1

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

3

Outline

Theoretical background

Fabrication of gratings

Energy analysis on a reflectometer using gratings

4

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

22

( )

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