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Soft X-Ray
Reflectivity: from
quasi-perfect
mirrors
to accelerator
walls
Franz SchäfersInstitute for Nanometre
Optics and Technology (INT)
2The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Synchrotron Radiation
polarised
pulsed
energy
range
from infrared
to x-rays
calculable
very
intensive
collimated
Synchrotron Radiation
in all colours
Charged particles,moving close to the speed of light
when deflected by Magnets irradiate a “special light”:
BESSY-II
15 Dip-beamlines
~50 mrad
15 kW total power
~ 1 % used
3The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Undulators
and Wigglers
intensité
Devices with a periodic array of magnets (Undulators, Wigglers) implemented in the straight sections of the storage ring produce coherent, polarised
radiation.
3rd Generation Light -
our
Product
4The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
TitlesPhoton-matter interaction (basic optics)
From mirrors to accelerator walls
Reflectometry
Experimental data at BESSY-II
OUTLINE
5The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
A. Simionovici
SAS Berlin 1/2012
6The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
A. Simionovici
SAS Berlin 1/2012
XU
V
7The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Fresnel equations: Reflectance, Transmission
Es,p (r,t)=Eos,p ei(ωt-kr-φs,p)
rs,p =|r|e-iδs,p
Rs,p =|rs,p |2
Ts,p =|ts,p |2
Io =|Eo |2
θ i
θ t
θ i
Snells law:sinθi / sinθt = n1 /n2
n1
n2
Index of refraction:n(λ) = 1 - δ
- ik
Augustin Fresnel1788 - 1827
Willebrord von Ruijen Snell1580 - 1626
8The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
1E-3 0.01 0.1 1 10 100
Photon Energy (keV)
CROMER (Z=2-92) f1 , f2
HENKE (Z=1-92) f1 , f2
MOLECULES (Al2 O3 , SiC, SiO2 …) n, k
PALIK (Al, Au, C, Cr, Cu, Ir, Ni, Os, Pt, Si,…) n, k
OPTICAL DATA TABLES
STRUCTURE FACTORS fo , fH , fHCZinkblendeHexagonalBeryl
Calculation of
• Reflectivity• Efficiency• Transmission• Rocking curves• Photon Flux• Resolving power• Polarisation
EUV VUV XUV soft X hard XVIS UV
9The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
0 10 20 30 40 50 60 70 80 9010-9
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
10 eV
100 eV
1000 eV
Incidence angle (deg.)
Reflectometry
for
beginners:
Phas
eshi
ft Δ
0o
180o
100 eV
0 10 20 30 40 50 60 70 80 900.0
0.2
0.4
0.6
0.8
1.0
Incidence angle (deg.)
10 eV
1000 eV
Rs
Rp
Δ
Fresnel Equations
Ref
lect
ivity
Brewster
angleTotal external
reflection
θC
mirror, n
vacuum
I0
Ir
nC arccos=Θ
⎟⎠⎞
⎜⎝⎛=ΘnB1arctan
θB
E'pmirror, n
vacuum
I0 Ir
It
θB
Normal incidence
Rs,p = ¼ (δ2+β2)
<< 1~45°
SA
RIO
ES
EP
θ
Multilayer nλ=2dsinθ
10The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Fresnel
reflectivity
Al, Cu, SS
100 1000 1000010-4
10-3
10-2
10-1
100
10°15°
20°
6°4°
1°2°
Ref
lect
ivity
Photon energy (eV)
Cuσ=0 nm
0.5°
100 1000 1000010-4
10-3
10-2
10-1
100
10°15°
20°
6°4°
1°2°
Ref
lect
ivity
Photon energy (eV)
Feσ=0 nm
0.5°
100 1000 1000010-4
10-3
10-2
10-1
100
10°15°
20°
6° 4°
1°2°
Ref
lect
ivity
Photon energy (eV)
Alσ=0 nm
0.5°
11The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
TitlesPhoton matter interaction (basic optics)
From mirrors to accelerator walls
Reflectometry
Experimental data at BESSY-II
OUTLINE
12The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
surface with facets
Δα
• Surface
composed
of facets
with
angle Δαi
• beams
are
deflected
by
2·Δαi
• Slope
error
is
the
rms-value
of the
(gaussian)
angular
distribution
of the
surface
facets
Δαi
• Slope
error
gives
rise
to a blurring
of the
image
• Reduction
of specular
intensity
• Debye-Waller
factor
reduces
reflectance
R0
σ: rms
value
of the
height
deviation
Note that
FWHM = 2.3·σ
Real Optics: Slope
errors, Surface
roughness
2sin4
0
⎟⎠⎞
⎜⎝⎛−
= λθπσ i
eRR θi θs
λ
σ
13The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Debye
Waller
factor
XUV-
mirr
orqu
ality
0.1 1 10 100 100010-6
10-5
10-4
10-3
10-2
10-1
100
90°45°
20°
10°
5°
1°
Spe
cula
r ref
lect
ivity
Roughness σ (nm)
Cu λ = 100 nmhν = 12.4 eV
2°
0.1 1 10 100 100010-6
10-5
10-4
10-3
10-2
10-1
100
90°
45°
20°10°
5°
2°
1°
Cu λ = 1 nmhν = 1240 eV
Spe
cula
r ref
lect
ivity
Roughness σ (nm)0 20 40 60 80
10-6
10-5
10-4
10-3
10-2
10-1
100
Cu
Fe
Al
σ = 100 nm λ = 100 nmhν = 12.4 eV
Spe
cula
r ref
lect
ivity
Incidence angle θ (°)
mac
hine
dsu
rfac
es
14The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Courtesy
of V. Yashchuk, ALS
Slop
e
roug
hnes
s
Metrology
on surfaces: PSD -
Power spectral
density
LSFE MSFE HSFE
wide
angle scattersmall
angle scatterwavefront
distortion
λθϕ sin2 hΔ
=
15The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
( ) ( ) ( )( )2
32D, 2 sided4
0
1 16 in idP R s PSD
P dπ θ
ω λ⎛ ⎞
= ⎜ ⎟⎝ ⎠
f
Angular
distribution
of scattered
power
=++…
Rayleigh scattering‚blue
sky‘
factor Mat
eria
l pr
oper
ties
Gra
zing
inci
denc
e
Power spectral
density
• Scattering goes up with energy of the light--fast• Scattering goes down with higher incidence angle• Valid in the ‘smooth surface’
limit!!!
Courtesy
of V. Yashchuk, ALS
Surface
is
sum
over
gratings
16The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Metrology at BESSY NOM -
The Nanometer Optics Measuring Machine
Penta
Prism
idealreal
Reticle
image α = 0
Autocollimator
Illumination
+ reticle
Beam
splitter
CCD line
Collimator
objective
Surface
under
testSurface
under
test
17The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Surface
under
test
Moving
Penta
Prism
idealreal
Reticle
image α = 0
Autocollimator
Illumination
+ reticle
Beam
splitter
CCD line
Collimator
objective
Scanning Penta
Prism –
Set up
α
Reticle
image at angle α
d = f tan(2α)
d
f: focal
length
18The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy18
-0,5
-0,3
-0,1
0,1
0,3
0,5
0 50 100 150 200 250 300
x-position [mm]
slop
e [µ
rad]
A-BB-A
Mirrror
Requirements for todays
X-Ray Optics
achieved: BESSY-II Plane mirrors 300 mm 0.1 μrad (0.02“)
LCLS Refoc. mirror 350 mm 0.05 μrad <1 nm rms
goal: XFEL Plane mirror
800 mm 0.05 μrad (2 nm pv) XFEL Refoc. mirror
800 mm 0.05 μrad
the
tip
of the
needle, not
the
head!
19The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
TitlesPhoton matter interaction (basic optics)
From mirrors to accelerator walls
Reflectometry
Experimental data at BESSY-II
OUTLINE
20The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
eig
ht a
bo
ve
oo
r le
ve
l [m
m]
wal l t oroidal mir ror
pl anemir ror
pl ane grat ing366 l/mm, 1228 l/mm
exi t sli t
dipol
sample
M4GM1 M2
1412
R= 498000
M3
t oroidal mi rror
cyl indri cal mi rr or
re fl ectomet erapertureaperture
rho=1116.3
176.093° 176.8°
177.8°
rho=689.4
rho=33.4R= 74610
+0.5 mrad
top view
side view
2.2 mrad
Collimated
Plane Grating
Monochromator
(PGM)• 10 -
2000 eV
• polarization
linear/elliptical• higher
order light suppression
• low
divergence
At-wavelength
Metrology
-
Optics
Beamline
@BESSY-II
21The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Reflectometer
@ Optics
Beamline
•
3 axis
goniometer•
Vertical
reflecion
(s-pol)•
In sitù
´sample
in-out´: R=I/Io•
Incidence
angle 0°-
87.5°
22The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Optics
beamline
10 100 1000108
109
1010
1011
1012
360 l/mm
150 l/mm
n flu
x (1
/s/0
.1A)
10 100 10001
10
100
1000
Photon flux Energy resolution
23The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
White light irradiation
tests
1 10 100 1000 10000106
107
108
109
1010
1011
1012
1013
1014 photonsat sample in 0-order
4 Au-mirrors (@1.6°,2°,4°,4°)
+ 10 mm MgF2-window
5.3 1015 photons
Pho
tons
(s-1eV
-1)
Photon energy (eV)
7.8 1014 photonsat sample in 0-order
4 Au-mirrors
(@1.6°,2°,4°,4°)
BESSY-II 0.23x1.3 mrad2
100 mA
24The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
0 5 10 15 20 25 3010-6
10-5
10-4
10-3
10-2
10-1
100
E = 340eVTiO2(10 nm)/Si
Ref
lect
ivity
Grazing angle (deg)520 530 540 550
0.4
0.5
0.6O K-edge
A'Ref
lect
ivity
Energy (eV)
HfO2
20nm 100nm
θ=2o
0 5 10 15 20
Cou
nts
(a.u
.)
Detector angle (deg)
substrate
θ θdet
d(θ)
DETECTOR
DETECTOREhν
Reflectometry
-
Reflectivity-
surface
roughness
-
interface
quality-
layer
thickness
-
chemical
composition-
optical
constants
-
TEST DRIVE for
Optics
25The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
1 10 100 1000 100000.1
1
10
100 GaAsP photodiode
Ele
ctro
ns /
phot
on
Photon energy (eV)
I
0 10 20 30 40 50 60 70 80 900.0
0.2
0.4
0.6
0.8
1.0
Incidence angle (deg.)
Reflectometry
facing
reality
beam
heighth=0.25 mm θtan
hL =
θSample
θ=0.5°
L=29 mmθ=1.0°
L=15 mm
• θ−rotation
axis
not
in beam
center• Sample not
in rotation axis• Both• Sample too
short
for
grazing
geometry• Detector
larger than
beam
cross section
• Angular
coupling
θ −
2θ
incorrect:problems
at small
angles• Sample tilt:
problems
at large angles
hν 2θ
no in
form
atio
n
Ref
lect
ivity
Au10 eV
I DetectorGaAsP-diode
Photoyield:electrons/photon
Theory
Experiment
Straylight
26The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
TitlesPhoton matter interaction (basic optics)
From mirrors to accelerator walls
Reflectometry
Experimental data at BESSY-II(Roberto, Takuya, Laura)
OUTLINE
27The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
During three beam periods, we measured six samples:
-
Two Al samples (Al#1 and #2) and two Cu samples (Cu#1 and #2) of Cornell,
-
One Cu sample and one SS sample of ANKA Light Source.
The samples are isolated from the sample holder by Kapton
to also measure the photo yield.
Samples and Sample holder
120 mm
48 mm
28The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Photon Reflectivity vs Photon Energy (CESR Cu sample1)
Photon Energy [eV]
Ref
lect
ivity
Nor
m.
theta:1.5, twotheta:3, HG, rc_ref_0.241theta:1.5, twotheta:3, LG, rc_ref_0.203theta:3, twotheta:6, HG, rc_ref_0.242theta:3, twotheta:6, LG, rc_ref_0.204theta:5, twotheta:10, HG, rc_ref_0.243theta:5, twotheta10, LG, rc_ref_0.205theta:10, twotheta:20, HG, rc_ref_0.244theta:10, twotheta:20, LG, rc_ref_0.206theta:20, twotheta:40, HG, rc_ref_0.245theta:20, twotheta:40, LG, rc_ref_0.207
20 178 336 494 652 810 968 1126 1284 1442 1600
0.00
00.
024
0.04
80.
072
0.09
60.
120
Energy dependence
of Reflectivity
C K-edge
O K-edge
C-edge
O-edge
Reflectivity vs Photon Energy (APS Al flat sample)
Photon Energy [eV]
Ref
lect
ivity
Nor
m.
theta:1.5, twotheta:3, HG, ST_ref_0.28theta:1.5, twotheta:3, LG, ST_ref_0.103theta:3, twotheta:6, HG, ST_ref_0.29theta:3, twotheta:6, LG, ST_ref_0.104theta:5, twotheta:10, HG, ST_ref_0.30theta:5, twotheta:10, LG, ST_ref_0.105theta:10, twotheta:20, HG, ST_ref_0.31theta:10, twotheta:20, LG, ST_ref_0.106theta:20, twotheta:40, HG, ST_ref_0.32theta:20, twotheta:40, LG, ST_ref_0.107
20 336 652 968 1284 1600
0.00
0.08
0.16
0.24
0.32
0.40
Cu L-edge
data from Takuya Ishibashi
29The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Al (ILC) Specular
reflectivity
-
Photoyield
0 200 400 600 800 1000 1200 1400 1600 18000,00E+000
2,00E-012
4,00E-012
6,00E-012
8,00E-012
1,00E-011
1,20E-011
1,40E-011
1,60E-011
Al ILC
phot
oyie
ld n
orm
. to
Iring
=100
mA
energy (eV)
photoyield norm. to Iring=100 mA
d e m o d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o d e m o
0 200 400 600 800 1000 1200 1400 1600 18001E-6
1E-5
1E-4
1E-3
0,01
0,1
phot
oref
lect
ivity
energy (eV)
θ (deg) 1.5 3 5 10
Al ILCd e m o d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o d e m o
d e m o d e m o d e m o d e m o d e m o
30The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Straylight
distribution
(twotheta
scans)
5 10 1510-6
10-5
10-4
10-3
10-2
10-1
100
124 eV
twotheta°
Si
Ref
lect
ivity
θ=5°
●●●●●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
Twotheta scan (CESR Al sample1, 150 eV)
Twotheta [degree]
Inte
nsity
●●●●●●●●●●●●●
●
●
●
●
●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●
●
●
●
●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●
●
●
●
●
●
●
●●●●
●
●
●
●
●
●
●
●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
●
●
●
●
theta:1.5, rc_ref_0.14theta:3, rc_ref_0.18thta:5, rc_ref_0.22theta:10, rc_ref_0.24
0 5 10 15 20 25
0.0e
+00
1.5e−1
03.
0e−1
04.
5e−1
06.
0e−1
07.
5e−1
0
quasi-perfect
mirror accelerator
wall
small angle scatter
wide angle scatter
specular
reflection
31The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Photoyield
250 500 750 1000 1250 15000.0
0.1
0.2
0.3
0.4
0.5
θ=20
θ=10
θ=5
θ=3
Ele
ctro
ns /
phot
on
Photon energy (eV)
CHESR Cu sample #1
θ=1.5
C-k
O-k
Cu 2p
32The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Conclusion
•
Reflectometry
is a nice and indispensible tool for a quality check of optical elements
•
It delivers information on the slope and roughness of the surface and the optical properties -
at the design wavelength
•
Reflectometry
is a multi-dimensional experimental challenge: photon energy, angle, substrate, contamination, non-perfect surfaces (up to sandpaper quality)
•
Scattering is difficult to be treated mathematically -
just on a statistical basis
•
Sample alignment is always a serious issue -
a source of misinterpreting the measured data
•
Nevertheless we’ve measured photon reflectivity and photoyield
for some samples (Al, Cu, and SS) of vacuum chambers at BESSY II
•
Photoyield
data can be transformed quantitatively (electrons/photon)
•
We need to analyze all the data (total 630 data sets) and see how it compares with theory
33The BESSY raytrace program RAYFranz Schäfers, Soft x-ray reflectivity… 5th Electron-cloud Workshop ECLOUD‘12, June 5-9 2012, La Biodola, Italy
Roberto Cimino; LNF, INFN, Italy
Takuya Ishibashi; KEK Accelerator Laboratory, JapanLEPP, Cornell University
Sara Casalbuoni; ANKA, KIT, Germany
Laura Boon; APS
Silvio Künstner; HZB, Institute for Nanometre Optics
Acknowlegement