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Analisi delle proprietà ottiche di un materiale Mediante ellissometria spettroscopica ad angolo variabile: in riflessione e trasmissione dall’UV (300nm) al vicino infrarosso (1700nm) angolo variabile controllo in temperatura fino a 200°C Fasi dell’esperienza: 1.Studio della letteratura sulla tecnica e sul materiale scelto 2.Acquisizione dati 3.Modellizzazione ed analisi dei dati Possibili materiali da analizzare: Cristalli liquidi antiferroelettrici Fluoruro di Lantanio Sistemi ed elevata correlazione elettronica (perovskiti e manganiti)

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L’ellissometria Polarized light is reflected at an oblique angle to a surface The change to or from a generally elliptical polarization is measured. From these measurements, the complex index of refraction and/or the thickness of the material can be obtained. Ratio of the complex Fresnel reflection coefficients for the p and s polarizations : It is often convenient to write it in the form

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L’ellissometria Using Jones Matrix notation: –where and are complex Fresnel reflection coefficients.

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L’ellissometria Ellipsometry measures the change in polarization of light reflected (transmitted) from sample.By determining complex ratio of output/input E-fields

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Generalized Ellipsometry Measure diagonal and off-diagonal elements of the sample Jones Matrix Muller Matrix Ellipsometry for depolarising samples p out s r pp r sp r ps r ss p in s S = Stokes vector. Measured data: M ij

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Caratteristiche dell’ellissometria Repeatable & accurate: –self-referencing (single-beam experiment) ellipsometry measures ratio of orthogonal light components E p /E s Thus, reduced problems with: Source Fluctuation Light Beam Overlapping Small Sample Sensitive: –Phase term D is very sensitive to film thickness Measure only two parameters

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L’ellissometria, lo schema dell’apparato Optical Fiber Sample Polarizer Photoelastic Modulator Analyzer Detector Monochromator Data Acquisition and Computer Xe lamp Shutter

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Cosa ci può dire l’ellissometria Geometrical properties: Layer thickness Surface roughness Interfacial roughness Material Properties: Alloy ratio Doping concentration Microstructure Depth profile Optical Properties: Refractive index Extinction coefficient Anisotropy

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Modellizzazione No direct access to optical and dielectric constants. Modeling is required to determine sample’s properties from measured data. A model is an idealized mathematical representation of the sample. To construct a model, one has to assume each layer’s: a. thickness b. dielectric functions c. composition Remember: if the model is no good, then the interpretation of the data isn’t good either.

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Inversione dei dati Load Experimental Data. Build Model that represents the sample. Generate data from model. Compare calculated and measured curves. “Normal” Fit finds best match (lowest MSE). Is this the correct answer? Check your model for reliability Crosscheck, if possible, with one of the “direct” measurement technique: TEM, SEM, XAFS,.... Results Fit Optical Model and Measurement Experimental Data Multilayers model Generated Data Generated Data Exp. Data Comparison n e, n o thickness roughness uniformity

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Mean Squared Error MSE We use the Mean Squared Error (MSE) to quantify the difference between experimental and model-generated data. A smaller MSE implies a better fit. MSE is weighted by the error bars of each measurement, so noisy data are weighted less.

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Il Setup Automatizzato

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Esempio: cristalli liquidi Dispersion curves of 5CB for different temperatures are found to be well approximated by the 3-parameter Cauchy formula

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Esempio: cristalli liquidi (VANs) “Small angle” model for voltage under 6V (corresponds to the theoretical solution) “Saturated” model for voltage over 6V. Bottom part: Central part: Top part: d – cell gap fraction Condition: Error bars: ± 1°-2°

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Esempio: silicio poroso infiltrato con CL Effective Medium Approximation (EMA) layer and a Graded anisotropic Layer Ordinary and extraordinary refractive indices as a function of and depth can be immediately calculated from the fitted data resulting from the described model. Effective n o and n e values for the whole samples, obtained by the simple following formula, 5CB

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Esempio: silicio poroso infiltrato con CL PS sample infiltrated with 5CB (19%Si, 52% 5CB) Infiltration of a nematic increases anisotropy of samples in the infrared and decreases in the visible. For temperature above T C LC escapes from the pores partially! PS sample infiltrated with E7 (30%Si, 13% E7)

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Esempio: Thue-Morse quasi-crystals Multilayer structures can be organized in a quasi-crystal structure like the Thue-Morse. A→AB B→BA S0=AS0=A S 1 =AB S 2 =ABBA S 3 =ABBABAAB S 4 =ABBABAABBAABABBA S N → 2 N layers

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Esempio: Thue-Morse quasi-crystals Jeffrey O. Shallit Professor School of Computer Science University of Waterloo Waterloo, Ontario N2L 3G1 Canada

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Esempio: Thue-Morse quasi-crystals “Photonic band gaps analysis of Thue-Morse multilayers made of porous silicon” Optics Express, Vol. 14, pp (2006). d) e) The photonic bandgap properties of the Thue- Morse multilayers have been theoretically investigated by means of the transfer matrix method and the integrated density of states. Experimental (solid curves) and calculate (dashed curves) reflectivity for (a) S 3 T-M structure, (b) S 4 T-M structure and (c) S 5 T-M structure. (d) S 6 T-M structure: 64 PSi layers (e) S 7 T-M structure: 128 PSi layers

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Esempio: Fluoruro di Lantanio LAYER 1 = rugosità del materiale ~9nm; LAYER 2 = LaF 3 biassiale di 350μm. Lo strato biassiale è stato modellizzato come composto da due materiali con due diversi indice di rifrazione, che sono l’ordinario e lo straordinario. Ciascuno di questi è stato descritto delle equazioni di dispersione di Cauchy.

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Esempio: Fluoruro di Lantanio

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In futuro, l’ellissometria nel Terahertz Bal. Ph-diodes Si Ti:Sa laser MHz 10 fs 100 nm BW MHz 10 fs 100 nm BW

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