1. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications 1
Laboratoire de Physique des Interfaces et
des Couches Minces
Polarized and polarimetric Raman
spectroscopy and applications
A. Frigout, M. Richert, M. Lamy de la Chapelle &
R. Ossikovski
LPICM, Ecole Polytechnique, CNRS
alexandre.frigout@polytechnique.edu

2. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications2
Outline
• Motivation
• Experimental setup
• Polarized Raman
– Theory
– Application: stress characterization in semiconductors
• Polarimetric Raman
– Motivation
– Setup calibration
– Application example: Rayleigh-Stokes measurement
• Conclusion

3. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications3
Motivation
• Objective : Fully exploit the capabilities of « classic »
characterization techniques (Raman and Rayleigh
scattering, fluorescence)
• Means: Combine Raman spectroscopy and related
techniques (Rayleigh scattering, fluorescence) with full
polarized light control (generation and analysis)
• Expected results : Stokes vector and Mueller matrix
measurements within « classic » characterization
techniques resulting in advanced characterization methods

4. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications4
Experimental setup
• High Resolution Raman
spectroscopy
• Scanning probe
microscope
Oblique backscattering configuration
Piezo X,Y
Piezo Z
Microscope
Laser
grating
Notch filter
Detector
PSIA XE100 HORIBA JY Labram 800
X
Y
Z

5. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications5
Polarization control:
1. half-wave plate
2. analyzer
(photos à ajouter)
Generation and analysis of linear polarization states (incident and bacscattered light)
Polarized Raman setup
spectrometer
Laser
objectives
Removable
mirror
Half wave
plate
Analyzer
Edge
filter
spectrometer
Laser
objectives
Removable
mirror
Half wave
plate
Analyzer
Edge
filter

6. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications6
• Raman intensity : I ~ ∑|eS
T
Rjei|2
Rj : Raman tensor of the j phonon (3 for c-Si at 521 cm-1
)
eS : scattered polarization state (Analyzer A)
ei : incident polarization state (half wave plate P)
n

θ
ie

se

analyseur
A
Half wave plate
P










=










=










=
000
00
00
00
000
00
00
00
000
321 d
d
R
d
d
R
d
dR
azimuth
sample S
In the normal backscattering, the third phonon (LO) is the only
one wich can be observed !
Raman intensity depends on the polarization states eS and ei as well as
the sample azimuth !
Thoery of polarized Raman on crystals

7. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications7
Principle : Shift of the optical Si-Si phonon (at 521 cm-1
)
caused by internal mechanical strain : Δw = f(σ)
Observations + model + corrections => stress
1. Model for Δω
(analytical ou FE )
2. Corrections pour
profil du faisceau,
pénétration (l) ???
3. Result:
s = g (Δω)0 200 400 600
0
10
20
30
40
50
60
70
Ramanintensity(a.u.)
Raman shift (cm
-1
)
Si-Si phonon
(3 degenerated modes:
TO1, TO2 et LO)
Rayleigh diffusion
Raman spectrum of c-Si
Stress analysis in Si by
Raman spectroscopy

8. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications8
• In oblique configuration:
– Vary the azimuth sample or the incident polarization
– Fitting the intensity, frequency shift and the FWMH of the Si-Si line with a strain
model
80 nmsSi
SiGe
Si / SiGe structure:
MPa σ11
σ12
σ22
σ33
sSi 980 0 980 0
SiGe -650 0 -650 0
-20 0 20 40 60 80 100 120 140 160 180 200
509
515
516
517
Frequency(cm
-1
)
Sample azimuth (°)
FSiGe
FsSi
-20 0 20 40 60 80 100 120 140 160 180 200
2,8
3,0
3,2
3,4
3,6
3,8
4,0
4,2
4,4
4,6
4,8
FWHM(cm
-1
)
Sample azimuth (°)
strained-SiGe
strained-Si
Phonon position FWMHintensity
R. Ossikovski, Q. Nguyen, G. Picardi, J. Schreiber, J. Appl. Phys. 103, 093525 (2008)
R. Ossikovski, Q. Nguyen, G. Picardi, J. Schreiber, P. Morin, J. Raman Spectrosc. 39, 661 (2008)
bisotropic strain:
Strain measurement in
μRaman : strained Si/SiGe
Incident polarizationIncident polarization Incident polarization
σ11= σ22

9. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications9
• Same experimental configuration but fitted with a biaxial
stress tensor: σ11 ≠ σ22
sSi
SiO2
substrat Si
Strained Si stripes (200nm width, 10nm thick): for CMOS transistor
channel
-20 0 20 40 60 80 100 120 140 160 180 200
3.2
3.3
3.4
3.5
3.6
3.7
3.8
FWMH
Polarization
-20 0 20 40 60 80 100 120 140 160 180 200
516.54
516.55
516.56
516.57
516.58
516.59
516.60
516.61
516.62
516.63
516.64
Shift
Polarization
sSipeakFWMH
sSipeakposition
Incident polarization
Biaxial strain : 1300 / 400 MPa (confirmed by XRays !)
Stress measurement in μRaman:
Si stripes on strained SiO2
Biaxial strain results in asymmetric polarization curves

10. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications10
• Same experimental configuration.
-20 0 20 40 60 80 100 120 140 160 180 200
518.1
518.2
518.3
518.4
518.5
518.6
Experiment
Simulation
SipeakFWMH
Sipeakposition
Incident polarization
-20 0 20 40 60 80 100 120 140 160 180 200
5.20
5.25
5.30
Experiment
Simulation
Incident polarization
• SiNW optical image, 100x objective, 400nm diameter.
Fitted with an isotropic biaxial strain tensor with σ11 = σ22 = 450Mpa
and a (111) cristalline orientation
Stress measurement in
μRaman : SiNWs

11. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications11
• Integration of a polarimeter in the HR-800
Raman spectrometer (from Horiba Jobin Yvon):
– Polarimetric calibration of the spectrometer
– Measurements of Stokes vector and Mueller matrix:
• in Rayleigh scattering regime (coherent illumination)
• of Raman bands (inelastic scattering)
• of fluorescence bands
Motivation for
polarimetric Raman

12. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications12












−
−
−
=












=
−+
DG
yx
II
II
II
I
S
S
S
S
S
4545
0
3
2
1
0
• Description of polarized light (tottaly or not)
• Stokes vector:
• S0 : total intensity
• S1 : ligth polarized parallel
• S2 : light polarized perpendicular
• S3 : light circulary polarized
• DOP : fraction of polarized light
S / S0
Bijective
relationship
0
2
3
2
2
2
1
S
SSS
DOP
++
=
DOP < 1 : light partially polarized
DOP = 1 : light totally polarized
Polarimetry: Stokes
formalism

13. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications13
Polarization control:
1. liquid crystals
2. motorized rotating plates
Complete control of the « input / output » polarization
Polarimetric Raman setup
spectrometer
Laser
objectives
Removable
mirror
PSG
PSA
Edge
filter
spectrometer
Laser
objectives
Removable
mirror
PSG
PSA
Edge
filter
λ/4 rotating
plate
Analyzer

14. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications14
• Determination of the physical charectiristics of the scattered light path
• Measurements of stokes vectors with differents inputs polarizations:
– A rotating linear polarizer
– A rotating quarter wave plate
• Stokes vectors obtained by Fast Fourier Transform
Laser source
Microscope Spectrometer
rotating
polarirzer
λ/2 rotating
plate
45° mirror
Laser source
Microscope Spectrometer
λ/4 rotating
plate
rotating
polarizer
λ/2 rotating
plate
45° mirror
Linear polarized light input circular polarized light input
Polarimetric Raman:
calibration approach
PSAPSA

15. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications15
Stokes vector components vs input linear polarization
DOP
S1
S2
S3
Uncalibrated Raman spectrometer
response
Incident polarization Incident polarization
Incident polarizationIncident polarization
• Experimentals results:
– DOP varies between 0.8 and 1.1
– S1 and S2 have sinusoïdal trends but
do not fit with cosine and sine
– S3 varies between -0.5 and 0.4
• In theory:
– DOP = 1
– S1, S2 exhibit a sinusoïdal trend
– S3 = 0
The system is not passive with
respect to the polarization!
Simulated stokes vector
measured stokes vector
Laser source
Microscope Spectrometer
rotating
polarirzer
λ/2 rotating
plate
45° mirror

16. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications16
Poincaré sphere representation
of the uncalibrated response

17. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications17
IRaw
FFT {α, θ, Δ, D, R}
S = MΔ
-1
MD
-1
MR
-1
SRaw
Depolarizer
Diattenuator
Retarder
DOP ~ 1
S3 ~ 0
• Reasons of this modelisation:
– Depolarizer : DOP close to 1
– Diattenuator : uniform distribution of the polarization state on the ecuador
– Retarder : cancel the S3, bring the plane of the polarization states on the ecuador
• Recursive function with α, θ and Δ as initial conditions
– Calculation of R and D
• R, D and Δ have the sames axes (our reference frame), in that case their matrices
commute
Scattered light path
modeling

18. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications18
• Input parameters [α a θ] = [0 1 0]
• Adjusted parameters:
– λ/4 first angle α: -1.7133°
– Analyzer orientation θ: 0.8817°
– Depolarizer a: 0.9279
– diattenuator D: 0.5154
– Retardance R: 28.6639°
Stokes vector components vs input linear polarization
Laser source
Microscope Spectrometer
P
45°
mirror
Calibration with linear
polarization input
σS = < | Sexp- Stheo | >
= 10-2
[ 4.83 5.38 1.65 ]
Incident polarization
Incident polarizationIncident polarization
Incident polarization
PSA
Simulated stokes vector
measured stokes vector

19. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications19
Poincaré sphere representation of
the calibrated system response
• Polarization states close to the
ecuador and uniformly distributed
• Missmatch between first and
second loop of the polarization
states:
– misalignement of the retarder with
respect to the laser beam

20. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications20
Stokes vector components vs input elliptical polarization
Laser source
Microscope Spectrometer
λ/4
P
45°
mirror
Response to an elliptical
polarization input
σS = < | Sexp- Stheo | >
= 10-2
[ 2.39 3.12 5.71 ]
Incident polarization Incident polarization
Incident polarizationIncident polarization
PSA
Simulated stokes vector of a
retarder plates (adjustment :
R = 74.03° theta Sin = ???)
measured stokes vector

21. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications21
Poincaré sphere system
response
• Polarization states close to
the simulated curve
• Mismatch between first and
second loop of the
polarization states:
– misalignement of the retarder
with respect to the laser beam
measured stokes vector
Simulation with R = 74.03°
Measurement MM16:
R = 74.3°
=> Good agreement
Input : retarder plate at different azimuths

22. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications22
DOP
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
P S P S P S
514 nm 458nm
633 nm
S1
-1
-0.5
0
0.5
1
P S P S P S
514 nm 458nm633 nm
S2
-1
-0.5
0
0.5
1
P S P S P S
514 nm 458nm633 nm
S3
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
P S P S P S
514 nm 458nm633 nm
Stokes-Rayleigh measurement
of STM gold tips
• DOP : competition
between Rayleigh
regime scattering
(458nm) & plasmonic
excitation (633nm)
• A « strong » S3
component at 633 nm :
resulting from
plasmonic excitation (?)
Stokes vector components vs wavelength
Characterization of near field probes through their polairzation response
tiptip

23. 2009/12/07 Polarized and Polarimetric Raman spectroscopy and applications23
Conclusion & outlook
• Polarization control is an important « degree of freedom » that
can be advantageously exploited in scattering and spectroscopic
techniques (Rayleigh, Raman, fluorescence…)
• Polarization control is applied with success to industrial
applications of Raman such as stress characterization in
semiconductors
• Extension from polarized to polarimetric Rayleigh and Raman
scattering opens up the way to novel measurement opportunities
(Mueller-Rayleigh, Mueller-Raman matrices) and applications
(plasmonics)
WE ARE ONLY IN THE BEGINNING,
THE MOST EXCITING IS TO COME!