Soft X-Ray Reflectivity: from quasi-perfect mirrors to ......Beryl Calculation of • Reflectivity...

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


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


TitlesPhoton-matter interaction (basic optics)

From mirrors to accelerator walls

Reflectometry

Experimental data at BESSY-II

OUTLINE


A. Simionovici

SAS Berlin 1/2012


A. Simionovici

SAS Berlin 1/2012

XU

V


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


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


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


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


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°


TitlesPhoton matter interaction (basic optics)


Reflectometry


OUTLINE


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


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


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

=


( ) ( ) ( )( )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


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


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!




Reflectometry


OUTLINE


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


Reflectometer

@ Optics

Beamline

•

3 axis

goniometer•

Vertical

reflecion

(s-pol)•

In sitù

´sample

in-out´: R=I/Io•

Incidence

angle 0°-

87.5°


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


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


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


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


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




Reflectometry

Experimental data at BESSY-II(Roberto, Takuya, Laura)

OUTLINE


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


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


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






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







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


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


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


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

http://ankaweb.fzk.de/conferences/Anka%2520student%2520day/ANKA.gif

Soft X-Ray Reflectivity: from quasi-perfect mirrors to ......Beryl Calculation of • Reflectivity...

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Transcript of Soft X-Ray Reflectivity: from quasi-perfect mirrors to ......Beryl Calculation of • Reflectivity...