Report

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 light over the past decades. 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 LET’S TALK ABOUT POLARIZATION 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 A word about polarimeters 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 Aperture Mask 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 More about optical techniques 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 THE ITRS RoadMap 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 Manually selected mask Kept constant for all measurements of the same CD comination Scalar estimator : E = <E14>mask 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. Gold standard established by Advanced 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 Max(E14(mask)) simu -0.2 Mean(E14(mask)) simu -0.3 Mean(E14(mask)) exp 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 chosen mask 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 with@633nm cSi and 633nm SiO2 Objective calibrated with@532nm 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