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Angle resolved Mueller Polarimetry, Applications to periodic structures

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

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Angle resolved Mueller Polarimetry, Applications to periodic structures

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  1. Angle resolved Mueller Polarimetry, Applications to periodic structures PhDDefense Clément Fallet Under the supervision of Antonello de Martino

  2. Outline of the presentation Motivations and introduction to polarization Design and optimization of a Mueller microscope Fourier spacemeasurements : application to semiconductormetrology Real spacemeasurements : example of characterization of beetles Conclusions and perspectives PhD Defense - Clément Fallet - October 18th

  3. Motivations of the study • Various applications of polarization of light over the pastdecades. • A lot of studies, but mainlydriven by classicalellipsometry spectral resolution(discrete angle, averaged over the illuminatedregion) • Spatial dependency of polarimetricpropertiesisonlyqualitativelyassessed PhD Defense - Clément Fallet - October 18th

  4. Motivations of the study • Whatwe propose, discretewavelength : • Angularresolution (averaged over the field) • Spatial resolution (averaged over the angles) • Possibility to use the same system for bothmeasurements. • Evolution of a classicalbright-field microscope  ease of use PhD Defense - Clément Fallet - October 18th

  5. Let’s talk about polarization PhD Defense - Clément Fallet - October 18th

  6. Introduction to polarization M= PhD Defense - Clément Fallet - October 18th

  7. A word about polarimeters Mueller Polarimeter B = A.M.W  M = A-1.B.W-1 (Stokes Polarimeter) CCD camera PSA PSG At = [S’1, S’2, S’3, S’4] PSA Basis Stokes vectors W = [S1, S2, S3’ S4] PSG Basis Stokes vectors Calibration : eigenvaluemethod No instrument modelling (E.Compain, Appl. Opt38, 3490 1999) Aand W must be as close as possible to unitary Their condition numbers must beoptimized (E.Compain 1999, S. Tyo 2000, M. Smith, 2002) PhD Defense - Clément Fallet - October 18th

  8. Design & optimization of a Mueller microscope PhD Defense - Clément Fallet - October 18th

  9. Specifications of the set-up • Complete Mueller polarimeter atdiscreteλ • Completemeasurement of the Mueller Matrix (4 by 4 matrix). First setup by S. Ben Hatit. • 2 imaging modes • Fourier Space • we’re not imaging the sampleitself but the back focal plane of a high-aperture microscope objective • Real space • Design based on classicalmicroscopy PhD Defense - Clément Fallet - October 18th

  10. Epi-Illumination scheme CCD Aperture image : angularly resolved Interferentialfilter Lim3 Real image : spatially resolved 5 1 – Aperture diaphragm 2 – Field diaphragm 3 – PSG : Polarization State Generator 4 – PSA : Polarization State Analyser 5 – Aperture Mask Lim2 retractablelens Lim1 4 1 2 3 Source Beamsplitter Back focal plane LColl L1 L2 Strain-free Microscope objective Sample PhD Defense - Clément Fallet - October 18th

  11. Illumination arm Collection lens L2 L1 Rays emergingfrom the source Field diaphragm Back focal plane Aperture diaphragm PhD Defense - Clément Fallet - October 18th

  12. Detection arm 400nm pitch grating PhD Defense - Clément Fallet - October 18th

  13. Choice of the objectives • Strain-free Nikon objectives • Specified for quantitative polarization • No polarimetric signature in real space • But smalldichroism and birefringencewhenused in Fourier space calibration of the objective with well-characterized reference samples (c-Si, SiO2 on c-Si) (method explained in the manuscript) PhD Defense - Clément Fallet - October 18th

  14. Aperture Vs Field withourcurrentpinhole, the field (spot size) canbediscreased down to 10µm  Use of a pinholewithsmallerdiameter to achieve 5µm PhD Defense - Clément Fallet - October 18th

  15. 0.2 0.2 -0.2 -0.2 Description of the measurements c-Si wafer, 633nm dichroism retardance PhD Defense - Clément Fallet - October 18th

  16. 0.2 0.2 -0.2 -0.2 From (x,y) to (s,p) p s y x (s,p) Isotropicsample (x,y) PhD Defense - Clément Fallet - October 18th

  17. PhD Defense - Clément Fallet - October 18th

  18. Application to overlay characterization in the semiconductorindustry PhD Defense - Clément Fallet - October 18th

  19. Motivations • To keepincreasing the power of microprocessors, weneed to decrease the size of the transistors • Transistor fabrication = layer by layer • With the decrease in size (currently 22nm), bettermetrologyisrequired PhD Defense - Clément Fallet - October 18th

  20. Metrologyrequirements • We engrave speciallydesigned marks in the scribe lines • Wemeasure : • The profile (critical dimension …) : ASML contract • The overlay (shift between the 2 structures) : MuellerFouriercontractwithHoribaJobin Yvon and CEA-LETI CD PhD Defense - Clément Fallet - October 18th

  21. Overview of the metrology techniques • State of the art AFM (gold standard for CD metrology) • CD-SEM • Optical techniques : • Reflectometry, classicalellipsometry (q = 70°, f =0°, 0.75 – 6.3 eV) • Mueller matrix polarimetry (spectroscopic or angle-resolved) PhD Defense - Clément Fallet - October 18th

  22. Image Based overlay (IBO) : box in box or bar in bar marks imagedwith a bright-field microscope. Gratingbased 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 calibratedtargets Model-Based DBO : overlay as a parameter of the fit. Only 1 measurementneeded but model-dependent. Limited by the model and the size of the marks (30x60µm², ASML Yieldstar) More about optical techniques PhD Defense - Clément Fallet - October 18th

  23. THE ITRS RoadMap 2011  1.6nm 2012  1.4nm PhD Defense - Clément Fallet - October 18th

  24. 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 : where left and right stand for the direction of the shift in the structure. PhD Defense - Clément Fallet - October 18th

  25. Simulations and RCWA • Simulation of the Mueller matrix of a superposition of 2 gratingswith the same pitch but with a lateral shift • Simulation by Rigorouscoupledwaveanalysis : 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

  26. Piece-wise layer dielectricfunction Continuity of fieldassured by Lalanne / Li factorizationrules Propagation of S matrices Based on ourknowledge on Mueller matrix symmetries, wecompute to define possible estimators Simulations of structures of interest PhD Defense - Clément Fallet - October 18th

  27. Description of the test samples • Test samplesdesigned and manufactured @ CEA-LETI Nominal overlays (nm) : ±150, ± 100, ± 50, ± 40, ± 30, ± 20 ± 10, 0 Nominal CDs L1 and L2alsovary to extensively test the simulations  84 differentgratingcombinations 50µm PhD Defense - Clément Fallet - October 18th

  28. 0.2 0.2 -0.2 -0.2 Sample 1 : CD N1 150 N2 300 Estimator Normalized Mueller matrix measurement PhD Defense - Clément Fallet - October 18th

  29. Scalarestimator Manuallyselectedmask Kept constant for all measurements of the same CD comination Scalarestimator : E = <E14>mask E14 PhD Defense - Clément Fallet - October 18th

  30. How to use ourestimator? • 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

  31. Validation of the linearity of estimator e14 PhD Defense - Clément Fallet - October 18th

  32. Sample 1 (N1 150 N2 300) : Linearity PhD Defense - Clément Fallet - October 18th

  33. Sample 1 : comparisonwith simulations PhD Defense - Clément Fallet - October 18th

  34. Sample 2 : CD N1 130 N2 300 PhD Defense - Clément Fallet - October 18th

  35. Sample 2 : CD N1 130 N2 300 PhD Defense - Clément Fallet - October 18th

  36. Influence of the CD PhD Defense - Clément Fallet - October 18th

  37. Conclusion • Estimator OK linearwith overlay measured by AIM, whichisconsidered as gold standard. • Consistencybetween X and Y overlays. • The slopehighlydepends on the CD of the gratings. • Value of the experimentalestimatorsmallerthanpredicted by simulations. PhD Defense - Clément Fallet - October 18th

  38. Measurements of the uncontrolled overlay PhD Defense - Clément Fallet - October 18th

  39. Definitions • Wedistinguish the nominal overlay (specified) and real overlay • The nominal overlay is a controlledbias, intentionallyintroduced. • Only the uncontrolled overlay is relevant PhD Defense - Clément Fallet - October 18th

  40. Method 1 • I • Linear fit on the measurements   Given by linearregression PhD Defense - Clément Fallet - October 18th

  41. Method 2 (H) PhD Defense - Clément Fallet - October 18th

  42. Verification of H Module 10 N1 170 N2 300, overlay Y Method 2 isvalidated for high nominal overlays Method 1 Method2 AIM overlay (nm) PhD Defense - Clément Fallet - October 18th

  43. Correlationbetween AIM et Mueller PhD Defense - Clément Fallet - October 18th

  44. Correlationbetween AIM et Mueller PhD Defense - Clément Fallet - October 18th

  45. Map of the overlay on a field • Map of the uncontrolled overlay (all measurement in nm) PhD Defense - Clément Fallet - October 18th

  46. A few qualityestimators • TMU : total measurementuncertainty PhD Defense - Clément Fallet - October 18th

  47. Comparisonswithexistingapparatus • Total measurementuncertainty (TMU) for commercial instruments • AIM : TMU ~ 2nm (2008) • Yieldstar : TMU = 0,2nm (2011) • Nanometrics : TMU ~ 0,4nm (2010) PhD Defense - Clément Fallet - October 18th

  48. Conclusions • Characterization of the overlay with a (fast), non-destructive technique. No modellingrequired but 2 very-wellcharacterized structures for calibration • Uncertaintyrelativelysmall ~ 2nm • Measurements in 20 x 20µm² boxes PhD Defense - Clément Fallet - October 18th

  49. Conclusions (2) • Very good linearity of the scalarestimator respect to the overlay defect (R² between 0,94 and 0,99) • However, experimental values of the estimators are lowerthanwhat simulation predicted. • Estimators are very sensitive to the chosenmask PhD Defense - Clément Fallet - October 18th

  50. Perspectives • Possibility to go down to 5 x 5µm² boxes with the correct pinhole • Automaticselection of the mask • Increase the repeatability of the measurements to decreaseToolInduced Shift and itsvariability to decrease total uncertainty • Integrate CD measurementthroughfitting of the Mueller matrix to approachAusschnitt’s MOXIE (Metrology Of eXtremely Irrational Exuberance) PhD Defense - Clément Fallet - October 18th

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