### soutenance V1

```Angle resolved Mueller Polarimetry,
Applications to periodic structures
PhD Defense
Clément Fallet
Under the supervision of Antonello de Martino
Outline of the presentation
Motivations and introduction to polarization
Design and optimization of a Mueller microscope
Fourier space measurements : application to
semiconductor metrology
Real space measurements : example of characterization
of beetles
Conclusions and perspectives
PhD Defense - Clément Fallet - October 18th
2
Motivations of the study
 Various applications of polarization of
 A lot of studies, but mainly driven by
classical ellipsometry  spectral
resolution (discrete angle, averaged over
the illuminated region)
 Spatial dependency of polarimetric
properties is only qualitatively assessed
PhD Defense - Clément Fallet - October 18th
3
Motivations of the study
 What we propose, discrete wavelength :
 Angular resolution (averaged over the field)
 Spatial resolution (averaged over the angles)
 Possibility to use the same system for
both measurements.
 Evolution of a classical bright-field
microscope  ease of use
PhD Defense - Clément Fallet - October 18th
4
PhD Defense - Clément Fallet - October 18th
5
Introduction to polarization

−
=
45° − −45°
−

= .
M=
PhD Defense - Clément Fallet - October 18th
 M 11

M
 21
 M 31

 M 41
M 12
M 13
M 22
M 23
M 32
M 33
M 42
M 43
M 14 

M 24

M 34 

M 44 
6
Mueller Polarimeter)
Polarimeter
(Stokes
B = A.M.W
 M = A-1.B.W-1
At = [S’1, S’2, S’3, S’4]
PSA Basis Stokes vectors
W = [S1, S2, S3’ S4]
PSG Basis Stokes vectors
A and W must be as close as possible to unitary Calibration : eigenvalue method
No instrument modelling
Their condition numbers must be optimized
(E.Compain 1999, S. Tyo 2000, M. Smith, 2002)
(E.Compain, Appl. Opt 38, 3490 1999)
PhD Defense - Clément Fallet - October 18th
7
DESIGN & OPTIMIZATION OF A
MUELLER MICROSCOPE
PhD Defense - Clément Fallet - October 18th
8
Specifications of the set-up
 Complete Mueller polarimeter at discrete λ
▪
Complete measurement of the Mueller Matrix
(4 by 4 matrix). First setup by S. Ben Hatit.
 2 imaging modes
▪ Fourier Space
 we’re not imaging the sample itself but the back
focal plane of a high-aperture microscope
objective
▪ Real space
 Design based on classical microscopy
PhD Defense - Clément Fallet - October 18th
9
Epi-Illumination scheme
CCD
Aperture image : angularly resolved
Lim3
Real image : spatially resolved
Interferential
filter
5
1
2
3
4
5
–
–
–
–
–
Aperture diaphragm
Field diaphragm
PSG : Polarization State Generator
PSA : Polarization State Analyser
Lim2
retractable lens
Lim1
4
1
2
3
Source
Beamsplitter
LColl
L1
L2
Back focal plane
Strain-free
Microscope objective
Sample
PhD Defense - Clément Fallet - October 18th
10
Illumination arm
Collection
lens
L2
Rays emerging
from the source
L1
Aperture
diaphragm
Field
diaphragm
PhD Defense - Clément Fallet - October 18th
Back focal
plane
11
Detection arm
400nm pitch grating
PhD Defense - Clément Fallet - October 18th
12
Choice of the objectives
 Strain-free Nikon objectives
▪
▪
Specified for quantitative polarization
No polarimetric signature in real space
 But small dichroism and birefringence
when used in Fourier space
 calibration of the objective with wellcharacterized reference samples (c-Si, SiO2 on
c-Si) (method explained in the manuscript)
PhD Defense - Clément Fallet - October 18th
13
Aperture Vs Field
objective
Full Field
Maximum Aperture
5x
360µm
0-8°
20x
90µm
0-26°
50x
36µm
0-53°
100x
18µm
0-64°
with our current pinhole, the field (spot size) can be discreased
down to 10µm
 Use of a pinhole with smaller diameter to achieve 5µm
PhD Defense - Clément Fallet - October 18th
14
Description of the measurements
0.2
0.2
-0.2
∝ sin -0.2

= tan(Ψ)

dichroism
Δ
c-Si wafer, 633nm
retardance
PhD Defense - Clément Fallet - October 18th
15
From (x,y) to (s,p)
,  =   .  ,  . (−)
y
x
(x,y)
0.2
0.2
-0.2
-0.2
PhD Defense - Clément Fallet - October 18th
(s,p)
Isotropic sample
16
PhD Defense - Clément Fallet - October 18th
17
APPLICATION TO OVERLAY
CHARACTERIZATION IN THE
SEMICONDUCTOR INDUSTRY
PhD Defense - Clément Fallet - October 18th
18
Motivations
 To keep increasing the power of
microprocessors, we need to decrease
the size of the transistors
 Transistor fabrication = layer by layer
 With the decrease in size (currently
22nm), better metrology is required
PhD Defense - Clément Fallet - October 18th
19
Metrology requirements
 We engrave specially designed marks in the
CD
scribe lines
 We measure :
▪
The profile (critical dimension …) : ASML contract
▪
The overlay (shift between the 2 structures) :
MuellerFourier contract with Horiba Jobin Yvon and
CEA-LETI
PhD Defense - Clément Fallet - October 18th
20
Overview of the metrology techniques



State of the art AFM (gold standard for CD metrology)
CD-SEM
Optical techniques :
•Reflectometry, classical ellipsometry (q = 70°, f =0°, 0.75 – 6.3 eV)
•Mueller matrix polarimetry (spectroscopic or angle-resolved)
PhD Defense - Clément Fallet - October 18th
21

Image Based overlay (IBO) :
▪
box in box or bar in bar marks imaged with a bright-field microscope.
▪
Grating based Advanced Imaging Method (AIM) by KLA-TENCOR
▪
Limited by the aberrations and size of the marks ( 15x15 – 30x30 µm²)

Diffraction Based Overlay (DBO) : Collection of the light diffracted,
scattered and reflected by the sample and analysis as a function of either the wavelength
(spectroscopic) or the angle of incidence
▪
Empirical DBO : no modeling of the structure needed but at least 2 measurements of
calibrated targets
▪
Model-Based DBO : overlay as a parameter of the fit. Only 1 measurement needed
but model-dependent. Limited by the model and the size of the marks (30x60µm²,
ASML Yieldstar)
PhD Defense - Clément Fallet - October 18th
22
2011  1.6nm
2012  1.4nm
PhD Defense - Clément Fallet - October 18th
23
Properties of the Mueller matrix
The Mueller matrix elements are sensitive
to the profile structure and its asymmetry.
For a structure presenting an asymmetry,
we have :
 M ijleft  M left
ji

right
right
 M ij
i  1, 2
 M ij
 M left  M right
ij
ji

j  3, 4
where left and right stand
for the direction of the
shift in the structure.
PhD Defense - Clément Fallet - October 18th
24
Simulations and RCWA

Simulation of the Mueller matrix of a superposition of 2
gratings with the same pitch but with a lateral shift

Simulation by Rigorous coupled wave analysis : All the
electromagnetic quantities (E, H and ε,μ) are expanded
in Fourier series. Simulations by T.Novikova and
M.Foldyna PhD Defense - Clément Fallet - October 18th
25
Estimator
Simulations of structures of interest
0.3
0.2
0.1
0
R² = 1
0
10
20
30
Overlay (nm)




Piece-wise layer dielectric
function
Continuity of field assured by
Lalanne / Li factorization rules
Propagation of S matrices
Based on our knowledge on
Mueller matrix symmetries, we
t
compute M  M to define
possible estimators
PhD Defense - Clément Fallet - October 18th
M  M
t
26
Description of the test samples

Test samples designed and manufactured @ CEA-LETI
Nominal overlays (nm) : ±150, ± 100, ± 50, ± 40, ±50µm
30, ± 20 ± 10, 0
Nominal CDs L1 and L2 also vary to extensively test the simulations
 84 different grating combinations
PhD Defense - Clément Fallet - October 18th
27
Sample 1 : CD N1 150 N2 300
0.2
0.2
Normalized Mueller matrix measurement
-0.2
Estimator E  M  M
-0.2
PhD Defense - Clément Fallet - October 18th
28
t
Scalar estimator
Kept constant for all
measurements of the same CD
comination
Scalar estimator :
E14
PhD Defense - Clément Fallet - October 18th
29
How to use our estimator?
 2 possibilities
▪
▪
1 – Check the linearity of the estimator based
on the overlay actually present on the wafer.
Imaging Method (AIM)
2 – Measurement of the uncontrolled overlay
(overlay in addition of the nominal overlay)
PhD Defense - Clément Fallet - October 18th
30
VALIDATION OF THE LINEARITY OF
ESTIMATOR E14
PhD Defense - Clément Fallet - October 18th
31
Sample 1 (N1 150 N2 300) : Linearity
Estimator overlay Y
0.14
Value of the estimator
0.12
y = 0.0016x - 0.003
R² = 0.9936
0.1
0.08
0.06
0.04
0.02
0
-10
0
-0.02
-0.04
10
20
30
40
50
60
70
80
90
AIM overlay (nm)
Gold standard
PhD Defense - Clément Fallet - October 18th
32
Sample 1 : comparison with simulations
0.4
R² = 1
0.3
value of the estimator
R² = 0.9999
-60
0.2
0.1
R² = 0.9936
0
-40
-20
0
20
40
60
80
-0.1
-0.2
-0.3
100
-0.4
Overlay (nm)
PhD Defense - Clément Fallet - October 18th
33
Sample 2 : CD N1 130 N2 300
mean(E14) Overlay Y
y = 0.0043x + 0.0091
R² = 0.9667
0.35
0.3
0.25
0.2
estimator
0.15
-40.00
0.1
0.05
-20.00
0
0.00
-0.05
20.00
40.00
60.00
80.00
-0.1
-0.15
-0.2
AIM overlay (nm)
PhD Defense - Clément Fallet - October 18th
34
Sample 2 : CD N1 130 N2 300
mean(E14) Overlay X
0.3
0.2
y = -0.0055x - 0.0301
R² = 0.9978
estimator
0.1
0
-60
-40
-20
0
20
40
60
-0.1
-0.2
-0.3
-0.4
AIM overlay (nm)
PhD Defense - Clément Fallet - October 18th
35
Influence of the CD
Influence of the CD
-45nm
-25nm
0.15
overlay Y 200 200
value of the estimator
0.1
-60
overlay Y 200 220
0.05
0
-40
-20
0
20
40
60
-0.05
-0.1
-0.15
y = -0.0014x - 0.0664
-0.2
-0.25
-0.3
y = -0.0047x - 0.1185
-0.35
nominal overlay (nm)
Specified value
PhD Defense - Clément Fallet - October 18th
36
Conclusion
 Estimator OK linear with overlay
measured by AIM, which is considered as
gold standard.
 Consistency between X and Y overlays.
 The slope highly depends on the CD of
the gratings.
 Value of the experimental estimator
smaller than predicted by simulations.
PhD Defense - Clément Fallet - October 18th
37
MEASUREMENTS OF THE
UNCONTROLLED OVERLAY
PhD Defense - Clément Fallet - October 18th
38
Definitions
 We distinguish the nominal overlay
(specified) and real overlay
=  +

 The nominal overlay is a controlled bias,
intentionally introduced.
 Only the uncontrolled overlay is relevant
PhD Defense - Clément Fallet - October 18th
39
Method 1
 If  =  +  = 0  14 = 0
 Linear fit on the measurements
Overlay Y
14 =  ∗  +
0.04

Given by linear regression
-50

Estimator
0.02

=−

-30
0
-10
-0.02
y = -0.0014x - 0.0664
10
30
50
-0.04
-0.06
-0.08
-0.1
-0.12
-0.14
  =  +
PhD Defense - Clément Fallet - October 18th
-0.16
nominal overlay (nm)
40
Method 2
 14  ∝  +
 14 − ∝ − +
  =
14  +14(−)

14  −14(−)
  =  +
hypothesis ∶   (H)
PhD Defense - Clément Fallet - October 18th
41
Verification of H
Module 10 N1 170 N2 300, overlay Y
Method 2 is validated for high nominal overlays
Method 1
Method 2
AIM overlay (nm)
PhD Defense - Clément Fallet - October 18th
42
Correlation between AIM et Mueller
Correlation AIM - Mueller Overlay Y
200
Mueller overlay (nm)
150
-100
y = 1.0456x + 1.5293
R² = 0.9674
100
50
0
-50
0
50
100
150
-50
-100
AIM overlay (nm)
PhD Defense - Clément Fallet - October 18th
43
Correlation between AIM et Mueller
Correlation AIM - Mueller Overlay X
Mueller overlay (nm)
y = 0.945x + 0.709
R² = 0.9708
60
40
20
-80.00
-60.00
-40.00
-20.00
0
0.00
20.00
40.00
60.00
-20
-40
-60
-80
AIM overlay (nm)
PhD Defense - Clément Fallet - October 18th
44
Map of the overlay on a field
 Map of the uncontrolled overlay
(all measurement in nm)
PhD Defense - Clément Fallet - October 18th
45
A few quality estimators
  ∶   ℎ = 1,12
  = 1,1nm
  = 0,88
 TMU : total measurement uncertainty
=
² +  ² + ²
= 1,80
PhD Defense - Clément Fallet - October 18th
46
Comparisons with existing apparatus
 Total measurement uncertainty (TMU) for
commercial instruments
▪
AIM : TMU ~ 2nm (2008)
▪
Yieldstar : TMU = 0,2nm (2011)
▪
Nanometrics : TMU ~ 0,4nm (2010)
PhD Defense - Clément Fallet - October 18th
47
Conclusions
 Characterization of the overlay with a
(fast), non-destructive technique. No
modelling required but 2 very-well
characterized structures for calibration
 Uncertainty relatively small ~ 2nm
 Measurements in 20 x 20µm² boxes
PhD Defense - Clément Fallet - October 18th
48
Conclusions (2)
 Very good linearity of the scalar estimator
respect to the overlay defect (R² between
0,94 and 0,99)
 However, experimental values of the
estimators are lower than what simulation
predicted.
 Estimators are very sensitive to the
PhD Defense - Clément Fallet - October 18th
49
Perspectives
 Possibility to go down to 5 x 5µm² boxes
with the correct pinhole
 Automatic selection of the mask
 Increase the repeatability of the
measurements to decrease Tool Induced
Shift and its variability to decrease total
uncertainty
 Integrate CD measurement through fitting of
the Mueller matrix to approach Ausschnitt’s
MOXIE (Metrology Of eXtremely Irrational
Exuberance)
PhD Defense - Clément Fallet - October 18th
50
MEASUREMENTS
ON
BEETLES
PhD Defense - Clément Fallet - October 18th
51
Organization of the cuticle
 A twisted multilayer structure : Bouligand
structures
 Each layer consists of a chitin structure
with uniaxial anysotropy
L. Besseau and M.-M. Giraud-Guille, J. Mol. Biol., no. 251, pp.
197–202, 1995.
10µm
PhD Defense - Clément Fallet - October 18th
52
Modeling of the structure
 Fit of spectroscopic Mueller ellipsometry
 Optical model of the cuticle (K. Järrendahl)
Image from K. Järrendahl.
 Spatial homogeneity is assumed; but need of a
more complex model to take into account the
spatial variations
PhD Defense - Clément Fallet - October 18th
53
Purpose of this study
 Compare the results obtained on same
species with different characterization
methods
 Characterize the spatial variations of the
polarimetric response to improve the
model
PhD Defense - Clément Fallet - October 18th
54
Comparisons of the results
Variable Angle Spectroscopic
ellipsometer RC2
Angle resolved Mueller
polarimeter









Angular range 20°-70°
2θ configuration
Average on the field
Spectral resolution
Only the specular
reflection
All incidence at a time
Average on the angle
Spatial resolution
All the light emitted at a
certain angle (reflection
+ scattering)
PhD Defense - Clément Fallet - October 18th
55
Cetonia aurata
Cetonia aurata
5x image
Imaged area 360µm
PhD Defense - Clément Fallet - October 18th
20x image
Imaged area 90µm
56
Cetonia aurata
1 0
0
0 0
0 0
0
0
−
0
20X
1
0
0
−1
0
0
0
0
0
0
0
0
−1
0
0
1
M14
PhD Defense - Clément Fallet - October 18th
57
0
0
0

Chrysina argenteola
20x image
Imaged area 90µm
PhD Defense - Clément Fallet - October 18th
58
Chrysina argenteola
20X
M14
PhD Defense - Clément Fallet - October 18th
59
Conclusions
 Difficult to accurately compare the results
obtained with different techniques.
 But still, common features arise
 Only a preliminary work, a lot remains to
be done.
 To our knowledge, nobody has ever
published spatially resolved Mueller
matrices for beetles
PhD Defense - Clément Fallet - October 18th
60
CONCLUSIONS & PERSPECTIVES
PhD Defense - Clément Fallet - October 18th
61
PERSPECTIVES
PhD Defense - Clément Fallet - October 18th
62
Chiral structures
 Understand the
relationship
between helicoidal
structures and
circular dichroism
 Mimic the cuticle of
beetles
From G. z. Radnoczi et al. ,Physica status solidi. A. Applied
research, vol. 202, no. 7, pp. R76–R78.
Mueller Matrix @ 633nm
0.2
0.2
-0.2
-0.2
PhD Defense - Clément Fallet - October 18th
M14
63
Periodic structures
Sol-gel deposited silica spheres
M12
Real image with 100x
Angle resolved MM
 Hexagonal symmetry visible in both the structure
and the Mueller matrix
PhD Defense - Clément Fallet - October 18th
M34
64
CONCLUSIONS
PhD Defense - Clément Fallet - October 18th
65
Conclusions
 Optimization of a Mueller microscope
▪
▪
Better illumation scheme  Modified Köhler
Good calibration of the objective without any
prior modelling but only a (Ψ,Δ) matrix
assumption
 Measurements in both real and reciprocal
space, different kind of applications
presented
PhD Defense - Clément Fallet - October 18th
66
Conclusions
 In Fourier space
▪
▪
Characterization of the overlay with a (fast),
non-destructive technique. No modelling
required but 2 very-well characterized
structures
Uncertainty relatively small ~ 2nm
 In real space
▪
▪
Accurate spatial characterization of
entomological structures
Major step for the study of the autoorganized structures
PhD Defense - Clément Fallet - October 18th
67
Acknowledgements
 Financial support of the French National
Research Agency (ANR) through the joint
project MuellerFourier with CEA-LETI and
Horiba Jobin-Yvon.
 Hans Arwin, Kenneth Järrendahl and Roger
Magnusson at LiU.
 Special thanks to Tatiana Novikova and Bicher
Haj Ibrahim for their help and support.
PhD Defense - Clément Fallet - October 18th
68
PhD Defense - Clément Fallet - October 18th
69
PhD Defense - Clément Fallet - October 18th
70
M 1  T obj  M  T obj
o
i
M 1  T obj  M  T obj
o
i
M 1  T obj  M  T obj
o
i
Calibration of the objective
 Assumptions :
▪
▪
Objective can be described by a (Ψ,Δ)
matrix.
The MM in forward and backward directions
are equal = Mobj
 By measuring an isotropic sample (eg. cSi wafer), we can calibrate the objective
PhD Defense - Clément Fallet - October 18th
71
Calibration of the objective
 Mmeas = Mobj * McSi * Mobj
(Ψ,Δ) matrices commute
 Mmeas = Mobj² * McSi

Δmeas = 2 Δobj + ΔcSi
tanΨmeas = tanΨobj² * tanΨcSi
PhD Defense - Clément Fallet - October 18th
72
Results on objective calibration
Difference
between
calibration
Difference
between
calibration
[email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */
cSi and 633nm
SiO2
Objective
calibrated
[email protected]/* <![CDATA[ */!function(t,e,r,n,c,a,p){try{t=document.currentScript||function(){for(t=document.getElementsByTagName('script'),e=t.length;e--;)if(t[e].getAttribute('data-cfhash'))return t[e]}();if(t&&(c=t.previousSibling)){p=t.parentNode;if(a=c.getAttribute('data-cfemail')){for(e='',r='0x'+a.substr(0,2)|0,n=2;a.length-n;n+=2)e+='%'+('0'+('0x'+a.substr(n,2)^r).toString(16)).slice(-2);p.replaceChild(document.createTextNode(decodeURIComponent(e)),c)}p.removeChild(t)}}catch(u){}}()/* ]]> */
cSi
PhD Defense - Clément Fallet - October 18th
73
Calibration of reflectivity
 M11 is not calibrated in the ECM.
 B = τ A’.M.W’.Isource with τ, total
transmission of the device
 M = 1/c .A’-1.B.W’-1 with c= τ.Isource
 By measuring well-known samples, we
can calibrate the factor c.
PhD Defense - Clément Fallet - October 18th
74
Details of the mark
AIM marks
30x30 µ2
10
x marks
overlay specified
along Y
y marks
Overlay specified
along x
20
5
10
20
10
x grating
Level 1
Level 2
y grating
AIM marks
clockwise
anticlockwise
PhD Defense - Clément Fallet - October 18th
75
Best results so far, N1 300 N2 180
OVY
0.4
Value of E14 versus nominal
overlay in nm for overlay along
x and y axis
0.3
y = -0,0057x - 0,0047
R² = 0,9893
0.2
0.1
0
-60
-40
-20
0
20
40
60
Main features :
- the uncontrolled overlay is
close to 0.
- Highest slope in the
measured samples
-0.1
-0.2
-0.3
-0.4
OVX
0.4
0.3
Is there a correlation between
the slope and the uncontrolled
overlay?
y = -0.0069x - 0.0178
R² = 0.9947
0.2
0.1
0
-60
-40
-20
0
20
40
60
-0.1
-0.2
-0.3
-0.4
PhD Defense - Clément Fallet - October 18th
76
Intrensinc properties of the MM
A Stokes non-diagonalizable Mueller matrix (NSD MM) : theory
Image and equation from Ossikovski et al, Opt. Lett. 34, 974-976 (2009)
77
PhD Defense - Clément Fallet - October 18th
Intrensic properties of the MM
PhD Defense - Clément Fallet - October 18th
78
Beetles, natural occurrence of NSD MM
 The MM can be regarded as the weighted
average of 3 components
M  nd
1

0


0

1
0
0
0
0
0
0
0
0
LCP
 1
1


0
0
 
0
0 


 1
0
0
0
1
0
0
1
0
0
0

0

0

1
1

0

0

0
Mirror
0
0
1
0
0
1
0
0
0

0

0

1
HWP
From Ossikovski et al., Opt. Lett. 34, 2426-2428 (2009)
PhD Defense - Clément Fallet - October 18th
79
Sum decomposition of the MM
PhD Defense - Clément Fallet - October 18th
80
DOP ellipse
PhD Defense - Clément Fallet - October 18th
81
Calibration of Bouligand structures
PhD Defense - Clément Fallet - October 18th
82
```