![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](https://image.slidesharecdn.com/6be121a0-348c-4363-88ff-5ab9953105d8-160127191120/85/workshop_X_dec_2009_AF-18-320.jpg)
![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](https://image.slidesharecdn.com/6be121a0-348c-4363-88ff-5ab9953105d8-160127191120/85/workshop_X_dec_2009_AF-20-320.jpg)
workshop_X_dec_2009_AF
- 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!