch etching plant (VEECO)– two small etching guns
Chemical etching: element specific– ex: Ni,Fe: FeCl3
– fast and cheap even over very large areas
Reactive ion etching: element specific– oxygen, SF6, CH4
– no good for multilayers (ex. Ni/Ti)– one vacuum chamber for samples of 50x50
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Etching examples
0
10
20
30
40
0 10 20 30 40 50 60
x (µm)
heig
ht (
nm)
0
20
40
60
80
0 2 4 6 8 10 12
Hei
ght
(nm
)
Chemical etching(Ni etched by FeCl3)
0
100
200
300
0 10 20 30 40 50 60 70 80
X (microns)
Heig
ht
(A°)
Argon etch of a supermirror
Rie (SF6) of glass
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Deposition / Lithography facilities Deposition:
– Sputtering (3 inches)– MBE (limited areas) + sputtering (2 targets)
or use of standard supermirrors (e.g. Swiss Neutronics, Cilas)
Lithography: – clean room with U.V. lithography facility
But limited area: 50x50mm²– electron beam lithography:
very precise but limited in size too
Masks price: (ordered outside) from 1-2 k€
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Off-specular diffraction on a glass grating (periodicity 10 µm, lines width 7 µm)
0.10 0.20 0.30 0.40
-0.003
-0.002
-0.001
0.000
0.001
0.002
0.003
qz (nm-1)
qx (
nm-1
)
Measurement on the time of flight reflectometer EROS (LLB)Detector fixed at 1.5°, scan in the reciprocal space obtained by rocking curves around 0.75°
Specular reflection line
Off-specular diffraction modes
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Increase of the diffraction efficiencies
Increase of the contrast between the incidence medium and the diffraction grating.
Three possibilities :– grating made out of a high index material (Nickel)– incidence medium with an index >1 (Titanium)– use of materials with an «high artificial index» : supermirrors.
Results– under some conditions, efficiencies > 20%– increase of the “diffraction bandwidth”:
- high efficiency for a wide wavelength spectrum- or for a large range of incidence angles.
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Glass grating with and without a Ni coating
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
0 0.01 0.02 0.03 0.04 0.05 0.06
qz (A°-1)
Réfl
ectiv
ity (lo
g sc
ale)
bare glass
Ni coating
Modes 1 (x 10-2)
Modes 2 (x 10-2)
Specular
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Titanium coating(1st order diffraction mode efficiencies)
-3
-2.5
-2
-1.5
-1
-0.5
0
0 0.005 0.01 0.015 0.02 0.025 0.03
qz (A°-1)
Ref
lect
ivity
(lo
g)
0.4°0.75°1.2°
30%
3%
10%
Rocking curves around
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Supermirror gratings
0.001
0.01
0.1
1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
qx = 0
Mode +1 (qx = 0.003 nm-1)
Simulation
Simulation
Réfl
ect
ivit
y
qz (nm-1)
0
0.01
0.02
0.03
0.04
0.05
-0.05 0 0.05
Inte
nsité
(u.
a.)
Qx (100 x Å-1)
Ordre +1
Ordre -1
Spéculaire
The diffracted beam is not much widerthan the specular reflected beam
It is possible to obtain good diffractionefficiencies over a large qz range(0.3 - 0.6 nm-1)
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Time of flight reflectivity
k1
q1
q2k2
x
z
kii r
kr
q
échantillon0.00001
0.0001
0.001
0.01
0.1
1
0 0.5 1 1.5
qz (nm-1)
Refl
ectivi
ty
Cu (30nm) sur Si
q
5 µs pulse Spatial spread
= 2 - 0.2 nm
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Application in neutron instrumentation: Energy analysis.
r i d2 2 2
The diffraction directionis a function of the wavelength
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 0.5 1 1.5 2 2.5
Incidence 0.8°
Diff
ract
ion
dir
ect
ion
(d
eg
ree
s)
Wavelength (nm)
20 µm
10 µm
5 µm
2 µm
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Application on a time of flight spectrometer for energy analysis.
sample
grating
Position sensitivedetector
white beam = 4 to 25 A°
specular reflexion(white beam)
m=0m=+1
m=-1
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Detector view
Specular reflection
Mode 1
200
mm
Mode -1
1.5 nm
0.2 nm
1.5 nm
0.2 nm
Sample horizon
I
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Intensity gain
Use of a white beam a reflectivity curve in a single “shot”.
Study of the evolution of materials or liquids on a time scale of a few minutes
Examples: – liquid interfaces– diffusion, sticking, breaking
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Example: PS-PPMA di-block copolymers Study of the ordering
0 0.1 0.2 0.3 0.4
q (n m -1)
0.00001
0.0001
0.001
0.01
0.1
1
0 200T h ick ness (nm )
0.00
0.04m ark ed p olym er
su bstrate
0 0.1 0.2 0.3 0.4
q (nm -1)
0.00001
0.0001
0.001
0.01
0.1
1
0 200T h ick ness (nm )
0.00
0.04
Su bstrat
M arqu ed p olym er
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Techni project
Fabrication and tests of small prototypes (20x20mm²)
– choice of materials, periodicities, shape of the grating– optimisation in the resolution, useful q range
Comparison with simulations Extension to large surfaces (100x50mm²) Integration on the EROS reflectometer for
measurements on liquids Data processing (deconvolution)
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Conclusion
Off-specular diffraction on grating:– We have shown that is is possible to produce grating which have
diffraction efficiencies as high as 30%– The good diffraction efficiency can be obtained over a rather broad
range of qz or incidence angles.
– This suggests the possibility of building a neutron energy analyser by separating a white neutron beam by diffraction on a grating.
Next steps– Production of gratings over large surfaces– Obtain good diffraction resolutions– Use for the study of the reflectivity on liquids