Friedrich-Schiller-Universit¨

at 
Jena 
Physikalisch-Astronomische 
Fakult¨

at 


Light 
scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


Dissertation 


zur 
Erlangung 
des 
akademischen 
Grades 
doctor 
rerum 
naturalium 
(Dr. 
rer. 
nat.) 



vorgelegt 
dem 
Rat 
der 
Physikalisch-Astronomischen 
Fakult¨

at 


der 
Friedrich-Schiller-Universit¨

at 
Jena 
von 
Dipl.-Phys. 
Sven 
Schr¨

oder 
geboren 
am 
30. 
Juli 
1975 
in 
Erfurt 



Gutachter 


1. 
Prof. 
Dr. 
rer. 
unnermann 
nat. 
Andreas 
T¨

2. 
Prof. 
Dr. 
rer. 
nat. 
H. 
Angus 
Macleod 
3. 
Prof. 
Dr. 
rer. 
nat. 
Theo 
Tschudi 
Tag 
der 
letzten 
Rigorosumspr¨
ufung: 
8. 
Juli 
2008 
Tag 
der 
¨

offentlichen 
Verteidigung: 
17. 
Juli 
2008 



Contents 


1 
Introduction 
1 


2 
Definitions 
4 


2.1 
Specularreflectanceandtransmittance 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
5 


2.2 
Lightscattering 
............................... 
5 


2.2.1 
Totalscattering 
........................... 
5 


2.2.2 
Angleresolvedscattering 
...................... 
5 


2.2.3 
Bulkscatteringcoefficient 
..................... 
6 


2.3 
Roughness 
.................................. 
6 


2.3.1 
Rmsroughness 
........................... 
6 


2.3.2 
PowerSpectralDensityfunction.................. 
6 


3 
Theoretical 
models 
of 
scattering 
and 
roughness 
9 


3.1 
Specular 
reflectance 
and 
transmittance 
of 
imperfect 
interfaces 
. 
. 
. 
. 
. 
9 


3.2 
Scatteringofsinglesurfaces 
........................ 
10 


3.3 
Scatteringofthinfilmcoatings 
...................... 
12 


3.3.1 
Theoriesforthevisiblespectralrange. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
13 


3.3.2 
X-rayscatteringtheories 
...................... 
15 


3.3.3 
Harmonizationofthesolutions 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
15 


3.4 
Roughness 
and 
roughness 
evolution 
models 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
16 


3.5 
Volumescatteringofbulkmaterials 
.................... 
20 


4 
Independent 
roughness 
measurement 
techniques 
22 


4.1 
Opticalprofilometry 
............................ 
22 


4.2 
Electronmicroscopy 
............................ 
23 


4.3 
X-raymethods 
............................... 
24 


4.4 
Atomicforcemicroscopy 
.......................... 
25 


4.5 
R´esum´e 
................................... 
26 


5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 
28 


5.1 
Instrumentationfor193nm 
........................ 
29 


5.1.1 
Vacuumsystem 
........................... 
30 


5.1.2 
Lightsource 
............................. 
31 



5.1.3 
Beampreparationsystem 
..................... 
31 


5.1.4 
TSset-up 
.............................. 
32 


5.1.5 
ARSset-up 
............................. 
32 


5.1.6 
Detectionsystem 
.......................... 
33 


5.1.7 
Operationandperformance 
.................... 
34 


5.2 
Instrumentationfor13.5nm 
........................ 
36 


5.2.1 
Vacuumsystem 
.......................... 
36 


5.2.2 
Lightsource 
............................ 
37 


5.2.3 
Beampreparationsystem 
..................... 
37 


5.2.4 
Spectralpurityfiltersystem 
.................... 
38 


5.2.5 
ARSset-up 
............................. 
40 


5.2.6 
Detectionsystem 
.......................... 
40 


5.2.7 
Operationandperformance 
.................... 
40 


5.3 
Uncertaintybudget 
............................. 
41 


6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 
44 


6.1 
Coatings 
and 
bulk 
materials 
for 
applications 
at 
193 
nm 
. 
. 
. 
. 
. 
. 
. 
. 
. 
44 


6.1.1 
ARSmodelingmethodology 
.................... 
45 


6.1.2 
Fluoride 
HR 
coatings 
on 
CaF2: 
influence 
of 
substrate 
polish 
. 
. 
53 


6.1.3 
Bulk 
scattering 
of 
synthetic 
fused 
silica 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
62 


6.2 
Coatingsforapplicationsat13.5nm. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
. 
68 


6.2.1 
Roughness 
measurements 
of 
EUV 
mirrors 
using 
193 
nm 
scattering 
69 


6.2.2 
Mo/Si 
mirrors 
on 
fused 
silica: 
influence 
of 
substrate 
polish 
. 
. 
. 
74 


6.2.3 
Characterization 
of 
degradation 
effects 
of 
EUV 
mirrors 
. 
. 
. 
. 
. 
83 


7 
Conclusions 
87 


Bibliography 
90 



Nomenclature 


ACF 
autocorrelation 
function 
AFM 
atomic 
force 
microscopy 
ARS 
angle 
resolved 
scattering 
CS 
Coblentz 
sphere 
DUV 
deep 
ultraviolet 
DWBA 
distorted-wave 
Born 
approximation 
EUV 
extreme 
ultraviolet 
GHS 
generalized 
Harvey-Shack 
theory 
HSFR 
high-spatial 
frequency 
roughness 
LGT 
linear 
growth 
theory 
MSFR 
mid-spatial 
frequency 
roughness 
PMT 
photomultiplier 
tube 
PSD 
power 
spectral 
density 
function 
PSI 
phase-shift 
interferometry 
RR 
Rayleigh-Rice 
theory 
SEM 
scanning 
electron 
microscopy 
TEM 
transmission 
electron 
microscopy 
TS 
total 
scattering 
VPT 
vector 
perturbation 
theory 
XRR 
X-ray 
reflectivity 
XRS 
X-ray 
diffuse 
scattering 



a 
bulk 
scattering 
coefficient 


ß 
dynamic 
scaling 
exponent 


T 
isothermal 
compressibility 


d 
optical 
layer 
thickness 
deviation 




s 
detector 
solid 
angle 


. 
wavelength 


s 
(bandwidth 
limited) 
rms 
roughness 


8 
rms 
roughness 


c 
(lateral) 
correlation 
length 


TSb 
total 
backscattering 


TSf 
total 
forward 
scattering 


d 
thickness 


F 
focal 
length 


f 
spatial 
frequency 


H 
thickness 
of 
one 
multilayer 
period 


kB 
Boltzmann 
constant 
length 
of 
illuminated 
volume 


M 
number 
of 
layers 


N 
multilayer 
period 


n 
index 
of 
refraction 


p 
photoelastic 
coefficient 


Pi 
incident 
power 


R 
specular 
reflectance 


R0 
specular 
reflectance 
of 
ideally 
smooth 
interface 


T 
specular 
transmittance 


Tf 
fictive 
temperature 



1 
Introduction 


The 
progress 
of 
optical 
technology 
towards 
ever 
shorter 
wavelengths 
is 
accompanied 
by 
drastically 
increasing 
demands 
on 
optical 
components. 
For 
optics 
at 
193 
nm 
in 
the 
DUV1 
and 
13.5 
nm 
in 
the 
EUV2 
spectral 
ranges, 
in 
particular 
light 
scattering 
from 
interface 
and 
bulk 
imperfections 
becomes 
crucially 
important 
[2] 
and 
must 
be 
quantified. 
On 
the 
other 
hand, 
scattered 
light 
carries 
information 
about 
its 
origins, 
which 
can 
be 
exploited 
to 
improve 
DUV 
and 
EUV 
optics. 
Unfortunately, 
there 
is 
a 
serious 
lack 
of 
appropriate 
measurement 
and 
analysis 
tools. 
This 
thesis 
is 
therefore 
dedicated 
to 
the 
development 
of 
instrumentation 
as 
well 
as 
of 
measurement 
and 
analysis 
techniques 
for 
the 
thorough 
investigation 
of 
light 
scattering 
at 
193 
nm 
and 
13.5 
nm. 


Semiconductor 
projection 
lithography 
is 
the 
major 
driving 
force 
for 
technological 
developments 
at 
these 
wavelengths. 
However, 
DUV 
radiation 
is 
also 
utilized 
for 
micromachining, 
micro 
surgery, 
and 
ophthalmology 
[3]; 
and 
EUV 
(or 
soft 
X-ray) 
radiation 
enables 
new 
methods 
in 
spectroscopy, 
interferometry, 
and 
astronomy 
[4]. 


The 
resolution 
of 
a 
lithographic 
reduction 
projection 
system 
can 
be 
expressed 
as 
[5]: 
W 
~ 
/NA, 
where 
W 
is 
the 
minimum 
half 
pitch 
of 
the 
structures, 
. 
is 
the 
exposure 
wavelength, 
and 
NA 
is 
the 
numerical 
aperture. 
Consequently, 
the 
urgent 
demand 
for 
ever 
decreasing 
structure 
dimensions 
imposed 
by 
Moore’s 
law 
[6, 
7] 
can 
be 
met 
by 
increasing 
NA 
or 
by 
reducing 
. 
The 
latter 
was 
the 
most 
convenient 
approach 
in 
the 
past. 


Meanwhile, 
DUV 
lithography 
at 
the 
ArF 
excimer 
wavelength 
of 
193 
nm 
has 
become 
the 
state-of-the-art 
technology. 
Further 
reductions 
in 
wavelength, 
however, 
require 
enormous 
effort. 
EUV 
lithography 
at 
13.5 
nm 
is 
the 
most 
promising 
candidate 
for 
next-generation 
lithography. 
Nevertheless, 
several 
critical 
problems 
have 
to 
be 
solved, 
not 
the 
least 
regarding 
optical 
components 
with 
high 
throughput 
and 
stability 
[8, 
9]. 
Full 
implementation 
of 
EUV 
lithography 
is 
planned 
between 
2013 
and 
2016 
[10]. 


To 
bridge 
the 
gap 
until 
EUV 
lithography 
is 
ready 
for 
application, 
193 
nm 
lithography 
is 
being 
pushed 
to 
its 
ultimate 
limit 
using 
sophisticated 
imaging 
techniques 
in 
order 
to 
keep 
pace 
with 
Moore’s 
law 
[7]. 
Recently, 
a 
catadioptric 
immersion 
objective 
with 
NA 
= 
1.35 
was 
presented 
which 
enables 
W 
= 
45 
nm 
utilizing 
193 
nm 
radiation 
[11]. 


1Deep 
ultraviolet 
spectral 
range, 
reaching 
from 
approximately 
300 
nm 
down 
to 
190 
nm. 
2Extreme 
ultraviolet 
spectral 
range, 
between 
5 
nm 
and 
40 
nm 
[1]. 


1 



These 
radical 
developments 
at 
DUV 
and 
EUV 
wavelengths 
lead 
to 
extraordinary 
demands 
on 
optical 
components 
regarding 
low 
losses 
and 
high 
image 
quality. 
Optical 
scattering, 
on 
the 
one 
hand, 
withdraws 
power 
from 
the 
specular 
direction 
and 
reduces 
the 
throughput. 
On 
the 
other 
hand, 
scattered 
radiation 
may 
propagate 
through 
the 
optical 
system. 
In 
particular 
scattering 
within 
the 
field 
of 
view 
of 
an 
imaging 
element 
(near-angle 
scattering 
or 
flare) 
crucially 
influences 
contrast 
and 
resolution 
[12, 
13, 
14]. 
Since 
scattering 
constitutes 
a 
diffraction 
problem, 
it 
exhibits 
a 
strong 
wavelength 
dependence 
(~ 
-2 
, 
~ 
-4). 
Scattering 
becomes 
thus 
even 
more 
critical 
as 
the 
wavelengths 
of 
application 
shift 
from 
the 
visible 
to 
the 
deep 
or 
extreme 
UV 
spectral 
ranges. 


Surfaces, 
coatings, 
and 
materials 
suitable 
for 
DUV 
or 
EUV 
optics 
are 
generally 
much 
more 
difficult 
to 
process 
and 
to 
handle 
than 
their 
counterparts 
for 
longer 
wavelengths 
and 
can 
hardly 
be 
optimized 
with 
respect 
to 
all 
relevant 
parameters 
at 
the 
same 
time 
[15]. 
Therefore, 
thorough 
investigations 
are 
required 
for 
target-oriented 
optimization. 


Yet 
there 
is 
a 
lack 
of 
detailed 
information 
about 
the 
scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 
and 
the 
fundamental 
scattering 
mechanisms. 
Although 
interface 
roughness 
has 
widely 
become 
identified 
as 
a 
crucial 
limiting 
factor 
for 
the 
performance 
of 
DUV 
coatings 
[16, 
17], 
the 
exact 
influence 
of 
the 
substrate 
quality, 
thin 
film 
roughness 
evolution, 
interface 
cross-correlation 
functions, 
and 
layer 
thickness 
deviations 
on 
the 
scattering 
properties 
has 
not 
yet 
been 
completely 
clarified. 
At 
13.5 
nm, 
fundamental 
theoretical 
and 
experimental 
work 
was 
done 
by 
one 
group 
[18, 
14], 
but 
the 
investigations 
were 
performed 
from 
a 
viewpoint 
of 
X-ray 
scattering 
only 
and 
there 
are 
no 
links 
to 
the 
scattering 
of 
optical 
components 
at 
193 
nm. 


Investigating 
the 
scattering 
of 
DUV 
and 
EUV 
optical 
components 
requires 
a 
combination 
of 
appropriate 
measurement 
and 
analysis 
tools. 


Only 
few 
instruments 
have 
become 
available 
that 
are 
capable 
of 
sensitive 
scatter 
measurements 
at 
these 
wavelengths. 
For 
193 
nm, 
only 
instruments 
for 
total 
scatter 
measurements 
are 
reported 
[19, 
17, 
20, 
21]. 
Yet 
angle 
resolved 
scatter 
measurements 
are 
required 
for 
detailed 
investigations 
of 
the 
origins 
of 
scattering. 
Scattering 
measurements 
at 
13.5 
nm 
have 
only 
been 
reported 
from 
synchrotron 
facilities 
in 
the 
US 
and 
Japan 
[18, 
22]. 
Moreover, 
laboratory-size 
instruments 
are 
needed 
for 
investigations 
close 
to 
the 
manufacturing 
process 
of 
optical 
components 
in 
order 
to 
avoid 
extrinsic 
contamination 
and 
degradation 
effects 
from 
obscuring 
the 
intrinsic 
scattering. 


Scattering 
theories 
existing 
for 
the 
visible 
and 
X-ray 
spectral 
ranges 
generally 
require 
a 
large 
number 
of 
input 
parameters, 
which 
often 
inhibits 
the 
analysis 
of 
real 
coatings. 
A 
small 
set 
of 
descriptive 
parameters 
must 
be 
found 
which 
characterize 
the 
scattering 
properties 
and 
clearly 
reveal 
the 
fundamental 
mechanisms. 
Moreover, 
from 
a 
scientific 
point 
of 
view 
as 
well 
as 
for 
the 
optics 
manufacturer, 
it 
is 
interesting 
to 
compare 
the 
relevant 
effects 
in 
the 
two 
different 
spectral 
ranges. 


Therefore, 
a 
self-contained 
concept 
is 
needed 
that 
comprises 
the 
characterization 
of 
the 


2 



scattering 
of 
optical 
components 
at 
both 
wavelengths 
as 
well 
as 
the 
interpretation 
of 
the 
observations 
under 
consolidated 
aspects. 
This 
means, 
a 
comprehensive 
set 
of 
tools 
is 
required 
with 
the 
following 
properties: 
(i) 
compact, 
laboratory-size 
measurement 
systems 
for 
angle 
resolved 
and 
total 
scattering, 
(ii) 
operation 
at 
both 
wavelengths, 
193 
nm 
and 
13.5 
nm, 
(iii) 
implementation 
of 
confirmed 
theoretical 
models 
to 
analyze 
the 
observed 
scattering. 


To 
the 
best 
of 
the 
author’s 
knowledge, 
there 
is 
no 
laboratory 
so 
far 
to 
fulfill 
these 
demands. 
Consequently, 
the 
development 
of 
appropriate 
measurement 
and 
analysis 
tools 
for 
193 
nm 
and 
13.5 
nm 
was 
the 
main 
task 
of 
the 
work 
described 
in 
this 
thesis. 
The 
tools 
were 
then 
utilized 
to 
analyze 
the 
scattering 
properties 
of 
DUV 
and 
EUV 
optical 
components 
in 
order 
to 
understand 
the 
fundamental 
processes, 
to 
develop 
suitable 
scattering 
models, 
and 
to 
support 
further 
improvements 
in 
DUV 
and 
EUV 
optics. 


The 
thesis 
is 
organized 
as 
follows: 


After 
giving 
the 
most 
relevant 
definitions 
required 
for 
this 
thesis 
in 
Sec. 
2, 
theories 
linking 
the 
structural 
properties 
and 
scattering 
of 
single 
surfaces, 
thin 
film 
coatings, 
and 
bulk 
materials 
are 
reviewed 
and 
discussed 
in 
Sec. 
3 
with 
respect 
to 
their 
applicability 
at 
193 
nm 
and 
13.5 
nm. 


Independent 
roughness 
measurement 
techniques 
are 
required 
as 
input 
for 
the 
theories 
to 
investigate 
the 
fundamental 
scattering 
mechanisms. 
Sec. 
4 
therefore 
provides 
a 
survey 
of 
optical, 
X-ray, 
electron, 
and 
scanning 
probe 
methods 
with 
regard 
to 
the 
information 
content 
relevant 
for 
the 
analysis 
of 
DUV 
and 
EUV 
scattering. 


In 
Sec. 
5, 
the 
instruments 
developed 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 
are 
presented. 
The 
description 
of 
each 
instrument 
includes 
a 
detailed 
review 
of 
the 
current 
state-of-the-art 
of 
such 
tools. 


In 
Sec. 
6, 
the 
developed 
measurement 
and 
analysis 
tools 
are 
applied 
to 
investigate 
the 
scattering 
of 
optical 
components 
for 
193 
nm 
and 
13.5 
nm. 
For 
multilayer 
coatings, 
a 
modeling 
procedure 
is 
presented 
which 
enables 
describing 
the 
relevant 
structural 
properties 
using 
a 
small 
set 
of 
illustrative 
parameters. 
The 
impact 
of 
substrate 
roughness 
and 
intrinsic 
thin 
film 
roughness 
on 
the 
scattering 
properties 
of 
multilayer 
coatings 
is 
investigated 
in 
detail, 
and 
quite 
different 
results 
are 
obtained 
for 
DUV 
and 
EUV 
coatings. 
Furthermore, 
several 
methods 
are 
discussed 
to 
investigate 
the 
bulk 
scattering 
of 
synthetic 
fused 
silica 
at 
193 
nm 
by 
separating 
surface 
and 
bulk 
effects. 


3 



2 
Definitions 


For 
the 
investigation 
of 
light 
scattering 
properties 
of 
optical 
components, 
well-defined 
quantities 
are 
required 
to 
provide 
comparable 
and 
reproducible 
measurement 
results. 
Moreover, 
such 
definitions 
are 
essential 
to 
compare 
experimental 
observations 
with 
theoretical 
predictions 
in 
order 
to 
investigate 
the 
fundamental 
scattering 
mechanisms. 
As 
will 
be 
discussed 
in 
Sec. 
3, 
there 
is 
a 
strong 
link 
between 
interface 
roughness 
and 
scattering, 
and 
careful 
roughness 
analysis 
is 
necessary 
to 
compare 
theory 
and 
experiment. 
The 
most 
important 
quantities 
used 
in 
this 
work 
are 
defined 
in 
this 
section. 


The 
basic 
geometry 
for 
the 
definitions 
of 
specular 
and 
scattering 
quantities 
is 
shown 
in 
Fig. 
2.1. 
The 
sample 
(1) 
is 
illuminated 
with 
a 
collimated 
beam 
(2) 
at 
an 
angle 
of 
incidence 
i. 
The 
power 
of 
the 
specularly 
reflected 
beam 
(3) 
leaving 
the 
sample 
at 
r 
= 
i 
depends 
on 
the 
specular 
reflectance 
defined 
in 
Sec. 
2.1. 
Part 
of 
the 
incident 
light 
is 
scattered 
into 
off-specular 
directions 
expressed 
by 
the 
polar 
and 
azimuthal 
angles 
of 
scattering 
s 
and 
s 
(4). 
The 
definition 
of 
angle 
resolved 
scattering 
given 
in 
Sec.2.2 
requires 
normalization 
to 
the 
solid 
angle 


s 
covered 
by 
the 
detector. 
In 
contrast 
to 
interface 
scattering, 
scattering 
generated 
in 
the 
bulk 
of 
the 
sample 
is 
called 
bulk 
or 
volume 
scattering 
(5). 


ir
qq
z
fs
qsDWsyx12345
Figure 
2.1: 
Basic 
geometry 
for 
the 
definitions 
of 
specular 
quantities 
and 
scattering. 
1 
sample, 
2 
-incident 
beam, 
3 
-specularly 
reflected 
beam, 
4 
-scattered 
beam, 
5 
-volume 
scattering, 
i 
-angle 
of 
incidence, 
r 
-angle 
of 
specular 
reflection, 
s 
-scattering 
angle, 
s 
-azimuthal 
angle 
of 
scattering, 


s 
-detector 
solid 
angle. 


4 



2 
Definitions 


2.1 
Specular 
reflectance 
and 
transmittance 
The 
specular 
reflectance 
R 
is 
defined 
as 
the 
specularly 
reflected 
power 
PR 
normalized 


to 
the 
incident 
power 
Pi 
[23]: 
PR

R 
= 
. 
Pi 


The 
specular 
transmittance 
T 
is 
defined 
accordingly 
as 
the 
specularly 
transmitted 
power 
normalized 
to 
Pi 
[23]. 


2.2 
Light 
scattering 
2.2.1 
Total 
scattering 
Total 
backscattering 
TSb 
is 
defined 
as 
the 
backscattered 
power 
Ps 
normalized 
to 
Pi 
[24]: 


Pb

TSb 
= 
, 
(2.1) 
Pi 


where 
the 
range 
of 
scattered 
radiation 
to 
be 
detected 
(range 
of 
acceptance 
angles) 
is 
s 
=2. 
...85. 
and 
s 
=0. 
...360. 
. 


Total 
forward 
scattering 
TSf 
is 
defined 
accordingly 
in 
the 
forward 
hemisphere. 


In 
contrast 
to 
total 
integrated 
scattering 
(TIS) 
[25], 
TS 
is 
defined 
for 
both 
backward 
and 
forward 
scattering 
of 
opaque 
and 
transparent 
samples. 
Moreover, 
TS 
directly 
represents 
the 
scatter 
loss 
of 
an 
optical 
component 
such 
that 
R 
+ 
T 
+ 
A 
+ 
TSb 
+ 
TSf 
should 
yield 
unity 
(energy 
balance), 
where 
A 
denotes 
the 
absorptance. 


2.2.2 
Angle 
resolved 
scattering 
Angle 
resolved 
scattering 
ARS 
is 
defined 
as 
the 
power 

Ps 
scattered 
into 
the 
solid 
angle 


s, 
normalized 
to 


s 
and 
Pi 
[26]: 



Ps(s,s)

ARS(s,s)= 
. 
(2.2) 


Pi

s 




s 
is 
determined 
by 
the 
size 
of 
the 
detector 
aperture 
and 
its 
distance 
to 
the 
sample. 


ARS 
is 
equal 
to 
the 
cosine 
corrected 
BSDF 
(bidirectional 
scatter 
distribution 
function) 
[27, 
28], 
where 
BSDF 
= 
ARS/ 
cos 
s. 


TS 
can 
be 
calculated 
from 
ARS 
by 
integrating 
the 
scattered 
power 
within 
the 
corresponding 
hemisphere. 
For 
the 
simple 
case 
of 
normal 
incidence 
and 
isotropic 
scattering 


5 



2 
Definitions 


(ARS 
independent 
of 
s) 
TSb 
is 
calculated 
as: 


. 
85° 


TSb 
=2p 
ARS 
(s) 
sin 
s 
ds 
. 
(2.3) 


2° 


2.2.3 
Bulk 
scattering 
coefficient 
In 
lossy 
bulk 
materials, 
the 
decrease 
of 
the 
internal 
transmittance 
Tint 
along 
the 
path 
length 
d 
can 
be 
described 
by 
the 
Lambert-Beer 
law 
[29]: 


Tint 
~ 
exp 
{- 
(µ 
+ 
) 
d} 
, 
(2.4) 


where 
µ 
denotes 
the 
absorption 
coefficient 
and 
a 
is 
the 
bulk 
scattering 
coefficient. 


The 
total 
loss 
coefficient 
(µ 
+ 
) 
can 
be 
determined 
via 
T 
measurements. 
However, 
this 
does 
not 
allow 
distinguishing 
between 
absorption 
and 
scatter 
losses. 


2.3 
Roughness 
Several 
works 
are 
dedicated 
to 
the 
statistical 
formulation 
of 
roughness 
properties 
in 
detail 
[27, 
30, 
31, 
32]. 
The 
most 
important 
fundamentals 
required 
in 
this 
work 
are 
summarized 
in 
this 
section. 


2.3.1 
Rms 
roughness 
The 
rms 
roughness 
is 
defined 
as 
the 
standard 
deviation 
of 
the 
interface 
topography 
z(x, 
y) 
from 
the 
mean 
value 
z: 


1 
. 
L. 
L 
21 


[z 
(x, 
y) 
- 
z¯]2 
dx 
dy

8 
= 
lim 


. 


(2.5) 
L!8 
L200 


The 
rms 
roughness 
is 
a 
measure 
for 
the 
vertical 
distribution 
of 
surface 
heights. 
To 
describe 
also 
the 
lateral 
structural 
properties, 
a 
more 
general 
function 
is 
needed. 


2.3.2 
Power 
Spectral 
Density 
function 
The 
2-dimensional 
power 
spectral 
density 
function 
PSD 
is 
defined 
as 
the 
squared 
modulus 
of 
the 
Fourier 
transform 
of 
the 
interface 
topography: 


. 
L. 
L 


z 
(x, 
y) 
e 


-j2(fxx+fyy)dx 
dy 


2 


. 
(2.6) 


1 


PSD2 
(fx,fy) 
= 
lim 


L!8 


L2 


00 


6 



2 
Definitions 


The 
PSD 
expresses 
the 
power 
of 
different 
roughness 
components 
in 
terms 
of 
the 
(lateral) 


surface 
spatial 
frequencies 
fx 
and 
fy. 


Surfaces 
generated 
by 
stochastic 
processes, 
such 
as 
grinding, 
polishing, 
etching, 
and 
thin 
film 
growth, 
often 
exhibit 
isotropic 
roughness 
corresponding 
to 
a 
PSD 
with 
a 
polar 
symmetry. 
The 
2D-isotropic 
PSD, 
which 
is 
used 
throughout 
this 
work 
after 
verification 
of 
isotropy, 
is 
calculated 
by 
averaging 
the 
2D 
PSD 
over 
all 
azimuthal 
directions: 


. 
2

1 


PSD 
(f) 
= 
PSD2 
(f, 
')d. 
(2.7) 


2p 


0 


using 
the 
transformations: 


fy

f 
= 
fx 
2 
+ 
fy 
2 
,. 
= 
arctan 
. 
(2.8) 
fx 


Every 
real 
profile 
or 
roughness 
measurement 
technique 
is 
confined 
to 
a 
certain 
spatial 
frequency 
range, 
which 
is 
limited, 
for 
instance, 
by 
the 
investigated 
surface 
area 
and 
the 
instrumental 
resolution. 
The 
(bandwidth 
limited) 
rms 
roughness 
can 
be 
calculated 
as 
integral 
of 
the 
PSD: 


. 
fmax 
21 


s 
=2f 
PSD 
(f)df, 
(2.9) 


fmin 
where 
the 
integration 
limits 
depend 
on 
the 
application 
at 
hand 
(or 
measurement 
technique 
used). 


In 
the 
limits 
fmin 
. 
0 
and 
fmax 
!8 
it 
can 
be 
shown 
that 
s 
. 
1. 
A 
review 
of 
the 


bandwidth 
limits 
of 
relevant 
roughness 
measurement 
techniques 
is 
given 
in 
Sec. 
4. 


A 
theoretically 
equivalent 
description 
of 
surface 
roughness 
is 
provided 
by 
the 
surface 
autocorrelation 
function 
ACF, 
which 
for 
isotropic 
roughness 
is 
defined 
as 
[33]: 


. 
L

1 


ACF() 
= 
lim 
z 
(x)z(x 
+ 
)dx, 
(2.10) 


L!8 
L 


0 


with 
the 
lag 
length 
. 


The 
correlation 
length 
c 
is 
defined 
as 
the 
lateral 
spacing 
at 
which 
the 
ACF 
drops 
to 
1/e 
of 
its 
maximum 
value. 
ACF 
and 
PSD 
contain 
both 
vertical 
and 
lateral 
information 
about 
surface 
roughness 
(e.g. 
rms 
roughness 
and 
correlation 
length). 
They 
form 
a 
Fourier 
transform 
pair 
and 
are 
thus 
equivalent. 


However, 
only 
PSDs 
provide 
a 
direct 
representation 
of 
bandwidth 
limits. 
Use 
of 
PSDs 
enables 
a 
quantitative 
comparison 
and 
combination 
of 
different 
roughness 
measurement 
techniques, 
which 
will 
be 
shown 
to 
be 
essential 
for 
the 
interpretation 
of 
roughnessinduced 
light 
scattering. 
Furthermore, 
as 
will 
be 
shown 
in 
Sec. 
3, 
ARS 
of 
rough 
surfaces 
is 
directly 
proportional 
to 
the 
PSD. 
Hence, 
the 
PSD 
is 
regarded 
as 
the 
most 
convenient 
description 
of 
the 
roughness 
properties 
of 
the 
surfaces 
investigated 
in 
this 
work. 


7 



2 
Definitions 


In 
practice, 
surface 
topography 
is 
sampled 
with 
a 
finite 
number 
of 
points. 
The 
integral 
expressions 
given 
above 
are 
therefore 
replaced 
by 
discrete 
forms 
[34], 
sometimes 
introducing 
apodization 
functions 
to 
suppress 
numerical 
artifacts 
[35]. 


In 
the 
next 
section, 
theories 
will 
be 
presented 
which 
provide 
a 
direct 
link 
between 
the 
structural 
properties 
and 
the 
scattering 
of 
surfaces, 
thin 
film 
coatings, 
and 
bulk 
materials. 


8 



3 
Theoretical 
models 
of 
scattering 
and 
roughness 


Appropriate 
theoretical 
models 
for 
the 
scattering 
from 
surfaces, 
thin 
film 
coatings, 
and 
bulk 
materials 
are 
required 
for 
two 
reasons: 
On 
the 
one 
hand, 
comparing 
theories 
and 
measurement 
results 
enables 
investigations 
of 
the 
origins 
of 
the 
observed 
scattering. 
On 
the 
other 
hand, 
theories 
allow 
predicting 
the 
scattering 
of 
optical 
components 
in 
arbitrary 
practical 
situations 
or 
prior 
to 
manufacturing. 
The 
most 
relevant 
scattering 
theories 
and 
roughness 
models 
existing 
in 
the 
literature 
are 
summarized 
in 
this 
section. 


3.1 
Specular 
reflectance 
and 
transmittance 
of 
imperfect 
interfaces 
The 
specular 
reflectance 
and 
transmittance 
of 
a 
plane 
surface 
depend 
on 
the 
optical 
properties 
of 
the 
media 
involved 
as 
well 
as 
on 
the 
conditions 
of 
illumination 
(angle 
of 
incidence, 
polarization). 
Calculations 
for 
perfectly 
smooth 
interfaces 
can 
be 
performed 
using 
the 
Fresnel 
equations, 
which 
can 
be 
found 
in 
practically 
every 
text 
book 
concerned 
with 
physical 
optics, 
e.g. 
in 
[36]. 


The 
specular 
properties 
of 
ideally 
smooth 
multilayer 
coatings 
are 
advantageously 
calculated 
via 
matrix 
formalisms 
[37, 
38, 
36]. 
Throughout 
this 
work, 
optical 
constants 
were 
obtained 
from 
the 
database 
implemented 
in 
the 
thin 
film 
software 
IMD 
[39], 
which 
contains 
data 
of 
[40] 
and 
[41]. 
Alternatively, 
data 
were 
provided 
directly 
by 
the 
manufacturers 
of 
the 
corresponding 
samples. 


Interface 
roughness 
reduces 
the 
specular 
reflectance 
expected 
for 
an 
ideally 
sharp 
and 
smooth 
boundary. 
Part 
of 
the 
specular 
power 
is 
redistributed 
into 
off-specular 
scattering. 
Roughness 
components 
with 
lateral 
dimensions 
below 
the 
wavelength 
of 
light 
(sub-wavelength 
roughness) 
induce 
a 
redistribution 
of 
specular 
power 
between 
the 
reflection 
and 
transmission 
directions 
[14, 
42, 
43]. 


For 
a 
single 
interface, 
the 
roughness-induced 
modification 
of 
the 
specular 
reflectance 
is 
usually 
calculated 
using 
a 
Debye-Waller 
factor 
[42, 
44, 
45]: 


9 



3 
Theoretical 
models 
of 
scattering 
and 
roughness 


2

4s 


R 
= 
R0 
exp 
- 
cos 
i 
, 
(3.1) 


. 


where 
R0 
denotes 
the 
reflectance 
of 
the 
ideal 
surface. 
The 
limitations 
of 
this 
estimation 
are 
discussed 
in 
connection 
with 
the 
scattering 
theories 
presented 
in 
the 
next 
section. 


N´evot 
and 
Croce 
described 
the 
effect 
of 
finite 
interface 
width 
by 
modified 
Fresnel 
amplitude 
coefficients. 
For 
the 
reflection 
coefficient 
r 
[46, 
47]: 


r 
= 
r0 
exp 
-2k0k12 
, 
(3.2) 


where 
k0 
and 
k1 
are 
the 
perpendicular 
components 
(with 
respect 
to 
the 
interface) 
of 
the 
incident 
and 
refracted 
waves, 
respectively. 
Equation 
(3.2) 
was 
argued 
to 
be 
valid 
for 
c 
. 
. 
only. 


For 
multilayer 
coatings, 
the 
effect 
of 
interface 
roughness 
is 
typically 
included 
by 
using 
modified 
Fresnel 
amplitude 
coefficients 
at 
each 
interface 
as 
described 
in 
[14, 
39]. 


3.2 
Scattering 
of 
single 
surfaces 
In 
the 
last 
century, 
theories 
were 
developed 
to 
describe 
the 
light 
scattering 
from 
rough 
and 
slightly 
rough 
surfaces. 
Scalar 
theories 
are 
based 
on 
Kirchhoff 
diffraction 
theory 
[45]. 
However, 
vector 
theory 
is 
required 
to 
accurately 
describe 
the 
angular 
distribution 
of 
scattering 
[48]. 


Vector 
perturbation 
theories 
(VPTs) 
were 
first 
developed 
by 
Rayleigh 
[49] 
and 
Rice 
[50]. 
Church 
introduced 
the 
approach 
into 
the 
optics 
literature 
[51]. 


The 
basic 
procedure 
of 
VPT 
is 
to 
solve 
Maxwell’s 
equations 
for 
the 
ideally 
smooth 
surface 
and 
to 
replace 
the 
interface 
roughness, 
which 
induces 
the 
perturbation 
of 
the 
specular 
field, 
by 
a 
plane 
carrying 
surface 
currents 
which 
act 
as 
sources 
of 
scattered 
plane 
waves 
[52]. 


The 
Rayleigh-Rice 
VPT 
result 
for 
the 
ARS 
of 
a 
slightly 
rough 
single 
surface 
is 
[27]: 


ARS 
(s)= 
16


42 
cos 
i 
cos 
2 
sQ 
PSD 
(f) 
. 
(3.3) 


. 
denotes 
the 
wavelength 
of 
light. 
Q 
is 
the 
optical 
factor 
and 
contains 
all 
information 
on 
the 
corresponding 
perfectly 
smooth 
surface 
such 
as 
the 
dielectric 
constant 
and 
the 
conditions 
of 
illumination 
and 
observation 
(angles 
of 
incidence 
and 
scattering, 
polarization 
states). 
Q 
can 
be 
interpreted 
as 
a 
generalized 
Fresnel 
reflectance 
of 
the 
scattering 
surface. 
Explicit 
formulas 
are 
given 
in 
[27]. 


10 



3 
Theoretical 
models 
of 
scattering 
and 
roughness 


The 
link 
between 
spatial 
frequencies 
and 
scattering 
angles 
is 
given 
by 
the 
grating 
equation. 
For 
in-plane 
scattering 
(s 
= 
0): 


|sin 
s 
- 
sin 
i|

f 
= 
. 
(3.4) 


. 


Hence, 
considering 
the 
surface 
as 
superposition 
of 
gratings 
with 
different 
amplitudes, 
periods 
(~ 
1/f), 
and 
phases, 
the 
scattering 
distribution 
is 
simply 
a 
composition 
of 
the 
corresponding 
first 
order 
diffracted 
intensities1 
. 


Eq. 
(3.4) 
illustrates 
that 
the 
actual 
impact 
of 
a 
certain 
roughness 
component 
onto 
the 
scattering 
properties 
depends 
on 
both 
f 
and 
. 
In 
the 
EUV 
community, 
bandwidthlimited 
roughness 
values 
were 
defined 
with 
respect 
to 
their 
influence 
on 
the 
performance 
[54]. 
Mid-spatial 
frequency 
roughness 
(MSFR, 
0.001 
µm-1 
<f< 
1 
µm-1) 
is 
relevant 
for 
near-angle 
scattering 
at 
13.5 
nm 
with 
0.001. 
<s 
< 
1, 
which 
reduces 
the 
image 
contrast 
[12]. 
High-spatial 
frequency 
roughness 
(HSFR, 
f> 
1 
µm-1) 
is 
associated 
with 
losses 
caused 
by 
diffuse 
scattering 
(1 
µm-1 
<f< 
74 
µm-1) 
and 
redistribution 
of 
power 


-1) 
2

from 
specular 
reflection 
to 
transmission 
(f> 
74 
µm. 
Nevertheless, 
the 
relevant 
bandwidth 
limits 
depend 
on 
the 
actual 
wavelength 
of 
interest 
and 
the 
application 
at 
hand 
(e.g. 
field 
of 
view). 
Spatial 
frequencies 
corresponding 
to 
important 
scatter 
angles 
at 
193 
nm 
and 
13.5 
nm 
for 
normal 
incidence 
are 
shown 
in 
Tab. 
3.1. 


s 
193 
nm, 
f 
(µm-1) 
13.5 
nm, 
f 
(µm-1) 


0.1. 
0.01 
0.1 
2. 
0.2 
2.6 
85. 
5.2 
73.8 


Table 
3.1: 
Spatial 
frequencies 
corresponding 
to 
important 
scatter 
angles 
at 
193 
nm 
and 


13.5 
nm 
(i 
= 
0). 
The 
Rayleigh-Rice 
(RR) 
result 
(Eq. 
(3.3)) 
provides 
a 
direct 
solution 
to 
the 
inverse 
scattering 
problem; 
PSD 
can 
be 
measured 
via 
ARS: 


4 
PSDRR 
(f) 
= 
ARS(s) 
. 
(3.5) 


162 
cos 
i 
cos2 
sQ

Roughness 
measurements 
via 
light 
scattering 
have 
the 
advantage 
of 
avoiding 
numerical 
problems 
arising 
if 
PSDs 
are 
calculated 
by 
using 
discrete 
Fourier 
transforms 
of 
sampled 
surface 
data. 


Recently, 
a 
new 
”quasi-vectorized” 
scalar 
scattering 
theory, 
the 
generalized 
Harvey-
Shack 
(GHS) 
theory, 
was 
proposed 
[55]. 
The 
GHS 
result 
suggests 
a 
correction 
to 
the 
Rayleigh-Rice 
result: 


1Higher 
diffraction 
orders 
can 
be 
neglected 
as 
long 
as 
s 
. 
. 
[53]. 
2A 
slightly 
different 
definition 
of 
the 
bandwidth 
limits 
for 
HSFR, 
1 
µm-1 
<f 
< 
50 
µm-1, 
was 
used 
in 
[54]. 
It 
turns 
out, 
however, 
that 
the 
quantitative 
difference 
for 
typical 
surfaces 
is 
negligible. 


11 



3 
Theoretical 
models 
of 
scattering 
and 
roughness 


cos 
i 
cos 
s

PSDGHS(f)=4 
PSDRR(f) 
. 
(3.6) 


(cos 
i 
+ 
cos 
s)2 


The 
correction 
factor 
is 
˜ 
1 
for 
small 
i 
and 
s, 
but 
decreases 
rapidly 
as 
these 
angles 


approach 
90. 
. 
Although 
still 
under 
discussion 
[56, 
57], 
both 
the 
RR 
and 
the 
GHS 
results 
will 
be 
considered 
in 
this 
work. 


Theoretical 
expressions 
for 
the 
TS 
of 
single 
surfaces 
have 
been 
retrieved 
from 
scalar 
theories 
[42] 
as 
well 
as 
by 
integration 
of 
Eq. 
(3.3) 
[44]. 
For 
total 
backscattering: 


..
2 


TSb 
= 
R04s 
if 
c 
. 
. 
(3.7) 


. 
64422 


c

TSb 
= 
R034 
if 
c 
. 
. 
(3.8) 


Hence, 
the 
scatter 
loss 
exhibits 
a 
wavelength 
scaling 
between 
~ 
-2 
and 
~ 
-4 
de


pending 
on 
the 
lateral 
dimension 
of 
the 
dominating 
structures. 
For 
c 
. 
, 
the 
rms 
roughness 
can 
be 
directly 
measured 
via 
TS. 
It 
is 
interesting 
to 
note 
that 
Eq. 
(3.7) 
is 
identical 
with 
the 
first 
order 
Taylor 
expansion 
of 
Eq. 
(3.1). 


On 
transparent 
samples, 
scattering 
occurs 
at 
the 
front 
and 
the 
rear 
surfaces. 
Theories 
for 
this 
case 
are 
given 
in 
[42, 
58]. 
As 
a 
rule 
of 
thumb, 
for 
a 
sample 
with 
an 
index 
of 
refraction 
of 
n 
˜ 
1.5 
and 
identical 
front 
and 
rear 
surfaces, 
TSb 
is 
approximately 
3 
times 
the 
value 
of 
a 
single 
surface 
[59]. 


3.3 
Scattering 
of 
thin 
film 
coatings 
Scattering 
of 
thin 
film 
coatings 
arises 
from 
roughness 
of 
the 
interfaces 
between 
different 
layers 
as 
well 
as 
from 
fluctuations 
of 
the 
dielectric 
properties 
in 
the 
bulk 
of 
the 
layers. 
However, 
because 
of 
the 
large 
variation 
of 
the 
dielectric 
function 
at 
the 
interfaces, 
roughness-induced 
scattering 
usually 
dominates 
the 
overall 
scattering 
[60]. 


During 
the 
past 
decades, 
several 
theories 
for 
the 
description 
of 
the 
scattering 
of 
multilayer 
coatings 
were 
developed 
in 
different 
scientific 
communities. 
In 
the 
visible 
light 
optics 
community, 
vector 
perturbation 
theories 
based 
on 
the 
results 
for 
single 
surfaces 
(Sec. 
3.2) 
are 
generally 
used. 
For 
x-ray 
and 
neutron 
optics, 
theories 
have 
been 
developed 
in 
the 
so 
called 
distorted-wave 
Born 
approximation 
(DWBA). 
The 
individual 
approaches 
provoked 
the 
development 
of 
different 
terms 
and 
views. 
As 
a 
result, 
DUV 
scattering 
was 
initially 
only 
modeled 
using 
VPT, 
while 
EUV 
scattering 
was 
interpreted 
using 
DWBA. 
A 
harmonization 
of 
the 
different 
approaches 
and 
a 
transfer 
of 
concepts 
could 
bring 
benefits 
for 
both 
communities. 
In 
[61], 
VPT 
and 
DWBA 
were 
compared 
for 
single 
layers. 
However, 
no 
attempts 
have 
been 
reported 
so 
far 
to 
investigate 
the 
similarities 
of 
the 
theories 
or 
to 
extend 
the 
comparison 
to 
multilayer 
coatings. 


12 



3 
Theoretical 
models 
of 
scattering 
and 
roughness 


3.3.1 
Theories 
for 
the 
visible 
spectral 
range 
Based 
on 
theories 
for 
single 
surfaces, 
scalar 
and 
vector 
theories 
were 
developed 
to 
describe 
the 
scattering 
from 
multilayer 
coatings 
in 
the 
visible 
spectral 
range 
[42, 
52, 
62]. 
Again, 
vector 
theory 
is 
required 
to 
accurately 
model 
ARS. 


The 
basic 
procedure 
of 
VPT 
for 
multilayer 
coatings 
is 
to 
solve 
Maxwell’s 
equations 
for 
the 
perfectly 
smooth 
multilayer. 
The 
roughness 
of 
the 
i-th 
interface 
induces 
scattered 
plane 
waves 
driven 
by 
the 
field 
intensities 
at 
the 
interface. 
The 
scattered 
fields 
from 
all 
interfaces 
are 
propagated 
through 
the 
multilayer. 
Superposition 
of 
the 
contributions 
of 
all 
interfaces 
results 
in 
interference 
effects 
of 
the 
scattered 
radiation 
depending 
on 
the 
degree 
of 
coherence 
of 
the 
roughness 
of 
the 
interfaces. 
For 
a 
multilayer 
consisting 
of 
M 
layers, 
ARS 
can 
be 
modeled 
as 
[48, 
52, 
63, 
64]: 


MM

1 


ARS 
(s)= 
4 
CiCj 
* 
PSDij 
(f) 
. 
(3.9) 
i=0 
j=0 


The 
optical 
factors 
Ci 
contain 
all 
information 
about 
the 
corresponding 
perfectly 
smooth 
multilayer 
(without 
the 
roughness 
properties), 
such 
as 
the 
dielectric 
constants 
and 
the 
conditions 
of 
illumination 
and 
observation 
(wavelength 
of 
light, 
angles 
of 
incidence 
and 
scattering, 
polarization 
states). 
The 
PSDij 
are 
interface 
cross-correlation 
PSDs 
(i 
6

= 
j), 
and 
PSDii 
is 
the 
PSD 
of 
the 
i-th 
interface 
(see 
Fig. 
3.1). 



Figure 
3.1: 
Schematic 
of 
scattering 
of 
a 
multilayer 
coating. 


As 
will 
be 
shown 
in 
this 
work, 
the 
interference 
of 
scattered 
light 
from 
different 
interfaces 
(through 
optical 
factors 
and 
cross-correlation 
functions) 
crucially 
influences 
the 
scattering 
properties 
of 
multilayer 
coatings 
in 
addition 
to 
the 
purely 
roughness-induced 
effects. 


Exact 
calculation 
of 
Eq. 
(3.9) 
requires 
knowledge 
of 
M 
+ 
1 
interface 
PSDs 
and 
M(M 
+ 
1)/2 
cross-correlation 
PSDs, 
hence 
~ 
M2 
functions. 
In 
particular 
for 
HR 
coatings 


13 



3 
Theoretical 
models 
of 
scattering 
and 
roughness 


with 
M 
. 
10 
(DUV 
mirrors) 
to 
M 
. 
40 
(EUV 
mirrors), 
this 
means 
a 
practically 
intractable 
task. 
Yet 
the 
number 
of 
parameters 
can 
be 
drastically 
reduced 
using 
appropriate 
roughness 
and 
cross-correlation 
models 
for 
the 
relevant 
interfaces 
[16]. 
The 
most 
common 
cross-correlation 
models 
are 
uncorrelated, 
fully 
correlated, 
and 
partially 
correlated 
roughness. 


The 
uncorrelated 
roughness 
model 
assumes 
that 
the 
roughness 
of 
each 
layer 
is 
entirely 
independent 
of 
the 
underlying 
structure. 
Hence, 
all 
cross-correlation 
PSDs 
vanish. 


The 
fully 
correlated 
roughness 
model 
assumes 
that 
all 
layers 
perfectly 
replicate 
the 
underlying 
structure. 
Consequently, 
all 
interface 
and 
cross-correlation 
PSDs 
are 
identical 
to 
the 
substrate 
PSD. 
The 
top-down 
correlated 
roughness 
model 
is 
similar 
to 
the 
fully 
correlated 
roughness 
model, 
but 
all 
PSDs 
are 
assumed 
to 
be 
equal 
to 
the 
top-surface 
PSD. 


The 
most 
general 
model 
is 
the 
partial 
correlation 
model, 
which 
represents 
a 
transition 
between 
fully 
correlated 
and 
uncorrelated 
roughness, 
as 
will 
be 
discussed 
in 
the 
next 
section. 
In 
[64], 
the 
corresponding 
cross-correlation 
PSDs 
are 
explicitly 
given 
as 
low-pass 
filters. 
Low-spatial 
frequency 
roughness 
components 
are 
perfectly 
replicated, 
and 
uncorrelated 
intrinsic 
thin 
film 
roughness 
components 
enhance 
the 
high-spatial 
frequency 
roughness. 
A 
similar 
approximation 
presented 
in 
[16]: 
PSDij 
= 
PSDkk 
with 
k 
= 
min{i, 
j} 
is 
used 
for 
the 
calculations 
in 
this 
thesis. 


Already 
in 
[48], 
experimental 
data 
of 
ARS 
curves 
at 
. 
= 
633 
nm 
were 
found 
to 
be 
in 
good 
agreement 
with 
VPT 
modeling 
based 
on 
PSDs 
from 
profilometric 
data. 
In 
[65], 
Elson’s 
results 
were 
fitted 
to 
ARS 
curves 
of 
single 
surfaces 
measured 
in 
the 
soft 
x-ray 
spectral 
range. 
Prior 
to 
the 
present 
work, 
comparisons 
of 
theory 
and 
experiment 
at 
193 
nm 
could 
only 
be 
performed 
for 
total 
scattering 
[16]. 
However, 
as 
will 
be 
shown 
in 
this 
thesis, 
there 
are 
considerable 
scattering 
effects 
which 
can 
only 
be 
observed 
by 
analyzing 
the 
angle 
resolved 
scattering. 


For 
ARS 
calculations, 
a 
software 
code 
based 
on 
the 
vector 
perturbation 
theory 
of 
[52] 
is 
used 
[66]. 
The 
TS 
of 
multilayer 
coatings 
can 
be 
determined 
from 
the 
ARS 
curves 
by 
numerical 
integration, 
which 
avoids 
the 
difficulties 
associated 
with 
the 
ranges 
of 
validity 
of 
Eqs. 
(3.7) 
and 
(3.8). 
Only 
for 
the 
special 
case 
of 
fully 
correlated 
interfaces 
and 
c 
. 
, 
TS 
can 
also 
be 
approximated 
using 
Eq. 
(3.7) 
by 
replacing 
R 
with 
the 
effective 
reflectance 
of 
the 
multilayer 
(single-surface 
approximation). 
Consequently, 
applying 
Eq. 
(3.1) 
to 
multilayer 
coatings 
[67, 
68] 
inherently 
implies 
fully 
correlated 
interfaces. 


Theories 
describing 
volume 
scattering 
in 
thin 
film 
layers 
are 
discussed 
in 
[26, 
69, 
70, 
71]. 
However, 
because 
of 
the 
typically 
larger 
discontinuity 
of 
the 
dielectric 
properties 
at 
the 
boundary 
between 
two 
media, 
interface 
scattering 
is 
expected 
to 
be 
the 
dominant 
mechanism 
for 
the 
scattering 
of 
thin 
film 
coatings 
[72]. 


14 



3 
Theoretical 
models 
of 
scattering 
and 
roughness 


3.3.2 
X-ray 
scattering 
theories 
In 
the 
1980s 
and 
1990s, 
theories 
were 
developed 
in 
the 
distorted-wave 
Born 
approximation 
(DWBA) 
to 
describe 
the 
x-ray 
scattering 
from 
single 
surfaces 
[73] 
and 
multilayer 
coatings 
[69, 
74, 
75]. 
DWBA 
assumes 
that 
incident 
and 
scattered 
fields 
are 
two 
solutions 
of 
the 
wave 
equations 
for 
the 
ideally 
smooth 
multilayer. 
The 
interface 
roughness 
leads 
to 
coupling 
of 
energy 
from 
the 
incident 
into 
the 
scattered 
wave 
mode. 
The 
general 
result 
is 
an 
integral 
expression 
for 
the 
ARS 
[74, 
75] 
which 
can 
be 
written 
as: 


MM33

1 
I 


ARS 
(s)= 
i+1 
j+1 
AikA 
* 
jlDikDjl 


4 
q 
(q)* 


i=0 
j=0 
k=0 
l=0 
kz 
lz 
. 
(3.10) 


. 
... 
	
. 


i+1 
j+1

× 
dt 
exp 
{-2ift 
} 
exp 
q 
(q) 
* 
ACFij() 
- 
1

kz 
lz 
I 


A 
are 
optical 
factors, 
D 
are 
damping 
factors, 
I 
is 
the 
illuminated 
surface 
area, 
and 
q 
are 
transfer 
vectors 
between 
scattered 
and 
incident 
wave 
vectors. 


Calculations 
in 
the 
DWBA 
are 
performed 
using 
IMD 
[39], 
which 
implements 
the 
theories 
presented 
in 
[14, 
73, 
74, 
75]. 


3.3.3 
Harmonization 
of 
the 
solutions 
Although 
VPT 
and 
DWBA 
are 
fundamentally 
different 
approaches 
to 
describe 
the 
scattering 
of 
single 
surfaces 
and 
multilayer 
coatings, 
they 
ultimately 
approximate 
the 
same 
reality 
and 
should 
therefore 
yield 
the 
same 
results 
in 
their 
ranges 
of 
validity. 
A 
theoretical 
comparison 
of 
VPT 
and 
DWBA 
for 
single 
surfaces 
can 
be 
found 
in 
[61]. 
A 
heuristic 
comparison, 
which 
also 
includes 
multilayer 
coatings, 
was 
performed 
in 
the 
frame 
of 
this 
work 
and 
is 
discussed 
in 
detail 
in 
[76]. 


The 
first 
step 
was 
to 
bring 
the 
results 
of 
both 
theories 
to 
similar 
forms. 
The 
DWBA 
result 
(Eq. 
(3.10)) 
can 
be 
simplified 
in 
the 
small-roughness 
approximation 
(s 
. 
). 
In 
this 
case, 
the 
damping 
terms 
can 
be 
set 
equal 
to 
unity 
(no 
damping). 
Furthermore, 
the 
exponential 
containing 
the 
ACF 
can 
be 
approximated 
by 
its 
first-order 
Taylor 
expansion, 
since 
ACF= 
s 
[34]. 
The 
resulting 
integrals 
are 
simply 
the 
cross-correlation 
PSDs 
as 
discussed 
in 
Sec. 
2.3.2. 
The 
approximated 
DWBA 
result 
can 
be 
rewritten 
as: 


MM33

1 


ARS 
(s)= 
4 
A 
* 
PSDij 
. 
(3.11) 


Aik 
jl 
i=0 
j=0 
k=0 
l=0 


Hence, 
in 
the 
small-roughness 
approximation, 
the 
DWBA 
result 
takes 
a 
similar 
form 
as 
the 
VPT 
result 
(Eq. 
(3.9)). 


15 



3 
Theoretical 
models 
of 
scattering 
and 
roughness 


Simulation 
results 
using 
VPT 
and 
DWBA 
for 
an 
EUV 
mirror 
(Mo/Si 
coating 
for 
normal 
incidence 
with 
N 
= 
60, 
identical 
and 
fully 
correlated 
interfaces 
with 
s 
=0.3 
nm) 
at 
. 
= 
13.5 
nm 
at 
two 
angles 
of 
incidence 
are 
shown 
in 
Fig. 
3.2. 
For 
s-polarized 
light, 
the 
calculated 
ARS 
curves 
are 
identical 
at 
all 
scatter 
angles3 
. 
The 
good 
agreement 
of 
the 
results 
suggests 
that 
both 
theories 
should 
be 
valid 
at 
193 
nm 
and 
13.5 
nm. 
It 
is 
the 
first 
time 
that 
the 
results 
of 
the 
two 
different 
approaches 
developed 
for 
the 
optical 
scattering 
and 
the 
x-ray 
scattering 
of 
multilayer 
coatings 
are 
shown 
to 
be 
congruent 
both 
formally 
and 
numerically. 


-90-60-300306090
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100i = 67° 
VPT (s) 
VPT (p) 
DWBA (s)
ARS (sr-1)s (°)
i = 0° 
VPT (s) 
VPT (p) 
DWBA (s)
Figure 
3.2: 
Comparison 
of 
VPT 
and 
DWBA 
simulation 
results 
for 
s-polarized 
(s) 
and 
p-polarized 
(p) 
incident 
light. 


All 
theories 
presented 
in 
this 
section 
assumed 
that 
interface 
roughness 
is 
small 
compared 
to 
. 
Following 
Ref. 
[53], 
”small” 
means 
/. 
. 
10-2 
. 
For 
193 
nm 
and 
13.5 
nm 
radiation, 
this 
means 
that 
s 
must 
not 
exceed 
2 
nm 
and 
0.1 
nm, 
respectively. 
Since 
the 
typical 
roughness 
of 
DUV 
and 
EUV 
optical 
components 
is 
in 
the 
order 
of 
these 
values, 
the 
theories 
have 
to 
be 
verified 
at 
the 
wavelengths 
of 
application. 


3.4 
Roughness 
and 
roughness 
evolution 
models 
Theoretical 
modeling 
of 
scattering 
of 
surfaces 
and 
thin 
film 
coatings 
requires 
detailed 
knowledge 
of 
their 
roughness 
properties. 
Use 
of 
analytical 
model-PSDs 
enables 
roughness 
spectra 
to 
be 
described 
by 
a 
small 
set 
of 
characteristic 
parameters 
and 
allows 
identifying 
and 
eliminating 
measurement 
artifacts 
[77]. 
Moreover, 
for 
multilayer 
coatings 
it 
is 
impossible 
to 
measure 
all 
interface 
PSDs, 
and 
appropriate 
roughness 
and 
roughness 
evolution 
models 
have 
to 
be 
used. 
The 
most 
relevant 
results 
discussed 
in 
the 
literature 
are 
summarized 
in 
this 
section. 


3Although 
not 
a 
general 
restriction 
of 
the 
DWBA, 
the 
formalism 
implemented 
in 
IMD 
does 
not 
allow 
for 
calculations 
for 
p-polarized 
light. 


16 



3 
Theoretical 
models 
of 
scattering 
and 
roughness 


Many 
polished 
surfaces 
exhibit 
a 
self-similar 
topography 
over 
a 
wide 
lateral 
scale 
and 
are 
sufficiently 
described 
by 
a 
fractal 
model-PSD 
[78, 
79]: 


A 


PSDfractal 
(f)= 
. 
(3.12) 


f. 


Parameter 
. 
is 
related 
to 
the 
fractal 
dimension 
of 
the 
surface. 
On 
a 
log-log 
scale 
the 
fractal 
PSD 
is 
a 
straight 
line 
with 
slope 
-. 
(see 
Fig. 
3.3). 


The 
morphology 
of 
a 
thin 
film 
growing 
on 
a 
perfectly 
smooth 
substrate 
results 
from 
a 
competition 
of: 
(i) 
shot 
noise 
of 
the 
flux 
of 
incoming 
particles 
causing 
a 
flat 
(white 
noise) 
PSD, 
(ii) 
local 
relaxation 
and 
smoothing 
on 
a 
small 
lateral 
scale 
causing 
a 
cut-off 
in 
the 
PSD 
depending 
on 
the 
adatom 
mobility, 
and 
(iii) 
shadowing 
effects 
leading 
to 


columnar 
growth4 
. 


The 
extent 
of 
each 
of 
these 
effects 
depends 
on 
the 
deposition 
conditions 
(i.e. 
process, 
substrate 
temperature, 
pressure, 
deposition 
rate) 
and 
substantially 
influences 
the 
thin 
film 
properties 
[81]. 
Popular 
structure 
zone 
models 
[82, 
83] 
qualitatively 
describe 
the 
resulting 
thin 
film 
structure 
by 
introducing 
the 
reduced 
temperature 
Ts/Tm, 
where 
Ts 
is 
the 
substrate 
temperature 
and 
Tm 
is 
the 
melting 
temperature 
of 
the 
material 
deposited. 
Ts/Tm 
is 
related 
to 
the 
free 
energy 
and 
mobility 
of 
the 
adatoms. 
A 
more 
detailed 
review 
is 
given 
in 
[84]. 
In 
particular 
for 
Ts/Tm 
˜ 
0.3, 
a 
transition 
occurs 
from 
porous 
(zone 
I) 
to 
dense 
(zone 
II) 
columnar 
growth 
as 
a 
result 
of 
enhanced 
surface 
diffusion. 
Considering 
that 
typical 
melting 
points 
of 
metal 
fluorides 
are 
. 
1000 
K, 
extensive 
substrate 
heating 
is 
required 
to 
improve 
the 
structural 
properties 
of 
fluoride 
coatings 
deposited 
by 
low-energetic 
deposition 
processes 
like 
thermal 
boat 
evaporation. 
Nonetheless, 
such 
films 
will 
always 
exhibit 
pronounced 
columnar 
structures 
and 
cuspshaped 
surface 
features 
[80, 
85]. 
The 
corresponding 
surface 
PSD 
is 
described 
by 
the 


ABC 
model5 
[27, 
77]: 


A 


PSDABC 
(f)= 
C+1 
(3.13) 
2

(1 
+ 
B2f2) 


where 
A, 
B, 
and 
C 
are 
free 
parameters. 


Using 
the 
definitions 
given 
in 
Sec. 
2.3, 
it 
is 
straightforward 
to 
show 
that 
[77, 
86]: 


2A 
(C 
- 
1)2B2 


ABC 
= 
,ABC 
= 
. 
(3.14) 


B2(C 
- 
1) 
22C 


The 
vertical 
and 
lateral 
evolution 
of 
surface 
morphology 
as 
a 
function 
of 
film 
thickness 


4In 
particular 
if 
the 
flux 
of 
incoming 
particles 
has 
a 
random 
orientation, 
the 
growth 
rate 
depends 


on 
the 
local 
slope 
of 
the 
topography. 
Ariving 
particles 
tend 
to 
stick 
on 
hills 
rather 
than 
in 
valleys 


which 
results 
in 
a 
competitive 
growth 
of 
cone 
shaped 
columns 
[80]. 


5also 
known 
as 
K-correlation 
model 


17 



3 
Theoretical 
models 
of 
scattering 
and 
roughness 


d 
is 
often 
described 
by 
power 
laws 
[85, 
87, 
88, 
89, 
90]: 


~ 
d/. 


s 
~ 
dß 
,c 
, 
(3.15) 


where 
ß 
is 
the 
dynamic 
scaling 
exponent 
for 
roughness 
components 
larger 
than 
the 


correlation 
length 
(f< 
1/c) 
and 
. 
is 
the 
static 
scaling 
exponent 
[87]. 
The 
scaling 
exponents 
are 
related 
to 
the 
fundamental 
growth 
processes 
[87, 
89]. 
The 
case 
ß 
=0.5 
is 
referred 
to 
as 
stochastic 
roughening 
or 
random 
deposition 
limit, 
> 
0.5 
indicates 
rapid 
roughening, 
and 
ß 
= 
0 
occurs 
for 
saturated 
roughness 
or 
epitaxial 
growth. 


The 
PSD 
of 
a 
thin 
film 
deposited 
on 
a 
rough 
substrate 
can 
be 
expressed 
as 
a 
superposition 
of 
the 
PSDs 
of 
the 
substrate 
PSDsub 
and 
the 
intrinsic 
PSD 
of 
the 
thin 
film 
PSDint 
[86, 
91]: 


PSDcoating 
= 
PSDint 
+ 
aPSDsub 
, 
(3.16) 


where 
a 
is 
a 
spatial-frequency 
dependent 
replication 
factor. 


Equation 
(3.16) 
enables 
extracting 
the 
intrinsic 
thin 
film 
roughness 
out 
of 
the 
total 
roughness 
spectrum 
using 
model-PSDs, 
as 
presented 
in 
[86]. 
So 
far, 
roughness 
modeling 
only 
allows 
a 
phenomenological 
description 
of 
measured 


PSDs. 
A 
completely 
different 
approach 
starts 
with 
kinetic 
continuum 
equations 
to 
model 
the 
deposition 
process 
itself 
[87, 
92]. 
A 
special 
case, 
the 
linear 
growth 
theory 
(LGT) 
is 
based 
on 
the 
most 
simple, 
linear 
version 
of 
the 
more 
general 
Kardar-Parisi-
Zhang 
equation 
[92]. 
LGT 
provides 
an 
analytical 
solution 
to 
the 
problem 
and 
predicts 
a 
PSD 
of 
the 
form 
[14, 
93]: 


1 
- 
exp 
{-2. 
|2f|. 
d}

PSDLGT 
=O 
. 
(3.17) 


2. 
|2f|. 


The 
model 
parameters 
are 
directly 
related 
to 
physical 
quantities: 
O 
is 
the 
volume 
of 
a 
constituent 
of 
the 
film 
(atom, 
cluster, 
microcrystallite), 
. 
is 
a 
growth 
parameter, 
and 
. 
is 
the 
relaxation 
exponent 
which 
indicates 
the 
relevant 
relaxation 
mechanism 
during 
thin 
film 
growth. 


Although 
the 
analytic 
expressions 
in 
Eqs. 
(3.13) 
and 
(3.17) 
are 
different, 
Fig. 
3.3 
reveals 
that 
the 
corresponding 
graphs 
have 
similar 
shapes. 
Equating 
the 
PSDs 
for 
f 
. 
0 
and 
f 
!8 
leads 
to: 
A 
=
d, 
B 
=2p 
(2d)1/, 
and 
C 
= 
-1. 
Thus, 
ABC-and 
LGT-PSDs 
can 
be 
translated 
into 
each 
other. 


The 
linear 
growth 
theory 
was 
used 
in 
[14] 
to 
model 
the 
roughness 
properties 
of 
magnetron 
sputtered 
EUV 
coatings 
and 
is 
therefore 
expected 
to 
be 
valid 
also 
for 
the 
EUV 
coatings 
investigated 
in 
this 
work. 
However, 
as 
pointed 
out 
in 
[14], 
LGT 
is 
a 
linear 
and 
local 
description 
of 
the 
roughening 
process 
and 
can 
not 
be 
expected 
to 
hold 
for 
DUV 
coatings 
fabricated 
using 
low-energetic 
processes. 


18 



3 
Theoretical 
models 
of 
scattering 
and 
roughness 


0.010.1110100
10-2
10-1
100
101
102
103
104
105
106
107
PSD (nm4)f (µm-1) 
fractal 
ABC 
LGT 
Figure 
3.3: 
Model-PSDs 
used 
in 
this 
work. 
PSD 
model 
parameters 
used 
for 
figure: 


PSDfractal: 
A 
=0.006 
nm2 
, 
. 
= 
2; 
PSDABC: 
A 
= 
1000 
nm4 
, 
B 
= 
300 
nm, 


C 
= 
3; 
PSDLGT: 
O 
= 
333nm3 
, 
. 
= 
86620 
nm3 
, 
. 
= 
4, 
d 
= 
30 
nm. 


In 
the 
range 
of 
validity 
of 
LGT, 
an 
explicit 
expression 
for 
the 
PSD 
of 
multilayer 
coatings 
can 
be 
derived. 
For 
a 
coating 
containing 
M 
alternating 
L 
and 
H 
layers, 
the 
top-surface 
PSD 
after 
N 
periods 
(N 
= 
M/2) 
is 
[14]: 


22 
)N

1 
- 
(aLaH 
. 
(L)2 
(H) 
. 
22

PSDN 
= 
22 
PSDint 
+ 
aLPSDint 
+(aLaH 
)N 
PSDsub 
. 
(3.18) 


1 
- 
aLaH 


(L/H)

PSDint 
are 
the 
intrinsic 
PSDs 
of 
L 
and 
H 
single 
layers 
described 
by 
Eq. 
(3.17). 
aL/H 


describes 
the 
replication 
of 
different 
roughness 
components 
and 
has 
the 
form 
of 
a 
lowpass 
filter: 


aL/H 
= 
exp 
-2L/H 
|2f|. 
dL/H 
. 
(3.19) 


At 
high 
spatial 
frequencies, 
the 
adatom 
mobility 
leads 
to 
local 
smoothing. 
At 
low 
spatial 
frequencies, 
the 
replication 
factors 
are 
approximately 
unity, 
which 
corresponds 
to 
perfect 
replication 
of 
long-range 
roughness 
components. 


The 
similarity 
of 
Eq. 
3.18 
and 
Eq. 
3.16 
is 
obvious. 
For 
a 
= 
1, 
Eq. 
(3.18) 
can 
be 
approximated 
as: 


(L)(H)
PSDN 
= 
N 
PSD+PSD+PSDsub 
. 
(3.20) 


int 
int 


The 
corresponding 
rms 
roughness 
for 
fmin 
= 
0 
and 
fmax< 
1/c 
is 
(Eq. 
(2.9)): 


2 
2

(L)(H) 
+ 
2
N 
= 
Nint 
+ 
Nint 
sub 
. 
(3.21) 


Hence, 
LGT 
predicts 
an 
evolution 
of 
the 
intrinsic 
thin 
film 
roughness 
according 
to 


~ 
N0.5 


. 
Unfortunately, 
there 
is 
no 
general 
roughness 
evolution 
model 
which 
also 
holds 
for 
multilayers 
exhibiting 
columnar 
growth. 
A 
new 
approach 
for 
arbitrary 
coatings 
is 
presented 
in 
Sec. 
6.1.1. 


19 



3 
Theoretical 
models 
of 
scattering 
and 
roughness 


3.5 
Volume 
scattering 
of 
bulk 
materials 
Aside 
from 
scattering 
induced 
by 
roughness 
of 
the 
interfaces 
between 
two 
media, 
scattering 
in 
the 
bulk 
of 
optical 
materials 
can 
be 
of 
crucial 
importance. 
This 
volume 
scattering 
can 
be 
separated 
into 
extrinsic 
scattering 
by 
inclusions 
and 
particulate 
defects 
and 
intrinsic 
scattering 
resulting 
from 
imperfections 
of 
the 
molecular 
or 
crystalline 
structure 
of 
the 
material. 
In 
particular 
for 
the 
scattering 
of 
synthetic 
fused 
silica6 
at 
193 
nm, 
which 
is 
discussed 
in 
detail 
in 
this 
work, 
a 
convenient 
theoretical 
model 
is 
needed. 


The 
first 
investigations 
of 
light 
scattering 
in 
glasses 
were 
motivated 
by 
the 
need 
for 
extremely 
low-loss 
media 
for 
optical 
waveguides 
in 
the 
infrared. 
The 
intrinsic 
scattering 
was 
explained 
by 
thermally-induced 
density 
fluctuations 
in 
the 
melt 
which 
are 
”frozen” 
during 
quenching 
of 
the 
material 
[94, 
95, 
96]. 
The 
structural 
disorder 
in 
the 
nonequilibrium, 
glassy 
state 
is 
therefore 
associated 
to 
a 
fictive 
temperature 
Tf 
. 


The 
theories 
predict 
a 
Rayleigh 
scattering 
distribution 
[97]. 
For 
in-plane 
scattering, 
the 
ARS 
of 
a 
finite 
scattering 
volume 
can 
be 
modeled 
as 
[98]: 


. 
.


C 
, 
for 
s-polarized 


ARS 
= 
incident 
light 
. 
(3.22) 


:

C 
cos 
s 
, 
for 
p-polarized 


The 
constant 
C 
is 
proportional 
to 
the 
Rayleigh 
bulk 
scattering 
coefficient 
. 
A 
theoretical 
expression 
for 
fused 
silica 
is 
given 
in 
[96]: 


83 


a 
= 
n 
8 
p 
2T 
kBTf 
, 
(3.23) 


34 


where 
p 
is 
the 
photoelastic 
coefficient, 
T 
the 
isothermal 
compressibility 
at 
Tf 
, 
and 
kB 


the 
Boltzmann 
constant. 


By 
integrating 
Eq. 
(3.22) 
in 
full 
space 
and 
equating 
a 
with 
the 
total 
scatter 
loss 
normalized 
to 
the 
length 
L 
of 
the 
illuminated 
volume, 
it 
is 
straightforward 
to 
show 
that: 


8C 


a 
= 
. 
(3.24) 


3L 


Thereby 
it 
is 
assumed 
that 
L 
. 
1 
(ARS 
constant 
along 
L). 


Based 
on 
data 
obtained 
for 
fused 
silica 
in 
the 
visible 
and 
near 
infrared 
spectral 
regions, 
theoretical 
values 
for 
the 
scatter 
loss 
of 
fused 
silica 
at 
193 
nm 
can 
be 
estimated: 
A 
lower 
limit 
for 
the 
attenuation7 
caused 
by 
bulk 
scattering 
of 
3.9 
dB/km 
at 
633 
nm 
was 


6amorphous 
SiO2 


An 
attenuation 
a 
measured 
in 
dB/km 
is 
equivalent 
to 
an 
attenuation 
coefficient 
of 
a 
= 


ln 
(10a) 
x10-5 
cm-1 
. 


20 



3 
Theoretical 
models 
of 
scattering 
and 
roughness 


suggested 
in 
[96]. 
This 
corresponds 
to 
a 
˜ 
9x10-6 
cm-1 
. 
Using 
Eq. 
(3.23), 
the 
bulk 
scattering 
coefficient 
of 
fused 
silica 
at 
193 
nm 
should 
be 
in 
the 
order 
of 
1x10-3 
cm-1 
. 


Yet 
the 
Rayleigh 
scattering 
model 
implies 
the 
presumption 
that 
the 
scattering 
centers 
are 
small 
compared 
to 
. 
This 
is 
fulfilled 
for 
visible 
and 
near-infrared 
wavelengths 
if 
scattering 
is 
indeed 
caused 
by 
density 
fluctuations 
at 
molecular 
scale. 
But 
certainly, 
the 
shorter 
the 
wavelength, 
the 
more 
likely 
the 
theory 
will 
fail. 


This 
clearly 
holds 
for 
both 
surface 
and 
bulk 
scattering 
theories 
developed 
for 
the 
visible 
spectral 
range 
by 
assuming 
small 
(compared 
to 
the 
wavelength) 
scattering 
centers 
or 
roughness. 
Most 
of 
the 
theories 
presented 
in 
this 
section 
have 
never 
been 
verified 
at 
deep-or 
extreme 
ultraviolet 
wavelengths, 
mainly 
because 
of 
the 
lack 
of 
sensitive 
measurement 
tools 
and 
appropriate 
measurement 
and 
analysis 
techniques. 
This 
thesis 
is 
dedicated 
to 
overcome 
these 
limitations. 
However, 
in 
particular 
the 
modeling 
of 
surface 
scattering 
requires 
appropriate, 
independent 
roughness 
measurements. 
Therefore, 
different 
methods 
are 
surveyed 
in 
the 
next 
section. 


21 



4 
Independent 
roughness 
measurement 
techniques 


The 
investigation 
of 
the 
causes 
of 
scattering 
of 
optical 
components 
relies 
on 
the 
comparison 
of 
modeled 
scattering 
and 
actual 
measurement 
results. 
Accurate 
modeling 
of 
roughness-induced 
scattering 
using 
the 
theories 
presented 
in 
the 
preceding 
section 
in 
turn 
requires 
the 
input 
of 
appropriate 
roughness 
data. 
Furthermore, 
additional 
roughness 
information 
is 
valuable 
to 
reduce 
the 
number 
of 
parameters 
for 
the 
scatter 
analysis 
of 
multilayer 
coatings 
or 
to 
separate 
surface 
from 
bulk 
effects 
[99]. 


For 
the 
measurement 
of 
the 
structural 
properties 
relevant 
for 
scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm, 
characterization 
techniques 
are 
required 
which 
fulfill 
the 
following 
demands: 


• 
Quantitative 
topographic 
information 
or 
direct 
determination 
of 
roughness 
• 
Spatial 
frequency 
range 
between 
0.01 
µm-1 
and 
200 
µm-1 
• 
Vertical 
resolution 
<0.1 
nm 
The 
most 
prominent 
roughness 
measurement 
techniques 
used 
or 
considered 
in 
this 
thesis 
are 
briefly 
surveyed 
in 
this 
section 
with 
respect 
to 
their 
suitability 
for 
investigations 
of 
roughness-induced 
scattering 
at 
193 
nm 
and 
13.5 
nm. 


4.1 
Optical 
profilometry 
Optical 
profilometry 
characterizes 
a 
variety 
of 
optical 
techniques 
to 
measure 
surface 
topography. 
White 
light 
interferometry 
(WLI) 
combines 
interferometry 
and 
optical 
microscopy. 
Collimated 
light 
is 
split 
and 
focused 
on 
both 
the 
test 
surface 
and 
a 
reference 
surface. 
By 
scanning 
the 
sample 
surface 
along 
the 
optical 
axis, 
phase 
information 
is 
retrieved 
from 
the 
interference 
pattern. 
Analysis 
of 
the 
intensity 
and 
phase 
of 
the 
complex 
interference 
pattern 
provides 
topographic 
information 
about 
the 
test 
surface 
[100]. 


Phase-shift 
interferometry 
(PSI) 
utilizes 
monochromatic 
light. 
In 
the 
interference 
pattern, 
all 
points 
with 
the 
same 
intensity 
have 
a 
vertical 
distance 
of 
i/2, 
where 
i 
is 
an 


22 



4 
Independent 
roughness 
measurement 
techniques 


integer. 
For 
the 
reconstruction 
of 
the 
surface 
topography, 
several 
images 
with 
slightly 
shifted 
phases 
are 
analyzed 
[100, 
101]. 
PSI 
is 
restricted 
to 
rather 
smooth 
surfaces 
but 
typically 
offers 
higher 
vertical 
resolution 
than 
WLI. 
The 
PSI 
measurements 
in 
this 
thesis 
were 
performed 
using 
a 
white 
light 
interferometer 
Atos 
Micromap 
512 
operated 
in 
PSI 
mode 
at 
a 
wavelength 
of 
532 
nm. 


Optical 
profilometry 
is 
well 
suited 
for 
the 
measurement 
of 
mid-spatial 
frequency 
roughness 
with 
a 
vertical 
resolution 
better 
than 
1 
nm. 
Yet 
the 
high-spatial 
frequency 
limit 
is 
in 
the 
order 
of 
the 
inverse 
of 
the 
wavelength 
employed. 
Moreover, 
low-pass 
filtering 
effects 
in 
the 
measured 
PSD 
resulting 
from 
the 
transfer 
function 
of 
the 
optical 
system 
near 
the 
resolution 
limit 
have 
to 
be 
considered. 
Hence, 
optical 
profilometry 
(using 
visible 
light) 
can 
not 
provide 
all 
structural 
information 
relevant 
for 
light 
scattering 
at 
wavelengths 
shorter 
than 
200 
nm. 


4.2 
Electron 
microscopy 
Electron 
microscopy 
(EM) 
can 
be 
used 
to 
analyze 
the 
top-surface 
or 
a 
cross-section 
of 
a 
thin 
film 
coating 
based 
on 
the 
interaction 
of 
high-energetic 
electrons 
with 
the 
sample 
under 
investigation. 
A 
narrow, 
intense 
electron 
beam 
is 
focused 
to 
the 
sample. 
Incident 
electrons 
scattered 
back 
or 
transmitted 
as 
well 
as 
secondary 
electrons 
or 
xray 
fluorescence 
radiation 
emitted 
by 
the 
sample 
can 
be 
used 
for 
the 
analysis. 
EM 
provides 
a 
very 
high 
lateral 
resolution 
limited 
by 
the 
spot 
diameter 
of 
the 
electron 
beam 
and 
the 
volume 
of 
interaction. 
As 
a 
result 
of 
the 
short 
de 
Broglie 
wavelength 
of 
the 
electrons 
(determined 
by 
the 
acceleration 
voltage), 
the 
theoretical 
resolution 
is 
in 
the 
order 
of 
0.01 
nm. 
However, 
because 
of 
the 
complex 
electron 
optics 
required, 
which 
provide 
only 
small 
numerical 
apertures 
(˜ 
0.01), 
the 
practical 
resolution 
is 
limited 
to 
a 
few 
nanometers 
[102]. 


In 
scanning 
electron 
microscopy 
(SEM), 
the 
beam 
is 
deflected 
to 
scan 
the 
sample 
surface 
and 
backscattered 
or 
secondary 
electrons 
are 
detected. 
The 
amount 
of 
detected 
electrons 
and 
their 
energy 
distribution 
is 
a 
function 
of 
the 
surface 
topography, 
local 
composition, 
crystal 
structure, 
and 
electronic 
properties 
of 
the 
sample. 
Unfortunately, 
SEM 
provides 
only 
semi-quantitative 
topographic 
data 
unless 
advanced 
calibration 
techniques 
are 
applied 
[103]. 
Moreover, 
it 
has 
to 
be 
considered 
that 
secondary 
electrons 
may 
originate 
from 
far 
below 
the 
surface 
(˜ 
100 
nm) 
and 
the 
local 
geometry 
of 
the 
surface 
affects 
the 
secondary 
electron 
yield 
[102]. 


While, 
conventional 
SEM 
requires 
a 
conducting 
surface 
to 
prevent 
surface 
charging, 
new 
instruments 
have 
been 
developed 
which 
also 
allow 
nonconducting 
surfaces 
to 
be 
investigated 
by 
utilizing 
lower 
acceleration 
voltages 
[104]. 
The 
SEM 
measurements 
presented 
in 
this 
thesis 
were 
performed 
with 
a 
field 
emission 
SEM 
Hitachi 
S-4800 
UHR 


23 



4 
Independent 
roughness 
measurement 
techniques 


at 
the 
Institute 
of 
Applied 
Physics 
of 
the 
Friedrich-Schiller-University 
Jena. 
Acceleration 
voltages 
between 
1 
kV 
and 
15 
kV 
were 
applied, 
and 
backscattered 
electrons 
were 
analyzed. 
The 
instrument 
exhibits 
a 
lateral 
resolution 
down 
to 
1 
nm. 


In 
transmission 
electron 
microscopy 
(TEM), 
the 
electron 
beam 
transmitted 
through 
a 
thin 
sample 
is 
analyzed. 
TEM 
reveals 
information 
about 
the 
structure, 
composition, 
and 
crystalline 
properties 
of 
the 
sample, 
as 
well 
as 
quasi-topographic 
information. 


Unfortunately, 
EM 
studies 
are 
usually 
destructive 
and 
require 
elaborate 
sample 
preparation 
techniques 
to 
generate 
clean 
cross 
sections. 
These 
cross-sections, 
however, 
are 
rather 
sensitive 
to 
the 
fracturing 
conditions. 
Moreover, 
cross-sectional 
analysis 
is 
limited 
to 
a 
single 
fracture 
plane, 
which 
might 
not 
be 
representative 
for 
the 
whole 
three 
dimensional 
interface 
structure 
in 
general. 
Finally, 
the 
high-energetic 
electrons 
may 
induce 
a 
change 
of 
the 
structure 
under 
investigation, 
as 
was 
observed 
in 
[105]. 


4.3 
X-ray 
methods 
X-ray 
reflectivity 
(XRR) 
measurements 
are 
performed 
by 
irradiating 
the 
sample 
surface 
with 
quasi-monochromatic 
x-ray 
radiation 
and 
measuring 
the 
specular 
reflectance 
as 
a 
function 
of 
the 
angle 
of 
incidence. 
Information 
about 
layer 
thicknesses, 
electron 
densities, 
and 
interface 
widths 
are 
obtained 
by 
utilizing 
X-ray 
scattering 
theories 
[75] 
to 
fit 
a 
theoretical 
model 
to 
the 
measured 
curve. 


Unfortunately, 
XRR 
like 
any 
specular 
technique 
does 
not 
distinguish 
between 
topological 
roughness 
and 
gradings 
of 
composition 
or 
density 
at 
an 
interface 
which 
both 
result 
in 
effective 
electron 
density 
gradients 
[106]. 
Hence, 
no 
information 
about 
the 
lateral 
distribution 
of 
roughness 
can 
be 
retrieved 
from 
XRR 
measurements. 
Moreover, 
the 
lower 
bandwidth 
limit 
sensitively 
depends 
on 
the 
detector 
aperture 
and, 
thus, 
on 
the 
actual 
set-up 
used. 


The 
roughness 
spectrum 
can 
only 
be 
obtained 
by 
measurement 
of 
x-ray 
diffuse 
scattering 
(XRS). 
In 
this 
case, 
the 
lower 
bandwidth 
limit 
is 
determined 
by 
the 
smallest 
detectable 
scatter 
angle 
and 
the 
wavelength. 
For 
typical 
x-ray 
wavelengths 
in 
the 
range 
of 
0.1 
nm, 
this 
means 
that 
measurements 
have 
to 
be 
performed 
extremely 
close 
(< 
0.01) 
to 
the 
specular 
beam 
in 
order 
to 
measure 
the 
PSD 
around 
f 
˜ 
1 
µm-1 
. 
The 
upper 
bandwidth 
limit 
is 
determined 
by 
the 
power 
of 
the 
x-ray 
source 
and 
the 
sensitivity 
of 
the 
detector. 
In 
[107], 
PSDs 
were 
determined 
in 
the 
spatial 
frequency 
range 
between 
1 
µm-1 
and 
5 
µm-1 
by 
XRS 
at 
0.154 
nm 
(Cu 
Kline). 
Recently, 
XRS 
measurements 
based 
on 
synchrotron 
radiation 
were 
reported 
[90]. 
Provided 
by 
the 
high-power 
light 
source, 
a 
substantially 
increased 
dynamic 
range 
could 
be 
achieved. 
As 
a 
result, 
the 
spatial 
frequency 
range 
covered 
extends 
up 
to 
50 
µm-1 
and 
can 
be 
extended 
even 
further 
[108]. 


24 



4 
Independent 
roughness 
measurement 
techniques 


4.4 
Atomic 
force 
microscopy 
Atomic 
force 
microscopy 
(AFM) 
belongs 
to 
the 
family 
of 
scanning 
microscopes. 
A 
sharp 
probe 
tip 
(diameter 
˜ 
10 
nm) 
mounted 
on 
a 
cantilever 
is 
scanned 
over 
the 
sample 
surface. 
Inter-atomic 
forces 
between 
sample 
and 
tip 
lead 
to 
a 
deflection 
of 
the 
cantilever 
(contact 
mode) 
or 
a 
change 
of 
its 
elastic 
properties 
(noncontact 
mode, 
Tapping 
Mode 
[109]) 
which 
are 
detected. 
From 
this 
information, 
a 
3D 
topographic 
map 
of 
the 
surface 
is 
retrieved 
with 
extremely 
high 
vertical 
resolution 
of 
<0.02 
nm. 
In 
contrast 
to 
scanning 
tunneling 
microscopy 
[110], 
AFM 
allows 
also 
nonconductive 
surfaces 
to 
be 
investigated. 


The 
AFM 
measurements 
in 
this 
thesis 
were 
performed 
with 
an 
atomic 
force 
microscope 
VEECO 
D3100 
operated 
in 
Tapping 
Mode. 
Single 
crystalline 
Si 
probes 
(10 
nm 
nominal 
tip 
radius) 
and 
high-density 
carbon 
supersharp 
probes 
(tip 
radius 
5 
nm) 
were 
used. 
For 
each 
sample, 
several 
scans 
were 
performed 
at 
different 
positions 
and 
in 
different 
scan 
areas 
of 
1x1 
µm2, 
10x10 
µm2, 
and 
50x50 
µm2 
. 
Each 
scan 
contained 
512x512 
data 
points. 
PSDs 
were 
calculated 
from 
the 
topographic 
data 
using 
Eqs. 
(2.6) 
and 
(2.7). 
A 
combination 
algorithm 
described 
detail 
in 
[32] 
was 
then 
applied 
to 
determine 
a 
single 
Master 
PSD 
for 
each 
sample. 


The 
lower 
bandwidth 
limit 
of 
AFM 
is 
theoretically 
given 
by 
the 
scan 
area. 
Yet 
the 
practical 
limit 
is 
determined 
by 
the 
bow 
of 
the 
piezo 
scanning 
tube 
and 
is 
fmin 
0.1 
µm-1 
for 
the 
AFM 
utilized 
in 
this 
work 
[72]. 
The 
upper 
bandwidth 
limit 
depends 
on 
the 
tip 


v 


diameter 
r 
and 
can 
be 
estimated 
as 
[72, 
111]: 
fmax 
=1/(2p 
ar), 
where 
a 
is 
the 
amplitude 
of 
a 
sine 
profile. 
For 
extremely 
smooth 
surfaces 
with 
a 
in 
the 
order 
of 
0.1 
nm 
and 
r 
˜ 
10 
nm, 
the 
upper 
bandwidth 
limit 
is 
beyond 
160 
µm-1 
(but 
is 
practically 
limited 
by 
instrumental 
noise). 
For 
a 
thin 
film 
coating 
with 
a 
˜ 
1 
nm, 
however, 
an 
influence 
of 
tip 
effects 
can 
be 
expected 
also 
at 
scatter-relevant 
spatial 
frequencies. 
In 
addition, 
tip 
degradation 
and 
contamination 
during 
measurement 
results 
in 
a 
gradual 
decrease 
of 
resolution 
and 
additional 
measurement 
artifacts. 


During 
the 
last 
years, 
a 
lot 
of 
progress 
has 
been 
achieved 
regarding 
the 
control 
and 
suppression 
of 
noise 
and 
artifacts 
in 
AFM 
measurements 
and 
the 
interpretation 
of 
their 
impact 
on 
measured 
PSDs 
[112, 
113, 
114]. 
It 
was 
observed 
that 
tip 
degradation 
does 
not 
only 
lead 
to 
suppression 
of 
high-spatial 
frequency 
components. 
Moreover, 
low-spatial 
frequency 
components 
can 
be 
enhanced 
substantially 
[114]. 
Therefore, 
particular 
attention 
had 
to 
be 
paid 
on 
the 
condition 
of 
the 
tip 
and 
the 
suppression 
of 
measurement 
artifacts 
in 
order 
to 
achieve 
reliable 
results1 
. 


Nevertheless, 
no 
standardized 
calibration 
procedures 
for 
AFM 
measurements 
are 
established 
yet, 
and 
the 
measurement 
process 
involves 
several 
mechanical 
and 
electronical 
steps 
with 
linear 
and 
nonlinear 
sources 
of 
uncertainty. 
Hence, 
the 
calibration 
of 
AFM 
measurements 
is 
still 
a 
topic 
of 
research 
[115]. 


1For 
high-resolution 
measurements, 
a 
new 
tip 
is 
usually 
inserted 
for 
each 
scan. 


25 



4 
Independent 
roughness 
measurement 
techniques 


Furthermore, 
the 
small 
surface 
areas 
covered 
by 
single 
AFM 
scans 
lead 
to 
a 
natural 
uncertainty 
in 
the 
roughness 
measurement 
as 
a 
result 
of 
statistical 
fluctuation 
effects. 
These 
statistical 
effects 
are 
connected 
to 
the 
question 
to 
which 
extent 
the 
sampled 
topography 
is 
representative 
for 
the 
entire 
(infinitely 
large) 
surface 
and 
can 
be 
reduced 
by 
averaging 
the 
results 
retrieved 
at 
different 
scan 
positions. 
The 
relative 
uncertainty 
of 
the 
calculated 
Master 
PSDs, 
which 
was 
estimated 
as 
the 
standard 
deviation 
of 
PSDs 
obtained 
for 
one 
sample 
at 
different 
positions, 
is 
typically 
below 
15% 
[116]. 


4.5 
R´esum´e 
The 
spatial 
frequency 
ranges 
covered 
by 
the 
measurement 
techniques 
described 
above 
and 
those 
corresponding 
to 
light 
scattering 
at 
193 
nm 
and 
13.5 
nm 
are 
shown 
in 
Fig. 
4.1. 
The 
shaded 
areas 
mark 
regions 
in 
which 
quantitative 
information 
is 
difficult 
to 
be 
obtained 
or 
only 
qualitative 
or 
semi-quantitative 
information 
can 
be 
retrieved. 


Figure 
4.1 
reveals 
that 
a 
combination 
of 
AFM 
measurements 
in 
different 
scan 
areas 
is 
best 
suited 
for 
the 
analysis 
of 
roughness 
components 
that 
lead 
to 
scatter 
losses 
at 
193 
nm 
and 
13.5 
nm. 
Information 
about 
roughness 
components 
at 
lower 
spatial 
frequencies 
corresponding 
to 
near-angle 
scattering 
at 
193 
nm 
(scatter 
angles 
below 
2) 
and 
13.5 
nm 
(scatter 
angles 
below 
0.1) 
can 
be 
obtained 
by 
optical 
profilometry. 
The 
measurement 
results 
in 
the 
different 
scales 
can 
be 
combined 
directly 
in 
spatial 
frequency 
space 
by 
using 
PSDs, 
as 
described 
in 
Sec. 
(4.4). 


It 
is 
obvious 
that 
optical, 
X-ray, 
and 
electron 
microscopy 
methods 
resolve 
lateral 
structures 
in 
the 
order 
of 
magnitude 
of 
the 
wavelength 
used. 
For 
the 
measurement 
of 
structures 
relevant 
for 
scattering 
at 
193 
nm 
or 
13.5 
nm, 
the 
resolution 
of 
optical 
profilometry 
is 
too 
small. 
On 
the 
other 
hand, 
X-ray-and 
electron-based 
techniques 
are 
well 
suited 
for 
the 
resolution 
of 
very 
high 
spatial 
frequencies, 
which, 
however, 
are 
not 
relevant 
for 
scattering 
at 
the 
comparatively 
much 
longer 
wavelengths 
of 
interest 
for 
the 
application. 


In 
addition 
to 
the 
techniques 
discussed 
in 
this 
section, 
scatter 
measurements 
themselves 
can 
be 
used 
for 
roughness 
measurements 
[27, 
117] 
by 
exploiting 
the 
theories 
presented 
in 
Sec. 
(3.2). 
Yet 
accurate 
and 
absolute 
scatter 
measurements 
are 
mandatory 
for 
this 
purpose. 
Moreover, 
the 
validity 
of 
the 
theories 
must 
be 
checked 
at 
the 
wavelengths 
of 
application. 


26 



4 
Independent 
roughness 
measurement 
techniques 


1E-30.010.11101001000f (µm-1)
AFM50x50 µm²
10x10 µm²
1x1 µm²
ARS 193 nm0.1°2°90°
ARS 13.5 nm0.1°2°90°
XRS 0.154 nmEMWLI/PSI0.01°0.05°0.5°
XRR 0.154 nm
Figure 
4.1: 
Spatial 
frequency 
regions 
relevant 
for 
scattering 
at 
193 
nm 
and 
13.5 
nm 
and 
bandwidth 
limits 
of 
different 
roughness 
measurement 
and 
inspection 
techniques. 
The 
shaded 
areas 
represent 
regions 
in 
which 
only 
qualitative 
structural 
information 
can 
be 
obtained. 
EM 
-electron 
microscopy, 
XRS/XRR 
X-
ray 
scattering 
and 
reflectivity, 
WLI/PSI 
-white 
light 
and 
phase-shift 
interferometry, 
AFM 
-atomic 
force 
microscopy, 
ARS 
-angle 
resolved 
scattering. 


27 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 


13.5 
nm 
The 
development 
of 
capable 
instrumentation 
for 
the 
measurement 
of 
optical 
scattering 
at 
193 
nm 
and 
13.5 
nm, 
which 
constitute 
the 
basis 
for 
investigations 
of 
the 
scattering 
properties 
of 
DUV 
and 
EUV 
optical 
components, 
was 
one 
major 
challenge 
for 
the 
work 
presented 
in 
this 
thesis. 


There 
are 
some 
essential 
demands 
on 
instrumentation 
for 
scattering 
measurements 
in 
general: 


• 
High 
spectral 
purity 
is 
required 
because 
scattering 
strongly 
depends 
on 
. 
(see 
Sec. 
3). 
• 
High 
spatial 
purity 
(a 
clean 
core 
beam) 
and 
suppression 
of 
stray-light 
at 
the 
beam 
preparation 
optics 
is 
essential 
to 
prevent 
obstruction 
of 
the 
scattering 
of 
high-quality 
samples. 
• 
Low 
divergence 
of 
the 
incident 
beam 
is 
required 
to 
achieve 
a 
small 
beam 
diameter 
at 
both 
the 
sample 
position 
and 
the 
detector 
aperture 
(for 
ARS) 
or 
at 
the 
entrance 
and 
exit 
ports 
of 
the 
Coblentz 
sphere 
(for 
TS). 
The 
width 
of 
the 
specular 
beam 
at 
the 
detector 
aperture 
determines 
the 
near-angle 
limit 
for 
ARS 
measurements. 
• 
A 
high 
dynamic 
range 
is 
necessary 
to 
measure 
both 
specular 
and 
off-specular 
quantities, 
which 
are 
typically 
separated 
by 
several 
orders 
of 
magnitude. 
Thus, 
all 
of 
the 
requirements 
above 
have 
to 
be 
met 
by 
maintaining 
as 
much 
intensity 
in 
the 
incident 
beam 
as 
possible. 
The 
variety 
of 
components 
to 
be 
measured 
extends 
from 
supersmooth 
substrates 
with 
sub-nanometer 
roughness 
to 
multilayer 
systems 
with 
pronounced 
nanostructures. 
The 
sensitivity 
required 
can 
be 
estimated 
using 
the 
theoretical 
background 
presented 
in 
Sec. 
3. 


A 
super-polished 
fused 
silica 
substrate 
with 
an 
rms 
roughness 
of 
0.1 
nm 
can 
be 
assumed 
to 
be 
a 
state-of-the-art 
smooth 
surface1 
. 
At 
193 
nm, 
TSb 
˜ 
2x10-6 
is 
expected 
for 
the 


1The 
influence 
of 
bandwidth 
limits 
is 
neglected 
for 
the 
following 
rough 
estimations. 


28 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 


front 
surface 
according 
to 
Eq. 
(3.7) 
(R 
˜ 
4.8%, 
c 
. 
). 
At 
13.5 
nm, 
the 
reflectance 
of 
an 
uncoated 
fused 
silica 
substrate 
is 
as 
low 
as 
2x10-4 
leading 
to 
TSb 
˜ 
8x10-6 
. 
If 
the 
substrate 
is 
coated 
with 
an 
EUV 
mirror 
(R 
˜ 
70%), 
the 
scatter 
loss 
estimated 
in 
the 
single-surface 
approximation 
(assuming 
all 
interfaces 
to 
be 
identical 
with 
the 
substrate 
surface) 
is 
TSb 
˜ 
0.6%. 
Assuming 
ideally 
diffuse 
(Lambertian) 
scattering 
with 
ARS 
~ 
cos 
s, 
as 
a 
rough 
estimation, 
ARS 
levels 
of 
about 
one 
third 
of 
the 
TSb 
values 
can 
be 
expected2 
. 


For 
accurate 
measurements, 
the 
TS 
and 
ARS 
background 
scattering 
levels 
should 
be 
well 
below 
the 
measurement 
values3 
. 
To 
meet 
these 
stringent 
demands, 
an 
elaborated 
beam 
preparation 
is 
necessary 
which 
constitutes 
a 
challenging 
task 
even 
at 
visible 
wavelengths 
[118]. 
The 
design 
of 
such 
instruments 
for 
shorter 
wavelengths 
is 
even 
more 
demanding 
because 
of 
the 
limitations 
of 
the 
usable 
optics 
as 
well 
as 
the 
necessity 
to 
operate 
in 
inert 
purge 
gas, 
such 
as 
nitrogen 
for 
193 
nm, 
or 
even 
in 
high-vacuum 
(193 
nm, 
13.5 
nm). 
Hence, 
set-ups 
are 
required 
which 
combine 
a 
sophisticated 
optical 
system 
with 
the 
ability 
to 
tolerate 
harsh 
environmental 
conditions 
(pressure, 
vibrations, 
heating, 
etc.) 
In 
fact, 
instruments 
for 
scatter 
measurements 
at 
193 
nm 
or 
13.5 
nm 
share 
some 
crucial 
demands 
with 
corresponding 
lithographic 
tools. 


A 
variety 
of 
instruments 
have 
been 
developed 
for 
scattering 
measurements 
in 
the 
visible, 
near-infrared, 
and 
ultraviolet 
spectral 
ranges 
[2, 
27, 
118, 
119, 
120, 
121, 
122, 
123] 
and 
even 
for 
the 
hard-x-ray 
range 
[107]. 
However, 
there 
are 
only 
few 
instruments 
capable 
of 
scatter 
measurements 
in 
the 
DUV 
and 
EUV 
spectral 
ranges. 


5.1 
Instrumentation 
for 
193 
nm 
Instruments 
for 
TS 
at 
193 
nm 
and 
157 
nm 
were 
presented 
in 
[17, 
19, 
20]. 
Background 
scattering 
levels 
between 
10-3 
and 
10-5 
have 
been 
reported. 
A 
more 
detailed 
review 
is 
given 
in 
[99]. 
A 
laser 
based 
device 
for 
ARS 
measurements 
at 
157 
nm 
with 
a 
dynamic 
range 
of 
7 
orders 
of 
magnitude 
was 
presented 
in 
[124]. 
A 
scatterometer 
for 
160 
nm 
was 
used 
in 
[125]. 
An 
instrument 
for 
ARS 
measurements 
between 
58 
nm 
and 
120 
nm 
was 
presented 
in 
[126]. 
Recently, 
a 
scatterometer 
for 
wavelengths 
between 
190 
nm 
and 
840 
nm 
was 
developed 
[127], 
which 
was 
designed 
for 
the 
measurement 
of 
diffraction 
efficiencies 
and 
their 
numerical 
evaluation 
rather 
than 
for 
the 
sensitive 
characterization 
of 
optical 
components. 
In 
[99] 
it 
was 
discussed 
that 
none 
of 
the 
instruments 
existing 
for 
193 
nm 
has 
a 
sensitivity 
sufficient 
for 
investigations 
of 
arbitrary 
state-of-the-art 
optical 
components; 
use 
of 
laser 
light 
sources 
with 
appropriate 
output 
powers 
was 
found 
to 
be 
one 
of 
the 
basic 
requirements. 


2Often 
the 
performance 
of 
ARS 
measurement 
tools 
is 
given 
as 
a 
dynamic 
range 
(DR) 
of 
the 
instru


ments. 
The 
effective 
DR 
is 
the 
difference 
between 
the 
maximum 
ARS 
value 
(1/

s) 
and 
the 


noise-equivalent 
ARS. 


3A 
good 
signal 
to 
background 
(noise) 
ratio 
would 
be 
. 
10. 


29 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 


The 
instrumentation 
for 
scatter 
measurements 
at 
193 
nm 
implemented 
in 
this 
work 
is 
based 
on 
an 
existing 
system 
for 
total 
scatter 
measurements 
at 
157 
nm 
and 
193 
nm 
[21]. 
Several 
modifications 
were 
introduced 
and 
a 
novel 
calibration 
procedure 
for 
193 
nm 
was 
developed 
in 
order 
to 
obtain 
absolute 
and 
accurate 
TS 
values. 
Furthermore, 
a 
unique 
set-up 
for 
angle 
resolved 
scatter 
measurements 
at 
193 
nm 
was 
implemented. 
A 
detailed 
description 
of 
the 
instrument 
is 
given 
in 
[99]. 
The 
main 
components 
are 
schematically 
shown 
in 
5.1. 


1
TS modeARS mode
2345678910CSDGBCMC
Figure 
5.1: 
Instrumentation 
for 
193 
nm. 
BC 
-beam 
preparation 
chamber, 
MC 
measurement 
chamber, 
1 
-excimer 
laser, 
2 
-attenuator, 
3 
-aperture 
stop, 
4 
-baffle, 
5 
-focusing 
mirror, 
6 
-pinhole, 
7 
-focusing 
mirror, 
8 
-beam 
splitter, 
9 
-attenuator, 
10 
-reference 
detector. 
CS 
-Coblentz 
sphere 
for 
TS, 
DG 
double-
goniometer 
for 
ARS. 


Although, 
optical 
measurements 
at 
193 
nm 
can 
be 
performed 
in 
nitrogen 
atmosphere, 
Rayleigh 
scattering 
at 
the 
gas 
molecules 
leads 
to 
enhanced 
background 
scattering 
[27, 
128]. 
A 
10 
cm 
long 
illuminated 
gas 
channel 
at 
atmospheric 
pressure 
causes 
a 
TS 
background 
scattering 
of 
approximately 
1x10-4 
[99]. 
Hence, 
measurements 
of 
rather 
high-scattering 
samples 
can 
be 
performed 
in 
nitrogen 
atmosphere, 
but 
operation 
in 
vacuum 
is 
mandatory 
for 
extremely 
low-scattering 
samples. 
The 
vacuum 
system 
allows 
for 
both 
modes 
of 
operation. 


5.1.1 
Vacuum 
system 
The 
vacuum 
system 
consists 
of 
two 
chambers, 
the 
beam 
preparation 
chamber 
(BC) 
and 
the 
measurement 
chamber 
(MC). 
The 
chambers 
can 
be 
flushed 
with 
nitrogen 
or 


30 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 


operated 
in 
vacuum. 
A 
rotary 
pump 
(Leybold 
TRIVAC 
D 
65 
B) 
with 
an 
adsorption 
filter 
is 
used 
as 
roughing 
pump. 
A 
250 
mm 
diameter 
turbo-molecular 
pump 
(TURBOVAC 
1100 
C) 
is 
used 
to 
achieve 
high-vacuum. 
A 
base 
pressure 
of 
about 
5x10-6 
mbar 
is 
achieved 
after 
20 
minutes 
pumping 
time4 
. 


5.1.2 
Light 
source 
The 
light 
source 
(1) 
is 
an 
ArF* 
excimer 
laser 
(LPF 
220i, 
Lambda 
Physik) 
[3]. 
The 
excimer 
laser 
supplies 
pulsed 
radiation 
at 
a 
wavelength 
of 
193.4 
nm 
with 
a 
pulse 
length 
of 
~ 
15 
ns 
FWHM 
(full 
width 
at 
half 
maximum) 
and 
a 
pulse 
energy 
of 
approximately 
200 
mJ. 
The 
laser 
is 
operated 
at 
a 
repetition 
rate 
of 
50 
Hz. 


5.1.3 
Beam 
preparation 
system 
In 
order 
to 
suppress 
the 
generation 
of 
stray 
light 
of 
the 
illumination 
system, 
great 
care 
had 
been 
taken 
to 
choose 
particularly 
low-scattering 
optical 
components 
throughout 
the 
optical 
system. 
For 
example, 
superpolished 
Si 
wafers 
(rms 
roughness 
<0.1 
nm) 
are 
used 
as 
plane 
deflecting 
mirrors. 


The 
intensity 
of 
the 
incident 
beam 
is 
adjusted 
at 
an 
attenuator 
(2) 
consisting 
of 
up 
to 
three 
metal 
coated 
fused 
silica 
filters. 
The 
beam 
diameter 
is 
adjusted 
using 
a 
variable 
aperture 
stop 
(3), 
and 
a 
baffle 
(4) 
blocks 
stray 
light 
generated 
at 
the 
aperture. 


The 
beam 
is 
focused 
by 
a 
spherical 
aluminum 
coated 
mirror 
(5) 
with 
a 
focal 
length 
of 
F 
= 
300 
mm 
on 
a 
pinhole 
(6) 
with 
a 
diameter 
of 
100 
µm. 
The 
pinhole 
is 
imaged 
by 
a 
second 
spherical 
mirror 
(7, 
F 
= 
431 
mm) 
into 
the 
measurement 
chamber. 
The 
spatial 
filter 
consisting 
of 
the 
two 
focusing 
mirrors 
and 
the 
pinhole 
turned 
out 
to 
be 
essential 
to 
achieve 
a 
narrow, 
clean 
beam 
required 
for 
high-sensitive 
scatter 
measurements. 


During 
operation, 
the 
laser 
exhibits 
short-time 
fluctuations 
of 
the 
pulse 
energy 
as 
well 
as 
a 
long-term 
drift 
of 
the 
output 
power 
as 
a 
result 
of 
laser 
gas 
degradation 
[129]. 
In 
addition, 
laser-induced 
formation 
of 
absorbing 
carbon 
layers 
at 
the 
beam 
preparation 
optics 
leads 
to 
a 
gradually 
decreasing 
incident 
power 
at 
the 
sample 
position. 
Therefore, 
a 
reference 
channel 
has 
been 
implemented 
to 
correct 
for 
theses 
effects. 
A 
superpolished 
CaF2 
plate 
(8) 
is 
used 
as 
beam 
splitter. 
The 
reflected 
beam 
is 
attenuated 
(9) 
and 
enters 
a 
reference 
detector 
(10). 
Interchanging 
of 
the 
attenuators 
between 
pos. 
9 
and 
2 
allows 
for 
adjusting 
the 
intensity 
of 
the 
incident 
beam 
while 
keeping 
the 
reference 
signal 
nearly 
constant 
during 
this 
procedure. 


Provided 
by 
the 
beam 
preparation 
system, 
the 
sample 
is 
illuminated 
with 
a 
clean 
beam 
with 
a 
diameter 
of 
1 
mm 
and 
an 
energy 
density 
of 
3 
mJ/cm2 
for 
both 
TS 
and 
ARS. 


41 
mbar'100 
Pa 


31 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 


5.1.4 
TS 
set-up 
The 
set-up 
for 
TS 
measurements 
is 
schematically 
shown 
in 
Fig. 
5.2 
in 
the 
backscatter 
mode. 
The 
sample 
(1) 
is 
illuminated 
at 
normal 
incidence. 
A 
Coblentz 
sphere 
(CS), 
an 
aluminized 
glass 
hemisphere 
(?350 
mm), 
is 
used 
to 
collect 
the 
scattered 
light. 
For 
TSb, 
the 
radiation 
scattered 
between 
s 
=2. 
and 
85, 
according 
to 
ISO 
13696, 
is 
focused 
by 
the 
CS 
to 
a 
CaF2 
diffuser 
(2) 
mounted 
in 
front 
of 
the 
detector 
(3). 
The 
specularly 
reflected 
(4) 
and 
transmitted 
(5) 
beams 
are 
directed 
out 
of 
the 
CS 
and 
absorbed 
by 
beam 
dumps. 


CS123456
Figure 
5.2: 
Instrumentation 
for 
193 
nm. 
TS 
set-up 
(backscatter 
mode). 
1 
-sample, 


2 
-diffuser, 
3 
-detector, 
4 
-reflected 
beam, 
5 
-transmitted 
beam, 
6 
-rotation 


axis. 


The 
sample 
can 
be 
scanned 
horizontally 
to 
perform 
linear 
TS 
scans 
or 
two-dimensional 
TS 
mappings. 
The 
scans 
can 
then 
be 
analyzed, 
for 
instance 
to 
determine 
an 
average 
TS 
value 
for 
the 
sample 
after 
applying 
a 
data 
reduction 
algorithm 
according 
to 
the 
international 
standard 
[24]. 


For 
TSf 
measurements, 
the 
CS 
together 
with 
the 
sample 
positioning 
and 
detector 
systems 
is 
rotated 
about 
a 
horizontal 
axis 
(6) 
through 
the 
sample 
surface 
to 
switch 
to 
forward 
scatter 
mode. 
This 
configuration 
ensures 
that 
all 
beam 
parameters 
(i.e. 
intensity 
profile, 
divergence, 
relative 
position 
sample-detector) 
and 
thus 
the 
transfer 
function 
of 
the 
system 
are 
maintained 
when 
switching 
between 
the 
two 
modes. 


5.1.5 
ARS 
set-up 
For 
ARS 
measurements, 
a 
precision 
double-goniometer 
module 
is 
inserted 
into 
the 
measurement 
chamber. 
A 
top-view 
of 
the 
set-up 
is 
shown 
in 
Fig. 
5.3. 
Angles 
of 
incidence 
and 
scattering 
can 
be 
adjusted 
between 
0. 
and 
360. 
in 
0.01. 
steps. 


The 
sample 
(1) 
is 
mounted 
onto 
the 
inner 
goniometer 
arm 
(2). 
The 
incident 
beam 
is 
inclined 
to 
the 
goniometer 
rotation 
plane 
by 
an 
angle 
of 
0.5. 
to 
permit 
measurements 


32 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 


1547823
DW
s
q
s
q
i6
Figure 
5.3: 
Instrumentation 
for 
193 
nm. 
ARS 
set-up. 
1 
-sample, 
2 
-inner 
goniometer 


arm, 
3 
-outer 
goniometer 
arm, 
4 
-aperture, 
5 
-focusing 
lens, 
6 
-spectral 
pu


rity 
filter, 
7 
-field 
stop, 
8 
-detector. 


within 
the 
entire 
scattering 
plane 
including 
the 
specularly 
reflected 
and 
transmitted 
beams 
by 
preventing 
masking 
of 
the 
incident 
beam. 
As 
a 
result 
of 
the 
four 
nonnormal 
reflections 
between 
the 
source 
and 
the 
sample, 
the 
incident 
beam 
is 
linearly 
polarized 
with 
a 
stronger 
p-polarized 
(70%) 
component, 
which 
has 
to 
be 
considered 
for 
comparisons 
of 
measurement 
and 
simulation 
results 
if 
no 
polarizer 
is 
used. 
Alternatively, 
the 
polarization 
states 
of 
the 
incident 
beam 
and 
the 
polarization 
sensitivity 
of 
the 
detector 
can 
be 
adjusted 
by 
utilizing 
MgF2 
Rochon 
polarizers. 


The 
detector 
is 
located 
at 
the 
outer 
goniometer 
arm 
(3). 
A 
variable 
aperture 
stop 
(4) 
enables 
detector 
solid 
angles 


s 
between 
1x10-6 
sr 
and 
1x10-4 
sr 
to 
be 
adjusted 
in 
order 
to 
optimize 
the 
system 
for 
near-angle 
scatter 
measurements 
(small 


s) 
or 
for 
maximum 
sensitivity 
(large 


s). 
A 
lens 
(5) 
focuses 
the 
scattered 
light 
to 
the 
detector. 
A 
spectral 
purity 
filter 
(6) 
consisting 
of 
four 
dielectric 
narrow-band 
mirrors 
for 
193 
nm 
deposited 
on 
absorbing 
black 
glass 
can 
be 
used 
to 
suppress 
fluorescent 
light 
of 
the 
sample. 
The 
field 
stop 
(7) 
limits 
the 
field 
of 
view 
of 
the 
detector 
(8) 
to 
a 
diameter 
of 
7 
mm 
at 
the 
sample 
position. 
This 
well-defined 
field 
of 
view 
is 
essential 
to 
quantify 
the 
volume 
scattering 
of 
bulk 
materials 
from 
ARS 
measurements. 


5.1.6 
Detection 
system 
Side-on 
photomultiplier 
tubes 
(PMTs) 
Hamamatsu 
type 
R1220 
and 
R1259 
are 
used 
as 
detectors, 
where 
the 
latter 
is 
insensitive 
to 
radiation 
at 
wavelengths 
>200 
nm 
but 
also 
less 
sensitive 
at 
193 
nm. 
Gated 
pulse 
integration 
(Le 
Croy 
Waverunner-2 
LT 
264 
digital 
oscilloscope) 
is 
used 
for 
noise 
suppression. 
In 
order 
to 
increase 
the 
dynamic 
range 
of 
the 
system, 
both 
the 
attenuation 
and 
the 
dynode 
gain 
voltage 
can 
be 
adjusted 
during 
measurements. 
This, 
however, 
results 
in 
a 
nearly 
exponential 
response 
function 
which 
was 
determined 
experimentally. 


33 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 


5.1.7 
Operation 
and 
performance 
Appropriate 
calibration 
of 
the 
TS 
and 
ARS 
measurements 
is 
essential 
in 
order 
to 
achieve 
reliable, 
reproducible, 
and 
comparable 
results. 
For 
example, 
only 
use 
of 
ARS 
(rather 
than 
scattered 
intensity) 
permits 
the 
total 
scatter 
loss 
to 
be 
calculated 
by 
numerical 
integration 
of 
the 
scattering 
distribution. 


Calibration 
of 
TS 
or 
ARS 
measurements 
is 
usually 
performed 
by 
comparison 
of 
the 
scattering 
signals 
of 
the 
samples 
under 
investigation 
with 
the 
corresponding 
signals 
of 
diffuse 
scattering 
standards 
with 
known 
(certified) 
scattering 
properties 
[24, 
25, 
28]. 


Unfortunately, 
there 
are 
no 
such 
standard 
scatterers 
for 
wavelengths 
below 
200 
nm. 
Although 
ARS 
measurements 
can 
also 
be 
calibrated 
by 
measuring 
the 
relevant 
quantities 
according 
to 
Eq. 
(2.2) 
directly, 
this 
usually 
requires 
the 
measurement 
of 
signals 
that 
are 
separated 
by 
several 
orders 
of 
magnitude. 
Moreover, 
calibration 
of 
TS 
measurements 
by 
direct 
measurement 
of 
the 
incident 
power 
as 
performed 
in 
[20] 
does 
not 
take 
into 
account 
the 
transfer 
function 
of 
the 
Coblentz 
sphere 
[99, 
130]. 
For 
these 
reasons, 
new 
calibration 
procedures 
for 
193 
nm 
were 
developed 
[99]. 


The 
procedures 
utilize 
CaF2 
diffuser 
disks 
as 
pseudo-standards 
assuming 
that 
the 
sum 
of 
all 
specular 
and 
diffuse 
quantities 
must 
be 
unity 
if 
bulk 
absorption 
and 
fluorescence 
effects 
can 
be 
neglected. 
For 
TS, 
the 
calibration 
factor 
is 
determined 
by 
postulating 
that 
for 
the 
CaF2 
diffuser 
T 
+ 
R 
+ 
TSb 
+ 
TSf 
˜ 
1. 
For 
ARS, 
the 
integrated 
scattered 
power 
of 
the 
diffuser 
in 
the 
entire 
hemisphere 
should 
yield 
unity. 
This 
allows 
a 
calibrated 
ARS 
curve 
of 
the 
diffuser 
to 
be 
determined 
which 
can 
be 
used 
as 
reference 
curve 
for 
the 
calibration 
of 
all 
measurements. 
This 
method 
yields 
results 
which 
are 
consistent 
with 
the 
calibration 
by 
direct 
measurement 
of 
the 
incident 
power 
and 
the 
detector 
solid 
angle 
but 
avoids 
some 
critical 
issues 
of 
the 
latter 
technique 
[99]. 


TS 
background 
scattering 
levels 
and 
ARS 
instrument 
signatures, 
both 
measured 
using 
an 
empty 
sample 
holder, 
are 
shown 
in 
Fig. 
5.4 
for 
operation 
in 
nitrogen 
atmosphere 
and 
in 
high-vacuum. 
In 
addition, 
TS 
and 
ARS 
measurement 
results 
of 
a 
superpolished 
Si 
wafer 
(rms 
roughness 
0.08 
nm 
determined 
by 
AFM 
in 
a 
1x1 
µm2 
scan 
area) 
are 
shown 
for 
comparison5 
. 


The 
diagrams 
reveal 
that 
in 
case 
of 
operation 
in 
nitrogen 
atmosphere 
Rayleigh 
scattering 
at 
the 
gas 
molecules 
limits 
the 
sensitivity 
of 
the 
instrument. 
Although 
this 
is 
sufficient 
for 
the 
investigation 
of 
samples 
with 
TS 
levels 
>10-4, 
operation 
in 
vacuum 
is 
mandatory 
for 
low-scattering 
samples 
such 
as 
superpolished 
surfaces. 
In 
this 
case, 
the 
background 
scattering 
is 
limited 
by 
electronic 
noise 
and 
residual 
stray 
light 
in 
the 
measurement 
chamber. 
Nevertheless, 
TS 
background 
scatter 
levels 
<10-6 
and 
ARS 


5Throughout 
this 
work, 
both 
ARS 
and 
TS 
curves 
are 
shown 
as 
solid 
lines. 
This 
representation 
is 
justified 
by 
appropriate 
selection 
of 
the 
measurement 
parameters 
for 
ARS 
(detector 
solid 
angle 
and 
angular 
resolution) 
and 
TS 
(spot 
diameter 
and 
lateral 
resolution) 
such 
that 
the 
information 
of 
adjacent 
data 
points 
overlap. 


34 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 


-4-2024
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
TSscan (mm)
background scattering
/  TSb vacuum/N2
/  TSf vacuum/N2
 TSb Si wafer (vacuum)
-90-4504590135180225270
10-8
10-6
10-4
10-2
100
102
104
106
instrument signature 
N2 
vacuum 
Si waferARS (sr-1)s ( ° )
Figure 
5.4: 
Instrumentation 
for 
193 
nm. 
Detection 
limits 
for 
operation 
in 
N2 
atmosphere 
(1 
bar) 
and 
vacuum 
(~ 
10-6 
mbar). 
Left: 
TS 
background 
scattering 
levels. 
Right: 
ARS 
instrument 
signature. 


instrument 
signatures 
<10-6, 
which 
corresponds 
to 
a 
dynamic 
range 
of 
more 
than 
12 
orders 
of 
magnitude, 
are 
achieved. 


Photographs 
of 
the 
vacuum 
chambers, 
the 
Coblentz 
sphere, 
and 
the 
double-goniometer 
are 
shown 
in 
Fig. 
5.5. 
The 
size 
of 
the 
instrument 
(without 
the 
laser) 
is 
about 
2.0x1.8x1.0 
m3 
. 



Figure 
5.5: 
Instrumentation 
for 
193 
nm. 
Photographs 
showing 
the 
vacuum 
chambers 
(right), 
the 
Coblentz-sphere 
(upper 
left) 
for 
TS, 
and 
the 
double 
goniometer 
(lower 
left) 
for 
ARS 
measurements. 


35 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 


5.2 
Instrumentation 
for 
13.5 
nm 
So 
far, 
scattering 
measurements 
at 
13.5 
nm 
have 
only 
been 
reported 
from 
synchrotronfacilities 
in 
the 
US 
[13] 
and 
Japan 
[22, 
131]. 
As 
far 
as 
can 
be 
judged 
from 
the 
few 
experimental 
data 
available, 
even 
though 
the 
instruments 
allow 
reflectance 
and 
angle 
resolved 
scatter 
measurements 
at 
arbitrary 
angles 
of 
incidence 
with 
dynamic 
ranges 
of 
up 
to 
7 
orders 
of 
magnitude 
(provided 
by 
the 
high 
brightness 
of 
synchrotron 
radiation), 
there 
seem 
to 
be 
difficulties 
in 
measuring 
near-angle 
scattering 
below 
4. 
or 
at 
quasi-normal 
incidence. 
Furthermore, 
stand-alone 
instruments 
are 
required 
for 
characterization 
close 
to 
manufacturing 
of 
optical 
components 
to 
prevent 
extrinsic 
contamination 
and 
degradation 
effects 
from 
interfering 
with 
the 
intrinsic 
scattering 
properties. 
Several 
laboratory-based 
instruments 
for 
the 
measurement 
of 
EUV 
reflectance 
were 
developed 
recently 
[132, 
133, 
134]. 
However, 
these 
instruments 
can 
not 
provide 
the 
beam 
properties 
and 
dynamic 
ranges 
required 
for 
scatter 
measurements 
of 
high-quality 
samples. 


A 
novel 
instrument 
for 
the 
measurement 
of 
EUV 
reflectance 
and 
scattering 
at 
13.5 
nm 
has 
been 
developed 
in 
the 
frame 
of 
this 
work. 
It 
represents 
the 
first 
laboratory-size, 
synchrotron-independent 
system 
capable 
of 
both 
reflectance 
and 
scatter 
measurements 
at 
13.5 
nm. 
The 
instrument 
first 
mentioned 
in 
[135] 
and 
[136] 
is 
briefly 
presented 
in 
this 
section. 
The 
set-up 
is 
schematically 
shown 
in 
Fig. 
5.6. 


In 
contrast 
to 
measurements 
at 
193 
nm, 
operation 
in 
high-vacuum 
is 
mandatory 
for 
measurements 
at 
13.5 
nm. 
The 
absorption 
coefficient 
[137] 
of 
EUV 
radiation 
in 
air 
(at 
atmospheric 
pressure) 
calculated 
using 
the 
data 
given 
in 
[40] 
is 
˜ 
70 
cm-1 
. 
This 
corresponds 
to 
a 
penetration 
depth 
of 
< 
200 
µm. 
Hence, 
pressures 
below 
10-3 
mbar 
are 
required6 
to 
reduce 
absorption 
losses 
to 
1% 
at 
a 
beam 
path 
length 
of 
~ 
1 
m. 


5.2.1 
Vacuum 
system 
The 
vacuum 
system 
consists 
of 
three 
chambers, 
the 
source 
chamber 
(SC), 
the 
beam 
preparation 
chamber 
(BC), 
and 
the 
measurement 
chamber 
(MC). 
The 
EUV 
source 
(1) 
is 
attached 
to 
the 
SC 
which 
contains 
the 
collector 
optics. 
A 
2 
mm 
diameter 
hole 
(2) 
between 
the 
SC 
and 
BC 
enables 
differential 
pumping, 
since 
the 
achievable 
base 
pressure 
in 
the 
SC 
is 
limited 
by 
the 
gas 
flow 
out 
of 
the 
light 
source. 
An 
oil-free 
piston 
pump 
attached 
to 
the 
BC 
and 
the 
MC 
is 
used 
as 
roughing 
pump. 
A 
250 
mm 
diameter 
turbo 
molecular 
pump 
(TURBOVAC 
1100 
C) 
is 
attached 
to 
the 
BC 
to 
achieve 
high-vacuum. 
A 
base 
pressure 
of 
about 
5x10-6 
mbar 
is 
achieved 
after 
15 
minutes 
pumping 
time. 


6The 
absorption 
coefficient 
decreases 
linearly 
with 
the 
pressure. 


36 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 


23147M1M2M386SCBCMCM4M55
q
s
qr
q
i
Figure 
5.6: 
Instrumentation 
for 
13.5 
nm. 
SC 
-source 
chamber, 
BC 
-beam 
preparation 
chamber, 
MC 
-measurement 
chamber, 
M1,..,M5 
-mirrors, 
1 
-EUV 
lamp, 
2 
hole, 
3 
-Zr 
filter, 
4 
-pinhole, 
5 
-reference 
detector, 
6 
-sample, 
7 
-doublegoniometer, 
8 
-detector. 


5.2.2 
Light 
source 
An 
EUV 
lamp, 
which 
is 
based 
on 
a 
Xe-gas 
discharge 
plasma 
(hollow-cathode 
Z-pinch 
plasma 
geometry) 
[138], 
is 
used 
as 
light 
source. 
The 
EUV 
lamp 
generates 
about 
1014 
photons 
with 
each 
pulse 
into 
2p 
sr 
within 
the 
EUV 
band 
of 
13.5 
nm 
±2%. 
This 
corresponds 
to 
approximately 
4 
mJ 
in-band 
power 
per 
pulse. 
The 
pulse 
length 
is 
100 
ns, 
and 
the 
source 
is 
operated 
at 
a 
repetition 
rate 
of 
50 
Hz. 
In 
addition 
to 
the 
EUV 
radiation, 
out-of-band 
radiation 
ranging 
from 
a 
few 
nanometers 
up 
to 
the 
visible 
spectral 
range 
as 
well 
as 
debris, 
a 
stream 
of 
high-energetic 
particles 
(mainly 
sputtered 
electrode 
material 
and 
Xe 
ions), 
is 
emitted 
[68, 
139]. 
Thus, 
the 
properties 
of 
the 
EUV 
source 
substantially 
differ 
from 
laser 
light 
sources, 
which 
represented 
a 
challenging 
task 
for 
the 
design 
of 
the 
measurement 
system. 


5.2.3 
Beam 
preparation 
system 
A 
Zr 
foil 
transmission 
filter 
(3) 
with 
a 
thickness 
of 
0.2 
µm 
is 
utilized 
to 
suppress 
outof-
band 
radiation 
and 
to 
protect 
the 
collector 
optics 
from 
source 
debris. 


Throughout 
the 
optical 
system, 
Mo/Si 
multilayer 
mirrors 
deposited 
on 
superpolished 
Si 
wafers 
(plane 
mirrors) 
and 
fused 
silica 
substrates 
(curved 
mirrors) 
are 
used. 
The 
mirrors 
were 
designed 
for 
highest 
reflectance 
at 
13.5 
nm 
at 
their 
respective 
angles 
of 
application. 
The 
collector 
optics 
consists 
of 
a 
focusing 
mirror 
(M1, 
?50 
mm, 
F 
= 
200 
mm) 
followed 
by 
two 
plane 
deflecting 
mirrors 
(M2, 
M3). 
An 
intermediate 
focus 
is 
formed 
between 
the 
SC 
and 
the 
BC 
(2). 


The 
beam 
entering 
the 
BC 
is 
focused 
by 
a 
spherical 
mirror 
(M4, 
?50 
mm, 
F 
= 
100 
mm) 
to 
a 
pinhole. 
The 
pinhole 
is 
imaged 
by 
a 
spherical 
mirror 
(M5, 
?50 
mm, 
F 
= 
200 
mm) 


37 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 


onto 
the 
detector 
in 
the 
MC. 
Pinhole 
diameters 
between 
0.1 
mm 
and 
0.5 
mm 
are 
used 
depending 
on 
the 
application; 
the 
size 
being 
a 
trade-off 
between 
high 
incident 
power 
and 
a 
small 
beam 
diameter 
at 
the 
detector 
aperture. 
Radiation 
scattered 
off 
the 
pinhole 
is 
exploited 
to 
measure 
a 
reference 
signal 
at 
the 
reference 
detector 
(6). 


The 
illumination 
spot 
at 
the 
sample 
position 
has 
a 
diameter 
of 
approximately 
1 
mm 
(depending 
on 
the 
pinhole 
diameter). 
The 
polarization 
of 
the 
incident 
beam, 
which 
has 
to 
be 
considered 
for 
the 
interpretation 
of 
the 
measured 
data, 
is 
nearly 
unpolarized 
(65% 
s-polarized) 
as 
calculated 
by 
multiplying 
the 
theoretical 
reflectance 
curves 
of 
the 
beam 
preparation 
mirrors. 


5.2.4 
Spectral 
purity 
filter 
system 
Spectral 
filtering 
of 
the 
broad-band 
radiation 
emitted 
by 
the 
EUV 
lamp 
is 
essential 
for 
measurements 
at 
13.5 
nm. 
However, 
this 
constitutes 
a 
challenging 
task. 
The 
incident 
spectrum 
should 
have 
a 
spectral 
bandwidth 
below 
0.5 
nm, 
which 
is 
the 
bandwidth 
of 
a 
typical 
EUV 
mirror, 
with 
as 
much 
power 
around 
13.5 
nm 
as 
possible. 
At 
the 
same 
time, 
out-of-band-radiation 
has 
to 
be 
suppressed 
by 
at 
least 
3 
orders 
of 
magnitude. 
Neither 
single 
transmissive 
filters 
nor 
diffraction 
gratings 
can 
fulfill 
these 
stringent 
demands. 
Yet 
this 
problem 
was 
solved 
along 
with 
the 
design 
of 
the 
beam 
preparation 
system: 
Through 
combination 
of 
the 
Zr 
filter, 
which 
suppresses 
radiation 
at 
> 
20 
nm, 
and 
the 
5 
Mo/Si 
mirrors, 
which 
act 
as 
narrow-band 
reflection 
filters, 
a 
highly 
efficient 
EUV 
band 
pass 
filter 
is 
achieved 
as 
illustrated 
in 
Fig. 
5.7. 


020406080100120
10-30
10-20
10-10
10-2
10-1
100
Intensity (a.u.) (nm) 
T Zr (thickness 0.2 µm) 
R (Mo/Si)60 (5 reflections) 
total filter function
Figure 
5.7: 
Instrumentation 
for 
13.5 
nm. 
Calculated 
spectral 
filter 
performance 
of 
the 
beam 
preparation 
system. 


The 
condition 
for 
maximum 
(resonant) 
reflectance 
of 
an 
ideal 
multilayer 
structure 
in 
the 
EUV 
can 
be 
approximated 
by 
the 
Bragg 
equation 
[140]: 
m. 
=2H 
cos 
i, 
where 
m 
is 
the 
diffraction 
order 
and 
H 
is 
the 
thickness 
of 
one 
multilayer 
period7 
. 
It 
is 
evident 


7The 
full 
expression 
contains 
a 
correction 
factor 
which 
accurately 
takes 
into 
account 
the 
slight 
deviations 
of 
the 
indices 
of 
refraction 
from 
unity 
[140]. 


38 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 


that 
for 
a 
given 
H 
measuring 
the 
reflectance 
as 
a 
function 
of 
the 
angle 
of 
incidence 
(-2. 
measurement) 
is 
equivalent 
to 
scanning 
the 
wavelength. 


This 
fact 
was 
exploited 
to 
determine 
the 
effective 
spectrum 
registered 
by 
the 
detector. 
-2. 
measurements 
were 
performed 
on 
a 
narrow-band 
reflector 
especially 
designed 
for 
this 
purpose. 
The 
design 
is 
(3.5 
nm 
Mo/31.5 
nm 
Si)30 
. 
Provided 
by 
the 
high 
Bragg 
diffraction 
order 
utilized 
(m 
= 
4) 
and 
the 
small 
thickness 
ratio 
dMo/H 
˜ 
0.1, 
the 
spectral 
bandwidth 
of 
the 
coating 
and 
thus 
the 
spectral 
resolution 
of 
the 
procedure 
is 
as 
low 
as 
0.1 
nm 
FWHM. 


Simulations 
of 
R(i; 
) 
were 
performed 
for 
discrete 
wavelengths 
between 
10 
nm 
and 
80 
nm 
using 
the 
software 
IMD 
[39]. 
The 
total 
reflectance 
curve 
was 
calculated 
as 
weighted 
average 
of 
the 
functions 
R(i; 
) 
by 
assuming 
a 
spectral 
intensity 
distribution 
I(). 
A 
recursive 
optimization 
algorithm 
for 
I() 
was 
developed 
to 
fit 
the 
theoretical 
2. 
curve 
to 
the 
measurement 
result 
(see 
Fig. 
5.8 
(left)). 
The 
resulting 
effective 
spectral 
distribution 
is 
shown 
in 
Fig. 
5.8 
(right). 
A 
strong 
peak 
at 
13.5 
nm 
and 
some 
residual 
secondary 
peaks 
can 
be 
observed, 
which 
correspond 
to 
electronic 
transitions 
of 
ten-fold 
ionized 
Xe 
[141] 
and 
could 
be 
expected 
from 
the 
emitted 
spectrum 
[142]. 
Nevertheless, 
the 
filtered 
spectrum 
can 
be 
considered 
quasi-monochromatic 
with 
a 
center 
wavelength 
of 
13.5 
nm 
and 
a 
bandwidth 
of 
±0.2 
nm 
FWHM. 


-1001020304050607080
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Ri (°) 
meas. 
sim. = 13.5 nm 
sim. filtered spectrum
12.513.013.514.0
0.0
0.2
0.4
0.6
0.8
1.0
Intensity (a.u.) (nm)
 emitted 
 after filtering
Figure 
5.8: 
Determination 
of 
the 
incident 
spectrum. 
Left: 
-2. 
measurement 
result 
compared 
to 
simulations 
using 
monochromatic 
light 
and 
the 
estimated 
spectrum. 
Right: 
Spectrum 
after 
filtering 
estimated 
by 
the 
simulation. 


The 
equivalence 
of 
R(i) 
and 
R() 
can 
generally 
be 
exploited 
to 
compensate 
the 
constraints 
of 
quasi-monochromatic 
illumination, 
as 
will 
be 
further 
discussed 
in 
Sec. 
6.2.2. 
Moreover, 
because 
the 
wavelength 
remains 
constant 
during 
-2. 
measurements, 
dispersion 
effects 
of 
the 
dielectric 
properties 
are 
eliminated. 
This 
could 
be 
useful 
if 
samples 
are 
to 
be 
compared 
that 
are 
not 
accurately 
centered 
at 
the 
same 
wavelength. 


39 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 


5.2.5 
ARS 
set-up 
The 
measurements 
are 
based 
on 
a 
precision 
double 
goniometer. 
The 
samples 
(6) 
are 
mounted 
on 
a 
horizontal 
x-y-positioning 
unit 
(7) 
onto 
the 
inner 
goniometer 
arm. 
The 
outer 
goniometer 
arm 
carries 
the 
detector 
(8). 
Both 
goniometer 
arms 
can 
be 
rotated 
within 
360. 
with 
a 
resolution 
of 
0.01. 
. 
The 
incident 
beam 
is 
tilted 
about 
0.9. 
with 
respect 
to 
the 
measurement 
plane 
to 
prevent 
any 
masking 
of 
the 
incident 
beam. 
This 
allows 
even 
near-angle 
scattering 
or 
specular 
reflectance 
to 
be 
measured 
at 
quasi-normal 
incidence. 


5.2.6 
Detection 
system 
Silicon 
photodiodes 
IRD 
AXUV100, 
uncoated 
or 
coated 
with 
an 
additional 
EUV 
band 
pass 
filter, 
are 
used 
as 
detectors 
[143]. 
The 
photodiodes 
are 
well-suited 
for 
this 
application 
because 
of 
their 
high 
quantum 
efficiency 
(˜ 
25 
electrons 
per 
incident 
photon 
at 


13.5 
nm), 
homogeneity, 
and 
radiation 
stability 
[143]. 
The 
detector 
signals 
are 
preprocessed 
using 
vacuum 
compatible 
pulse 
amplifiers 
and 
analyzed 
via 
gated 
pulse 
integration 
(Le 
Croy 
Waverunner 
6200 
digital 
oscilloscope) 
to 
suppress 
electronic 
noise. 
The 
reference 
pulse 
is 
used 
for 
triggering 
the 
oscilloscope 
to 
suppress 
the 
influence 
of 
time 
jitter 
of 
the 
plasma 
discharge 
and 
to 
correct 
the 
measurement 
signals 
for 
fluctuations 
of 
the 
output 
power 
of 
the 
source. 


5.2.7 
Operation 
and 
performance 
The 
calibration 
issue 
is 
even 
more 
critical 
for 
measurements 
at 
13.5 
nm 
since 
neither 
diffuse 
reflectance 
standards 
nor 
transparent 
materials 
exist 
that 
could 
be 
used 
as 
pseudo-standards. 
However, 
calibration 
can 
be 
performed 
by 
measuring 
the 
incident 
power 
and 


s 
directly. 
Alternatively, 
ARS 
measurements 
can 
be 
calibrated 
by 
measuring 
the 
scattering 
of 
a 
reference 
sample. 
An 
EUV 
mirror 
which 
is 
permanently 
mounted 
in 
the 
double 
sample 
holder 
and 
was 
originally 
calibrated 
using 
the 
first 
mentioned 
method 
is 
utilized 
for 
this 
purpose. 


The 
instrument 
signature 
of 
the 
system 
is 
shown 
in 
Fig. 
5.9. 
The 
incident 
beam 
corresponding 
to 
the 
peak 
at 
180. 
is 
slightly 
broadened 
as 
a 
result 
of 
scattering 
from 
the 
beam 
preparation 
system 
itself. 
The 
sensitivity 
of 
the 
instrument 
is 
limited 
by 
electronic 
noise. 
The 
dynamic 
range 
exceeds 
6 
orders 
of 
magnitude. 
Though, 
as 
discussed 
above, 
ARS 
levels 
down 
to 
10-3 
sr-1 
are 
expected 
for 
high-quality 
EUV 
mirrors. 
Hence, 
the 
effective 
angular 
range 
in 
which 
information 
about 
the 
scattering 
distribution 
of 
low-scattering 
samples 
can 
be 
retrieved 
will 
be 
limited. 
Nevertheless, 
the 
dynamic 
range 
achieved 
should 
be 
sufficient 
to 
investigate 
EUV 
mirrors 
in 
the 
most 
important 
angular 
regions 
around 
the 
specular 
direction. 


40 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 


-90-4504590135180225270
10-4
10-3
10-2
10-1
100
101
102
103 
instrument signatureARS (sr-1)s (°)
Figure 
5.9: 
Instrumentation 
for 
13.5 
nm. 
Instrument 
signature 
for 
ARS 
measurements. 
Photographs 
of 
the 
whole 
system 
and 
the 
double 
goniometer 
are 
shown 
in 
Fig. 
5.10. 



Figure 
5.10: 
Instrumentation 
for 
13.5 
nm. 
Photographs 
showing 
the 
vacuum 
chambers 
(right) 
and 
the 
double-goniometer 
(left). 


5.3 
Uncertainty 
budget 
The 
measurement, 
data 
acquisition, 
and 
evaluation 
procedures 
are 
similar 
for 
the 
instruments 
at 
193 
nm 
and 
13.5 
nm. 
For 
this 
reason, 
a 
general 
treatment 
of 
the 
measurement 
uncertainties 
is 
briefly 
presented 
in 
this 
section. 


An 
uncalibrated 
measurement 
value 
U 
obtained 
from 
an 
ARS, 
TS, 
or 
R 
measurement 
is 
determined 
by 
normalizing 
the 
detector 
signal 
Vs 
to 
the 
signal 
Vref 
measured 
at 
the 
reference 
detector 
and 
applying 
correction 
factors 
for 
the 
amplification 
Camp 
and 
attenuation 
Catt: 


Vs

U 
= 
CampCatt 
. 
(5.1) 
Vref 


41 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 


For 
low-level 
intensity 
measurements, 
noise 
from 
the 
detection 
system 
becomes 
crucially 
important. 
The 
dominating 
source 
of 
noise 
in 
photodiodes 
is 
dark 
current. 
In 
photomultipliers, 
the 
primary 
noise 
source 
is 
shot 
noise 
of 
the 
dark 
current 
arising 
from 
the 
quantum 
nature 
of 
the 
photons, 
the 
uncertainty 
in 
photon 
arrival 
rates, 
and 
electron 
emission 
probability. 
In 
addition, 
electromagnetic 
disturbances 
may 
couple 
into 
the 
detection 
system 
through 
cables 
and 
connectors. 
In 
particular 
the 
vacuum 
pumps 
and 
the 
light 
sources 
of 
the 
instruments 
used 
in 
this 
work 
are 
considerable 
sources 
of 
noise, 
and 
electromagnetic 
shielding 
is 
particularly 
important. 
All 
these 
noise 
effects 
act 
on 
Vs 
and 
Vref 
. 


The 
amplification 
factors 
of 
the 
PMTs 
in 
the 
DUV 
system 
were 
determined 
experimentally 
[99]. 
Sources 
of 
error 
are 
deviations 
from 
linearity 
as 
well 
as 
statistical 
fluctuations 
of 
the 
dynode 
gain 
(excess 
noise). 
The 
amplification 
factors 
of 
the 
EUV 
system 
were 
provided 
by 
the 
supplier. 
For 
both 
instruments, 
linearity 
was 
checked 
and 
the 
uncertainties 
of 
the 
amplification 
factors 
were 
determined 
experimentally. 


The 
attenuation 
factor 
is 
relevant 
for 
the 
DUV 
system 
only. 
Since 
it 
is 
strongly 
influenced 
by 
contamination 
and 
degradation 
effects, 
the 
factor 
is 
determined 
for 
each 
attenuator 
change. 


From 
Eq. 
(5.1), 
error 
propagation 
leads 
to 
a 
general 
expression 
for 
the 
relative 
uncer


tainty 
of 
U: 
. 

U 
U 
2 
= 
. 

Vs 
Vs 
2 
+ 
. 

Vref 
Vref 
2 
+ 
. 

Camp 
Camp 
2 
+ 
. 

Catt 
Catt 
2 
. 
(5.2) 


In 
order 
to 
determine 
ARS, 
TS, 
or 
R 
values, 
calibration 
of 
the 
measurement 
values 
is 
required. 
Calibration 
is 
performed 
by 
comparing 
U 
of 
the 
sample 
with 
the 
corresponding 
value 
of 
a 
calibration 
sample 
with 
known 
ARS, 
TS, 
or 
R 
resulting 
in 
a 
calibration 
factor 
Ccal. 
The 
resulting 
uncertainty 
of 
the 
final 
measurement 
value 
is 


2 
(
U/U)2 
+ 
(
Ccal/Ccal)2 
. 


The 
actual 
uncertainty 
of 
a 
particular 
measurement 
can 
be 
reduced 
by 
maintaining 
as 
much 
parameters 
constant 
as 
possible 
(e.g. 
variable 
attenuation 
and 
amplification 
are 
not 
necessary 
for 
R 
measurements). 
The 
estimated 
uncertainties 
for 
different 
measurement 
regimes 
are 
summarized 
in 
Tab. 
5.1 
together 
with 
some 
additional 
comments. 
Although 
not 
of 
the 
main 
interest 
in 
this 
work, 
the 
uncertainties 
for 
measurements 
of 
the 
specular 
reflectance 
and 
transmittance 
at 
193 
nm 
and 
13.5 
nm 
are 
also 
given. 


The 
comparatively 
high 
relative 
uncertainties 
of 
the 
scattering 
measurements 
at 
193 
nm 
are 
a 
consequence 
of 
the 
high 
dynamic 
ranges 
required, 
because 
the 
main 
sources 
of 
uncertainty 
are 
the 
variable 
amplification 
and 
attenuation. 
Nevertheless, 
considering 
the 
sensitivity 
of 
the 
instruments, 
the 
achieved 
parameters 
lead 
to 
superior 
absolute 
measurement 
uncertainties 
for 
investigations 
of 
low-scattering 
samples. 
For 
example, 


42 



5 
Experimental 
set-ups 
for 
scatter 
measurements 
at 
193 
nm 
and 
13.5 
nm 


Contributor 
ARS 
193 
nm 
TS 
193 
nm 
R, 
T 
193 
nm 
ARS 
13.5 
nm 
R, 
T 
13.5 
nm 


Vs, 
Vref 
1% 
1% 
1% 
1% 
1% 
Camp 
5% 
5% 
-1% 
-
Catt 
10% 
---4 
-
Ccal 
5% 
1 
17%2 
-5%1 
0.15%5 
Total 
17% 
19% 
2% 
(0.3%3) 
6% 
2% 
(0.3%3) 


Table 
5.1: 
Uncertainty 
budget 
for 
scatter 
and 
reflectance 
measurements 
at 
193 
nm 
and 


13.5 
nm. 
Relative 
uncertainties 
of 
contributing 
quantities 
and 
total 
relative 
measurement 
uncertainties 
of 
specified 
methods. 
*1 
calibration 
by 
direct 
measurement 
of 


s, 
*2 
calibration 
using 
reference 
sample 
with 
TS 
deterv 
mined 
from 
ARS 
measurements, 
*3 
~ 
1/K 
with 
K 
= 
100 
the 
number 
of 
independent 
measurement 
values, 
*4 
currently, 
no 
attenuation 
necessary 
because 
of 
limited 
source 
intensity 
and 
detector 
sensitivity. 
*5 
uncertainty 
of 
reflectance 
of 
reference 
sample 
measured 
by 
the 
PTB 
[144]. 


the 
set-up 
for 
TS 
at 
193 
nm 
allows 
a 
scatter 
loss 
of 
10-6 
(1 
ppm) 
to 
be 
measured 
with 


an 
uncertainty 
of 
2x10-7 
. 


43 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


In 
addition 
to 
the 
measurement 
equipment 
for 
scattering 
measurements 
at 
193 
nm 
and 
13.5 
nm 
presented 
in 
Sec. 
5, 
new 
measurement 
and 
analysis 
techniques 
had 
to 
be 
developed 
to 
interpret 
the 
results 
and 
to 
investigate 
the 
causes 
of 
the 
observed 
scattering. 
For 
example, 
combination 
of 
scattering 
measurements 
with 
independent 
roughness 
measurements 
is 
necessary 
to 
analyze 
multilayer 
coatings, 
or 
separation 
of 
interface 
and 
bulk 
scattering 
is 
essential 
to 
investigate 
optical 
bulk 
materials. 


DUV 
and 
EUV 
optical 
components 
are 
nearly 
without 
exception 
covered 
with 
optical 
coatings. 
Therefore, 
investigations 
of 
coatings 
are 
of 
particular 
importance. 
First, 
a 
new 
methodology 
for 
the 
scatter 
analysis 
for 
arbitrary 
coatings 
is 
discussed 
in 
detail 
for 
DUV 
coatings. 
Afterwards, 
the 
procedure 
is 
utilized 
for 
investigations 
of 
DUV 
and 
EUV 
coatings. 
Yet 
only 
investigations 
of 
HR 
coatings 
are 
discussed 
in 
detail, 
for 
two 
reasons: 
Because 
all 
effects 
can 
be 
expected 
to 
be 
more 
pronounced 
for 
coatings 
containing 
a 
larger 
number 
of 
layers, 
investigations 
of 
HR 
coatings 
provide 
a 
magnified 
view 
onto 
the 
thin 
film 
related 
scattering 
effects. 
Furthermore, 
because 
EUV 
coatings 
are 
HR 
coatings 
in 
general, 
this 
allows 
for 
comparing 
the 
scattering 
properties 
of 
DUV 
and 
EUV 
coatings 
directly. 
Nevertheless, 
the 
methods 
and 
results 
can 
be 
transferred 
to 
other 
types 
of 
coatings 
as 
well. 


6.1 
Coatings 
and 
bulk 
materials 
for 
applications 
at 
193 
nm 
The 
high 
photon 
energy 
of 
193 
nm 
radiation 
(6.4 
eV) 
demands 
bulk 
and 
coating 
materials 
with 
sufficiently 
high 
electronic 
band 
gaps 
in 
order 
to 
achieve 
tolerable 
absorption 
and 
to 
avoid 
radiation 
damage. 
This 
drastically 
reduces 
the 
number 
of 
suitable 
materials. 


Among 
oxides, 
only 
SiO2 
and 
Al2O3 
offer 
sufficiently 
high 
transparency 
at 
193 
nm. 
Metal 
fluorides 
are 
transparent 
down 
to 
120 
nm 
and 
are 
therefore 
preferred. 
However, 
fluoride 
films 
typically 
exhibit 
pronounced 
nanostructures 
with 
several 
nanometers 
roughness 
[86] 
giving 
rise 
to 
considerable 
scattering. 
Scatter 
losses 
of 
fluoride 
HR 


44 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


coatings 
ranging 
from 
0.2% 
up 
to 
13% 
were 
reported 
by 
different 
groups 
[19, 
21, 
145]. 
Yet 
systematic 
investigations 
of 
scattering 
at 
193 
nm 
with 
respect 
to 
the 
underlying 
mechanisms 
could 
hardly 
be 
found 
at 
the 
beginning 
of 
this 
work 
with 
only 
two 
exceptions 
[16, 
19]. 
Moreover, 
the 
general 
restriction 
to 
total 
scattering 
(a 
single 
number 
that 
characterizes 
the 
scatter 
loss) 
inhibited 
a 
detailed 
analysis. 


Angle 
resolved 
scattering 
should 
reveal 
more 
information 
about 
the 
fundamental 
scattering 
mechanisms. 
Unfortunately, 
in 
particular 
for 
multilayer 
coatings, 
the 
large 
number 
of 
parameters 
impedes 
the 
analysis. 
A 
methodology 
to 
analyze 
the 
ARS 
of 
multilayer 
coatings 
is 
presented 
in 
the 
following 
sections. 
The 
DUV 
coatings 
discussed 
in 
this 
thesis 
were 
provided 
by 
the 
Optical 
Coatings 
department 
of 
the 
Fraunhofer 
IOF, 
Jena 
and 
by 
Newport 
Corp., 
Irvine 
(CA). 
All 
films 
were 
deposited 
by 
thermal 
boat 
evaporation 
at 
elevated 
substrate 
temperatures 
(T 
˜ 
300C). 


Common 
substrate 
materials 
for 
193 
nm 
applications 
are 
CaF2 
and 
synthetic 
fused 
silica. 
Compared 
to 
CaF2, 
synthetic 
fused 
silica 
is 
much 
harder, 
easier 
to 
shape 
and 
to 
polish, 
and 
noticeably 
less 
expensive 
(considering 
that 
the 
typical 
diameter 
of 
lithography 
optics 
is 
about 
300 
mm) 
[15]. 
Though, 
considerable 
absorption 
and 
scattering 
can 
be 
expected 
[146], 
and 
their 
accurate 
determination 
and 
separation 
are 
of 
great 
importance, 
e.g. 
for 
the 
optical 
design 
to 
compensate 
thermal 
lensing 
effects. 
Detailed 
analysis 
of 
the 
scattering 
properties 
of 
synthetic 
fused 
silica 
at 
193 
nm 
is 
presented 
at 
the 
end 
of 
this 
section. 
The 
samples 
were 
provided 
by 
Heraeus 
Quarzglas 
GmbH 
& 
Co. 
KG, 
Hanau. 


6.1.1 
ARS 
modeling 
methodology 
In 
Sec. 
3.3, 
theories 
for 
the 
simulation 
of 
the 
ARS 
of 
multilayer 
coatings 
were 
presented 
which 
require 
knowledge 
of 
~ 
M2 
interface 
and 
cross-correlation 
PSDs. 
However, 
only 
the 
top-surface 
of 
a 
coating 
is 
generally 
accessible 
to 
direct 
topography 
measurements. 
Therefore, 
appropriate 
models 
for 
the 
roughness 
of 
the 
buried 
interfaces 
and 
their 
crosscorrelation 
properties 
are 
essential 
to 
simulate 
the 
scattering. 
The 
validity 
of 
such 
models 
has 
to 
be 
proven 
by 
comparison 
of 
the 
predicted 
scattering 
with 
the 
results 
of 
scattering 
measurements. 


In 
[16], 
simulations 
of 
the 
total 
scattering 
of 
fluoride 
quarter-wave 
stacks 
were 
compared 
to 
measurement 
results 
at 
193 
nm. 
The 
simple 
top-down 
model 
led 
to 
deviations 
of 
up 
to 
74%. 
A 
rather 
good 
agreement 
was 
achieved 
by 
using 
the 
partial 
correlation 
model, 
but 
M 
measured 
PSDs 
had 
to 
be 
known. 
In 
[72], 
a 
small 
subset 
of 
interface 
PSDs 
were 
approximated 
by 
the 
top-surface 
PSDs 
of 
similar 
multilayer 
stacks 
interrupted 
after 
different 
periods. 
The 
missing 
intermediate 
PSDs 
were 
estimated 
by 
linear 
interpolation. 
Yet 
also 
this 
method 
requires 
fabrication 
of 
a 
set 
of 
samples 
to 
emulate 
the 
actually 
buried 
interfaces 
and 
is 
based 
on 
rather 
heuristic 
assumptions. 
A 
more 


45 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


general 
approach 
which 
is 
consistent 
with 
existing 
physical 
models 
was 
developed 
in 
this 
work 
and 
will 
be 
illustrated 
for 
one 
DUV 
coating. 
First, 
the 
conventional 
procedure 
is 
discussed. 


Conventional 
scatter 
analysis 


In 
the 
frame 
of 
a 
study 
on 
stress-induced 
defects 
in 
fluoride 
multilayers 
for 
193 
nm 
deposited 
on 
fused 
silica, 
HR 
coatings 
for 
normal 
incidence 
were 
investigated 
[147]. 
One 
design, 
(L/H)20 
with 
H=LaF3 
and 
L=AlF3 
is 
discussed 
in 
detail 
here 
to 
demonstrate 
the 
modeling 
procedures. 


The 
results 
of 
ARS 
measurements 
at 
193 
nm 
are 
shown 
in 
Fig. 
6.1 
(left). 
The 
scattering 
of 
the 
coating 
is 
substantially 
higher 
than 
the 
scattering 
of 
the 
uncoated 
substrate. 
The 
TSb 
calculated 
from 
the 
ARS 
data1 
increases 
from 
(0.11 
± 
0.02)% 
for 
the 
uncoated 
substrate 
to 
(2.8±0.5)% 
for 
the 
coating. 
Considering 
Eq. 
(3.9), 
this 
can 
be 
qualitatively 
explained 
by 
a 
two-fold 
effect: 
(i) 
increased 
reflectance 
(optical 
factors) 
and 
(ii) 
increased 
roughness 
(roughness 
factors). 


-90-60-300306090
10-5
10-4
10-3
10-2
10-1
100 
meas. coating 
mod. coating 
meas. substrateARS (sr-1)s ( ° )
0.1110100
10-3
100
103
106 
N=20 
substratePSD (nm4)f (µm-1)
Figure 
6.1: 
AlF3/LaF3 
mirror 
for 
193 
nm. 
Left: 
ARS 
measured 
(”meas.”, 
blue) 
and 


modeled 
using 
the 
top-down 
model 
(”mod.”, 
red). 
Right: 
PSDs 
of 
the 


coating 
(blue) 
and 
the 
uncoated 
substrate 
(grey). 


To 
verify 
this 
assumption, 
top-surface 
roughness 
measurements 
of 
the 
coating 
and 
uncoated 
substrates 
were 
performed 
using 
AFM. 
Master 
PSDs, 
calculated 
by 
combining 
the 
AFM 
data 
of 
different 
scans 
for 
each 
sample, 
are 
shown 
in 
Fig. 
6.1 
(right). 
The 
substrate 
exhibits 
a 
fractal 
PSD 
while 
the 
PSD 
of 
the 
coating 
can 
be 
interpreted 
as 
a 
superposition 
of 
the 
fractal 
PSD 
and 
an 
ABC-PSD 
(see 
Sec. 
3.4). 
The 
corresponding 
AFM 
images 
shown 
in 
Fig. 
6.2 
reveal 
that 
pronounced 
nanocrystallites 
and 
agglomerates 
of 
crystallites 
in 
the 
coating 
are 
the 
cause 
for 
this 
effect. 
The 
roughness 
in 
the 


1The 
equivalence 
of 
TS 
values 
directly 
measured 
and 
calculated 
from 
ARS 
data 
was 
demonstrated 
in 
[148]. 


46 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


1x1 
µm2 
and 
10x10 
µm2 
scan 
areas 
increases 
from 
˜ 
0.3 
nm 
to 
˜ 
5 
nm 
after 
20 
layer 
pairs. 



Figure 
6.2: 
AlF3/LaF3 
mirror 
for 
193 
nm. 
AFM 
images 
of 
uncoated 
fused 
silica 
sub


strate 
(left) 
and 
HR 
coating 
(right). 
The 
roughness 
values 
in 
the 
insets 
are 


for 
the 
corresponding 
scans. 


The 
only 
structural 
information 
available 
so 
far 
is 
the 
top-surface 
roughness 
and 
the 
theoretical 
design. 
Consequently, 
ARS 
can 
only 
modeled 
using 
the 
top-down 
model 
by 
approximating 
all 
PSDs 
with 
the 
measured 
top-surface 
PSD. 
The 
result 
shown 
in 
Fig. 
6.1 
(left, 
red 
curve) 
is 
in 
rather 
poor 
agreement 
with 
the 
measured 
(blue) 
curve. 
The 
overestimated 
ARS 
at 
smaller 
scatter 
angles 
is 
presumably 
caused 
by 
the 
assumption 
that 
all 
interfaces 
are 
equal 
to 
the 
top-surface. 
The 
deviations 
at 
larger 
angles 
look 
similar 
to 
the 
effect 
of 
a 
mismatch 
of 
the 
incident 
and 
the 
resonance 
wavelengths 
of 
EUV 
coatings 
shown 
in 
[149]. 
A 
more 
realistic 
model 
that 
takes 
into 
account 
the 
roughness 
evolution 
and 
layer 
thickness 
deviations 
in 
the 
multilayer 
is 
presented 
in 
the 
next 
section. 


Derivation 
of 
ARS 
modeling 
procedure 


The 
linear 
growth 
theory 
provides 
explicit 
results 
for 
the 
roughness 
evolution 
of 
coatings 
in 
the 
stochastic 
limit 
but 
is 
not 
valid 
if 
columnar 
growth 
occurs. 
The 
more 
general 
scaling 
laws 
(Eq. 
(3.15)) 
describe 
the 
evolution 
of 
roughness 
as 
a 
function 
of 
film 
thickness 
but 
have 
been 
used 
for 
single 
layers 
only. 


Using 
the 
thickness 
of 
the 
multilayer 
D 
= 
N 
· 
H, 
where 
H 
is 
the 
geometrical 
thickness 
of 
one 
multilayer 
period, 
a 
generalized 
scaling 
approach 
is 
proposed: 
s 
~ 
Dß 
. 
N 
= 
aN, 
where 
a 
is 
a 
parameter. 


Following 
this 
simple 
approach, 
different 
roughness 
scalings 
can 
be 
identified 
in 
the 
literature: 
LGT 
predicts 
ß 
=0.5 
(see 
Eq. 
(3.21)), 
which 
represents 
the 
random 
deposition 


47 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


limit. 
In 
[150], 
ß 
= 
1 
was 
observed 
in 
ZnS/ThF4 
coatings 
for 
633 
nm. 


Multilayer 
stacks 
for 
193 
nm 
and 
157 
nm 
with 
N 
= 
5 
to 
25 
and 
L=AlF3 
and 
various 
H 
materials 
were 
investigated 
in 
the 
frame 
of 
this 
work 
[151]. 
The 
evolution 
of 
roughness 
for 
different 
material 
combinations 
was 
determined 
from 
AFM 
in 
10x10 
µm² 
scan 
areas. 
The 
results 
are 
shown 
in 
Fig. 
6.3 
(left) 
together 
with 
best 
fits 
according 
to 
s 
~ 
Nß 
with 
emphasis 
on 
the 
uppermost 
interfaces. 
ß 
ranging 
from 
0.15 
(nearly 
saturated 
roughness) 
to 
1 
(rapid 
roughening) 
are 
be 
observed. 
Although 
for 
several 
sample 
sets 
the 
simple 
scaling 
model 
does 
not 
hold 
for 
all 
N 
(which 
indicates 
transitions 
between 
different 
growth 
mechanisms), 
it 
accurately 
describes 
the 
roughness 
evolution 
down 
to 
15 
layer 
pairs 
below 
the 
top-surfaces 
of 
all 
coatings. 


0510152025
0
1
2
3
4
 SmF3 = 0.45
 YbF3 = 1.0
 GdF3 = 0.45
 LaF3 = 0.25
 YF3 = 0.15
 (nm)N
0.1110100
10-1
101
103
105
107
85°2° 
f (µm-1) PSD (nm4) 
N=25 
N=15 
N=10 
N=5 
ABC mod. 
different ATS at 193 nm
Figure 
6.3: 
Roughness 
evolution 
in 
multilayer 
stacks 
with 
different 
H 
materials 
(L=AlF3 
for 
all 
coatings) 
and 
different 
number 
of 
layer 
pairs. 
Left: 
Rms 
roughness 
(from 
AFM 
in 
10x10 
µm2 
scan 
areas). 
Right: 
PSDs 
for 
GdF3 
based 
coatings. 


The 
relevance 
of 
an 
interface 
for 
the 
overall 
scattering 
is 
proportional 
to 
the 
electric 
field 
intensity 
at 
that 
interface. 
For 
HR 
coatings, 
an 
effective 
information 
depth 
is 
defined 
as 
the 
depth 
in 
the 
coating 
at 
which 
the 
transmittance 
drops 
to 
1/e2 
˜ 
14%. 
For 
a 
free-standing 
HR 
coating 
[152]: 


. 
2 
2

1 
- 
(nH 
/nL)N 
nH

T 
=1 
- 
R 
= 
, 
(6.1) 


1+(nH 
/nL)N 
nH 
2 


where 
nH 
and 
nL 
are 
the 
indices 
of 
refraction 
of 
the 
H 
and 
L 
materials, 
respectively. 


Typical 
values 
of 
nH 
˜ 
1.67 
and 
nL 
˜ 
1.42 
for 
DUV 
coatings 
[153] 
lead 
to 
an 
information 
depth 
of 
7 
layer 
pairs. 
For 
EUV 
mirrors 
consisting 
of 
Mo 
(nH 
=0.9216) 
and 
Si 
(nL 
=0.99946)2, 
the 
estimated 
information 
depth 
is 
19 
layer 
pairs 
below 
the 


2The 
nomenclature 
of 
H 
and 
L 
was 
chosen 
with 
respect 
to 
the 
absolute 
deviation 
of 
the 
indices 
of 
refraction 
to 
unity. 


48 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


top-surface3 
. 
Hence, 
the 
proposed 
scaling 
model 
accurately 
describes 
the 
roughness 
of 
all 
relevant 
interfaces 
of 
typical 
DUV 
and 
EUV 
coatings 
provided 
either 
by 
the 
limited 
penetration 
depth, 
in 
particular 
in 
HR 
stacks, 
or 
by 
the 
smaller 
number 
of 
layers 
used, 
for 
instance 
in 
AR 
coatings 
[154]. 


The 
scaling 
approach 
can 
now 
be 
applied 
to 
calculate 
the 
evolution 
of 
the 
interface 
PSDs 
as 
a 
function 
of 
N. 
The 
intrinsic 
thin 
film 
roughness 
(i.e. 
excluding 
the 
substrate 
roughness) 
of 
a 
multilayer 
after 
N 
periods 
is 
modeled 
as 
ABC-PSD 
(see 
Eq. 
3.16). 
The 
parameters 
A, 
B, 
C, 
and 
a 
for 
the 
top-surface 
are 
obtained 
by 
fitting 
a 
model-PSD 
to 
a 
measured 
PSD. 
C, 
which 
indicates 
the 
dominant 
surface 
relaxation 
mechanism, 
is 
constant 
for 
all 
interfaces. 
Also 
the 
variation 
of 
B, 
corresponding 
to 
the 
lateral 
dimension 
of 
dominating 
surface 
features, 
is 
neglected 
because 
the 
alternating 
materials 
represent 
barriers 
for 
the 
granular 
growth 
[116, 
151, 
155]. 
This 
effect 
is 
illustrated 
in 
Fig. 
6.3 
(right) 
for 
GdF3-based 
stacks. 


Parameter 
A, 
which 
corresponds 
to 
the 
height 
of 
the 
PSD, 
is 
calculated 
as 
a 
function 
of 
N 
using 
the 
proposed 
scaling 
approach 
and 
Eq. 
(3.14): 


a2B2(C 
- 
1)

N2

AN 
()= 
, 
(6.2) 


2p 
where 
ß 
is 
the 
only 
free 
parameter 
describing 
the 
roughness 
evolution 
of 
the 
multilayer. 


This 
procedure 
allows 
both 
linear 
(ß 
=0.5) 
and 
nonlinear 
growth 
to 
be 
described. 
Extending 
this 
model 
to 
include 
variations 
of 
B 
and 
C 
or 
to 
model 
the 
evolution 
as 
a 
function 
of 
the 
layer 
number 
is 
straightforward. 


In 
addition 
to 
the 
roughness 
evolution 
in 
multilayer 
coatings, 
optical 
layer 
thickness 
deviations 
from 
the 
theoretical 
design 
have 
to 
be 
considered. 
Such 
thickness 
deviations 
may 
arise 
from 
nonuniformity 
effects 
during 
deposition 
[156] 
(geometrical 
thickness 
deviations) 
or 
refractive 
index 
variations 
associated 
with 
porosity 
and 
packing 
density 
[80, 
157]. 
In 
this 
thesis, 
these 
effects 
are 
approximated 
by 
introducing 
an 
average 
optical 
layer 
thickness 
deviation 
d 
of 
the 
realized 
layers 
from 
the 
ideal 
thickness. 


Based 
on 
ARS 
measurement 
and 
modeling, 
a 
procedure 
can 
be 
established 
for 
the 
estimation 
of 
the 
two 
parameters 
ß 
and 
: 


1. 
Determination 
of 
the 
top-surface 
PSD 
using 
appropriate 
roughness 
measurement 
techniques. 
As 
discussed 
in 
Sec. 
4, 
AFM 
is 
best-suited 
for 
this 
purpose. 
2. 
Parametrization 
of 
the 
measured 
PSD 
by 
using 
model-PSDs 
and 
separation 
of 
substrate 
and 
intrinsic 
thin 
film 
roughness 
components. 
3. 
Definition 
of 
appropriate 
start 
parameters, 
for 
instance 
ß 
= 
0 
and 
d 
= 
0. 
3In 
Eq. 
(6.1), 
absorption 
is 
neglected. 
Exact 
calculation 
of 
the 
electric 
field 
intensities 
including 
absorption 
by 
utilizing 
IMD 
yields 
an 
information 
depth 
of 
15 
layer 
pairs. 


49 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


4. 
Variation 
of 
ß 
and 
. 
5. 
Estimation 
of 
the 
PSDs 
of 
the 
buried 
interfaces 
assuming 
a 
roughness 
evolution 
with 
parameter 
ß 
(Eq. 
(6.2)): 
For 
k 
=1, 
..., 
N: 
PSDk(f; 
), 
PSD2k 
= 
PSD2k-1 
(subsequent 
interfaces 
of 
one 
period 
are 
assumed 
to 
be 
equal). 
6. 
Calculation 
of 
the 
cross-correlation 
PSDs 
according 
to 
the 
partial 
correlation 
model: 
PSDij 
= 
PSDkk 
with 
k 
= 
min{i, 
j} 
(see 
Sec. 
3.3). 
PM 
PM


7. 
Calculation 
of 
ARS: 
ARSmod(s; 
)= 
1 
Ci()Cj 
() 
PSDij 
(f; 
), 
where 
4 
i=0 
j=0 


M 
=2N. 


8. 
Comparison 
with 
measured 
ARS 
by 
determining 
the 
merit 
function 
. 
[86, 
158]: 
K

1 
X. 
. 
2 
= 
ln 
ARSmeas(s 
(k)) 
- 
ln 
ARSmod(s 
(k); 
, 
) 
2 
, 
(6.3) 


K 


k=1 


where 
K 
is 
the 
number 
of 
sampling 
points. 


9. 
Minimization 
of 
. 
via 
refinement 
of 
ß 
and 
d 
. 
return 
to 
step 
4. 
The 
final 
result 
is 
a 
model 
for 
the 
scatter-relevant 
structural 
properties 
of 
the 
coating 
with 
the 
new 
parameters 
ß 
and 
. 


Advanced 
scatter 
analysis 
using 
ARS 
modeling 
procedure 


The 
ARS 
modeling 
procedure 
can 
now 
be 
applied 
to 
analyze 
the 
scattering 
of 
the 
LaF3/AlF3 
coating 
described 
at 
the 
beginning 
of 
this 
section. 
The 
results 
for 
different 
ß 
and 
d 
compared 
to 
the 
measured 
ARS 
curves 
are 
shown 
in 
Fig. 
6.4. 


-90-60-300306090
10-5
10-4
10-3
10-2
10-1
100 
meas. 
mod. = 0 
mod. = 0.25 
mod. = 0.5 
mod. = 0.75 
mod. = 1ARS (sr-1)s ( ° )
-90-60-300306090
10-5
10-4
10-3
10-2
10-1
100 
meas. 
mod. = 0 
mod. = 0.01 
mod. = 0.02 
mod. = 0.03 
mod. = 0.04 
mod. = 0.05ARS (sr-1)s ( ° )
Figure 
6.4: 
ARS 
modeling 
procedure. 
Left: 
Effect 
of 
variation 
of 
. 
Right: 
Effect 
of 
variation 
of 
. 


50 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


Fig. 
6.4 
(left) 
reveals 
that 
variation 
of 
ß 
essentially 
shifts 
the 
near-specular 
ARS 
in 
height. 
In 
X-ray 
terminology, 
this 
effect 
is 
referred 
to 
as 
”resonant 
diffuse 
scattering” 
[149]: 
Scattering 
with 
|s| 
. 
30. 
is 
within 
the 
Bragg-peak 
of 
the 
HR 
coating. 
As 
a 
result, 
contributions 
of 
different 
interfaces 
add 
up 
in 
phase, 
provided 
that 
the 
interface 
roughness 
is 
highly 
correlated, 
and 
ARS 
is 
proportional 
to 
the 
average 
PSD. 


The 
best 
fit 
is 
achieved 
for 
ß 
= 
1. 
Considering 
the 
uncertainty 
of 
both 
the 
measured 
and 
the 
simulated 
ARS 
(through 
the 
PSD 
measured 
via 
AFM), 
the 
absolute 
uncertainty 
of 
the 
estimation 
of 
ß 
using 
the 
modeling 
procedure 
is 
0.3. 
This 
is 
sufficient 
to 
distinguish 
between 
saturated 
roughness, 
stochastic 
roughening, 
and 
rapid 
roughening. 


As 
can 
be 
observed 
from 
Fig. 
6.4 
(right), 
variation 
of 
d 
leads 
to 
a 
shift 
of 
the 
angular 
position 
of 
the 
characteristic 
wings 
of 
the 
ARS, 
while 
the 
ARS 
at 
small 
angles 
is 
nearly 
constant 
if 
d 
. 
0.05. 
The 
best 
fit 
is 
achieved 
for 
d 
=0.030 
± 
0.005. 
The 
sensitivity 
of 
the 
procedure 
allows 
layer 
thickness 
deviations 
of 
as 
low 
as 
0.3 
nm 
for 
DUV 
coatings 
and 
0.04 
nm 
for 
EUV 
coatings 
to 
be 
detected. 


The 
effect 
of 
d 
on 
the 
scattering 
characteristics 
can 
be 
explained 
by 
enhanced 
electric 
field 
intensities 
in 
the 
coating 
as 
illustrated 
in 
Fig. 
6.5 
(calculations 
were 
performed 
with 
IMD). 
The 
enhanced 
fields 
lead 
to 
increased 
scattering 
through 
the 
optical 
factor 
in 
Eq. 
(3.9). 
For 
radiation 
propagating 
at 
|s| 
. 
30. 
outside 
the 
multilayer 
resonance, 
the 
coating 
becomes 
transparent 
and 
the 
enhanced 
scattering 
from 
the 
innermost 
interfaces 
can 
penetrate 
through 
the 
multilayer. 
The 
transition 
between 
dominating 
influence 
of 
ß 
and 
d 
occurs 
at 
s 
˜ 
30. 
at 
the 
edge 
of 
the 
multilayer 
resonance4 
. 


02004006008001000
0
1
2
d= 0
d= 0.03
electricfieldintensity(a.u.)thickness (nm)
220
210
200
190
180
170
02004006008001000400
thickness (nm)
l(nm)
0
1
2
Figure 
6.5: 
Calculated 
standing 
wave 
electric 
field 
intensities 
for 
d 
= 
0 
and 
d 
=0.03. 
Vertical 
lines 
represent 
interfaces. 
Thickness 
is 
measured 
from 
the 
topsurface. 
For 
better 
comparability, 
d 
has 
been 
converted 
into 
a 
variation 
of 
the 
incident 
(not 
the 
design) 
wavelength: 
. 
= 
193.4 
nm/(1 
+ 
). 


4This 
means 
that 
the 
transition 
angle 
in 
general 
depends 
on 
the 
spectral 
bandwidth 
of 
the 
multilayer. 


51 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


As 
shown 
in 
Tab. 
6.1, 
aside 
from 
the 
scattering 
distribution, 
both 
ß 
and 
d 
crucially 
influence 
the 
scatter 
loss 
(For 
HR 
coatings, 
TSb 
can 
be 
identified 
with 
the 
total 
scatter 
loss 
since 
forward 
scattering 
can 
be 
neglected 
[99]) 
and 
limit 
the 
reflectance 
of 
the 
LaF3/AlF3 
mirror 
at 
193 
nm. 


d 
TSb 
(%) 
R1 
(%) 


0 
0 
2.2 
96.7 
0.5 
0 
1.7 
97.2 
1 
0 
1.4 
97.6 
1 
0.03 
2.72 
96.1 
1 
0.05 
4.6 
92.0 
Table 
6.1: 
Influence 
of 
ß 
and 
d 
on 
the 
TSb 
and 
R 
of 
the 
LaF3/AlF3 
coating 
at 
193 
nm. 


*1 
calculated 
as 
R 
= 
R0 
- 
TSb, 
*2 
This 
value 
has 
to 
be 
compared 
to 
the 


measurement 
result 
of 
2.8%. 


The 
final 
results 
of 
the 
modeling 
procedure 
for 
ß 
= 
1 
and 
d 
=0.03 
are 
presented 
in 
Fig. 
6.6. 
The 
measured 
and 
some 
of 
the 
estimated 
PSDs 
of 
buried 
interfaces 
used 
for 
the 
ARS 
calculation 
are 
shown 
in 
Fig. 
6.6 
(right). 
The 
simulated 
ARS 
(Fig. 
6.6 
(left)) 
is 
in 
excellent 
agreement 
with 
the 
measured 
curve. 
This 
demonstrates 
the 
accuracy 
of 
the 
measurement 
and 
modeling 
procedures. 
This 
also 
proves 
that 
the 
scattering 
theory 
used 
(see 
Sec. 
3.3.1) 
is 
valid 
at 
193 
nm. 
Moreover, 
the 
results 
reveal 
that 
the 
observed 
scattering 
is 
in 
fact 
caused 
by 
the 
roughness 
of 
the 
uppermost 
interfaces 
(down 
to 
˜ 
7 
layer 
pairs 
below 
top-surface) 
and 
their 
cross-correlation 
properties 
but 
also 
depends 
on 
layer 
thickness 
deviations. 


-90-60-300306090
10-5
10-4
10-3
10-2
10-1
100 
meas. 
mod. = 0.03ARS (sr-1)s ( ° )
0.1110100
10-3
100
103
106meas. 
N=20 
substratemod. 
N=20 
N=15 
N=10 
N=5 
N=5 int.
PSD (nm4)f (µm-1)
85°2°TS at 193 nm
Figure 
6.6: 
ARS 
modeling 
procedure. 
Final 
results 
for 
ß 
= 
1 
and 
d 
=0.03. 
Left: 
Measured 
and 
modeled 
ARS 
curves. 
Right: 
Measured 
and 
estimated 
PSDs 
after 
N 
multilayer 
periods. 
In 
addition 
to 
the 
total 
PSDs, 
the 
intrinsic 
thin 
film 
component 
is 
shown 
exemplarily 
for 
N 
=5. 


The 
main 
aspects 
of 
the 
ARS 
modeling 
procedure 
presented 
in 
this 
section 
can 
be 
summarized 
as 
follows: 


52 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


• 
The 
scattering 
properties 
of 
multilayer 
coatings 
are 
the 
result 
of 
a 
combination 
of 
interface 
roughness 
and 
thin 
film 
interference 
effects. 
• 
An 
ARS 
modeling 
procedure 
was 
presented 
with 
two 
descriptive 
parameters: 
Parameter 
ß 
describes 
the 
roughness 
evolution 
as 
a 
function 
of 
the 
multilayer 
period, 
and 
parameter 
d 
represents 
optical 
layer 
thickness 
deviations. 
• 
For 
HR 
coatings, 
ß 
mainly 
influences 
the 
scattering 
around 
the 
specular 
direction, 
and 
d 
leads 
to 
enhanced 
large-angle 
scattering. 
The 
ARS 
modeling 
also 
enables 
investigating 
the 
scattering 
properties 
of 
coatings 
for 
situations 
which 
are 
not 
accessible 
to 
direct 
measurement. 
The 
procedure 
comprises: 
(i) 
scatter 
measurement 
under 
convenient 
conditions, 
(ii) 
ARS 
modeling 
to 
determine 
the 
top-surface 
roughness, 
, 
and 
, 
(iii) 
simulation 
of 
the 
scattering 
under 
any 
condition 
of 
interest. 


This 
procedure 
for 
the 
first 
time 
allowed 
the 
determination 
of 
the 
scatter 
losses 
of 
HR 
coatings 
at 
193 
nm 
at 
oblique 
incidence 
[116]. 
The 
investigations 
revealed 
a 
strong 
anisotropy 
of 
the 
hemispherical 
scatter 
distribution. 
Moreover, 
the 
total 
scattering 
was 
found 
to 
be 
substantially 
higher 
for 
p-polarized 
than 
for 
s-polarized 
incident 
light 
as 
a 
result 
of 
a 
different 
penetration 
depth 
into 
the 
multilayer. 


A 
combination 
of 
ARS 
measurement 
and 
modeling 
was 
also 
utilized 
to 
investigate 
the 
scattering 
of 
AR 
coatings 
for 
193 
nm 
immersion 
lithography 
when 
immersed 
in 
water. 
The 
main 
result 
of 
the 
investigations 
discussed 
in 
detail 
in 
[116] 
was 
that 
the 
scatter 
loss 
of 
the 
immersed 
coating 
would 
be 
as 
low 
as 
(1.1 
± 
0.2) 
× 
10-3 
. 
Moreover, 
it 
was 
found 
that 
the 
scattering 
was 
dominated 
by 
substrate 
roughness 
and 
intrinsic 
thin 
film 
roughness 
played 
a 
minor 
role. 


Significantly 
higher 
scattering 
can 
generally 
be 
expected 
for 
multilayer 
coatings 
because 
of 
the 
larger 
number 
of 
layers. 
The 
influence 
of 
the 
substrate 
polish 
on 
the 
scattering 
of 
fluoride 
HR 
coatings 
is 
investigated 
in 
detail 
in 
the 
next 
section. 


6.1.2 
Fluoride 
HR 
coatings 
on 
CaF2: 
influence 
of 
substrate 
polish 
The 
preparation 
of 
sufficiently 
smooth 
substrates 
for 
DUV 
applications 
requires 
enormous 
effort 
[15]. 
In 
order 
to 
analyze 
the 
actual 
impact 
of 
substrate 
roughness 
on 
the 
scattering 
of 
HR 
coatings 
at 
193 
nm, 
fluoride 
quarter-wave 
stacks 
were 
deposited 
on 
differently 
polished 
substrates, 
normal-polished 
(“n”, 
rms 
roughness 
<0.5 
nm) 
and 
superpolished 
(“s”, 
rms 
roughness 
<0.2 
nm) 
CaF2 
(diameter 
25 
mm). 


In 
addition 
to 
the 
different 
substrates, 
an 
unconventional 
coating 
material 
combination 
was 
employed 
with 
the 
objective 
of 
achieving 
smoother 
interfaces 
and 
lower 
intrinsic 
scattering. 
In 
fluoride 
coatings 
for 
193 
nm, 
usually 
MgF2 
or 
AlF3 
is 
used 
as 
low-index 


53 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


material 
[159]. 
The 
latter 
was 
shown 
to 
grow 
in 
an 
X-ray 
amorphous 
structure 
with 
lower 
surface 
roughness 
[153, 
160] 
offering 
reduced 
scatter 
losses. 
LaF3 
is 
used 
almost 
exclusively 
as 
high-index 
material 
[153], 
although 
recently 
coatings 
with 
H=GdF3 
[161, 
162] 
were 
reported. 
In 
search 
of 
alternative 
materials, 
a 
variety 
of 
metal 
fluorides 
were 
investigated 
in 
the 
past 
[163] 
and 
also 
during 
this 
work 
[151, 
153]. 
AFM 
measurements 
of 
30 
nm 
thick 
single 
layers 
of 
LaF3 
and 
YbF3 
deposited 
on 
Si 
wafer 
substrates 
revealed 
promising 
nanostructural 
properties 
of 
YbF3 
in 
1x1 
µm² 
scan 
areas 
(rms 
roughness 


0.48 
nm 
compared 
to 
0.87 
nm) 
[153]. 
Therefore, 
HR 
coatings 
for 
normal 
incidence 
at 
193 
nm 
consisting 
of 
H=YbF3 
and 
L=AlF3 
with 
N 
= 
15 
were 
deposited 
at 
320C 
substrate 
temperature 
on 
the 
n-and 
spolished 
CaF2 
substrates 
(diameter 
25 
mm). 
The 
substrates 
were 
supplied 
as 
“random 
oriented” 
(i.e. 
no 
specification 
of 
the 
crystal 
orientation). 


The 
ARS 
of 
the 
coatings 
and 
the 
uncoated 
substrates 
were 
measured 
at 
193 
nm. 
The 
results 
shown 
in 
Fig. 
6.7 
reveal 
substantially 
higher 
ARS 
of 
the 
coatings 
compared 
to 
both 
substrates. 
Although 
the 
TSb 
of 
the 
uncoated 
substrates 
calculated 
from 
the 
ARS 
data 
of 
(1.2 
± 
0.2) 
× 
10-5 
(s) 
and 
(3.0 
± 
0.5)x10-4 
(n) 
differ 
by 
a 
factor 
of 
30, 
the 
TSb 
of 
the 
coatings 
of 
(0.9 
± 
0.2)% 
(s) 
and 
(1.0 
± 
0.2)% 
(n) 
are 
almost 
identical. 


-90-60-300306090
10-6
10-5
10-4
10-3
10-2
10-1
100
s-polish 
HR coating 
uncoated substr.
ARS (sr-1)s ( ° )
n-polish 
HR coating 
uncoated substr.
Figure 
6.7: 
YbF3/AlF3 
coatings 
on 
differently 
polished 
substrates. 
ARS 
at 
193 
nm 
of 
coatings 
deposited 
on 
superpolished 
(s) 
and 
normal-polished 
(n) 
CaF2, 
and 
ARS 
of 
uncoated 
substrates. 


Nevertheless, 
the 
ARS 
measurements 
reveal 
enhanced 
scattering 
of 
the 
coating 
on 
the 
n-substrate 
for 
s 
. 
40. 
. 
This 
effect 
could 
at 
first 
glance 
be 
misinterpreted 
as 
a 
result 
of 
the 
higher 
roughness 
of 
the 
n-substrate. 
On 
the 
other 
hand, 
the 
coating 
on 
the 
s-substrate 
exhibits 
enhanced 
scattering 
at 
s 
. 
40, 
which 
is 
in 
contradiction 
to 
the 
results 
of 
the 
uncoated 
substrates. 


To 
investigate 
the 
actual 
origins 
of 
the 
different 
scattering 
effects, 
the 
ARS 
modeling 
procedure 
was 
applied. 


Representative 
AFM 
images 
of 
the 
coatings 
and 
the 
uncoated 
substrates 
are 
shown 
in 


54 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


Fig. 
6.8. 
A 
granular 
structure 
of 
the 
YbF3 
top-layers 
can 
be 
observed 
in 
the 
1x1 
µm² 
scan 
areas. 
The 
coating 
on 
the 
s-substrate 
exhibits 
a 
slightly 
denser 
nanostructure 
resulting 
in 
a 
lower 
small-scale 
roughness. 
In 
contrast, 
a 
more 
pronounced 
long-range 
roughness 
(superstructure) 
of 
the 
coating 
deposited 
on 
the 
s-substrate 
can 
be 
observed. 



Figure 
6.8: 
YbF3/AlF3 
coatings 
on 
differently 
polished 
substrates. 
AFM 
images 
of 


coatings 
and 
uncoated 
substrates. 
The 
rms 
roughness 
values 
calculated 


from 
the 
image 
data 
are 
given 
in 
the 
insets. 


The 
observed 
morphologies 
indicate 
columnar 
growth. 
Considering 
the 
melting 
temperature 
of 
YbF3 
(Tm 
= 
1160 
C 
[164]), 
a 
reduced 
substrate 
temperature 
of 
Ts/Tm 
˜ 
0.4 
is 
calculated 
corresponding 
to 
zone 
II 
in 
the 
structure 
zone 
models. 
The 
reduced 
temperature 
is 
higher 
than 
that 
of 
a 
similarly 
fabricated 
coating 
containing 
H=LaF3 
(Tm 
= 
1493 
C 
[165]). 
This 
could 
explain 
the 
lower 
roughness 
observed 
for 
the 
YbF3 
single 
layer 
and 
the 
considerably 
lower 
TS 
values 
of 
the 
YbF3-based 
mirrors 
compared 
to 
the 
LaF3-based 
coating 
of 
the 
previous 
section. 


PSDs 
were 
calculated 
from 
the 
AFM 
data 
as 
described 
in 
Sec. 
4.4. 
The 
scatter-relevant 
roughness 
calculated 
by 
numerical 
integration 
of 
the 
Master 
PSDs 
and 
the 
measured 
TSb 
values 
of 
the 
coatings 
are 
shown 
in 
Tab. 
6.2. 
No 
reasonable 
correlation 
between 
the 
roughness 
before 
and 
after 
coating 
or 
the 
scatter 
losses 
can 
be 
observed. 
This 
demonstrates 
that 
knowledge 
of 
the 
top-surface 
roughness 
of 
multilayer 
coatings 
alone 


55 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


does 
not 
permit 
conclusions 
about 
the 
scatter 
losses; 
a 
more 
detailed 
scatter 
analysis 
is 
necessary. 


s-polish 
n-polish 


s 
relevant 
for 
TS 
(nm) 
2.24 
(0.16)1 
1.86 
(0.43) 
TSb 
measured 
(%) 
(0.9 
± 
0.2)% 
(1.0 
± 
0.2)% 


Table 
6.2: 
YbF3/AlF3 
coatings 
on 
differently 
polished 
substrates. 
Measured 
rms 
roughness 
and 
total 
backscattering. 
*1 
values 
in 
parenthesis 
are 
for 
the 
uncoated 
substrates. 


The 
PSDs 
were 
modeled 
utilizing 
a 
combination 
of 
two 
shifted 
ABC 
model-PSDs 
with 


-1 
-1

roll-off-spatial 
frequencies 
near 
1 
µmand 
30 
µmto 
take 
into 
account 
the 
longrange 
and 
small-scale 
structures, 
respectively. 
Additional 
AFM 
measurements 
were 
performed 
on 
similar 
multilayer 
stacks 
with 
N 
= 
5 
and 
N 
= 
10 
to 
support 
the 
roughness 
evolution 
model. 
The 
parameters 
of 
the 
model-PSDs 
were 
fitted 
according 
to 
s 
~ 
Nß 
to 
estimate 
the 
intermediate 
interface 
PSDs. 


The 
ARS 
modeling 
was 
then 
utilized 
to 
verify 
and 
refine 
this 
initial 
roughness 
evolution 
model. 
The 
final 
results 
of 
the 
ARS 
modeling 
compared 
to 
the 
measured 
curves 
are 
shown 
in 
Fig. 
6.9. 
Both 
ß 
and 
d 
were 
found 
to 
be 
different 
for 
the 
coatings 
deposited 
on 
different 
substrates. 


-90-60-300306090
10-5
10-4
10-3
10-2
10-1
ARS (sr-1)s ( ° ) 
s meas. 
s mod. = 1.1, = 0.02 
n meas. 
n mod. = 0.6, = 0.035
Figure 
6.9: 
YbF3/AlF3 
coatings 
on 
differently 
polished 
substrates. 
ARS 
at 
193 
nm 
and 
modeling 
results. 


The 
final 
PSD 
results 
are 
shown 
in 
Fig. 
6.10. 
A 
transition 
from 
replication 
of 
substrate 
roughness 
to 
dominating 
intrinsic 
thin 
film 
roughness 
can 
be 
observed 
at 
f 
˜ 
0.2 
µm-1 
for 
both 
coatings. 
Consequently, 
near-angle 
scattering 
with 
s 
. 
2 
is 
dominated 
by 
replicated 
substrate 
roughness. 
However, 
provided 
by 
the 
dominant 
intrinsic 
thin 
film 
roughness 
at 
higher 
spatial 
frequencies 
and 
the 
low 
effective 
penetration 
depth 
of 
approximately 
7 
layer 
pairs, 
the 
scatter 
losses 
can 
be 
entirely 
attributed 
to 
thin 
film 
roughness 
efffects. 


56 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


0.1110100
10-2
10-1
100
101
102
103
104
105
106
PSD (nm4)f (m-1)
 substrate
 N=5
 N=10
 N=15
 model N=5,10,15
 model intermediate PSDs
0.1110100
10-2
10-1
100
101
102
103
104
105
106
PSD (nm4)f (m-1)
 substrate
 N=5
 N=10
 N=15
 model N=5,..,15
 model intermediate PSDs
Figure 
6.10: 
YbF3/AlF3 
coatings 
on 
differently 
polished 
substrates 
-roughness 
evolution. 
PSDs 
calculated 
directly 
from 
AFM 
data 
(solid 
lines) 
and 
PSDs 
determined 
using 
the 
ARS 
modeling 
procedure 
(interrupted 
lines) 
with 
parameter 
. 
Left: 
s-polish, 
ß 
=1.1. 
Right: 
n-polish, 
ß 
=0.6. 


The 
coating 
deposited 
on 
the 
n-substrate 
exhibits 
stochastic 
roughening 
with 
ß 
= 


0.6. 
In 
contrast, 
rapid 
roughening 
with 
ß 
=1.1 
is 
observed 
for 
the 
coating 
on 
the 
s-substrate. 
This 
indicates 
that 
the 
enhanced 
scattering 
at 
smaller 
angles 
observed 
for 
this 
sample 
is 
caused 
by 
the 
pronounced 
superstructures 
which 
can 
be 
related 
to 
island 
growth 
on 
the 
uncoated 
substrates 
and 
transitions 
between 
different 
crystal 
structures 
[163]. 
A 
more 
detailed 
structural 
analysis 
based 
on 
large-angle 
XRR 
and 
TEM 
measurements, 
however, 
is 
beyond 
the 
scope 
of 
this 
thesis. 
The 
roughness 
analysis 
also 
reveals 
information 
which 
is 
not 
directly 
relevant 
for 
scattering 
at 
193 
nm: 
First, 
the 
slope 
of 
the 
measured 
PSDs 
at 
high 
spatial 
frequencies 
corresponds 
to 
C 
= 
. 
- 
1 
˜ 
3 
(the 
deviation 
of 
the 
model-PSDs 
is 
an 
artifact). 
This 
indicates 
surface 
diffusion 
as 
the 
dominating 
relaxation 
process 
[14] 
for 
thermal 
boat 
evaporated 
fluoride 
coatings 
in 
agreement 
with 
the 
structure 
zone 
models. 
Second, 
the 
strength 
of 
the 
small-scale 
roughness 
component 
at 
f 
˜ 
35 
µm-1 
is 
slightly 
higher 
for 
the 
coating 
on 
the 
n-substrate 
(700 
nm4 
compared 
to 
500 
nm4). 
Since 
surface 
defects 
are 
preferred 
nucleation 
sites 
[166], 
this 
effect 
is 
attributed 
to 
the 
different 
substrate 
qualities. 


In 
addition 
to 
the 
observed 
, 
different 
layer 
thickness 
deviations 
of 
d 
˜ 
0.020 
and 
d 
˜ 
0.035 
for 
the 
coatings 
on 
the 
s-and 
on 
the 
n-substrates, 
respectively, 
are 
observed. 
These 
values 
in 
fact 
explain 
the 
different 
large-angle 
scattering. 
Nonuniformity 
effects 
during 
deposition 
can 
be 
excluded 
as 
cause 
of 
the 
different 
; 
the 
coatings 
were 
deposited 
in 
the 
same 
run, 
and 
the 
substrates 
were 
placed 
side-by-side 
with 
the 
same 
radial 
distance 
on 
the 
rotating 
calotte. 
Therefore, 
it 
is 
concluded 
that 
the 
observed 
d 
are 
related 
to 
different 
porosities 
of 
the 
coatings 
in 
agreement 
with 
the 
different 
smallscale 
roughness 
of 
the 
samples. 
When 
exposed 
to 
air, 
the 
pores 
fill 
with 
water 
and 
hydrocarbons 
leading 
to 
an 
increased 
effective 
refractive 
index 
[80, 
157, 
167, 
168]. 
The 


57 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


laser 
irradiation 
during 
the 
scatter 
measurements 
removes 
hydrocarbons 
adsorbed 
near 
the 
surface 
(in-situ 
cleaning), 
but 
adsorbed 
water 
is 
inert 
to 
DUV 
radiation 
and 
may 
only 
be 
removed 
by 
long-term 
baking 
[169]. 
Adsorbed 
water 
(n 
=1.44 
at 
193 
nm) 
leads 
to 
an 
increased 
effective 
index 
and, 
therewith, 
a 
larger 
optical 
thickness. 


The 
effect 
of 
d 
can 
also 
be 
observed 
as 
shifts 
of 
the 
center 
wavelength 
of 
the 
HR 
coatings 
away 
from 
the 
design 
wavelength 
193 
nm. 
It 
is 
straightforward 
to 
show 
that 
the 
center 
wavelength 
shift 
is 

c 
= 
c. 
Using 
the 
values 
d 
obtained 
from 
the 
scatter 
analysis, 

c 
˜ 
3 
nm 
and 

c 
˜ 
7 
nm 
are 
predicted 
for 
the 
coatings 
on 
the 
s-and 
the 
n-substrates, 
respectively. 
This 
is 
in 
agreement 
with 
the 
results 
of 
spectral 
reflectance 
measurements 
(performed 
with 
Perkin-Elmer 
spectro-photometer 
Lambda900) 
shown 
in 
Fig. 
6.11. 
A 
more 
detailed 
review 
of 
porosity-induced 
wavelength 
shifts 
of 
optical 
coatings 
is 
given 
in 
[170]. 


190195200205210215220
1
10
100
200 nm
197 nm
R, T (%) (nm)
s-polishn-polish
 R R
 T T
193.4 nm
Figure 
6.11: 
YbF3/AlF3 
coatings 
on 
differently 
polished 
substrates. 
Spectral 
reflectance 
and 
transmittance. 
The 
green 
and 
red 
arrows 
indicate 
the 
center 
wavelengths 
as 
predicted 
from 
the 
ARS 
modeling 
results. 


To 
illustrate 
the 
effect 
of 
the 
different 
substrates 
on 
the 
roughness 
evolution 
inside 
the 
coatings, 
cross-sectional 
SEM 
measurements 
were 
performed. 
The 
results 
are 
shown 
in 
Fig. 
6.12. 
The 
multilayer 
structure 
can 
be 
clearly 
perceived 
provided 
by 
the 
high 
material 
contrast 
between 
the 
H 
and 
L 
materials 
(higher 
atomic 
number 
Z 
of 
Yb 
(Z 
= 
70) 
compared 
to 
Al 
(Z 
= 
13) 
corresponding 
to 
a 
higher 
electron 
scattering 
cross-section). 


The 
SEM 
images 
reveal 
a 
higher 
degree 
of 
disorder 
in 
the 
coating 
on 
the 
n-substrate. 
This 
is 
correlated 
to 
higher 
small-scale 
roughness, 
porosity, 
and 
layer 
thickness 
deviations. 
The 
total 
geometrical 
thicknesses5 
of 
the 
coatings 
on 
the 
s-and 
n-substrates, 
respectively, 
are 
994 
nm 
compared 
to 
1013 
nm. 
Assuming 
equal 
deposition 
rates, 
the 


5measured 
assuming 
that 
the 
fracture 
planes 
are 
perpendicular 
to 
the 
sample 
surfaces 
and 
parallel 
to 
the 
measurement 
planes 
-Admittedly, 
such 
dimensional 
measurements 
from 
SEM 
data 
have 
to 
be 
treated 
with 
great 
care 
because 
the 
absolute 
values 
depend 
on 
the 
position 
and 
declination 
of 
the 
cross-sectional 
plane 
with 
respect 
to 
the 
virtual 
plane 
containing 
the 
reference 
scale. 


58 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 



Figure 
6.12: 
YbF3/AlF3 
coatings 
on 
differently 
polished 
substrates. 
SEM 
images. 


coating 
on 
the 
n-substrate 
exhibits 
a 
lower 
packing 
density 
(higher 
porosity) 
in 
agreement 
with 
the 
results 
of 
the 
scatter 
analysis. 


Yet 
the 
structures 
actually 
inducing 
scattering 
are 
only 
vaguely 
perceptible 
from 
the 
SEM 
images. 
The 
problem 
is 
that 
the 
relevant 
vertical 
roughness 
is 
in 
the 
order 
of 
a 
few 
nanometers 
while 
the 
lateral 
dimension 
of 
the 
structures 
corresponding 
to 
first-order 
diffraction 
at 
193 
nm 
is 
in 
the 
order 
of 
a 
micrometer. 
Thus, 
there 
is 
a 
fundamental 
clash 
of 
interests 
between 
high 
vertical 
resolution 
and 
sufficiently 
large 
field 
of 
view 
for 
the 
cross-sectional 
analysis 
of 
high-quality 
multilayers. 


One 
question 
is 
often 
asked: 
Why 
is 
a 
strong 
correlation 
of 
interface 
roughness 
observed 
in 
the 
scattering 
patterns 
of 
fluoride 
HR 
coatings? 
Does 
this 
mean 
that 
grains 
of 
different 
layers 
grow 
exactly 
upon 
each 
other? 
The 
answer 
is 
no. 
Fig. 
6.12 
reveals 
that 
structural 
defects 
caused 
by 
randomly 
enlarged 
grains 
are 
replicated 
and 
amplified 
by 
the 
subsequent 
layers 
as 
a 
result 
of 
shadowing 
effects 
which 
lead 
to 
columnar 
growth. 
These 
superstructures 
with 
f 
. 
1/. 
rather 
than 
the 
granular 
structure 
itself 
(f 
. 
1/) 
cause 
scattering 
at 
193 
nm. 
Furthermore, 
while 
the 
granular 
growth 
of 
adjacent 
layers 
is 
uncorrelated, 
the 
long-range 
roughness 
is 
replicated 
and 
enhanced 
through 
the 
multilayer 
structure 
which 
explains 
the 
strong 
cross-correlation 
observed 
by 
the 
scatter 
analysis. 


The 
observed 
relationships 
between 
the 
nanostructural 
properties 
and 
the 
scattering 
of 
thin 
film 
coatings 
are 
illustrated 
schematically 
in 
Fig. 
6.13. 
Although 
small-scale 
roughness 
does 
not 
induce 
scattering 
directly, 
it 
influences 
the 
optical 
properties 
of 
the 
coating 
which 
in 
turn 
influence 
the 
scattering 
properties 
through 
the 
optical 
factors. 


High-energy 
deposition 
processes 
such 
as 
ion-assisted 
deposition 
[163, 
171] 
or 
ion


59 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


?
?nano
granular growth
crystallites
porosity
scattering
?substrate (roughness, contaminations, defects, crystal orientation, ...)
deposition conditions (process,T/T, pressure, contaminations, ...)
coating materials (T, crystallinity, ...)
?
?
sm
m
optical layer thickness
deviations ()d
structural properties
?
?
substrate replication
shadowing effects
agglomeration
?
small-scale roughness
f  > 1/l
long-range roughness
f  < 1/l
effective
refractive index
adsorption
roughness
evolution ()b
randomly enlarged
grains
Figure 
6.13: 
Proposed 
model 
for 
the 
structure-property 
relationship 
for 
thin 
film 
coatings. 
Grains 
do 
not 
produce 
scattering 
at 
193 
nm 
directly, 
but 
structural 
defects 
can 
be 
amplified 
as 
a 
result 
of 
columnar 
growth. 
The 
resulting 
superstructures 
in 
turn 
give 
rise 
to 
scattering. 


beam 
sputter 
deposition 
[159] 
should 
result 
in 
smoother 
interfaces 
because 
of 
enhanced 
adatom 
mobilities. 
Though, 
the 
formation 
of 
superstructures 
is 
possibly 
not 
affected 
or 
even 
initiated 
[86, 
172]. 
Furthermore, 
fluoride 
films 
deposited 
by 
highenergetic 
processes 
often 
exhibit 
stoichiometric 
mismatches 
leading 
to 
enhanced 
absorption 
[163, 
171, 
173]. 
However, 
the 
bivalent/trivalent 
nature 
of 
Yb 
(YbF3 
exists 
as 
well 
as 
YbF2) 
[163], 
YbF3 
films 
offers 
a 
self-organized 
compensation 
of 
fluorine 
deficiencies 
[174]. 
Thus, 
YbF3 
may 
be 
an 
interesting 
material 
for 
future 
studies, 
but 
further 
investigations 
regarding 
the 
suppression 
of 
superstructures 
are 
necessary 
to 
achieve 
DUV 
coatings 
with 
both 
low 
absorption 
and 
low 
scattering. 


A 
non-trivial 
question 
for 
radiometric 
measurements 
is 
weather 
the 
sum 
of 
the 
specular 
quantities 
and 
all 
losses 
yields 
unity 
(energy 
balance). 
For 
this 
reason, 
the 
energy 
balance 
was 
checked 
for 
the 
two 
HR 
coatings 
by 
adding 
up 
the 
TSb, 
R, 
and 
T 
values 
at 
193 
nm. 
In 
addition, 
the 
absorptance 
A 
at 
193 
nm 
was 
measured 
at 
the 
Institute 
of 
Photonic 
Technology 
(IPHT), 
Jena 
by 
a 
laser-induced 
deflection 
technique 
[175, 
176]. 
The 
results 
are 
summarized 
in 
Tab. 
6.3. 


All 
contributions 
add 
up 
to 
unity 
within 
the 
uncertainty 
bars 
for 
both 
samples. 
This 
demonstrates 
the 
consistence 
of 
the 
different 
measurement 
techniques 
developed 
for 
193 
nm. 
Such 
a 
comprehensive 
verification 
of 
radiometric 
measurements 
at 
193 
nm 
has 
not 
been 
reported 
elsewhere 
so 
far. 


60 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


HR 
on 
s-polish 
HR 
on 
n-polish 


R 
(%) 
96.9±0.2 
94.6±0.2 
T 
(%) 
1.6±0.2 
3.2±0.2 
A 
(%) 
0.82±0.06 
0.94±0.06 
TSb 
(%) 
0.9±0.2 
1.0±0.2 
total 
(%) 
100.2±0.4 
99.7±0.4 


Table 
6.3: 
YbF3/AlF3 
coatings 
on 
differently 
polished 
substrates. 
Energy 
balance 
at 
193 
nm. 


The 
results 
also 
demonstrate 
that 
scattering 
and 
absorption 
are 
in 
the 
same 
order 
of 
magnitude. 
The 
slightly 
different 
absorptance 
of 
the 
coatings 
can 
also 
be 
explained 
by 
the 
enhanced 
fields 
and 
is 
therefore 
directly 
related 
to 
d 
as 
well. 
It 
should 
be 
noted, 
however, 
that 
the 
cause 
of 
the 
enhanced 
total 
loss 
L 
= 
TSb 
+ 
A, 
different 
, 
can 
only 
be 
observed 
via 
ARS 
analysis. 


Up 
to 
this 
point, 
the 
ARS 
modeling 
procedure 
was 
utilized 
to 
analyze 
the 
scattering 
and 
to 
separate 
roughness-induced 
and 
optical 
effects 
on 
the 
scattering 
properties. 
This 
in 
turn 
enables 
predicting 
the 
scattering 
for 
the 
case 
of 
ideal 
layer 
thicknesses 
(d 
= 
0). 
The 
results 
of 
this 
remodeling 
are 
shown 
in 
Fig. 
6.14. 
TSb 
values 
of 
as 
low 
as 
0.74% 
for 
the 
coating 
on 
the 
s-substrate 
and 
surprisingly 
0.69% 
for 
the 
coating 
on 
the 
n-substrate 
(because 
of 
the 
lower 
long-range 
roughness) 
are 
predicted. 
These 
for 
fluoride 
HR 
coatings 
exceptionally 
low 
values 
are 
the 
result 
of 
superior 
intrinsic 
thin 
film 
roughness 
but 
do 
not 
depend 
on 
the 
substrate 
polish. 


-90-60-300306090
10-5
10-4
10-3
10-2
10-1
ARS (sr-1)s ( ° ) 
s meas. 
s mod. = 1.1, = 0 
n meas. 
n mod. = 0.6, = 0
Figure 
6.14: 
YbF3/AlF3 
coatings 
on 
differently 
polished 
substrates. 
Remodeling 
of 
ARS 
for 
the 
case 
of 
ideal 
layer 
thicknesses. 


Considering 
the 
residual 
transmittance 
of 
the 
coatings, 
the 
reflectance 
could 
be 
further 
increased 
by 
increasing 
N. 
This 
will, 
however, 
be 
accompanied 
by 
higher 
roughness 
and 
enhanced 
scatter 
losses. 
Nevertheless, 
utilizing 
the 
material 
combination 
of 
YbF3 
and 
AlF3 
has 
the 
potential 
to 
enhance 
the 
reflectance 
up 
to 
about 
98% 
by 
using 
N 
˜ 
20. 


61 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


Moreover, 
from 
the 
viewpoint 
of 
scattering, 
it 
is 
not 
necessary 
to 
use 
superpolished 
substrates. 


The 
results 
of 
the 
investigations 
of 
the 
YbF3/AlF3 
coatings 
for 
193 
nm 
presented 
in 
this 
section 
can 
be 
summarized 
as 
follows: 


• 
The 
scatter-relevant 
roughness 
properties 
are 
dominated 
by 
intrinsic 
thin 
film 
roughness 
effects, 
in 
particular 
by 
superstructures 
resulting 
from 
columnar 
growth 
with 
f 
. 
1/. 
˜ 
5 
µm-1 
. 
• 
The 
substrate 
roughness 
does 
not 
influence 
the 
scattering 
of 
the 
HR 
coatings 
directly, 
but 
it 
crucially 
influences 
the 
growth 
properties 
of 
the 
films 
leading 
to 
different 
porosities. 
• 
Scatter 
losses 
of 
as 
low 
as 
0.7% 
at 
193 
nm 
can 
be 
achieved 
if 
layer 
thickness 
errors 
can 
be 
suppressed. 
A 
reflectance 
of 
>98% 
could 
be 
accomplished 
by 
increasing 
the 
number 
of 
layer 
pairs 
to 
N 
˜ 
20, 
while 
it 
is 
not 
necessary 
to 
use 
superpolished 
substrates. 
Considering 
the 
results 
of 
investigations 
of 
other 
material 
combinations 
[151], 
these 
results 
can 
be 
regarded 
as 
representative 
for 
high-quality 
fluoride 
coatings 
deposited 
by 
thermal 
boat 
evaporation 
in 
general. 


6.1.3 
Bulk 
scattering 
of 
synthetic 
fused 
silica 
In 
transmissive 
optical 
components 
for 
193 
nm, 
in 
addition 
to 
roughness-induced 
scattering 
at 
interfaces, 
scattering 
in 
the 
bulk 
of 
the 
materials 
has 
to 
be 
taken 
into 
account. 
Investigations 
of 
bulk 
scattering 
of 
optical 
materials 
at 
193 
nm 
have 
a 
two-fold 
importance: 
On 
the 
one 
hand, 
bulk 
scattering 
itself 
leads 
to 
reduced 
throughput 
and 
straylight. 
On 
the 
other 
hand, 
knowledge 
of 
the 
bulk 
scattering 
coefficient 
allows 
absorption 
to 
be 
determined 
from 
total 
loss 
measurements 
(L 
= 
A 
+TS 
= 
1 
- 
R 
- 
T 
). 
This 
is 
of 
particular 
interest, 
since 
existing 
direct 
methods 
to 
measure 
absorptance 
at 
193 
nm 
[176, 
177, 
178] 
sometimes 
lead 
to 
inconsistent 
results 
[179]. 
Critical 
challenges 
for 
bulk 
scattering 
measurements 
are, 
however, 
the 
separation 
of 
surface 
and 
bulk 
effects 
and 
the 
calibration 
of 
the 
scatter 
signals 
in 
order 
to 
obtain 
absolute 
results. 


A 
common 
substrate 
material 
for 
193 
nm 
is 
CaF2 
because 
of 
its 
high 
transparency 
and 
optical 
isotropy. 
Bulk 
scattering 
coefficients 
at 
193 
nm 
of 
as 
low 
as 
10-5 
cm-1 
were 
presented 
in 
[146]. 
This 
can 
be 
explained 
by 
the 
crystalline 
structure 
of 
the 
material6 
. 
The 
residual 
scattering 
results 
from 
lattice 
defects 
and 
impurities 
[180, 
181], 
which 


6In 
an 
ideal 
crystal, 
all 
scatter 
centers 
radiate 
coherently 
in 
phase 
and, 
except 
for 
the 
specular 
directions, 
the 
total 
scattering 
vanishes. 


62 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


have 
been 
considerably 
reduced 
during 
the 
last 
years 
[182]. 
Hence, 
volume 
scattering 
of 
high-quality 
CaF2 
does 
not 
play 
a 
critical 
role 
at 
193 
nm. 


As 
stated 
before, 
synthetic 
fused 
silica 
has 
a 
variety 
of 
promising 
properties, 
but 
absorption 
and 
scattering 
are 
considerably 
higher 
than 
in 
CaF2 
[146]. 
A 
variety 
of 
synthetic 
fused 
silica 
exists, 
which 
are 
manufactured 
by 
different 
process 
chains 
leading 
to 
different 
chemical 
and 
physical 
properties. 
Although 
extensively 
investigated 
in 
the 
near 
infrared 
spectral 
range 
in 
connection 
with 
the 
development 
of 
fiber 
optics, 
only 
little 
has 
been 
known 
about 
the 
scattering 
properties 
at 
shorter 
wavelengths. 


In 
[98], 
scatter 
measurements 
were 
performed 
at 
442 
nm 
and 
at 
633 
nm. 
A 
Rayleigh 
type 
scatter 
distribution 
was 
reported, 
but 
the 
expected 
-4 
scaling 
could 
not 
be 
observed. 
A 
scattering 
coefficient 
of 
a 
= 
(1.5 
± 
0.3)x10-3 
cm-1 
for 
”high-purity 
fused 
silica” 
at 
193 
nm 
was 
reported 
in 
[183] 
without 
further 
investigations 
regarding 
its 
causes. 
Yet 
there 
is 
still 
a 
lack 
of 
information 
about 
the 
scattering 
properties 
of 
different 
fused 
silica, 
their 
dependence 
on 
the 
material 
properties, 
and 
the 
correlation 
to 
theoretical 
models. 


First, 
a 
reliable 
method 
for 
the 
absolute 
determination 
of 
a 
at 
193 
nm 
is 
required. 
Moreover, 
the 
results 
have 
to 
be 
analyzed 
with 
respect 
to 
theory 
to 
investigate 
the 
fundamental 
scattering 
mechanisms 
and 
to 
optimize 
the 
materials. 
The 
equipment 
developed 
for 
193 
nm 
enables 
sensitive 
scattering 
measurements. 
However, 
well-considered 
methodologies 
and 
careful 
analysis 
are 
needed 
to 
separate 
bulk 
and 
interface 
effects. 
A 
detailed 
description 
of 
the 
investigations 
presented 
in 
this 
section 
is 
given 
in 
[184]. 


Three 
types 
of 
fused 
silica 
were 
investigated. 
The 
base 
materials, 
denoted 
by 
A, 
B, 
and 
C, 
had 
been 
fabricated 
by 
three 
different 
manufacturing 
processes 
resulting 
in 
different 
amounts 
of 
hydroxyl. 
A 
detailed 
description 
of 
the 
materials 
is 
given 
in 
[184]. 


Considering 
the 
results 
obtained 
at 
longer 
wavelengths, 
a 
strong 
dependence 
of 
the 
bulk 
scattering 
properties 
on 
the 
fictive 
temperature 
could 
be 
expected. 
Therefore, 
from 
each 
base 
material, 
sample 
sets 
with 
different 
Tf 
were 
generated 
at 
Heraeus 
Quarzglas 
by 
annealing 
at 
the 
desired 
temperature 
and 
subsequent 
quenching 
in 
water 
mist. 


The 
fictive 
temperature 
and 
the 
OH 
content 
of 
each 
sample 
were 
determined 
by 
Raman 
spectroscopy 
(data 
provided 
by 
Heraeus 
Quarzglas). 
Tf 
was 
estimated 
by 
evaluation 
of 
the 
606 
cm-1 
defect 
band 
(uncertainty 
10C), 
which 
is 
related 
to 
the 
breathing 
mode 
of 
planar 
3-fold 
Si-O 
rings 
[185]. 
The 
OH 
content 
was 
determined 
by 
measuring 
the 
strength 
of 
the 
3695 
cm-1 
band 
(relative 
uncertainty 
5%), 
which 
represents 
the 
O-H 
stretching 
[186]. 
Tab. 
6.4 
gives 
an 
overview 
of 
the 
results. 


As 
demonstrated 
in 
the 
preceding 
sections, 
ARS 
analysis, 
in 
addition 
to 
the 
scatter 
loss, 
provides 
more 
information 
about 
the 
scattering 
mechanisms. 
Therefore, 
ARS 
measurements 
were 
performed 
to 
investigate 
the 
nature 
of 
the 
volume 
scattering 
of 
fused 
silica 
at 
193 
nm. 
In 
order 
to 
separate 
surface 
from 
bulk 
effects, 
a 
special 
sample 


63 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


Base 
material 
OH 
(ppm) 
1 
Sample 
Set 
Tf 
(C) 


A 
1168 
A1 
A2 
A3 
992 
1086 
1173 
B 
276 
B1 
B2 
B3 
1038 
1129 
1211 
C 
26 
C1 
C2 
C3 
1057 
1216 
1282 


Table 
6.4: 
Bulk 
scattering 
of 
synthetic 
fused 
silica. 
Sample 
overview. 
*1 
mean 
value 
of 
all 
corresponding 
sample 
sets. 


disk 
was 
designed 
and 
manufactured 
for 
this 
purpose. 
The 
disk 
material 
is 
equivalent 
to 
the 
material 
of 
sample 
set 
B1. 


Figure 
6.15 
(left) 
shows 
the 
sample 
geometry 
and 
the 
illumination 
conditions. 
The 
sample 
disk 
has 
a 
diameter 
of 
200 
mm. 
In 
order 
to 
avoid 
focusing 
effects 
of 
the 
specular 
beams, 
flat 
entrance 
(1) 
and 
exit 
(2) 
surfaces 
were 
prepared 
and 
mechanically 
polished. 
Only 
radiation 
emitted 
from 
the 
center 
of 
the 
sample 
(3) 
is 
in 
the 
field 
of 
view 
of 
the 
detector. 
Hence, 
the 
large 
sample 
diameter 
and 
the 
measurement 
set-up 
prevent 
surface 
scattering 
from 
disturbing 
the 
bulk 
scattering 
measurements. 
The 
cylindrical 
shape 
of 
the 
sample 
ensures 
that 
the 
detected 
scattered 
radiation 
is 
transmitted 
through 
the 
sample 
surface 
at 
normal 
incidence 
to 
avoid 
refraction 
and 
polarization 
effects. 


q
s123
-90090180270
10-5
10-4
10-3
10-2
ARS (sr-1)s ( ° )
s-pol.p-pol. 
meas. meas. 
fit ~ fit ~ cos²(s)
Figure 
6.15: 
Bulk 
scattering 
of 
synthetic 
fused 
silica. 
ARS 
of 
disk 
sample. 
Left: 
Set-up. 


(1) 
entrance 
and 
(2) 
exit 
surfaces 
of 
the 
sample 
for 
the 
specular 
beams. 
(3) 
detected 
scattering 
volume 
defined 
by 
the 
field 
of 
view 
of 
the 
detector. 
Right: 
Measurement 
results 
and 
fits 
according 
to 
a 
Rayleigh 
scattering 
distribution. 
The 
results 
of 
the 
ARS 
measurements, 
performed 
with 
the 
incident 
light 
polarized 
parallel 
(p-pol.) 
and 
perpendicular 
(s-pol.) 
to 
the 
measurement 
plane, 
are 
shown 
in 


64 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


Fig. 
6.15 
(right). 
Because 
the 
detected 
scattering 
volume 
varies 
with 
the 
direction 
of 
observation, 
the 
measured 
curves 
were 
corrected 
by 
a 
factor 
|sin 
s|. 


In 
the 
angular 
ranges 
around 
0. 
and 
180, 
the 
entrance 
and 
exit 
points 
of 
the 
incident 
beam 
are 
in 
the 
field 
of 
view 
of 
the 
detector. 
As 
a 
result, 
the 
ARS 
is 
dominated 
by 
surface 
scattering 
in 
these 
regions. 
In 
the 
off-specular 
directions, 
however, 
a 
Rayleigh 
scattering 
distribution 
can 
be 
observed. 
This 
is 
the 
first 
indication 
that 
the 
theory 
described 
in 
Sec. 
3.5 
is 
valid 
at 
193 
nm. 
Using 
Eq. 
(3.24) 
with 
the 
field 
of 
view 
of 
the 
detector 
being 
L 
= 
(0.7 
± 
0.1) 
cm, 
the 
bulk 
scattering 
coefficient 
of 
the 
material 
is 
a 
= 
(1.14 
± 
0.27)x10-3 
cm-1 
. 


It 
is 
interesting 
to 
note 
that 
only 
the 
constant 
C 
has 
to 
be 
determined 
to 
calculate 
a 
via 
ARS. 
Hence, 
for 
s-polarized 
incident 
light, 
a 
can 
theoretically 
be 
measured 
at 
any 
(fixed) 
angle 
provided 
that 
the 
scattering 
is 
of 
the 
Rayleigh 
type 
and 
interface 
scattering 
does 
not 
contribute 
to 
the 
measured 
signal. 


Unfortunately, 
the 
ARS 
method 
requires 
a 
rather 
complex 
sample 
geometry 
and 
its 
accuracy 
depends 
on 
the 
knowledge 
of 
L. 
In 
contrast, 
measurement 
of 
TS 
is 
a 
direct 
and 
fast 
method 
to 
determine 
the 
scatter 
loss. 
However, 
a 
different 
approach 
is 
required 
to 
separate 
surface 
from 
bulk 
effects. 


The 
total 
scattering 
of 
a 
sample 
is 
the 
sum 
of 
the 
actual 
bulk 
scattering 
TSbulk 
and 
roughness-and 
defect-induced 
surface 
and 
subsurface 
effects. 
TSbulk 
is 
a 
function 
of 
the 
sample 
thickness 
d 
and 
a 
which 
for 
a 
. 
1 
can 
be 
approximated 
by 
a 
linear 
relationship7: 


TSbulk(d)=1 
- 
e 
-d 
˜ 
d 
. 


Thus, 
plotting 
measured 
TS 
values 
against 
d 
should 
yield 
a 
linear 
function 
with 
slope 
. 


For 
this 
reason, 
rods 
with 
a 
diameter 
of 
25 
mm 
were 
manufactured 
from 
each 
material. 
A 
set 
of 
samples 
with 
thicknesses 
of 
2 
mm, 
5 
mm, 
10 
mm, 
15 
mm, 
and 
20 
mm 
was 
fabricated 
from 
each 
rod. 
The 
measurement 
methodology 
is 
illustrated 
in 
Fig. 
6.16 
(left). 


This 
technique 
eliminates 
surface 
and 
subsurface 
scattering 
effects. 
Admittedly, 
these 
contributions 
have 
to 
be 
constant 
throughout 
all 
samples 
with 
varying 
d. 
Therefore, 
the 
front 
and 
rear 
surfaces 
of 
the 
samples 
were 
superpolished 
to 
suppress 
surface 
scattering 
as 
far 
as 
possible. 
AFM 
inspection 
revealed 
a 
relevant 
roughness 
of 
(0.10±0.02) 
nm 
for 
all 
samples 
corresponding 
to 
a 
roughness-induced 
contribution 
to 
the 
TS 
signals 
below 
10-5 
. 


For 
each 
sample 
set, 
TSb 
and 
TSf 
measurements 
were 
performed 
as 
2D 
mappings 
by 
scanning 
the 
samples 
over 
the 
entrance 
surfaces 
in 
7x7 
mm2 
areas 
to 
check 
the 


7The 
extinction 
arising 
from 
bulk 
absorption 
can 
be 
neglected 
in 
this 
procedure 
because 
the 
scattering 
is 
investigated 
directly 
rather 
than 
the 
internal 
transmittance. 


65 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


sample 
homogeneity 
and 
to 
suppress 
the 
influence 
of 
local 
(surface) 
defects. 
From 
each 
mapping, 
an 
average 
TS 
value 
was 
determined. 
The 
total 
scattering 
TS 
= 
TSb 
+ 
TSf 
was 
calculated 
and 
corrected 
to 
take 
into 
account 
radiation 
that 
leaves 
the 
sample 
through 
the 
sidewalls 
as 
described 
in 
[184]. 
In 
Fig. 
6.16 
(right), 
the 
resulting 
TS 
values 
are 
exemplarily 
shown 
for 
sample 
set 
A1. 


detectorCoblentzsphere
05101520
0.2
0.4
0.6
0.8
1.0
1.2
TS / 10-3d (mm)
Figure 
6.16: 
Bulk 
scattering 
of 
synthetic 
fused 
silica. 
Determination 
of 
a 
via 
TS. 
Left: 
Mesurement 
set-up. 
Right: 
TS 
versus 
sample 
thickness 
for 
sample 
set 
A1. 


The 
total 
scattering 
increases 
nearly 
linearly 
for 
d 
. 
15 
mm. 
For 
d 
. 
15mm, 
a 
nonlinear 
decrease 
can 
be 
observed 
for 
all 
samples, 
which 
can 
be 
explained 
by 
the 
imaging 
properties 
of 
the 
Coblentz 
sphere: 
Only 
light 
scattered 
from 
a 
small 
volume 
located 
conjugate 
to 
the 
detector 
position 
is 
completely 
detected 
[21, 
99, 
187]. 
This 
causes 
the 
deviation 
from 
the 
linear 
relationship 
for 
thicker 
samples. 
Therefore, 
only 
the 
TS 
values 
for 
d 
= 
10 
mm 
were 
used 
for 
the 
linear 
regression 
to 
determine 
. 


The 
results 
for 
all 
sample 
sets 
are 
plotted 
in 
Fig. 
6.17 
(left) 
against 
Tf 
. 
The 
uncertainty 
values 

a 
contain 
the 
uncertainties 
of 
both 
the 
TS 
measurements 
and 
the 
linear 


-1 
-1

regression. 
The 
scattering 
coefficients 
are 
between 
0.6x10-3 
cmand 
1.7x10-3 
cmdepending 
on 
the 
OH 
content 
and 
the 
fictive 
temperature. 
It 
is 
noteworthy 
that 
these 
values 
are 
in 
the 
same 
order 
of 
magnitude 
as 
typical 
bulk 
absorption 
coefficients 
of 
fused 
silica 
at 
193 
nm 
[188]. 


A 
linear 
relationship 
a 
~ 
Tf 
within 
the 
uncertainty 
bars 
can 
be 
observed 
for 
each 
sample 
group 
with 
similar 
OH 
content. 
The 
deviations 
for 
two 
samples 
at 
Tf 
> 
1200C 
could 
be 
an 
indication 
of 
a 
relaxation 
of 
longer 
correlated 
structural 
disorder 
at 
higher 
temperatures, 
because 
Raman 
spectroscopy 
is 
sensitive 
only 
to 
local 
disorder 
while 
the 
light 
scatter 
technique 
also 
includes 
such 
large-scale 
effects 
(although 
measurement 
errors 
can 
not 
be 
entirely 
excluded). 
Nevertheless, 
the 
correlation 
found 
between 
a 
and 
Tf 
below 
1200C 
is 
in 
agreement 
with 
the 
theory 
presented 
in 
Sec. 
3.5. 


It 
should 
be 
noted 
that 
the 
result 
for 
sample 
B1 
determined 
by 
TS 
is 
in 
good 
agreement 
with 
the 
value 
of 
the 
disk 
sample 
(which 
has 
similar 
properties) 
obtained 
by 
ARS. 
This 


66 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


9501000105011001150120012501300
4.0x10-4
6.0x10-4
8.0x10-4
1.0x10-3
1.2x10-3
1.4x10-3
1.6x10-3
1.8x10-3
2.0x10-3
A1
A2
A3
B1
B2
B3C1
C2
C3
 (cm-1)Tf (°C)
100200300400500600700
10-6
10-5
10-4
10-3
10-2 
fit ~n8/ 
(cm-1) (nm)
A1 B1 C1A2 B2 C2A3 B3 C3
Figure 
6.17: 
Bulk 
scattering 
of 
synthetic 
fused 
silica. 
Left: 
Dependence 
on 
fictive 
temperature. 
Right: 
Wavelength 
scaling. 


demonstrates 
the 
consistence 
and 
absolute 
accuracies 
of 
the 
TS 
and 
ARS 
methods. 


In 
order 
to 
verify 
the 
wavelength 
scaling 
predicted 
in 
Eq. 
(3.23), 
similar 
TS 
investigations 
were 
performed 
at 
325 
nm 
and 
633 
nm 
with 
the 
set-up 
described 
in 
[118]. 
The 
results 
shown 
in 
Fig. 
6.16 
(right) 
demonstrate 
that 
the 
wavelength 
scaling 
predicted 
by 
theory, 
a 
~ 
n8/4, 
holds 
down 
to 
193 
nm. 


Using 
Eq. 
(3.23), 
theoretical 
values 
of 
a 
can 
be 
calculated: 
The 
term 
n8p2 
can 
be 
approximated 
by 
(n2 
- 
1)2 
[96] 
with 
n 
=1.561 
for 
fused 
silica 
at 
193 
nm. 
T 
between 
5.7x10-11ms2/kg 
and 
6.2x10-11ms2/kg 
depending 
on 
Tf 
are 
given 
in 
[189]. 
Thus, 
theoretical 
a 
are 
obtained 
between 
1.41x10-3cm-1 
for 
Tf 
= 
1050C 
and 
1.54x10-3cm-1 
for 
Tf 
= 
1300C. 
This 
is 
in 
good 
agreement 
with 
the 
values 
measured 
for 
the 
high-purity 
(low 
OH) 
fused 
silica 
(material 
C). 


Significantly 
lower 
a 
were 
obtained 
for 
materials 
with 
higher 
OH 
concentrations. 
This 
can 
be 
explained 
by 
additional 
structural 
relaxation 
and 
alteration 
of 
the 
thermodynamic 
and 
elastic 
properties 
caused 
by 
the 
integration 
of 
the 
impurities 
into 
the 
network, 
which 
enables 
lower 
Tf 
(see 
Fig. 
6.17 
(left)) 
and 
leads 
to 
decreased 
T 
[190]. 


It 
can 
be 
concluded 
that 
the 
theory 
described 
in 
Sec. 
3.5 
is 
valid 
at 
193 
nm. 
Consequently, 
the 
scattering 
at 
193 
nm 
is 
related 
to 
the 
concentration 
of 
planar 
3-fold 
rings 
and 
therefore 
to 
strained 
Si-O 
bonds 
in 
the 
silica 
network 
[191]. 
Even 
small 
impurity 
levels 
and 
the 
thermal 
history 
influence 
the 
network 
structure 
and, 
thus, 
the 
scattering 
properties. 


The 
investigations 
of 
the 
bulk 
scattering 
of 
fused 
silica 
at 
193 
nm 
reveal: 


• 
Two 
independent 
methods 
based 
on 
TS 
and 
ARS 
measurements 
can 
be 
used 
to 
determine 
the 
bulk 
scattering 
coefficient. 
-1 
-1

• 
The 
bulk 
scattering 
coefficient 
is 
between 
0.6x10-3 
cmand 
1.7x10-3 
cmdepending 
on 
the 
OH 
content 
and 
the 
fictive 
temperature. 
67 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


• 
The 
scattering 
distribution 
is 
of 
the 
Rayleigh 
type. 
Moreover, 
a 
~ 
Tf 
and 
a 
~ 
n8/4 
were 
observed. 
Thus, 
the 
theory 
developed 
for 
the 
near 
infrared 
spectral 
range 
holds 
down 
to 
193 
nm. 
• 
Consequently, 
the 
scattering 
of 
synthetic 
fused 
silica 
at 
193 
nm 
is 
caused 
by 
thermally-induced 
disorder 
in 
the 
amorphous 
structure 
of 
the 
material. 
At 
the 
beginning 
of 
this 
section, 
it 
was 
discussed 
that 
scattering 
measurements 
can 
be 
utilized 
for 
the 
determination 
of 
absorptance. 
Recently, 
the 
bulk 
scattering 
coefficients 
of 
synthetic 
fused 
silica 
measured 
at 
193 
nm 
were 
in 
fact 
used 
as 
independent 
method 
to 
verify 
the 
results 
of 
direct 
absorption 
measurements 
[192]. 


The 
results 
retrieved 
in 
this 
investigation 
suggest 
that 
the 
scattering 
coefficients 
of 
fused 
silica 
at 
193 
nm 
can 
be 
estimated 
by 
extrapolation 
from 
values 
measured 
at 
longer 
wavelengths. 
Vice 
versa, 
measurements 
at 
193 
nm 
can 
be 
utilized 
to 
characterize 
materials 
for 
longer 
wavelengths, 
e.g. 
for 
fiber 
optics 
applications. 
Although 
it 
has 
to 
be 
taken 
into 
account 
that 
drawing 
a 
fiber 
from 
a 
raw 
material 
alters 
the 
structural 
properties, 
which 
requires 
additional 
scaling 
models, 
measurement 
at 
193 
nm 
offers 
a 
superior 
sensitivity 
even 
for 
rather 
small 
samples. 
This 
method 
becomes 
even 
more 
attractive 
considering 
that 
bulk 
scattering 
exhibits 
a 
much 
stronger 
wavelength 
dependence 
(~ 
1/4) 
than 
interface 
scattering 
(~ 
1/2) 
which 
relaxes 
the 
stringent 
demands 
on 
the 
surface 
quality 
for 
such 
investigations. 


Further 
developments 
of 
DUV 
lithography 
suggest 
that 
bulk 
scattering 
will 
become 
even 
more 
critical 
for 
new 
high-index 
materials 
currently 
being 
developed 
to 
further 
increase 
the 
resolution 
of 
193 
nm 
lithography 
tools 
[193]. 
The 
measurement 
techniques 
presented 
in 
this 
section 
permit 
also 
these 
new 
materials 
to 
be 
investigated 
with 
high 
sensitivity 
and 
accuracy. 


6.2 
Coatings 
for 
applications 
at 
13.5 
nm 
In 
the 
EUV 
spectral 
range, 
all 
materials 
exhibit 
strong 
bulk 
absorption 
and 
indices 
of 
refraction 
close 
to 
unity. 
Therefore, 
only 
reflective 
optics 
can 
be 
used, 
and 
multilayer 
coatings 
consisting 
of 
alternating 
spacer 
(low 
absorption) 
and 
absorber 
(high 
Fresnel 
reflectance) 
materials 
are 
required. 
The 
combination 
of 
Mo 
and 
Si 
was 
found 
to 
be 
the 
most 
convenient 
to 
achieve 
highest 
reflectance 
at 
13.5 
nm 
[194]. 
The 
maximum 
theoretical 
reflectance 
of 
Mo/Si 
multilayers 
is 
R0 
˜ 
75% 
[195] 
limited 
by 
intrinsic 
absorption 
of 
the 
coating 
materials. 


In 
practice, 
however, 
reflectances 
of 
R> 
68% 
are 
hardly 
being 
achieved 
[196, 
197] 
as 
a 
result 
of 
intermixing 
and 
roughness 
at 
the 
boundaries 
between 
adjacent 
layers. 
The 
short 
wavelength 
imposes 
tremendous 
demands 
on 
the 
interface 
roughness. 
Supplying 


68 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


sufficiently 
smooth 
substrates 
(down 
to 
0.1 
nm 
rms 
[54]) 
and 
controlling 
the 
thin 
film 
morphology 
are 
some 
of 
the 
greatest 
challenges 
for 
EUV 
technology 
in 
order 
to 
achieve 
high 
throughput 
and 
low 
scattering. 


Yet 
there 
is 
still 
a 
lack 
of 
quantitative 
information 
about 
the 
influence 
of 
substrate 
and 
thin 
film 
roughness 
on 
the 
scattering 
distribution, 
the 
scatter 
losses, 
as 
well 
as 
the 
link 
to 
the 
specular 
reflectance. 
In 
addition, 
EUV-induced 
degradation 
effects 
which 
drastically 
reduce 
the 
throughput 
of 
Mo/Si 
mirrors 
were 
observed 
recently 
[68, 
198], 
but 
no 
investigations 
of 
the 
impact 
of 
the 
mirror 
degradation 
on 
the 
scattering 
properties 
had 
become 
known. 


Both 
issues 
will 
be 
addressed 
in 
this 
section 
using 
the 
instrumentation 
developed 
for 
scatter 
and 
reflectance 
measurements 
at 
13.5 
nm. 
The 
EUV 
coatings 
for 
these 
investigations 
were 
deposited 
by 
magnetron 
sputtering 
at 
the 
Optical 
Coatings 
department 
of 
the 
Fraunhofer 
IOF, 
Jena 
[197]. 


First, 
a 
method 
is 
presented 
to 
measure 
the 
roughness 
of 
EUV 
mirrors 
by 
utilizing 
scattering 
at 
193 
nm, 
which 
has 
some 
interesting 
capabilities 
compared 
to 
conventional 
roughness 
measurement 
techniques. 


6.2.1 
Roughness 
measurements 
of 
EUV 
mirrors 
using 
193 
nm 
scattering 
For 
lithographic 
imaging, 
near-angle 
scattering 
(flare) 
is 
of 
crucial 
importance 
because 
it 
leads 
to 
degradation 
of 
contrast 
and 
resolution. 
Measurement 
of 
near-angle 
scattering 
at 
the 
wavelength 
of 
application 
typically 
requires 
highly 
specialized 
set-ups 
to 
reduce 
the 
effects 
of 
the 
instrument 
signature 
close 
to 
the 
specular 
beam 
[199]. 
So 
far, 
direct 
measurements 
at 
13.5 
nm 
down 
to 
s 
˜ 
0.1. 
were 
only 
reported 
in 
[13]. 


The 
top-surface 
roughness 
is 
an 
indicator 
for 
the 
quality 
of 
EUV 
mirrors. 
According 
to 
Eq. 
(3.4), 
near-angle 
scattering 
at 
13.5 
nm 
in 
the 
angular 
range 
between 
0.1. 
and 
4. 
is 
caused 
by 
roughness 
components 
at 
spatial 
frequencies 
between 
0.1 
µm-1 
and 
5 
µm-1 
. 


Although 
phase-shift 
interferometry 
offers 
sufficiently 
high 
vertical 
resolution, 
its 
lateral 
resolution 
is 
limited 
to 
f 
. 
2 
µm-1 
. 
In 
contrast, 
AFM 
is 
well-suited 
for 
roughness 
analysis 
at 
f 
. 
1 
µm-1 
but 
has 
limited 
applicability 
at 
lower 
spatial 
frequencies. 
Hence, 
there 
is 
no 
sufficiently 
large 
overlapping 
range 
of 
established 
roughness 
measurement 
techniques 
around 
f 
=1 
µm-1 
which 
is 
particularly 
important 
for 
near-angle 
scattering 
at 
13.5 
nm. 
An 
additional 
technique 
is 
needed 
to 
bridge 
the 
gap 
between 
AFM 
and 
PSI 
data. 


Roughness 
measurements 
by 
utilizing 
light 
scattering 
techniques 
are 
robust, 
contactless, 
and 
directly 
traceable 
[117, 
200]. 
Investigations 
were 
reported 
previously 
in 
the 
visible 
[27, 
201] 
and 
X-ray 
[202] 
spectral 
ranges. 
For 
EUV 
optical 
components, 
however, 


69 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


utilizing 
visible 
light 
restricts 
roughness 
analysis 
to 
rather 
low 
f 
with 
limited 
significance 
for 
the 
application. 
The 
wavelength 
of 
X-rays, 
on 
the 
other 
hand, 
is 
two 
orders 
of 
magnitude 
below 
13.5 
nm 
and 
requires 
measurements 
at 
extremely 
small 
scatter 
angles 
(see 
Sec. 
4). 


Interestingly, 
as 
can 
be 
observed 
from 
Fig. 
4.1, 
the 
roughness 
components 
relevant 
for 
near-angle 
scattering 
at 
13.5 
nm 
also 
give 
rise 
to 
scattering 
at 
193 
nm 
but 
into 
a 
wider 
range 
of 
scatter 
angles 
between 
1. 
and 
85. 
. 
This 
corresponds 
to 
a 
zoom 
into 
the 
relevant 
spatial 
frequency 
range 
and 
a 
relaxation 
of 
the 
near-angle 
scattering 
limit 
required 
to 
measure 
roughness 
at 
f 
˜ 
0.1 
µm-1 
. 


Nevertheless, 
the 
penetration 
depth 
of 
193 
nm 
radiation 
should 
be 
smaller 
than 
a 
multilayer 
period 
of 
an 
EUV 
mirror 
(typically 
˜ 
7 
nm) 
in 
order 
to 
solve 
the 
inverse 
scattering 
problem 
directly 
without 
need 
for 
additional 
assumptions 
about 
the 
roughness 
evolution 
inside 
the 
coating. 
The 
spectral 
penetration 
depth 
into 
a 
typical 
Mo/Si 
mirror 
for 


13.5 
nm 
at 
normal 
incidence 
calculated 
using 
IMD 
is 
shown 
in 
Fig. 
6.18. 
10100
10
100
1000
3
1
penetration depth (nm) (nm)
2
4
Figure 
6.18: 
Penetration 
depth 
into 
Mo/Si 
multilayer 
as 
a 
function 
of 
the 
incident 


wavelength. 
1 
-Si 
L3 
edge, 
2 
-Bragg 
resonance 
at 
13.5 
nm, 
3 
-Mo 
N 
edges, 


4 
-193 
nm. 


The 
dips 
in 
the 
curve 
can 
be 
associated 
with 
the 
Si 
L3 
edge 
at 
12.5 
nm 
(1), 
the 
Bragg 
resonance 
at 
13.5 
nm 
(2), 
and 
the 
Mo 
N 
edges 
around 
30 
nm 
(3). 
At 
193 
nm 
(4), 
the 
penetration 
depth 
is 
smaller 
than 
one 
multilayer 
period 
(6 
nm 
compared 
to 
6.9 
nm). 
Thus, 
the 
scattering 
at 
193 
nm 
is 
particularly 
sensitive 
to 
the 
top-surface 
roughness 
of 
EUV 
mirrors. 


The 
fortunate 
circumstances 
of 
coincident 
spatial 
frequency 
ranges 
and 
the 
small 
penetration 
depth 
enable 
direct 
roughness 
measurements 
of 
EUV 
mirrors 
using 
193 
nm 
radiation 
with 
a 
direct 
link 
to 
the 
application 
at 
13.5 
nm. 
In 
the 
following, 
this 
is 
discussed 
in 
detail 
for 
a 
Mo/Si 
coating 
for 
13.5 
nm 
deposited 
on 
superpolished 
fused 
silica 
(diameter 
25 
mm) 
[135]. 


70 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


ARS 
measurements 
were 
performed 
at 
193 
nm 
at 
quasi-normal 
incidence. 
The 
resulting 
curve 
shown 
in 
Fig. 
6.19 
is 
well 
above 
the 
detection 
limit 
of 
the 
instrument. 


-90-60-300306090
10-8
10-7
10-6
10-5
10-4
10-3
10-2 
EUV mirror 
signatureARS (sr-1)s ( ° )
Figure 
6.19: 
ARS 
measurement 
at 
193 
nm 
of 
EUV 
mirror 
for 
13.5 
nm. 


PSDs 
determined 
by 
PSI 
and 
AFM 
are 
shown 
in 
Fig. 
6.20 
(left) 
and 
clearly 
reveal 
bandwidth 
limits 
and 
measurement 
artifacts. 
In 
particular 
around 
f 
=1 
µm-1 
,a 
strong 
variance 
of 
the 
PSDs 
of 
nearly 
one 
order 
of 
magnitude 
can 
be 
observed. 
These 
fluctuation 
effects 
are 
caused 
by 
the 
small 
areas 
(100 
µm²) 
covered 
by 
single 
measurements 
[117, 
136, 
203] 
and 
can 
be 
suppressed 
by 
averaging 
PSDs 
determined 
at 
different 
sample 
positions8 
. 
Although 
not 
evident, 
the 
PSDs 
of 
both 
PSI 
and 
AFM 
around 
f 
=0.1 
µm-1 
are 
expected 
to 
be 
underestimated 
as 
a 
result 
of 
the 
nonideal 
transfer 
function 
and 
filter 
effects. 
Nevertheless, 
a 
Master 
PSD 
was 
determined 
by 
combining 
PSI 
and 
AFM 
data 
as 
described 
in 
Sec. 
4.4. 


In 
addition, 
PSDs 
were 
calculated 
from 
the 
ARS 
data 
at 
193 
nm 
by 
applying 
both 
the 
Rayleigh-Rice 
theory 
(Eq. 
(3.5)) 
and 
the 
generalized 
Harvey-Shack 
theory 
(Eq. 
(3.6)). 
The 
results 
shown 
in 
Fig. 
6.20 
(right) 
are 
in 
good 
agreement 
with 
the 
Master 
PSD. 
The 
slight 
deviation 
at 
low 
f 
is 
explained 
by 
the 
underestimated 
Master 
PSD. 
Both 
scattering 
theories 
lead 
to 
nearly 
identical 
PSDs. 
Though, 
the 
GHS 
result 
avoids 
the 
hook 
at 
large 
f 
which 
is 
obviously 
an 
artifact 
resulting 
from 
limitations 
of 
the 
Rayleigh-
Rice 
theory 
for 
extremely 
large 
scatter 
angles 
[56]. 


The 
ARS-PSD 
provides 
a 
continuous 
transition 
between 
the 
PSDs 
determined 
from 
AFM 
and 
PSI 
data. 
This 
significantly 
enhances 
the 
information 
in 
the 
spatial 
frequency 
range 
relevant 
for 
near-angle 
scattering 
at 
13.5 
nm. 
Moreover, 
statistical 
fluctuation 
effects 
are 
automatically 
suppressed 
because 
the 
illumination 
spot 
diameter 
of 
1 
mm 
for 
the 
ARS 
measurements 
is 
equivalent 
to 
~ 
105 
AFM 
measurement 
areas. 
Furthermore, 
because 
the 
ARS-PSD 
is 
fully 
traceable 
(through 
Eqs. 
3.3 
and 
3.4), 
the 
method 
should 
be 
useful 
to 
verify 
and 
calibrate 
other 
roughness 
measurement 
techniques. 


8Similar 
fluctuation 
effects 
were 
observed 
in 
[204, 
Chap. 
10], 
where 
as 
much 
as 
30 
scanning 
tunneling 
microscope 
images 
were 
analyzed 
to 
estimate 
an 
average 
PSD. 


71 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


0.010.1110
100
101
102
103
104
105
106
107
108 PSI 10x 
AFM 50x50 µm² 
AFM 10x10 µm² 
AFM 1x1 µm² 
Master PSDPSD (nm4)f (µm-1)
0.1° EUV 4°
0.010.1110
100
101
102
103
104
105
106
107
108 Master PSD 
ARS 193 nm (RR) 
ARS 193 nm (GHS)
PSD (nm4)f (µm-1)
0.1° EUV 4°
Figure 
6.20: 
Roughness 
analysis 
of 
EUV 
mirror. 
Left: 
PSDs 
determined 
by 
PSI 
and 
AFM, 
and 
combination 
to 
Master 
PSD. 
Right: 
PSDs 
determined 
from 
ARS 
measurements 
at 
193 
nm 
using 
the 
Rayleigh-Rice 
theory 
and 
the 
generalized 
Harvey-Shack 
theory 
compared 
to 
the 
Master 
PSD. 


ARS 
at 
193 
nm 
provides 
roughness 
information 
at 
spatial 
frequencies 
relevant 
for 
EUV 
near-angle 
scattering 
in 
sample 
area 
of 
the 
size 
of 
the 
illumination 
spot 
(diameter 
1 
mm). 
Consequently, 
TS 
measurements 
at 
193 
nm 
provide 
the 
corresponding 
rms 
roughness 
but 
enable 
rapid, 
spatially 
resolved 
investigations 
of 
larger 
surface 
areas. 
A 
TSb 
mapping 
of 
the 
EUV 
mirror 
was 
performed 
at 
193 
nm 
in 
an 
area 
of 
100 
mm2 
. 
For 
each 
sample 
point, 
the 
measured 
TSb 
value 
was 
converted 
into 
an 
rms 
roughness 
value 
using 
Eq. 
(3.7). 
The 
resulting 
roughness 
map 
is 
shown 
in 
Fig. 
6.21. 



Figure 
6.21: 
Roughness 
map 
of 
EUV 
mirror 
measured 
via 
TS 
at 
193 
nm. 


The 
average 
TSb 
value 
is 
3.6x10-5 
corresponding 
to 
an 
rms 
roughness 
of 
(0.11 
± 
0.02) 
nm. 
This 
is 
in 
good 
agreement 
with 
the 
corresponding 
value 
of 
(0.12 
± 
0.02) 
nm 
determined 
by 
integrating 
the 
Master 
PSD 
from 
f 
=0.1 
µm-1 
to 
f 
=5 
µm-1 
. 
Assuming 
that 
the 
top-surface 
topography 
is 
dominated 
by 
substrate 
roughness 
replicated 
through 
the 
multilayer, 
the 
single-surface 
approximation 
(see 
Sec. 
3.3) 
can 
be 
used 
to 
calculate 
the 
scattering 
at 
the 
actual 
wavelength 
of 
application. 
At 
13.5 
nm, 
an 
inte


72 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


grated 
near-angle 
scattering 
(relative 
power 
scattered 
into 
the 
angular 
range 
between 
0.1. 
and 
4. 
from 
the 
specular 
direction) 
of 
(0.7 
± 
0.3)% 
is 
predicted. 
Yet 
at-wavelength 
scatter 
measurements 
are 
required 
to 
verify 
this 
assumption 
(see 
next 
section). 


In 
some 
areas 
the 
TS 
roughness 
map 
exhibits 
values 
of 
as 
high 
as 
(0.25±0.03) 
nm. 
The 
PSI 
images 
shown 
in 
Fig. 
6.22 
(left) 
illustrate 
that 
the 
roughness 
inhomogeneities 
are 
linked 
to 
a 
strong 
variation 
of 
the 
surface 
topographies 
and 
defect 
densities 
at 
different 
sample 
positions. 
The 
AFM 
image 
(Fig. 
6.22 
(right)) 
reveals 
that 
the 
defects 
are 
small 
holes 
(depth 
~ 
1 
nm) 
-a 
typical 
feature 
of 
imperfect 
superpolishings. 
This 
suggests 
that 
the 
observed 
roughness 
of 
the 
EUV 
coating 
is 
a 
result 
of 
replicated 
substrate 
roughness. 
A 
more 
detailed 
analysis 
will 
be 
presented 
in 
Sec. 
6.2.2. 



Figure 
6.22: 
Roughness 
measurements 
of 
EUV 
mirror. 
Left: 
PSI 
images 
at 
different 
positions. 
Right: 
AFM 
image. 


Finally, 
one 
issue 
that 
often 
led 
to 
misunderstandings 
in 
the 
past 
needs 
to 
be 
addressed: 
The 
rms 
roughness 
determined 
by 
PSI 
and 
AFM 
are 
almost 
equal. 
Yet 
this 
is 
just 
a 
consequence 
of 
the 
nearly 
fractal 
PSD 
of 
this 
sample. 
In 
fact, 
both 
techniques 
are 
sensitive 
to 
different 
spatial 
frequency 
regions 
and 
do 
not 
refer 
to 
the 
same 
structures. 
While 
fractal 
PSDs 
are 
often 
observed 
for 
conventionally 
polished 
optical 
surfaces 
[78, 
79], 
superpolishing 
comprises 
different 
mechanical 
and 
chemical 
process 
steps 
[15] 
which 
lead 
to 
considerable 
deviations 
from 
purely 
fractal 
surfaces. 
In 
Fig. 
6.20 
(right), 
this 
effect 
can 
be 
observed 
as 
deviation 
of 
the 
measured 
PSD 
from 
a 
straight 
line 
of 
as 
much 
as 
600% 
around 
f 
=1 
µm-1 
. 
Therefore, 
roughness 
data 
must 
always 
be 
interpreted 
with 
respect 
to 
the 
corresponding 
spatial 
frequency 
range. 


In 
this 
section, 
it 
was 
demonstrated 
that 
scattering 
measurements 
at 
193 
nm 
are 
a 
powerful 
technique 
to 
determine 
roughness 
relevant 
for 
near-angle 
scattering 
at 
13.5 
nm. 
Furthermore, 
in 
contrast 
to 
local 
techniques 
(AFM, 
PSI), 
in 
particular 
TS 
mappings 
enable 
rapid 
100% 
inspections 
of 
larger 
surface 
areas. 
Moreover, 
the 
technique 
could 
help 
to 
meet 
the 
eager 
demands 
for 
appropriate 
characterization 
of 
large 
and 
curved 
samples. 


The 
procedures 
can 
also 
be 
used 
for 
the 
characterization 
of 
substrates 
before 
coating. 


73 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


However, 
scattering 
from 
the 
backside 
of 
transparent 
substrates 
has 
to 
be 
suppressed 
methodically 
(e.g. 
using 
a 
thin 
metallic 
overlayer) 
or 
by 
separating 
the 
contributions 
using 
appropriate 
scattering 
theories 
[58, 
205]. 


Nevertheless, 
measurements 
directly 
at 
13.5 
nm 
are 
indispensable 
for 
the 
determination 
of 
the 
actual 
impact 
of 
roughness 
onto 
the 
scatter 
losses 
under 
application 
conditions. 
At-wavelength 
scatter 
measurements 
of 
EUV 
mirrors 
are 
presented 
in 
the 
next 
section, 
where 
the 
sample 
discussed 
in 
this 
section 
is 
identical 
with 
sample 
3. 


6.2.2 
Mo/Si 
mirrors 
on 
fused 
silica: 
influence 
of 
substrate 
polish 
As 
discussed 
in 
the 
preceding 
sections, 
top-surface 
roughness 
is 
only 
one 
indicator 
for 
the 
scattering 
of 
multilayer 
coatings. 
In 
fact, 
estimations 
based 
on 
top-surface 
roughness 
data 
do 
not 
take 
into 
account 
the 
roughness 
evolution 
of 
buried 
interfaces 
and 
their 
cross-correlation 
properties 
(or 
use 
simplified 
models). 
Moreover, 
surface 
or 
bulk 
defects 
not 
contained 
in 
the 
roughness 
analysis 
might 
induce 
additional 
scattering. 
At-wavelength 
scatter 
measurements 
are, 
thus, 
essential 
for 
substantiated 
statements. 


To 
investigate 
the 
influence 
of 
the 
substrate 
quality 
on 
the 
properties 
of 
EUV 
mirrors, 
Mo/Si 
multilayers 
with 
N 
= 
60 
designed 
for 
13.5 
nm 
at 
an 
angle 
of 
incidence 
of 
5. 
were 
deposited 
in 
the 
same 
run 
on 
differently 
polished 
fused 
silica 
substrates. 
The 
substrate 
of 
sample 
1 
represents 
the 
state-of-the-art 
of 
plane 
superpolished 
surfaces. 
The 
substrates 
of 
samples 
2 
and 
3 
are 
two 
research 
superpolishings 
from 
another 
manufacturer. 


The 
results 
of 
ARS 
measurements 
performed 
at 
13.5 
nm 
with 
i 
=5. 
using 
the 
instrumentation 
described 
in 
Sec. 
5.2 
are 
shown 
in 
Fig. 
6.23. 
The 
heights 
of 
the 
specular 
peaks 
at 
5. 
are 
related 
to 
the 
reflectance 
(R 
= 
ARS(s 
=5)

s). 
Nevertheless, 
reflectance 
values 
were 
determined 
in 
a 
separate 
step 
described 
below 
to 
increase 
the 
accuracy 
of 
the 
results. 
Furthermore, 
the 
ARS 
curves 
reveal 
significantly 
different 
offspecular 
scattering. 
Since 
all 
coatings 
were 
deposited 
in 
the 
same 
run, 
this 
is 
most 
likely 
a 
result 
of 
different 
substrate 
roughness. 


The 
scatter 
losses 
of 
the 
samples 
were 
determined 
by 
integrating 
the 
ARS 
curves 
after 
coordinate 
transformation 
to 
shift 
the 
specular 
peak 
to 
0. 
and 
by 
assuming 
isotropic 
scattering 
(a 
detailed 
discussion 
of 
this 
procedure 
is 
given 
in 
[116]). 
Significant 
scatter 
losses 
between 
(0.8 
± 
0.3)% 
for 
sample 
1 
and 
(3.9 
± 
1.0)% 
for 
sample 
2 
were 
observed. 
A 
complete 
overview 
over 
all 
measurement 
results 
is 
given 
in 
Tab. 
6.5 
on 
page 
76. 


As 
can 
be 
seen 
in 
Fig. 
6.23, 
scattering 
into 
angles 
> 
20. 
is 
below 
the 
current 
sensitivity 
limit 
of 
the 
instrument. 
Nevertheless, 
the 
total 
scatter 
loss 
is 
dominated 
by 
scattering 
into 
smaller 
scatter 
angles. 
In 
addition, 
the 
instrument 
signature 
obscures 
the 
diffuse 
scattering 
of 
the 
samples 
close 
to 
the 
specular 
peak 
(see 
inset 
in 
Fig. 
6.23), 
the 
nearangle 
limit 
being 
approximately 
0.5 
from 
the 
specular 
direction 
determined 
by 
the 


74 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


-20-1001020
10-3
10-2
10-1
100
101
102
103
104
0.1110
10-3
10-2
10-1
100
101
102
103 sample 2 
sample 3 
sample 1 
signatureARS (sr-1)s ( ° ) 
s - i ( ° )
Figure 
6.23: 
Mo/Si 
mirrors 
on 
different 
substrates. 
ARS 
at 
13.5 
nm. 
The 
inset 
shows 
the 
same 
graphs 
on 
a 
double-logarithmic 
scale. 


width 
of 
the 
specular 
peak. 
In 
particular 
for 
sample 
1, 
a 
significant 
influence 
of 
the 
signature 
up 
to 
5. 
from 
the 
specular 
direction 
is 
observed. 
This 
can 
be 
attributed 
to 
the 
effect 
of 
scattering 
from 
the 
beam 
preparation 
system. 
However, 
the 
signature 
equivalent 
contribution 
to 
the 
TS 
of 
the 
samples 
is 
below 
0.15% 
and 
can 
be 
neglected. 


The 
integrated 
near-angle 
scattering 
of 
sample 
3, 
calculated 
by 
integrating 
the 
ARS 
between 
0.5. 
and 
4. 
from 
the 
specular 
direction, 
amounts 
to 
(0.7 
±0.2)%. 
This 
value 
is 
in 
excellent 
agreement 
with 
the 
prediction 
based 
on 
ARS 
measurements 
at 
193 
nm 
(see 
Sec. 
6.2.1). 
Moreover, 
the 
validity 
of 
the 
single-surface 
approximation 
used 
indicates 
fully 
correlated 
roughness 
in 
the 
mid-spatial 
frequency 
range. 


While 
knowledge 
of 
the 
top-surface 
roughness 
seems 
to 
allow 
predicting 
the 
integrated 
near-angle 
scattering, 
a 
more 
detailed 
roughness 
analysis 
is 
necessary 
to 
explain 
this 
effect 
and 
to 
analyze 
the 
observed 
scattering 
distribution. 
Therefore, 
AFM 
measurements 
were 
performed 
before 
and 
after 
coating. 
Representative 
images 
are 
shown 
in 
Fig. 
6.24. 
The 
corresponding 
rms 
roughness 
values 
indicate 
both 
roughening 
and 
smoothing 
effects. 
In 
[131], 
such 
roughness 
values 
were 
empirically 
correlated 
to 
scattered 
intensity 
at 
rather 
arbitrary 
chosen 
scatter 
angles. 
In 
contrast, 
a 
direct 
link 
between 
roughness 
and 
scattering 
properties 
can 
be 
provided 
by 
ARS 
and 
roughness 
evolution 
modeling. 


Master 
PSDs 
determined 
from 
AFM 
data 
for 
each 
sample 
before 
and 
after 
coating 
are 
shown 
in 
Fig. 
6.25 
(left). 
The 
mid-spatial 
frequency 
roughness, 
which 
is 
relevant 
for 
near-angle 
scattering 
(see 
Sec. 
3.2), 
is 
dominated 
by 
the 
substrate 
roughness 
for 
all 
samples. 
The 
high-spatial 
frequency 
roughness, 
which 
is 
relevant 
for 
the 
scatter 
loss, 
is 
influenced 
by 
substrate 
roughness 
as 
well 
as 
by 
roughening 
and 
smoothing 
effects 
during 
thin 
film 
growth. 
The 
PSDs 
reveal 
that 
the 
transition 
from 
replication 
of 
substrate 
roughness 
to 
dominating 
influence 
of 
intrinsic 
thin 
film 
roughness 
occurs 
between 
2 
µm-1 
to 
20 
µm-1, 
depending 
on 
the 
substrate. 
This 
is 
more 
than 
one 
order 
of 
magnitude 
higher 
than 
the 
values 
observed 
for 
DUV 
coatings 
(Sec. 
6.1.2) 
and 
indicates 


75 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 



Figure 
6.24: 
Mo/Si 
mirrors 
on 
different 
substrates. 
AFM 
images 
before 
(bottom) 
and 
after 
(top) 
coating. 


a 
much 
lower 
intrinsic 
roughness 
of 
EUV 
coatings 
as 
a 
result 
of 
higher 
adatom 
mobility. 


Bandwidth-limited 
rms 
roughness 
values 
before 
and 
after 
coating 
and 
the 
measured 
scatter 
losses 
are 
summarized 
in 
Tab. 
6.5. 
It 
is 
interesting 
to 
note 
that 
all 
samples 
meet 
the 
specification 
for 
EUV 
lithography 
in 
the 
MSFR 
(0.2 
nm) 
but 
fail 
with 
regard 
to 
the 
HSFR 
(0.1 
nm) 
[54]. 
A 
linear 
correlation 
can 
be 
observed 
between 
the 
scatter 
loss 
and 
the 
roughness 
before 
or 
after 
coating9 
. 
Nevertheless, 
a 
quadratic 
correlation 
could 
be 
expected 
considering 
Eq. 
12. 
Moreover, 
the 
total 
scattering 
should 
vanish 
for 
s 
. 
0. 
Yet 
thorough 
scatter 
analysis 
requires 
knowledge 
about 
the 
roughness 
evolution 
inside 
the 
coatings. 


Sample 
1 
Sample 
2 
Sample 
3 


MSFR 
(nm) 
0.091 
(0.11)2 
0.15 
(0.15) 
0.17 
(0.16) 
HSFR 
(nm) 
0.21 
(0.13) 
0.30 
(0.34) 
0.25 
(0.25) 
s 
relevant 
for 
TS 
(nm) 
0.20 
(0.12) 
0.28 
(0.32) 
0.24 
(0.21) 
TSb 
(%) 
0.8±0.3 
3.9±1.0 
2.3±0.5 


Table 
6.5: 
Mo/Si 
mirrors 
on 
different 
substrates. 
Bandwidth-limited 
rms 
roughness 
and 
total 
backscattering. 
*1 
Uncertainty 
of 
rms 
roughness 
is 
0.02 
nm 
(rms). 
*2 
Values 
in 
parenthesis 
are 
for 
the 
uncoated 
substrates. 


In 
contrast 
to 
thermal 
boat 
evaporated 
DUV 
coatings, 
the 
linear 
growth 
theory 
can 
be 
expected 
to 
be 
valid 
for 
magnetron 
sputtered 
EUV 
coatings 
[14]. 
The 
main 
reason 
is 


9In 
the 
range 
of 
the 
measured 
roughness 
values 
between 
0.1 
nm 
and 
0.3 
nm, 
TSb 
˜ 
0.15s 
- 
0.01 
and 
TSb 
˜ 
0.4s 
- 
0.07 
using 
the 
roughness 
(in 
nm) 
before 
and 
after 
coating, 
respectively. 


76 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


0.1110100
10-2
10-1
100
101
102
103
104
105
TS (scatter loss)near-angle scatterHSFR 
Sample 2 
Sample 3 
Sample 1 
uncoated substrate 
EUV mirrorPSD (nm4)f (µm-1)
MSFR
0.1110100
10-2
10-1
100
101
102
103
104
105 AFM N=60 
mod. N=60 
mod. N=40 
mod. N=20 
mod. N=10 
AFM substratePSD (nm4)f (µm-1)
Figure 
6.25: 
Mo/Si 
mirrors 
on 
different 
substrates. 
Roughness 
analysis. 
(a) 
PSDs 
calculated 
from 
AFM 
measurement 
of 
samples 
before 
(dashed) 
and 
after 
(solid) 
coating. 
(b) 
Simulation 
of 
the 
roughness 
evolution 
for 
sample 
1 
using 
the 
linear 
growth 
theory. 


the 
much 
higher 
kinetic 
energy 
of 
the 
deposited 
particles 
(~ 
10 
eV 
[67, 
206] 
compared 
to 
< 
0.1 
eV 
[172, 
206]) 
leading 
to 
a 
higher 
adatom 
mobility 
and 
preventing 
shadowing 
effects 
and 
columnar 
growth 
if 
appropriate 
deposition 
parameters 
(pressure, 
bias, 
...) 
are 
found 
[67, 
206]. 
Consequently, 
the 
roughness 
evolution 
of 
the 
coatings 
could 
be 
modeled 
using 
Eq. 
(3.18) 
provided 
that 
the 
PSDs 
of 
the 
substrate 
or 
the 
coating, 
the 
multilayer 
design, 
and 
all 
growth 
parameters 
are 
known. 
The 
result 
of 
this 
procedure 
can 
be 
verified 
via 
scatter 
analysis. 


The 
parameters 
for 
the 
roughness 
modeling 
were 
determined 
by 
fitting 
simulated 
PSDs 
for 
N 
= 
60 
to 
the 
measured 
top-surface 
PSDs. 
The 
results 
are 
(
, 
, 
) 
=(0.015 
nm3 
, 
3 
nm3.5, 
4.5) 
for 
the 
Si 
layers 
and 
(0.03 
nm3, 
3nm3.5, 
4.5) 
for 
the 
Mo 
layers, 
which 
is 
in 
reasonable 
agreement 
with 
the 
values 
reported 
in 
[14]. 
The 
estimated 
O 
for 
the 
Si 
layers 
is 
close 
to 
the 
atomic 
volume 
(0.02 
nm3) 
indicating 
an 
amorphous 
structure 
[14]. 
The 
value 
for 
the 
Mo 
layers 
is 
considerably 
larger 
than 
the 
atomic 
volume 
(0.016 
nm3 
[164]), 
which 
indicates 
a 
partly 
polycrystalline 
structure 
as 
reported 
in 
[14, 
67, 
206]10 
. 
The 
observed 
relaxation 
exponent 
of 
. 
˜ 
4 
indicates 
that 
surface 
diffusion 
is 
the 
dominant 
relaxation 
process 
during 
thin 
film 
growth, 
as 
for 
the 
DUV 
coatings. 


The 
LGT 
in 
fact 
explains 
both 
the 
stochastic 
roughening 
and 
smoothing 
effects 
as 
a 
result 
of 
local 
relaxation 
via 
surface 
diffusion 
[14] 
observed 
via 
AFM. 
Selected 
model-
PSDs 
for 
sample 
1 
are 
shown 
in 
Fig. 
6.25 
(right). 
Smoothing 
only 
occurs 
at 
very 
high 
spatial 
frequencies. 
The 
effect 
could 
be 
shifted 
to 
lower 
spatial 
frequencies 
by 
adding 
more 
layer 
pairs 
but 
this 
would 
automatically 
lead 
to 
increased 
MSFR. 


Final 
verification 
of 
the 
linear 
growth 
theory 
can 
only 
be 
performed 
via 
light 
scattering 


10In 
fact, 
in 
[207] 
it 
was 
discussed 
that 
the 
thickness 
of 
the 
Mo 
layers 
triggers 
the 
transition 
from 
amorphous 
to 
polycrystalline 
growth. 


77 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


measurements, 
since 
roughness 
measurements 
do 
not 
provide 
information 
about 
the 
cross-correlation 
of 
different 
interfaces. 
Therefore, 
ARS 
was 
simulated 
using 
Eq. 
(3.9) 
and 
the 
roughness 
data 
predicted 
by 
LGT. 
The 
results 
are 
shown 
in 
Fig. 
6.26. 


-20-1001020
10-3
10-2
10-1
100
101
102
103
104 
s2 meas. 
s2 mod. = 0 
s3 meas. 
s3 mod. = 0.1 
s1 meas. 
s1 mod. = 0.3 
signatureARS (sr-1)s ( ° )
Figure 
6.26: 
Mo/Si 
mirrors 
on 
different 
substrates. 
ARS 
measurement 
and 
modeling 
results. 


The 
good 
agreement 
between 
the 
simulated 
and 
the 
measured 
curves 
proves 
the 
validity 
of 
both 
the 
scattering 
theory 
at 
13.5 
nm 
and 
the 
LGT 
for 
the 
Mo/Si 
coatings. 
Moreover, 
this 
demonstrates 
that 
interface 
roughness 
is 
the 
dominating 
source 
of 
scattering 
and 
the 
interfaces 
are 
highly 
correlated 
also 
in 
EUV 
coatings. 
This 
also 
means 
that 
the 
scattering 
of 
EUV 
mirrors 
can 
be 
predicted 
if 
the 
substrate 
PSD 
and 
the 
growth 
parameters 
are 
known. 


In 
contrast 
to 
the 
ARS 
modeling 
based 
on 
LGT, 
the 
procedure 
presented 
in 
Sec. 
6.1.1 
does 
not 
require 
any 
a-priori 
knowledge 
about 
the 
growth 
parameters. 
Using 
this 
procedure, 
a 
constant 
value 
of 
d 
=0.005 
was 
observed 
for 
all 
EUV 
coatings. 
Although, 
this 
may 
indicate 
a 
systematic 
layer 
thickness 
deviation, 
this 
effect 
has 
another, 
rather 
simple 
explanation, 
as 
will 
be 
shown 
below. 


Different 
ß 
were 
determined 
via 
scatter 
analysis, 
which 
represent 
the 
impact 
of 
substrate 
roughness 
on 
the 
scattering 
properties. 
Sample 
2 
(ß 
= 
0) 
exhibits 
fully 
correlated 
roughness 
indicating 
purely 
substrate-dominated 
interface 
roughness. 
In 
contrast, 
sample 
1 
(ß 
=0.3) 
exhibits 
a 
significant 
contribution 
of 
intrinsic 
thin 
film 
roughness 
close 
to 
the 
random 
deposition 
limit 
which 
would 
be 
expected 
for 
an 
ideally 
smooth 
substrate. 
Yet 
it 
can 
be 
concluded 
that, 
in 
contrast 
to 
DUV 
mirrors, 
substrate 
roughness 
is 
the 
most 
critical 
factor 
for 
the 
scattering 
of 
EUV 
mirrors 
even 
if 
high-end 
superpolished 
substrates 
are 
used. 


To 
investigate 
the 
impact 
of 
the 
observed 
scattering 
properties 
on 
the 
throughput 
of 
the 
EUV 
mirrors, 
specular 
reflectance 
measurements 
were 
performed 
as 
a 
function 
of 
the 
angle 
of 
incidence 
at 
13.5 
nm 
(-2. 
measurement). 
The 
results 
are 
shown 
in 
Fig. 
6.27 
(left) 
together 
with 
curves 
simulated 
using 
IMD 
by 
taking 
into 
account 
the 


78 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


finite 
bandwidth 
of 
the 
incident 
radiation. 
In 
addition, 
results 
of 
spectral 
reflectance 
measurements 
performed 
at 
the 
EUV 
metrology 
lab 
of 
the 
Physikalisch-Technische 
Bundesanstalt 
(PTB) 
at 
the 
electron 
storage 
ring 
BESSY 
II 
[144] 
at 
a 
fixed 
angle 
of 
incidence 
of 
5. 
are 
shown 
in 
Fig. 
6.27 
(right). 


0102030405060708090
10-2
10-1
100
Ri ( ° ) 
sample 1 
sample 3 
sample 2simulation (Mo/Si)60 
with capping layer: 
Si 
2 nm SiO2
12.813.013.213.413.613.814.014.2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
R (nm)
 sample 1
 sample 3
 sample 2
Figure 
6.27: 
Mo/Si 
mirrors 
on 
different 
substrates. 
Left: 
Results 
of 
-2-measurements 
at 
13.5 
nm. 
Right: 
Spectral 
reflectance 
curves. 


As 
discussed 
in 
Sec. 
5.2, 
-2. 
measurements 
at 
13.5 
nm 
are 
equivalent 
to 
spectral 
reflectance 
measurements 
by 
eliminating 
dispersion 
effects. 
The 
R 
values 
of 
the 
-2. 
curves 
at 
i 
=5. 
correspond 
to 
the 
specular 
reflectance 
at 
13.5 
nm 
at 
the 
design 
angle. 
The 
results 
listed 
in 
Tab. 
6.6 
were 
found 
to 
be 
in 
good 
agreement 
with 
the 
corresponding 
values 
of 
the 
spectral 
reflectance 
curves 
at 
13.5 
nm 
[136]. 


The 
actual 
peak 
values 
of 
the 
-2. 
curves 
are 
located 
at 
7.8. 
rather 
than 
at 
5.0. 
. 
Using 
the 
Bragg 
equation, 
this 
can 
be 
explained 
by 
a 
slight 
deviation 
of 
the 
multilayer 
period 
corresponding 
to 
a 
shift 
of 
the 
peak 
wavelength 
from 
13.50 
nm 
to: 


cos(5.0)

peak 
= 
13.50 
nm 
=13.57 
nm 
(6.4) 


cos(7.8) 


if 
the 
multilayers 
are 
illuminated 
at 
5. 
. 
In 
fact, 
Fig. 
6.27 
(right) 
reveals 
that 
the 
spectral 
position 
of 
the 
peak 
reflectance 
is 
located 
at 
13.57 
nm 
rather 
than 
at 
13.50 
nm. 
This 
asymmetry, 
which 
also 
explains 
the 
d 
determined 
via 
ARS 
analysis 
considering 
that 
(see 
Sec. 
6.1.2) 

. 
˜ 
d 
˜ 
0.07 
nm, 
can 
be 
attributed 
to 
the 
effect 
of 
absorption 
in 
the 
coating 
materials. 
Nevertheless, 
the 
coatings 
were 
designed 
with 
respect 
to 
the 
FWHM 
at 
13.5 
nm. 
This 
constitutes 
the 
more 
important 
condition 
regarding 
the 
throughput 


[208] 
and 
is 
clearly 
fulfilled 
for 
all 
mirrors. 
The 
-2. 
curves 
in 
Fig. 
6.27 
(left) 
are 
shown 
on 
a 
logarithmic 
scale 
to 
illustrate 
that 
this 
method 
provides 
additional 
information 
about 
the 
EUV 
mirrors. 
The 
positions 
and 
forms 
of 
the 
Bragg 
peaks 
indicate 
equal 
multilayer 
periods 
and 
bandwidths 
in 
agreement 
with 
the 
spectral 
reflectance 
curves. 
Furthermore, 
the 
steep 
increase 
near 


79 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


i 
= 
70, 
corresponding 
to 
the 
critical 
angle 
of 
total 
external 
reflection11, 
enables 
a 
sensitive 
analysis 
of 
the 
top-layers. 
Theoretical 
modeling 
using 
IMD 
revealed 
a 
naturally 
grown 
SiO2 
top-layer 
with 
a 
thickness 
of 
2 
nm 
in 
agreement 
with 
the 
literature 
[68, 
196]. 
The 
enhanced 
reflectance 
around 
50. 
were 
found 
to 
be 
caused 
by 
residual 
out-of-band 
radiation 
as 
a 
result 
of 
degradation 
of 
the 
Zr 
filter 
[76]. 


The 
investigation 
results 
demonstrate 
that 
the 
-2. 
measurements 
are 
consistent 
with 
the 
well-established 
spectral 
reflectance 
methods 
and 
provide 
similar 
and 
complementary 
information 
about 
the 
samples. 
Nevertheless, 
specular 
measurements 
do 
not 
distinguish 
between 
losses 
generated 
by 
absorption, 
intermixing, 
and 
scattering. 
The 
instrumentation 
developed 
in 
the 
frame 
of 
this 
work 
enables 
both 
specular 
reflectance 
and 
scatter 
measurements 
at 
13.5 
nm, 
which 
allows 
the 
transition 
from 
specular 
reflection 
to 
off-specular 
scattering 
to 
be 
analyzed. 


The 
TSb 
and 
R 
values 
determined 
at 
13.5 
nm 
are 
summarized 
in 
Tab. 
6.6. 
The 
sum 
of 
the 
TSb 
and 
R 
values 
are 
nearly 
identical 
for 
all 
samples 
as 
could 
be 
expected. 
This 
demonstrates 
that 
the 
reduced 
specular 
power 
reappears 
as 
diffuse 
scattering 
and 
the 
scatter 
loss 
is 
dominated 
by 
backscattering. 


Sample 
1 
Sample 
2 
Sample 
3 


TSb 
(%) 
0.8±0.3 
3.9±1.0 
2.3±0.5 
R 
(%) 
68.3±0.2 
65.0±0.3 
66.5±1.0 
R+TSb 
(%) 
69.1±0.4 
69.0±1.0 
68.8±0.7 


Table 
6.6: 
Mo/Si 
mirrors 
on 
different 
substrates. 
Results 
overview. 
*1 
Uncertainty 
of 
rms 
roughness 
values 
0.02 
nm. 
*2 
Values 
in 
parenthesis 
are 
for 
the 
uncoated 
substrates. 


It 
is 
interesting 
to 
note 
that 
commonly 
used 
estimations 
of 
the 
impact 
of 
roughness 
on 
the 
reflectance 
using 
either 
the 
Debye-Waller 
factor 
(Eq. 
(3.1)) 
with 
the 
single-surface 
approximation 
(method 
1) 
or 
the 
method 
of 
modified 
Fresnel 
amplitude 
coefficients 
(Eq. 
(3.2), 
method 
2) 
do 
not 
provide 
accurate 
results 
for 
real 
EUV 
mirrors. 


As 
an 
example, 
for 
sample 
1 
with 
a 
relevant 
roughness 
of 
0.2 
nm, 
a 
roughness-induced 
loss 
of 

R 
= 
R 
- 
R0 
=2.4% 
is 
predicted 
by 
method 
1. 
In 
contrast, 
method 
2 
leads 
to 

R 
=0.44%. 
Both 
results 
substantially 
differ 
from 
the 
measured 
value 
of 
0.8% 
considering 
that 

R 
˜ 
TSb 
12 
. 


This 
can 
be 
explained 
as 
follows: 
Method 
1 
assumes 
c 
. 
. 
and 
neglects 
the 
roughness 
evolution. 
As 
a 
result, 
the 
roughness-induced 
loss 
is 
overestimated. 
In 
method 
2, 
roughness 
evolution 
can 
be 
included, 
but 
c 
. 
. 
is 
assumed. 
Moreover, 
resonant 
scattering 
effects 
are 
not 
taken 
into 
account 
which 
results 
in 
an 
underestimation 
of 
the 
loss. 


11This 
effect 
is 
possible 
because 
the 
indices 
of 
refraction 
of 
all 
materials 
at 
13.5 
nm 
are 
smaller 
than 
unity. 
12This 
of 
cause 
only 
holds 
for 
the 
scatter-relevant 
roughness. 
However, 
the 
results 
in 
Tab. 
(6.5) 
indicate 
that 
most 
of 
the 
HSFR 
is 
in 
the 
scatter-relevant 
spatial 
frequency 
range. 


80 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


The 
actual 
impact 
of 
roughness 
can 
only 
be 
determined 
by 
accurate 
scatter 
modeling 
(which 
yields 
a 
scatter 
loss 
of 
0.79% 
for 
sample 
1) 
or 
direct 
scatter 
measurements. 


As 
discussed 
in 
the 
preceding 
sections, 
ARS 
modeling 
also 
allows 
predicting 
the 
scattering 
of 
EUV 
coatings 
prior 
to 
manufacturing. 
This 
can 
be 
exploited 
to 
determine 
the 
optimum 
number 
of 
layer 
pairs 
for 
a 
given 
substrate 
to 
achieve 
the 
highest 
reflectance 
possible 
by 
accurately 
taking 
into 
account 
roughness 
evolution 
effects. 
In 
Fig. 
6.28 
(left), 
the 
results 
of 
simulations 
of 
TSb 
as 
a 
function 
of 
N 
are 
shown 
for 
Mo/Si 
mirrors 
on 
ideally 
smooth 
substrates 
assuming 
identical 
deposition 
conditions 
as 
for 
the 
real 
coatings 
discussed 
above. 
A 
nearly 
linear 
increase 
of 
TSb(N) 
can 
be 
observed, 
which 


v 
can 
be 
explained 
considering 
TS 
~ 
2 
(Eq. 
(3.7)) 
and 
s 
~ 
N 
(Eq. 
(3.21)). 


The 
effect 
of 
the 
roughness 
evolution 
on 
the 
reflectance 
is 
illustrated 
in 
Fig. 
6.28 
(right). 
The 
reflectance 
of 
an 
ideal 
multilayer 
with 
smooth 
and 
sharp 
interfaces 
calculated 
using 
a 
simple 
2-layer 
model13 
converges 
to 
the 
theoretical 
value 
of 
75%. 
Real 
Mo/Si 
coatings 
exhibit 
intermixing 
and 
a 
naturally 
grown 
Si 
top-layer. 
This 
can 
be 
modeled 
using 
a 
4-layer 
approach14 
. 
Interface 
roughness 
is 
typically 
assumed 
to 
be 
independent 
of 
N. 
Hence, 
all 
of 
these 
effects 
lead 
to 
a 
constant 
offset 
to 
the 
theoretical 
reflectance 
limit. 


By 
accurately 
taking 
into 
account 
roughness 
and 
scattering 
as 
a 
function 
of 
N, 
it 
can 
be 
shown 
that 
R 
does 
not 
saturate 
but 
decreases 
for 
large 
N 
(Fig. 
6.28 
(right, 
violet 
curve)). 
For 
the 
ideally 
smooth 
substrate, 
the 
optimum 
is 
at 
N 
˜ 
64. 
This 
is 
close 
to 
the 
value 
of 
N 
= 
60 
of 
the 
coatings 
presented 
above, 
which 
was 
chosen 
in 
a 
rather 
heuristic 
manner 
as 
the 
value 
at 
which 
the 
gain 
of 
the 
theoretical 
reflectance 
becomes 
negligible 
[67]. 
However, 
the 
modeling 
procedure 
enables 
an 
optimum 
N 
to 
be 
customized 
to 
any 
given 
substrate 
by 
exploiting 
smoothing 
and 
controlling 
roughening 
effects. 
For 
rougher 
substrates, 
N 
can 
be 
increased 
to 
smoothen 
the 
HSFR 
up 
to 
the 
point 
when 
thin 
film 
roughness 
begins 
to 
increase 
the 
MSFR. 


It 
is 
interesting 
to 
note 
that 
the 
intrinsic 
scatter 
loss 
of 
the 
Mo/Si 
coatings 
investigated 
in 
this 
section 
is 
0.7%, 
which 
represents 
the 
potential 
for 
increasing 
the 
reflectance 
by 
further 
optimization 
of 
the 
deposition 
process. 
However, 
the 
investigation 
of 
the 
impact 
of 
the 
substrate 
roughness 
clearly 
demonstrates 
that 
there 
is 
a 
much 
higher 
potential 
if 
the 
substrate 
polishing 
can 
be 
improved 
or 
if 
smoothing 
effects 
can 
be 
exploited. 


The 
results 
of 
this 
section 
can 
be 
summarized 
as 
follows: 


• 
Even 
high-quality 
EUV 
mirrors 
on 
superpolished 
substrates 
exhibit 
significant 
scattering 
at 
13.5 
nm. 
The 
scatter 
losses 
of 
the 
analyzed 
samples 
are 
between 
(0.8 
± 
0.3)% 
and 
(3.9 
± 
1.0)%. 
13(2.63 
nm 
Mo/4.28 
nm 
Si)60 
14(1.75 
nm 
Mo/0.49 
nm 
MoSi2/3.40 
nm 
Si/1.27 
nm 
MoSi2)59/1.75 
nm 
Mo/0.49 
nm 
MoSi2/3.26 
nm 
Si/1.9 
nm 
SiO2) 


[68] 
81 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


0102030405060708090100
0.2
0.4
0.6
0.8
1.0
 sim.
 linear fit
TSb (%)N
2030405060708090100
65
70
75
 ideal multilayer: R0(N)
 + intermixing + SiO2
 + interm. + roughness evolution
R (%)N
Figure 
6.28: 
Mo/Si 
mirror 
on 
ideally 
smooth 
substrate. 
Total 
scatter 
loss 
(left) 
and 
its 
effect 
on 
the 
specular 
reflectance 
(right) 
as 
a 
function 
of 
the 
multilayer 
period. 


• 
The 
main 
source 
of 
scattering 
is 
interface 
roughness. 
Near-angle 
scattering 
is 
dominated 
by 
replicated 
substrate 
roughness. 
The 
scatter 
losses 
depend 
on 
both 
the 
substrate 
and 
intrinsic 
thin 
film 
roughness. 
• 
Estimating 
the 
effect 
of 
roughness 
on 
multilayer 
reflectance 
using 
the 
Debye-
Waller 
factor 
or 
modified 
amplitude 
coefficients 
can 
lead 
to 
substantial 
errors 
because 
either 
the 
roughness 
evolution 
or 
resonant 
scattering 
effects 
are 
neglected. 
Accurate 
determination 
of 
roughness-induced 
losses 
requires 
scatter 
modeling 
or 
direct 
measurements. 
• 
The 
linear 
growth 
theory 
accurately 
describes 
the 
roughness 
evolution 
of 
magnetron 
sputtered 
EUV 
coatings. 
For 
a 
given 
substrate, 
an 
optimum 
N 
can 
be 
determined 
with 
balanced 
roughening 
and 
smoothing 
to 
optimize 
the 
scattering 
and 
the 
specular 
reflectance. 
• 
On 
ideally 
smooth 
substrates, 
the 
intrinsic 
scattering 
of 
the 
Mo/Si 
coatings 
is 
0.7% 
and 
the 
optimum 
number 
of 
layer 
pairs 
is 
N 
= 
64. 
• 
The 
ARS 
modeling 
procedure 
presented 
in 
Sec. 
6.1.1 
enables 
the 
influence 
of 
substrate 
roughness 
on 
the 
scattering 
properties 
to 
be 
characterized 
by 
a 
single 
parameter, 
. 
For 
ß 
= 
0, 
the 
scattering 
can 
be 
entirely 
attributed 
to 
replicated 
substrate 
roughness. 
Finally, 
electron 
microscopy 
was 
performed 
to 
illustrate 
the 
scatter-relevant 
structures 
in 
EUV 
coatings. 
However, 
these 
structures 
are 
impossible 
to 
visualize 
via 
crosssectional 
analysis 
(vertical 
structures 
<0.5 
nm 
on 
a 
lateral 
scale 
~ 
100 
nm). 
Therefore, 
Mo/Si 
coatings 
with 
intentionally 
rough 
interfaces 
were 
generated. 
An 
SEM 
image 
of 
a 
coating 
deposited 
onto 
a 
standard 
polished 
substrate 
is 
shown 
in 
Fig. 
6.29 
(left). 


82 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


Despite 
the 
poor 
quality 
of 
the 
cross-section 
(no 
polishing 
applied), 
the 
replication 
of 
substrate 
defects 
through 
the 
multilayer 
can 
be 
observed. 
Fig. 
6.29 
(right) 
shows 
a 
TEM 
image 
of 
a 
coating 
which 
was 
roughened 
by 
intentionally 
detuning 
the 
deposition 
parameters 
(increased 
pressure) 
[209]. 
Columnar 
growth 
caused 
by 
lower 
adatom 
mobility 
leads 
to 
a 
roughness 
in 
the 
order 
of 
1 
nm. 
State-of-the-art 
EUV 
coatings 
generally 
exhibit 
much 
smoother 
interfaces 
[67, 
206, 
210]. 
Nevertheless, 
the 
results 
of 
this 
section 
demonstrated 
that 
even 
coatings 
with 
an 
rms 
roughness 
of 
as 
low 
as 
0.2 
nm 
exhibit 
significant 
scattering 
at 
13.5 
nm. 



Figure 
6.29: 
Cross-sectional 
electron 
microscopy 
images 
of 
intentionally 
roughened 


Mo/Si 
coatings. 
Left: 
SEM. 
Right: 
TEM 
(image 
provided 
by 
Stefan 


Braun, 
Fraunhofer 
IWS, 
Dresden). 


6.2.3 
Characterization 
of 
degradation 
effects 
of 
EUV 
mirrors 
The 
application 
of 
multilayer 
coatings 
for 
EUV 
lithography 
requires 
not 
only 
highest 
possible 
normal-incidence 
reflectance 
but 
also 
long-term 
thermal 
and 
radiation 
stability. 
Radiation-induced 
carbon 
growth, 
oxidation, 
and 
erosion 
of 
the 
multilayer 
structure 
are 
known 
processes 
that 
induce 
a 
degradation 
of 
the 
optical 
properties 
of 
EUV 
mirrors 
[68, 
139, 
198]. 


Investigations 
of 
the 
radiation-induced 
degradation 
of 
EUV 
mirrors 
were 
presented 
in 
[68]. 
Irradiation 
experiments 
were 
performed 
utilizing 
the 
Xe 
discharge 
plasma 
source 
described 
in 
Sec. 
5.2.2. 
EUV 
coatings 
were 
exposed 
directly 
to 
the 
plasma 
emission 
for 
up 
to 
8 
hours 
at 
a 
distance 
of 
140 
mm 
corresponding 
to 
an 
EUV-dose 
of 
approximately 
4 
J/cm2 
. 
A 
combination 
of 
different 
characterization 
techniques 
was 
used 
to 
analyze 
the 
degradation 
effects. 
The 
results 
for 
Si 
capped 
Mo/Si 
mirrors 
(N 
= 
60) 
are 
summarized 
as 
follows: 
Synchrotron-based 
EUV 
reflectometry 
[132] 
revealed 
a 
drastic 
decrease 
of 
the 
peak 
reflectance 
from 
68.4% 
to 
50.0% 
at 
13.44 
nm 
after 
irradiation. 
Total 
oxidation 
of 
the 
Si 
top-layer 
and 
partial 
oxidation 
of 
the 
Mo 
sub-layer 
after 
irradiation 
was 
detected 
by 
X-ray 
photon 
spectroscopy 
[211]. 
X-ray 
reflectivity 
was 
used 
to 
determine 
the 
top-layer 
thicknesses. 
AFM 
revealed 
a 
significantly 
increased 
top-surface 
roughness 
from 
0.14 
nm 
to 
0.49 
nm 
(see 
Fig. 
6.30). 


83 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 



Figure 
6.30: 
EUV-induced 
degradation 
of 
Mo/Si 
mirrors. 
AFM 
images 
before 
(left) 
and 
after 
(right) 
irradiation. 


Based 
on 
these 
results, 
a 
model 
was 
developed 
which 
explains 
the 
EUV-induced 
degradation 
of 
the 
Mo/Si 
mirrors 
by 
changes 
of 
the 
geometrical 
thicknesses 
(disturbed 
interference 
properties) 
and 
increased 
intrinsic 
absorption 
of 
the 
oxidized 
top-layers. 
Yet 
the 
question 
arises, 
how 
far 
the 
degradation, 
in 
particular 
the 
drastically 
increased 
roughness, 
alters 
the 
scattering 
properties 
of 
the 
EUV 
mirrors. 


In 
a 
subsequent 
study 
[139], 
the 
measurement 
and 
analysis 
techniques 
developed 
in 
this 
work 
were 
applied 
to 
investigate 
the 
degradation 
effects 
directly 
at 
13.5 
nm. 
The 
main 
results 
are 
presented 
in 
the 
following 
paragraphs. 


The 
results 
of 
-2. 
measurements 
at 
13.5 
nm 
are 
shown 
in 
Fig. 
6.31. 
The 
reflectance 
at 
normal 
incidence 
decreases 
from 
(66.9 
± 
0.3)% 
to 
(48.4 
± 
0.3)% 
during 
irradiation. 
These 
values 
are 
in 
good 
agreement 
with 
the 
corresponding 
values 
of 
(67.2 
± 
0.1)% 
and 
(49.0 
± 
0.1)% 
obtained 
from 
spectral 
reflectance 
curves 
at 
13.5 
nm 
measured 
at 
the 
PTB 
[132]. 
The 
nearly 
identical 
angular 
position 
of 
the 
Bragg 
peak 
before 
and 
after 
irradiation 
indicates 
that 
no 
spectral 
shift 
of 
the 
peak 
reflectance 
occurred 
during 
irradiation. 
The 
shapes 
of 
the 
curves 
above 
the 
critical 
angle 
at 
i 
˜ 
80. 
suggest 
different 
top-surface 
roughness, 
as 
will 
be 
discussed 
more 
precisely 
below. 


A 
strong 
impact 
of 
the 
mirror 
degradation 
on 
the 
-2. 
curve 
can 
be 
observed 
at 
i 
˜ 
30. 
and 
i 
˜ 
65. 
. 
Theoretical 
curves 
were 
fitted 
to 
the 
measurement 
results 
assuming 
a 
composition 
of 
unoxidized 
and 
oxidized 
layers 
with 
the 
layer 
thicknesses 
as 
free 
fitting 
parameters. 
The 
thicknesses 
of 
the 
uppermost 
layers 
estimated 
by 
the 
different 
methods 
are 
listed 
in 
Tab. 
6.7. 
Despite 
a 
considerable 
variation 
of 
the 
results 
for 
the 
thickness 
of 
the 
MoO2 
layer, 
which 
might 
be 
caused 
by 
sample 
inhomogeneities, 
there 
is 
a 
rather 
good 
agreement 
between 
the 
results 
of 
the 
different 
techniques. 


In 
order 
to 
investigate 
the 
impact 
of 
the 
irradiation-induced 
roughness 
enhancement 
on 
the 
scattering, 
ARS 
measurements 
were 
performed 
at 
13.5 
nm. 
The 
measurement 
results 
for 
normal 
incidence 
are 
shown 
in 
Fig. 
6.32 
(left). 
Surprisingly, 
the 
irradiated 
coating 
(with 
the 
rougher 
surface) 
exhibits 
a 
significantly 
lower 
ARS. 
TSb 
values 
of 


(0.9 
± 
0.2)% 
and 
(0.5 
± 
0.1)% 
were 
determined 
from 
the 
ARS 
data 
of 
the 
coating 
84 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


0102030405060708090
10-4
10-3
10-2
10-1
100
R (%)i ( ° ) 
as-deposited 
after irradiation 
modeling results
Figure 
6.31: 
EUV-induced 
degradation 
of 
Mo/Si 
mirrors. 
-2. 
measurement 
and 
modeling 
results. 


R() 
XRR 
. 
- 
2. 


SiO2 
7.7 
7.3 
9.5 
Si 
0 
0 
0 
MoO2 
4.3 
7.0 
1.4 
Mo 
0.7 
0.7 
0.7 


Table 
6.7: 
EUV-induced 
degradation 
of 
Mo/Si 
mirrors. 
Comparison 
of 
the 
top-layer 


thicknesses 
after 
irradiation 
as 
determined 
by 
different 
techniques. 
The 
un


certainty 
of 
the 
values 
is 
approximately 
1 
nm. 


before 
and 
after 
irradiation, 
respectively. 
Thus, 
the 
degradation 
does 
not 
deteriorate 
the 
scattering 
properties. 


This 
effect 
can 
only 
be 
explained 
by 
confinement 
of 
the 
roughness 
enhancement 
to 
the 
uppermost 
layer, 
which 
only 
contributes 
a 
small 
part 
to 
the 
total 
scattered 
power. 
Scattering 
from 
the 
buried 
interfaces 
is 
attenuated 
because 
of 
increased 
absorption 
in 
the 
oxidized 
layers. 


To 
verify 
this 
conclusion, 
ARS 
measurements 
were 
performed 
at 
i 
= 
80. 
near 
the 
critical 
angle 
of 
total 
external 
reflection. 
Because 
in 
this 
arrangement 
the 
penetration 
depth 
is 
only 
about 
10 
nm, 
this 
enables 
a 
surface-sensitive 
roughness 
measurement. 
The 
results 
shown 
in 
Fig. 
6.32 
(right) 
in 
fact 
reveal 
a 
higher 
ARS 
after 
irradiation. 
The 
TSb 
increases 
from 
(1.3 
± 
0.2)x10-3 
to 
(3.3 
± 
0.5)x10-3 
. 
The 
corresponding 
rms 
roughness 
values 
calculated 
using 
Eq. 
3.7 
are 
(0.27 
± 
0.03) 
nm 
and 
(0.42 
± 
0.05) 
nm 
before 
and 
after 
irradiation, 
respectively. 
Although 
the 
top-surface 
roughness 
of 
the 
as-deposited 
sample 
is 
slightly 
overestimated 
as 
a 
result 
of 
background 
noise, 
the 
result 
for 
the 
irradiated 
coating 
is 
in 
good 
agreement 
with 
the 
roughness 
measured 
by 
AFM. 


Further 
optimization 
of 
the 
instrument 
should 
allow 
for 
even 
more 
sensitive 
investigations 
of 
coated 
and 
uncoated 
surfaces 
at 
13.5 
nm. 
Though, 
the 
dynamic 
range 
has 
to 
be 
increased 
by 
approximately 
4 
orders 
of 
magnitude 
for 
this 
purpose. 
However, 
consider


85 



6 
Scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 


-30-20-100102030
10-4
10-3
10-2
10-1
100
101
102
103
104
ARS (sr-1)s ( ° ) 
as-deposited 
after irradiation 
signature
0102030405060708090
10-4
10-3
10-2
10-1
100
101
102
103
104
ARS (sr-1)s ( ° ) 
as-deposited 
after irradiation
Figure 
6.32: 
EUV-induced 
degradation 
of 
Mo/Si 
mirrors. 
Results 
of 
ARS 
measurements 
performed 
at 
i 
=0. 
(left), 
and 
i 
= 
80. 
(right). 


ing 
that 
the 
spatial 
frequency 
range 
relevant 
for 
scattering 
at 
13.5 
nm 
can 
be 
extended 
up 
to 
˜ 
2/. 
by 
increasing 
the 
angle 
of 
incidence, 
a 
higher 
sensitivity 
should 
enable 
roughness 
measurements 
at 
spatial 
frequencies 
where 
even 
AFM 
encounter 
limitations 
caused 
by 
the 
tip 
geometry. 


The 
results 
presented 
in 
this 
section 
demonstrate 
that 
the 
instrumentation 
developed 
for 
scattering 
and 
reflectance 
measurements 
at 
13.5 
nm 
together 
with 
innovative 
analysis 
methods 
enables 
investigating 
both 
the 
degradation 
effects 
of 
EUV 
coatings 
(decreased 
reflectance) 
and 
the 
origins 
of 
degradation 
(top-layer 
oxidation) 
directly 
at 
the 
wavelength 
of 
application. 
Moreover, 
the 
observed 
scattering 
properties 
can 
be 
exploited 
to 
monitor 
the 
degradation 
of 
EUV 
collector 
optics 
during 
operation 
without 
influencing 
the 
specular 
beam. 


In 
particular 
the 
capabilities 
of 
the 
-2. 
measurement 
technique 
demonstrated 
for 
the 
investigations 
at 
13.5 
nm 
can 
be 
useful 
also 
for 
investigations 
of 
DUV 
coatings 
at 
193 
nm. 
Furthermore, 
roughness 
measurements 
of 
DUV 
coatings 
using 
13.5 
nm 
radiation 
could 
provide 
more 
information 
about 
the 
link 
between 
small-scale 
roughness, 
porosity, 
and 
water 
content 
of 
fluoride 
films. 
Thus, 
the 
measurement 
and 
analysis 
methods 
developed 
at 
13.5 
nm 
give 
new 
impulses 
for 
further 
investigations 
of 
coatings 
for 
193 
nm. 


86 



7 
Conclusions 


The 
recent 
developments 
in 
semiconductor 
lithography 
place 
challenging 
demands 
on 
optical 
components 
for 
193 
nm 
and 
13.5 
nm. 
In 
particular 
light 
scattering 
becomes 
crucially 
important 
because 
of 
its 
strong 
wavelength 
dependence. 
However, 
information 
about 
the 
scattering 
of 
optical 
components 
at 
193 
nm 
and 
13.5 
nm 
and 
its 
origins 
had 
so 
far 
remained 
unsatisfactory. 
This 
was 
mainly 
caused 
by 
a 
lack 
of 
appropriate 
laboratory-size 
measurement 
and 
analysis 
tools. 


This 
thesis 
concentrates 
on 
the 
development 
of 
a 
complete 
methodology, 
comprising 
effective 
instruments 
for 
sensitive 
scattering 
measurements 
at 
193 
nm 
and 
13.5 
nm 
as 
well 
as 
the 
link 
to 
theoretical 
modeling 
and 
analysis 
tools 
to 
investigate 
the 
relevant 
scattering 
mechanisms 
at 
both 
wavelengths 
in 
a 
uniform 
manner. 


An 
excimer 
laser-based 
system 
for 
total 
scattering 
(TS) 
and 
angle 
resolved 
scattering 
(ARS) 
measurements 
at 
193 
nm 
has 
been 
accomplished. 
The 
TS 
set-up 
exhibits 
a 
sensitivity 
of 
better 
than 
10-6 
. 
The 
set-up 
for 
ARS 
enables 
measurements 
at 
arbitrary 
angles 
of 
incidence 
and 
scattering. 
A 
background-equivalent 
ARS 
below 
10-6 
sr-1 
corresponding 
to 
a 
dynamic 
range 
of 
12 
orders 
of 
magnitude 
has 
been 
achieved. 
This 
sensitivity 
makes 
the 
instrument 
capable 
for 
investigations 
of 
even 
superpolished 
substrates. 


For 
13.5 
nm, 
a 
novel 
instrument 
based 
on 
a 
Xe 
gas 
discharge 
plasma 
source 
has 
been 
developed. 
ARS 
can 
be 
measured 
in 
the 
entire 
scattering 
plane 
at 
arbitrary 
angles 
of 
incidence. 
The 
background-equivalent 
ARS 
is 
below 
10-3 
sr-1 
corresponding 
to 
a 
dynamic 
range 
of 
6 
orders 
of 
magnitude. 
TS 
values 
are 
obtained 
from 
ARS 
data 
by 
numerical 
integration. 
The 
system 
constitutes 
the 
first 
synchrotron-independent 
instrument 
for 
scatter 
measurements 
of 
EUV 
coatings. 


Along 
with 
scatter 
measurements, 
the 
goniometric 
set-ups 
for 
193 
nm 
and 
13.5 
nm 
allow 
reflectance 
and 
transmittance 
measurements 
at 
arbitrary 
angles 
of 
incidence. 
It 
was 
demonstrated 
that 
reflectance 
as 
a 
function 
of 
the 
angle 
of 
incidence 
yields 
information 
equivalent 
to 
spectral 
reflectance 
(peak 
reflectance, 
bandwidth, 
layer 
thickness, 
etc.) 
while 
excluding 
dispersion 
effects. 


In 
addition 
to 
the 
measurement 
equipment, 
theoretical 
tools 
were 
developed 
to 
analyze 
the 
observed 
scattering. 
Different 
theories 
for 
roughness-induced 
scattering 
in 
the 
visible 
and 
X-ray 
spectral 
ranges 
were 
shown 
to 
yield 
identical 
results. 
Following 
these 


87 



7 
Conclusions 


theories, 
the 
scattering 
from 
surfaces 
and 
thin 
film 
coatings 
can 
be 
interpreted 
as 
first-order 
diffraction 
at 
different 
roughness 
components 
and 
interference 
of 
radiation 
scattered 
at 
different 
interfaces. 


The 
theories 
proved 
to 
be 
valid 
at 
both 
193 
nm 
and 
13.5 
nm, 
and 
interface 
roughness 
was 
found 
to 
be 
the 
main 
source 
of 
scattering 
for 
both 
DUV 
and 
EUV 
coatings. 
A 
novel 
procedure 
for 
the 
characterization 
of 
multilayer 
coatings 
which 
combines 
scattering 
and 
roughness 
measurement 
and 
modeling 
was 
presented. 
The 
relevant 
structural 
properties 
are 
expressed 
by 
two 
descriptive 
parameters. 
The 
scaling 
exponent 
ß 
describes 
the 
roughness 
evolution 
in 
the 
multilayer, 
and 
d 
describes 
optical 
layer 
thickness 
deviations. 


It 
was 
found 
that 
methods 
using 
the 
Debye-Waller 
factor 
or 
modified 
amplitude 
coefficients 
lead 
to 
substantial 
errors 
in 
estimating 
the 
effect 
of 
roughness 
on 
multilayer 
coating 
reflectance. 
This 
is 
because 
either 
the 
roughness 
evolution 
or 
resonant 
scattering 
effects 
are 
neglected. 
Accurate 
determination 
of 
roughness-induced 
losses 
requires 
scatter 
modeling 
or 
direct 
measurements. 


Fluoride 
HR 
coatings 
for 
193 
nm 
applications 
exhibited 
total 
backscattering 
between 
0.9% 
and 
2.8% 
depending 
on 
the 
deposition 
conditions 
and 
coating 
materials, 
while 
TSb 
values 
of 
as 
low 
as 
1.2x10-5 
were 
observed 
for 
uncoated 
substrates. 
The 
drastically 
increased 
scattering 
was 
attributed 
to 
(i) 
increased 
interface 
roughness, 
(ii) 
increased 
reflectance, 
and 
(iii) 
strong 
correlation 
of 
different 
interfaces. 
In 
addition, 
even 
small 
deviations 
in 
optical 
layer 
thickness 
were 
determined 
to 
be 
crucial. 


Intrinsic 
thin 
film 
roughness 
was 
identified 
as 
the 
dominating 
factor 
for 
the 
scattering 
properties. 
The 
relevant 
thin 
film 
structures 
were 
found 
to 
be 
superstructures 
with 
spatial 
frequencies 
f 
. 
1/. 
˜ 
5 
µm-1 
resulting 
from 
columnar 
growth 
rather 
than 
the 
granular 
structure 
itself. 
In 
contrast, 
scattering 
is 
nearly 
independent 
of 
substrate 
roughness, 
i.e. 
superpolishing 
is 
not 
mandatory 
for 
low-loss 
HR 
coatings. 
On 
the 
other 
hand, 
optical 
layer 
thickness 
deviations 
of 
as 
low 
as 
1%, 
which 
were 
associated 
with 
different 
porosities 
and 
water 
adsorption 
of 
the 
films, 
induced 
enhanced 
scattering. 
Consequently, 
suppressing 
columnar 
growth, 
e.g. 
by 
ion-assisted 
deposition, 
should 
lead 
to 
substantially 
improved 
scattering 
properties. 


Bulk 
scattering 
from 
synthetic 
fused 
silica 
at 
193 
nm 
was 
found 
to 
be 
caused 
by 
Rayleigh 
scattering. 
Scattering 
coefficients 
a 
between 
0.6x10-3 
cm-1 
and 
1.7x10-3 
cm-1 
depending 
on 
the 
purity 
and 
thermal 
history 
of 
the 
materials 
were 
observed. 
The 
bulk 
scattering 
was 
related 
to 
the 
amorphous 
structure 
and 
exhibits 
a 
wavelength 
scaling 
of 
a 
~ 
1/4 
. 
As 
a 
result, 
measurements 
at 
193 
nm 
can 
be 
used 
to 
predict 
the 
scattering 
at 
longer 
wavelengths 
with 
superior 
sensitivity. 
Moreover, 
the 
developed 
methods 
are 
well-suited 
for 
investigations 
of 
new 
high-index 
bulk 
materials 
for 
DUV 
immersion 
lithography 
currently 
under 
development. 


Scatter 
measurements 
at 
193 
nm 
were 
demonstrated 
to 
be 
well-suited 
for 
surface 
rough


88 



7 
Conclusions 


ness 
measurements 
of 
EUV 
mirrors. 
Roughness 
associated 
with 
high-angle 
scattering 
at 
193 
nm 
causes 
near-angle 
scattering 
at 
13.5 
nm, 
which 
is 
more 
difficult 
to 
measure. 
This 
enables 
rapid 
investigations 
of 
the 
roughness 
and 
homogeneity 
of 
EUV 
coatings 
at 
193 
nm 
with 
a 
direct 
link 
to 
near-angle 
scattering 
at 
13.5 
nm. 


Investigations 
at 
13.5 
nm 
revealed 
that, 
unlike 
the 
scattering 
of 
DUV 
coatings, 
the 
scattering 
of 
EUV 
coatings 
is 
dominated 
by 
replicated 
substrate 
roughness, 
with 
increasing 
influence 
of 
intrinsic 
thin 
film 
roughness 
only 
at 
larger 
scatter 
angles 
(. 
10). 
Considerable 
scattering 
occurred 
even 
if 
supersmooth 
substrates 
with 
rms 
roughness 
of 
as 
low 
as 
0.1 
nm 
were 
used. 
Total 
backscattering 
between 
0.8% 
and 
3.9% 
depending 
on 
the 
substrate 
quality 
was 
determined. 
The 
intrinsic 
scattering 
of 
the 
investigated 
coatings, 
if 
deposited 
onto 
an 
ideally 
smooth 
substrate, 
would 
amount 
to 
0.7%. 
Therefore, 
increasing 
substrate 
quality 
has 
a 
higher 
potential 
for 
increasing 
the 
reflectance 
of 
EUV 
mirrors. 
The 
effect 
is 
presumably 
even 
more 
critical 
if 
curved 
substrates 
are 
used. 


Reflectance 
and 
scatter 
measurements 
at 
13.5 
nm 
enabled 
the 
investigation 
of 
the 
EUVinduced 
degradation 
of 
Mo/Si 
mirrors. 
The 
reduction 
of 
reflectance 
and 
the 
origin 
of 
degradation 
-oxidation 
of 
the 
top-layers 
-were 
analyzed 
directly 
at 
the 
wavelength 
of 
application. 
Although 
a 
drastic 
increase 
of 
surface 
roughness 
during 
irradiation 
was 
detected 
via 
scatter 
measurement 
at 
near-grazing 
incidence, 
scatter 
losses 
decreased 
from 
0.9% 
to 
0.5%. 
This 
indicates 
that 
the 
degradation 
is 
confined 
to 
the 
uppermost 
interfaces 
and 
does 
not 
deteriorate 
the 
scattering 
properties. 


The 
results 
presented 
in 
this 
thesis 
motivate 
further 
refinement 
of 
the 
measurement 
techniques 
for 
193 
nm 
and 
13.5 
nm. 
For 
example, 
reflectance 
and 
transmittance 
measurements 
at 
193 
nm 
as 
a 
function 
of 
the 
angle 
of 
incidence 
could 
provide 
more 
insight 
into 
the 
scattering 
properties 
of 
DUV 
coatings. 
Moreover, 
scatter 
measurements 
at 


13.5 
nm 
could 
be 
used 
to 
investigate 
porosity 
and 
surface 
adsorbates 
of 
fluoride 
coatings 
as 
well 
as 
the 
roughness 
of 
EUV 
substrate 
surfaces 
before 
coating. 
Because 
of 
the 
short 
wavelength, 
roughness 
can 
be 
measured 
with 
a 
lateral 
resolution 
of 
better 
than 
10 
nm 
where 
even 
atomic 
force 
microscopy 
encounters 
limitations 
by 
the 
tip 
geometry. 
However, 
because 
of 
the 
low 
single-surface 
reflectance 
of 
all 
materials 
at 
13.5 
nm, 
this 
requires 
measurements 
at 
grazing 
incidence 
(to 
exploit 
the 
total 
external 
reflection) 
or 
a 
further 
increase 
of 
the 
dynamic 
range 
of 
about 
4 
orders 
of 
magnitude. 
The 
roughness 
and 
scattering 
models 
presented 
in 
this 
thesis 
can 
be 
included 
in 
the 
design 
of 
thin 
film 
coatings. 
For 
example, 
the 
number 
of 
layer 
pairs 
can 
be 
adjusted 
to 
the 
substrate 
at 
hand 
by 
exploiting 
smoothing 
effects 
which 
enables 
to 
relax 
the 
stringent 
demands 
on 
DUV 
and 
EUV 
substrates. 


89 



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Acknowledgements 


I 
am 
deeply 
indebted 
to 
a 
number 
of 
people 
without 
whom 
this 
work 
would 
not 
have 
been 
possible. 


I 
would 
like 
to 
express 
my 
most 
sincere 
gratitude 
to 
my 
supervisor, 
Prof. 
Dr. 
Andreas 
T¨His 
con


unnermann, 
for 
his 
encouragement 
and 
support 
at 
all 
stages 
of 
my 
work. 
structive 
criticism 
and 
comments 
from 
the 
initial 
conception 
to 
the 
end 
of 
this 
thesis 
is 
highly 
appreciated. 


I 
am 
especially 
indebted 
to 
Dr. 
Angela 
Duparr´e 
(Fraunhofer 
Institute 
for 
Applied 
Optics 
and 
Precision 
Engineering 
(IOF), 
Jena) 
for 
her 
inspiration, 
guidance, 
and 
support 
from 
the 
very 
beginning 
of 
my 
work. 
Her 
fine 
balance 
between 
giving 
me 
the 
freedom 
to 
pursue 
what 
fascinated 
me 
and 
demanding 
a 
high 
quality 
of 
work 
greatly 
influenced 
my 
work, 
and 
the 
interesting 
and 
enlightening 
discussions 
in 
particular 
regarding 
the 
structure 
and 
scattering 
of 
thin 
film 
coatings 
had 
a 
great 
impact 
on 
this 
thesis. 
I 
would 
also 
like 
to 
express 
my 
gratitude 
to 
Dr. 
Gunther 
Notni 
for 
his 
continuous 
support. 


Special 
thanks 
and 
my 
deepest 
respect 
go 
to 
Dr. 
Stefan 
Gliech 
(IOF) 
who 
taught 
me 
the 
art 
of 
measuring 
light 
scattering. 
Dr. 
Marcel 
Flemming 
(IOF) 
gave 
me 
the 
pleasure 
to 
participate 
from 
his 
impressive 
knowledge 
regarding 
AFM 
measurements 
even 
on 
the 
most 
delicate 
samples, 
and 
Luisa 
Coriand 
and 
Carolin 
Voigt 
(IOF) 
supported 
me 
during 
numerous 
measurements. 


Moreover, 
I 
would 
like 
to 
thank 
all 
my 
colleagues 
at 
the 
Fraunhofer 
IOF. 
Many 
of 
them, 
in 
particular 
at 
the 
Optical 
Systems 
department, 
the 
Optical 
Coatings 
department, 
and 
the 
Precision 
Mechanical 
Workshop 
somehow 
contributed 
to 
this 
work, 
and 
I 
am 
very 
grateful 
for 
the 
kind 
support, 
the 
professional 
work, 
and 
the 
amicable 
atmosphere. 
My 
deep 
gratitude 
in 
particular 
goes 
to 
Mathias 
Kamprath, 
Tobias 
Herffurth, 
and 
Marcus 
Trost, 
undergraduate 
students 
at 
that 
time, 
for 
their 
valuable 
assistance 
during 
the 
past 
years. 


I 
am 
deeply 
indebted 
to 
all 
who 
designed, 
manufactured, 
and 
provided 
samples 
for 
the 
investigations 
presented 
in 
this 
thesis 
and 
for 
the 
enlightening 
discussions: 
Hein 
Uhlig, 
Dieter 
G¨

abler, 
Hanno 
Heiße 
(IOF), 
and 
Earl 
Rudisill 
(Newport 
Corp., 
Irvine 
(CA)) 
provided 
a 
lot 
of 
interesting 
DUV 
coatings. 
Bodo 
K¨

uhn 
and 
Dr. 
Ursula 
Klett 
(Heraeus 
Quarzglas, 
Hanau) 
generously 
prepared 
and 
provided 
both 
non-standard 
and 
high-end 
synthetic 
fused 
silica 
materials 
as 
well 
as 
additional 
information 
about 
the 



samples 
such 
as 
Raman 
spectroscopy 
data. 
Dr. 
Torsten 
Feigl, 
Dr. 
Sergiy 
Yulin, 
Dr. 
Nicolas 
Benoit, 
and 
Marco 
Perske 
(IOF) 
provided 
high-quality 
EUV 
coatings 
both 
for 
the 
EUV 
measurement 
system 
and 
for 
investigations. 


I 
would 
also 
like 
to 
express 
my 
gratitude 
to 
those 
who 
provided 
important 
additional 
measurement 
data 
or 
supported 
me 
during 
such 
measurements: 
Dr. 
uh-

Christian 
M¨
lig 
(Institute 
of 
Photonic 
Technology 
(IPHT), 
Jena) 
contributed 
sensitive 
absorption 
measurements. 
Detlef 
Schelle 
(Institute 
of 
Applied 
Physics 
(IAP) 
of 
the 
Friedrich-
Schiller 
University 
Jena) 
performed 
impressive 
SEM 
measurements 
in 
nearly 
no 
time. 
Dr. 
Stefan 
Braun 
(Fraunhofer 
IWS, 
Dresden) 
kindly 
provided 
a 
TEM 
image 
of 
one 
of 
his 
research 
samples 
for 
illustration 
purposes. 


Special 
thanks 
go 
to 
Dr. 
John 
Stover 
(The 
Scatter 
Works, 
Inc., 
Tucson, 
Arizona) 
for 
inspiring 
my 
way 
of 
seeing 
scattered 
light 
and 
for 
his 
kind 
support. 
I 
would 
also 
like 
to 
thank 
Dr. 
Igor 
Kozhevnikov 
(Institute 
of 
Crystallography, 
Moscow) 
and 
Prof. 
James 
Harvey 
(Center 
for 
Research 
and 
Education 
in 
Optics 
and 
Lasers 
(CREOL) 
at 
the 
University 
of 
Central 
Florida) 
for 
answering 
also 
the 
most 
tedious 
questions 
regarding 
scattering 
theories 
and 
the 
encouraging 
discussions 
about 
recent 
developments. 


I 
am 
very 
grateful 
to 
Dr. 
Nicolas 
Benoit 
and 
Dr. 
Christian 
M¨

uhlig 
for 
many 
detailed 
and 
enlightening 
discussions 
about 
critical 
issues 
for 
EUV 
and 
DUV 
optics, 
respectively. 
I 
wish 
to 
express 
my 
special 
thanks 
also 
to 
Dr. 
Marcel 
Flemming 
and 
Robert 
Leitel 
for 
the 
countless 
interesting 
and 
enjoyable 
discussions 
as 
well 
as 
for 
their 
kind 
and 
prompt 
support. 


I 
would 
also 
like 
to 
thank 
the 
Deutsche 
Forschungsgemeinschaft 
for 
funding 
my 
studies 
during 
the 
past 
years. 


Last 
but 
not 
least, 
I 
am 
much 
obliged 
to 
my 
family. 
My 
parents 
supported 
my 
interest 
in 
natural 
sciences 
since 
I 
was 
little, 
shaped 
my 
character 
to 
question 
things, 
and 
inspired 
my 
way 
of 
working. 


I 
am 
deeply 
grateful 
to 
my 
wife 
Jana 
for 
her 
nearly 
endless 
patience 
and 
understanding 
throughout 
the 
past 
years 
and 
for 
managing 
all 
the 
things 
I 
neglected. 
I 
am 
also 
most 
thankful 
to 
our 
wonderful 
children 
Sophia 
and 
Stella 
for 
the 
joy 
they 
bring 
to 
my 
life. 
Every 
smile 
you 
put 
on 
my 
face 
gave 
me 
new 
strength 
for 
this 
work. 



Kurzfassung 


Die 
aktuellen 
Entwicklungen 
auf 
dem 
Gebiet 
der 
Halbleiterlithographie 
ziehen 
enorme 
Herausforderungen 
an 
optische 
Komponenten 
f¨

ur 
193 
nm 
und 
13,5 
nm 
nach 
sich. 
Insbesondere 
Streulicht 
an 
optischen 
Oberfl¨

achen, 
Schichtsystemen 
und 
in 
Bulkmaterialien 
stellt 
einen 
kritischen 
Faktor 
dar. 
Hauptgegenstand 
dieser 
Arbeit 
war 
die 
Entwicklung 
eines 
Messinstrumentariums, 
das 
sowohl 
effektive 
Systeme 
zur 
sensitiven 
Streulichtmessung 
bei 
193 
nm 
und 
13,5 
nm 
als 
auch 
deren 
Verkn¨

upfung 
mit 
theoretischen 
Analysewerkzeugen 
umfasste, 
um 
die 
relevanten 
Streulichtmechanismen 
bei 
beiden 
Wellenl¨

angen 
zu 
untersuchen. 


Ein 
System 
zur 
Messung 
des 
totalen 
Streulichts 
(TS) 
und 
des 
winkelaufgel¨

osten 
Streulichts 
(ARS) 
bei 
193 
nm 
wird 
beschrieben. 
Das 
TS-System 
weist 
eine 
Sensitivit¨

at 
von 
besser 
als 
10-6 
auf. 
erm¨

Das 
ARS-System 
oglicht 
Messungen 
bei 
beliebigen 
Einfalls-und 
Streuwinkeln 
mit 
einem 
Dynamikbereich 
von 
mehr 
als 
12 
Gr¨ur 
Un


oßenordnungen. 
F¨
tersuchungen 
bei 
13,5 
nm 
wurde 
ein 
System 
f¨oste 
Streulicht-und 
Re-

ur 
winkelaufgel¨
flexionsmessungen 
mit 
einem 
Dynamikbereich 
von 
6 
Gr¨

oßenordnungen 
entwickelt. 


Es 
konnte 
gezeigt 
werden, 
dass 
existierende 
Theorien 
zur 
Beschreibung 
von 
rauheitsinduziertem 
Streulicht 
im 
sichtbaren 
und 
im 
R¨ultig 
bei 
193 
nm 


ontgen-Spektralbereich 
g¨
und 
13,5 
nm 
sind 
und 
Grenzfl¨

achenrauheit 
die 
wesentliche 
Streulichtursache 
sowohl 
bei 
DUV-als 
auch 
bei 
EUV-Schichtsystemen 
ist. 
Eine 
neuartige 
Methode 
zur 
Charakterisierung 
von 
Vielschichtsystemen 
durch 
Kombination 
von 
Streulicht-und 
Rauheitsmessungen 
wurde 
vorgestellt. 
Dabei 
werden 
die 
relevanten 
strukturellen 
Eigenschaften 
durch 
zwei 
anschauliche 
Parameter 
beschrieben: 
Der 
Skalierungsexponent 
ß 
beschreibt 
die 
Rauheitsentwicklung 
im 
Schichtsystem 
und 
d 
beschreibt 
Schichtdickenabweichungen. 


Fluoridische 
HR-Schichten 
f¨

ur 
Anwendungen 
bei 
193 
nm 
wiesen 
totale 
Streuverluste 
zwischen 
0, 
9% 
und 
2, 
8%, 
abh¨

angig 
von 
den 
Abscheidungsbedingungen 
und 
Schichtmaterialien, 
auf, 
w¨ur 
unbeschichtete 
Substrate 
TS-Werte 
von 
lediglich 
1, 
2 
× 
10-5

ahrend 
f¨
beobachtet 
wurden. 
Die 
drastisch 
erh¨

ohte 
Streuung 
der 
Beschichtungen 
konnte 
durch 
erh¨achenrauheit, 
erh¨

ohte 
Grenzfl¨ohten 
Reflexionsgrad 
und 
starke 
Korrelation 
unter¨ 


schiedlicher 
Grenzfl¨art 
werden. 


achen 
erkl¨Uberdies 
wurde 
ein 
kritischer 
Einfluss 
selbst 
kleiner 
Schichtdickenabweichungen 
festgestellt. 


Intrinsische 
Schichtrauheit 
infolge 
kolumnaren 
Wachstums 
stellte 
sich 
als 
dominierender 
Faktor 
f¨uber 
ist 
das 
Streulicht 
na-

ur 
die 
Streulichteigenschaften 
heraus. 
Demgegen¨


hezu 
unabh¨

angig 
von 
der 
Substratrauheit. 
Allerdings 
wurde 
eine 
teilweise 
drastische 
Streulichterh¨

ohung 
beobachtet, 
die 
durch 
Schichtdickenabweichungen 
infolge 
Substrat-
abh¨at 
erkl¨

angigen 
Schichtwachstums 
und 
Porosit¨art 
werden 
konnte. 


Die 
Untersuchung 
der 
Volumenstreuung 
von 
synthetischem 
Quarzglas 
bei 
193 
nm 
erforderte 
die 
Entwicklung 
geeigneter 
Methoden 
zur 
Trennung 
von 
Oberfl¨

achen-und 
Volumeneffekten. 
Volumenstreukoeffizienten 
a 
zwischen 
0,6x10-3 
cm-1 
und 
1,7x10-3 
cm-1 
, 
abh¨

angig 
vom 
Reinheitsgrad 
und 
der 
thermischen 
Vorgeschichte 
der 
Materialien, 
wurden 
ermittelt. 
Als 
wesentlicher 
Streulichtmechanismus 
konnte 
Rayleighstreuung 
an 
Dichtefluktuationen 
in 
der 
amorphen 
Struktur 
nachgewiesen 
werden. 


Neben 
der 
Untersuchung 
von 
optischen 
Komponenten 
f¨

ur 
DUV-Anwendungen 
wurde 
demonstriert, 
dass 
sich 
Streulichtmessungen 
bei 
193 
nm 
hervorragend 
zur 
Rauheitsmessung 
von 
EUV-Spiegeln 
eignen. 
Rauheitskomponenten 
die 
bei 
193 
nm 
Streulicht 
in 
gr¨ur 
Nahwinkelstreuung 
bei 
13,5 
nm 


oßere 
Winkel 
verursachen 
sind 
gleichzeitig 
auch 
f¨
verantwortlich, 
die 
besonders 
schwierig 
zu 
messen 
ist. 
Daher 
konnte 
die 
Rauheit 
und 
Homogenit¨

at 
von 
Mo/Si-Schichten 
bei 
193 
nm 
untersucht 
und 
die 
Ergebnisse 
direkt 
mit 
den 
Nahwinkelstreueigenschaften 
bei 
13,5 
nm 
korreliert 
werden. 


Untersuchungen 
an 
Mo/Si-Spiegeln 
bei 
13,5 
nm 
zeigten, 
dass 
im 
Gegensatz 
zum 
Streulicht 
bei 
DUV-Schichten, 
Streulicht 
von 
EUV-Schichten 
vor 
allem 
durch 
replizierte 
Substratrauheit 
hervorgerufen 
wird. 
Erst 
bei 
gr¨war 


oßeren 
Streuwinkeln 
(. 
10) 
ein 
zunehmender 
Einfluss 
von 
intrinsischer 
Schichtrauheit 
zu 
beobachten. 
Signifikante 
Streuverluste 
zwischen 
0, 
8% 
und 
3, 
9% 
wurden 
selbst 
bei 
Verwendung 
superpolierter 
Substrate 
festgestellt. 
Ein 
intrinsischer 
Streuverlust 
der 
untersuchten 
Schichten 
bei 
Abscheidung 
auf 
ein 
ideal 
glattes 
Substrat 
von 
0.7% 
wurde 
vorhergesagt. 


Der 
kombinierte 
Einsatz 
von 
winkelaufgel¨

osten 
Reflexions-und 
Streulichtmessungen 
bei 
13,5 
nm 
erm¨

oglichte 
die 
Untersuchung 
der 
bestrahlungsinduzierten 
Degradation 
von 
EUV-Spiegeln. 
F¨

ur 
Mo/Si-Schichtsysteme 
konnte 
sowohl 
die 
Reduzierung 
des 
Reflexionsgrads 
als 
auch 
deren 
Ursache, 
Oxidation 
der 
oberen 
Schichten, 
direkt 
bei 
der 
Anwendungswellenl
¨

ange 
untersucht 
werden. 
Obwohl 
eine 
drastische 
Zunahme 
der 
Rauheit 
nach 
Bestrahlung 
durch 
Streulichtmessungen 
bei 
schr¨

agem 
Einfall 
nachgewiesen 
wurde, 
nahm 
der 
Streuverlust 
bei 
quasi-normaler 
Beleuchtung 
von 
0, 
9% 
auf 
0, 
5% 
ab. 
Dies 
belegt, 
dass 
die 
Degradation 
auf 
die 
oberen 
Schichten 
beschr¨

ankt 
ist 
und 
nicht 
zur 
Verschlechterung 
der 
Streulichteigenschaften 
f¨

uhrt. 



Abstract 


The 
recent 
developments 
in 
semiconductor 
lithography 
place 
challenging 
demands 
on 
optical 
components 
for 
193 
nm 
and 
13.5 
nm. 
In 
particular 
light 
scattering 
from 
optical 
surfaces, 
thin 
film 
coatings, 
and 
bulk 
materials 
becomes 
crucially 
important. 
This 
thesis 
concentrates 
on 
the 
development 
of 
a 
complete 
methodology, 
comprising 
effective 
instruments 
for 
sensitive 
scattering 
measurements 
at 
193 
nm 
and 
13.5 
nm 
as 
well 
as 
the 
link 
to 
theoretical 
modeling 
and 
analysis 
tools 
in 
order 
to 
investigate 
the 
relevant 
scattering 
mechanisms 
at 
both 
wavelengths. 


A 
system 
for 
total 
scattering 
(TS) 
and 
angle 
resolved 
scattering 
(ARS) 
measurements 
at 
193 
nm 
is 
described. 
The 
TS 
set-up 
exhibits 
a 
sensitivity 
of 
better 
than 
10-6 
. 
The 
set-up 
for 
ARS 
enables 
measurements 
at 
arbitrary 
angles 
of 
incidence 
and 
scattering 
with 
a 
dynamic 
range 
of 
12 
orders 
of 
magnitude. 
For 
investigations 
at 
13.5 
nm, 
an 
instrument 
for 
angle 
resolved 
scatter 
and 
reflectance 
measurements 
has 
been 
developed. 
The 
dynamic 
range 
exceeds 
6 
orders 
of 
magnitude. 


Existing 
theories 
for 
roughness-induced 
scattering 
in 
the 
visible 
and 
X-ray 
spectral 
ranges 
proved 
to 
be 
valid 
at 
both 
193 
nm 
and 
13.5 
nm, 
and 
interface 
roughness 
was 
found 
to 
be 
the 
main 
source 
of 
scattering 
for 
both 
DUV 
and 
EUV 
coatings. 
A 
novel 
procedure 
for 
the 
characterization 
of 
multilayer 
coatings 
which 
combines 
scattering 
and 
roughness 
measurement 
and 
modeling 
was 
presented. 
The 
relevant 
structural 
properties 
are 
expressed 
by 
two 
descriptive 
parameters. 
The 
scaling 
exponent 
ß 
describes 
the 
roughness 
evolution 
in 
the 
multilayer, 
and 
d 
describes 
optical 
layer 
thickness 
deviations. 


Fluoride 
HR 
coatings 
for 
193 
nm 
applications 
exhibited 
total 
backscattering 
between 
0.9% 
and 
2.8% 
depending 
on 
the 
deposition 
conditions 
and 
coating 
materials, 
while 
TSb 
values 
of 
as 
low 
as 
1.2 
× 
10-5 
were 
observed 
for 
uncoated 
substrates. 
The 
drastically 
increased 
scattering 
of 
the 
coatings 
was 
attributed 
to 
increased 
interface 
roughness, 
increased 
reflectance, 
and 
strong 
correlation 
of 
different 
interfaces. 
In 
addition, 
even 
small 
deviations 
in 
optical 
layer 
thickness 
were 
determined 
to 
be 
crucial. 


Intrinsic 
thin 
film 
roughness 
resulting 
from 
columnar 
growth 
was 
identified 
as 
the 
dominating 
factor 
for 
the 
scattering 
properties. 
In 
contrast, 
scattering 
is 
nearly 
independent 
of 
substrate 
roughness. 
On 
the 
other 
hand, 
drastically 
increased 
scattering 
was 
observed 
which 
could 
be 
explained 
by 
optical 
layer 
thickness 
deviations 
caused 
by 
substrate-dependent 
growth 
properties 
and 
porosities. 



For 
the 
investigation 
of 
the 
bulk 
scattering 
from 
synthetic 
fused 
silica 
at 
193 
nm, 
methods 
had 
to 
be 
developed 
to 
separate 
surface 
from 
bulk 
effects. 
Bulk 
scattering 
co


-1 
-1

efficients 
a 
between 
0.6x10-3 
cmand 
1.7x10-3 
cmdepending 
on 
the 
purity 
and 
thermal 
history 
of 
the 
materials 
were 
observed. 
The 
relevant 
scattering 
mechanism 
was 
found 
to 
be 
Rayleigh 
scattering 
from 
density 
fluctuations 
in 
the 
amorphous 
structure. 


In 
addition 
to 
the 
investigation 
of 
optical 
components 
for 
DUV 
applications, 
scatter 
measurements 
at 
193 
nm 
were 
demonstrated 
to 
be 
well-suited 
for 
surface 
roughness 
measurements 
of 
EUV 
mirrors. 
Roughness 
associated 
with 
high-angle 
scattering 
at 
193 
nm 
also 
causes 
near-angle 
scattering 
at 
13.5 
nm, 
which 
is 
more 
difficult 
to 
measure. 
This 
enabled 
rapid 
investigations 
of 
the 
roughness 
and 
homogeneity 
of 
Mo/Si 
coatings 
at 
193 
nm 
with 
a 
direct 
link 
to 
their 
near-angle 
scattering 
properties 
at 
13.5 
nm. 


Investigations 
of 
Mo/Si 
mirrors 
at 
13.5 
nm 
revealed 
that, 
unlike 
the 
scattering 
of 
DUV 
coatings, 
the 
scattering 
of 
EUV 
coatings 
is 
dominated 
by 
replicated 
substrate 
roughness. 
Only 
at 
larger 
scatter 
angles 
(. 
10), 
an 
increasing 
influence 
of 
intrinsic 
thin 
film 
roughness 
was 
observed. 
Considerable 
scatter 
losses 
between 
0.8% 
and 
3.9% 
occurred 
even 
if 
superpolished 
substrates 
were 
used. 
The 
intrinsic 
scatter 
loss 
of 
the 
investigated 
coatings 
if 
deposited 
onto 
an 
ideally 
smooth 
substrate 
was 
predicted 
to 
be 
0.7%. 


A 
combination 
of 
reflectance 
and 
scatter 
measurements 
at 
13.5 
nm 
enabled 
the 
investigation 
of 
the 
radiation-induced 
degradation 
of 
EUV 
mirrors. 
For 
Mo/Si 
coatings, 
the 
reduction 
of 
reflectance 
as 
well 
as 
the 
origin 
of 
degradation 
-oxidation 
of 
the 
toplayers 
-were 
analyzed 
directly 
at 
the 
wavelength 
of 
application. 
Although 
a 
drastic 
increase 
of 
surface 
roughness 
during 
irradiation 
was 
detected 
via 
scatter 
measurement 
at 
near-grazing 
incidence, 
scatter 
losses 
at 
quasi-normal 
incidence 
decreased 
from 
0.9% 
to 
0.5%. 
This 
indicates 
that 
the 
degradation 
is 
confined 
to 
the 
uppermost 
interfaces 
and 
does 
not 
deteriorate 
the 
scattering 
properties. 



Ehrenw¨ 
arung

ortliche 
Erkl¨

Ich 
erkl¨hiermit 
ehrenw¨ 
andig, 
ohne 


are 
ortlich, 
dass 
ich 
die 
vorliegende 
Arbeit 
selbst¨
unzul¨

assige 
Hilfe 
Dritter 
und 
ohne 
Benutzung 
anderer 
als 
der 
angegebenen 
Hilfsmittel 
und 
Literatur 
angefertigt 
habe. 
Die 
aus 
anderen 
Quellen 
direkt 
oder 
indirekt 
uber


¨
nommenen 
Daten 
und 
Konzepte 
sind 
unter 
Angabe 
der 
Quelle 
gekennzeichnet. 


Bei 
der 
Auswahl 
und 
Auswertung 
folgenden 
Materials 
haben 
mir 
die 
nachstehend 
aufgef
¨

uhrten 
Personen 
in 
der 
jeweils 
beschriebenen 
Weise 
entgeltlich/unentgeltlich 
geholfen: 


1. 
Hein 
Uhlig, 
Hanno 
Heiße, 
Dr. 
Torsten 
Feigl, 
Dr. 
Sergiy 
Yulin, 
Marco 
Perske 
(Fraunhofer 
IOF, 
Jena), 
Earl 
Rudisill 
(Newport 
Corp., 
Irvine 
(CA)): 
Herstellung 
von 
DUV-und 
EUV-Schichtsystemen 
2. 
Bodo 
K¨
uhn 
(Heraeus 
Quarzglas, 
Hanau): 
Herstellung 
von 
fused 
silica 
Proben 
und 
Ramanspektroskopie 


3. 
Dr. 
Marcel 
Flemming: 
Unterst¨
utzung 
bei 
AFM-Messungen 


4. 
Dr. 
Christian 
M¨
uhlig 
(IPHT 
Jena): 
Absorptionsmessungen 


5. 
Dr. 
Nicolas 
Benoit 
(Fraunhofer 
IOF, 
Jena): 
Bestrahlung 
von 
EUV-Spiegeln 
6. 
Dr. 
Christian 
Laubis 
(PTB, 
Berlin): 
EUV-Spektralphotometrie 
7. 
Detlef 
Schelle 
(FSU 
IAP, 
Jena): 
SEM-Messungen 
Weitere 
Personen 
waren 
an 
der 
inhaltlich-materiellen 
Erstellung 
der 
vorliegenden 
Arbeit 
nicht 
beteiligt. 
Insbesondere 
habe 
ich 
hierf¨nicht 
die 
entgeltliche 
Hilfe 


ur 
von 
Vermittlungs-bzw. 
Beratungsdiensten 
(Promotionsberater 
oder 
andere 
Personen) 
in 
Anspruch 
genommen. 
Niemand 
hat 
von 
mir 
unmittelbar 
oder 
mittelbar 
geldwerte 
Leistungen 
f¨

ur 
Arbeiten 
erhalten, 
die 
im 
Zusammenhang 
mit 
der 
vorgelegten 
Dissertation 
stehen. 


Die 
Arbeit 
wurde 
bisher 
weder 
im 
In-noch 
im 
Ausland 
in 
gleicher 
oder 
¨

ahnlicher 
Form 
einer 
anderen 
Pr¨orde 
vorgelegt. 


ufungsbeh¨

Die 
geltende 
Promotionsordnung 
der 
Physikalisch-Astronomischen 
Fakult¨ist 
mir 


at 
bekannt. 


Ich 
versichere 
ehrenw¨

ortlich, 
dass 
ich 
nach 
bestem 
Wissen 
und 
Gewissen 
die 
reine 
Wahrheit 
gesagt 
und 
nichts 
verschwiegen 
habe. 


Jena, 
25. 
M¨arz 
2008 
Sven 
Schr¨

oder 



Lebenslauf 
Pers¨onliche 
Daten 
Name: 
Sven 
Schr¨oder 
Geburtsdatum: 
30. 
Juli 
1975 
Geburtsort: 
Erfurt 
Ausbildung 
1982-1991 
Polytechnische 
Oberschule 
“Wilhem 
Pieck”, 
Erfurt 
1991-2004 
1. 
Staatliche 
Integrierte 
Gesamtschule, 
Erfurt 
29. 
Juni 
1994 
Abitur 
1994-1998 
Wehrdienst, 
Fernmelderegiment 
320, 
Frankenberg/Eder 
1998-2004 
Studium 
der 
Physik 
an 
der 
Friedrich-Schiller-Universit¨at 
(FSU), 
Jena 
17. 
M¨arz 
2004 
Physik-Diplom 
2001-2004 
wissenschaftliche 
Hilfskraft 
am 
Fraunhofer 
Institut 
Angewandte 
Optik 
und 
Feinmechanik 
(IOF), 
Jena 
2004Doktorand 
Institut 
f¨ur 
Angewandte 
Physik 
der 
FSU 
/ 
Fraunhofer 
IOF