Analisi delle proprietà ottiche di un materiale

1. 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: • Studio della letteratura sulla tecnica e sul materiale scelto • Acquisizione dati • Modellizzazione ed analisi dei dati • Possibili materiali da analizzare: • Cristalli liquidi antiferroelettrici • Fluoruro di Lantanio • Sistemi ed elevata correlazione elettronica (perovskiti e manganiti)

2. 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

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

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

5. Generalized Ellipsometry é ù r r é ù é ù p p pp sp out in = × ê ú ê ú ê ú r r s s ê ú ps ss ë û ë û out in ë û • Measure diagonal and off-diagonal elements of the sample Jones Matrix • Muller Matrix Ellipsometry for depolarising samples S = Stokes vector. Measured data: Mij

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

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

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

9. 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.

10. Inversione dei dati Yand D Measurement Experimental Data Multilayers model Generated Data Optical Model Exp. Data Generated Data Fit Comparison ne, no thickness roughness uniformity Results • 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,....

11. Mean Squared Error • 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.

12. Il Setup Automatizzato

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

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

15. Esempio: silicio poroso infiltrato con CL Effective Medium Approximation (EMA) layer and a Graded anisotropic Layer 5CB Ordinary and extraordinary refractive indices as a function of l and depth can be immediately calculated from the fitted data resulting from the described model. Effective no and ne values for the whole samples, obtained by the simple following formula,

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

17. Esempio: Thue-Morse quasi-crystals • Multilayer structures can be organized in a quasi-crystal structure like the Thue-Morse. • A→AB • B→BA S0= A S1= AB S2= ABBA S3= ABBABAAB S4= ABBABAABBAABABBA SN → 2N layers

18. Esempio: Thue-Morse quasi-crystals http://www.cs.uwaterloo.ca/~shallit/ Jeffrey O. Shallit Professor School of Computer Science University of Waterloo Waterloo, Ontario N2L 3G1 Canada

19. Esempio: Thue-Morse quasi-crystals 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) S3 T-M structure, (b) S4 T-M structure and (c) S5 T-M structure. (d) S6 T-M structure: 64 PSi layers (e) S7 T-M structure: 128 PSi layers “Photonic band gaps analysis of Thue-Morse multilayers made of porous silicon” Optics Express, Vol. 14 , pp. 6264-6272 (2006).

20. Esempio: Fluoruro di Lantanio • LAYER 1 = rugosità del materiale ~9nm; • LAYER 2 = LaF3 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.

21. Esempio: Fluoruro di Lantanio

22. In futuro, l’ellissometria nel Terahertz Ti:Sa laser 800 mW @ 80 MHz 10 fs 100 nm BW Bal. Ph-diodes Si Si