antigone@na.infn.it

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 scelto2. Acquisizione dati3. Modellizzazione ed analisi dei dati

Possibili materiali da analizzare:• Cristalli liquidi antiferroelettrici• Fluoruro di Lantanio• Sistemi ed elevata correlazione elettronica (perovskiti e manganiti)

antigone@na.infn.it

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 :

r

rp

s

It is often convenient to write it in the form

tan ei

antigone@na.infn.it

L’ellissometria

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

ins

inp

s

p

outs

outp

E

E

r

r

E

E~0

0~

ins

inp

s

p

outs

outp

E

E

r

r

E

E~0

0~

spi

s

p

s

pins

outs

inp

outpi e

r

r

r

r

EE

EEe ~

~tan spi

s

p

s

pins

outs

inp

outpi e

r

r

r

r

EE

EEe ~

~tan

pr~

sr~

s

p

r

r)tan(

s

p

r

r)tan(

sp sp

tan ei

antigone@na.infn.it

L’ellissometria

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

ins

outs

inp

outpi

EE

EEe tan

ins

outs

inp

outpi

EE

EEe tan

antigone@na.infn.it

Generalized EllipsometryMeasure diagonal and off-diagonal elements of the sample Jones Matrix

Muller Matrix Ellipsometry for depolarising samples

poutsout

rpp rsprps rss

pinsin

INOUTS

S

S

S

MMMM

MMMM

MMMM

MMMM

S

S

S

S

3

2

1

0

44434241

34333231

24232221

14131211

3

2

1

0

S = Stokes vector.

Measured data: Mij

)exp(tan ppppppss

ppiJ

j

j

)exp(tan pspspspp

psiJ

j

j

)exp(tan spspspss

spiJ

j

j

antigone@na.infn.it

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 thickness

Measure only two parameters

antigone@na.infn.it

L’ellissometria, lo schema dell’apparato

Optical Fiber

Sample

PolarizerPhotoelasticModulator

Analyzer

Detector

Monochromator

Data Acquisitionand Computer

Xe lamp Shutter

antigone@na.infn.it

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

antigone@na.infn.it

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.

antigone@na.infn.it

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

ne, no

thicknessroughnessuniformity

antigone@na.infn.it

Mean Squared Error

We use the Mean Squared Error (MSEMSE) 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.

N

i i

ii

i

ii

MNMNMSE

1

2

2

exp,

expmod2

exp,

expmod

2

1

2

1

antigone@na.infn.it

Il Setup Automatizzato

antigone@na.infn.it

Esempio: cristalli liquidi

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

antigone@na.infn.it

Esempio: cristalli liquidi (VANs)

“Small angle” model for voltage under 6V (corresponds to the theoretical solution)

“Saturated” model for voltage over 6V.

11

11 0);2

( dddd

SinCAd Bottom part:

Central part:

Top part:

21;2/ dddd

1);22

( 22

22 dddd

SinCAd

)( dCSinBdAd

d – cell gap fraction

10 dCondition: 121 ddError bars: ± 1°-2°

antigone@na.infn.it

Esempio: silicio poroso infiltrato con CL

-4 cauchy 0 nm-3 delta_n 0 nm-2 ema void/20% si/0% (cauchy) 0 nm-1 sum_nk (ema)/100% (delta_n) 0 nm0 si 1 mm1 biaxial 0 nm2 graded (biaxial) 485.21 nm

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 no and ne values for

the whole samples, obtained by the simple

following formula,

d

eoeo dzznd

n0

,, )(1

5CB

antigone@na.infn.it

Esempio: silicio poroso infiltrato con CL

Wavelength (nm)300 600 900 1200 1500 1800

in

deg

rees

0

20

40

60

80

100Model Fit Exp E 60°, PSExp E 60°, PS+ E7 for t=65°C

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 TC LC escapes from the pores partially!

PS sample infiltrated with E7 (30%Si, 13% E7)

antigone@na.infn.it

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= ABBABAABBAABABBASN → 2N layers

antigone@na.infn.it

Esempio: Thue-Morse quasi-crystals

http://www.cs.uwaterloo.ca/~shallit/

Jeffrey O. ShallitProfessorSchool of Computer Science University of Waterloo Waterloo, Ontario N2L 3G1 Canada

antigone@na.infn.it

Esempio: Thue-Morse quasi-crystals

“Photonic band gaps analysis of Thue-Morse multilayers made of porous silicon”Optics Express, Vol. 14 , pp. 6264-6272 (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) 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

antigone@na.infn.it

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.

2

BAn

Generated and Experimental

Wavelength (nm)800 1000 1200 1400 1600

in

deg

rees

40

50

60

70

80

90

Model Fit Exp AnEt -0°Exp Apst -0°Exp Aspt -0°Exp AnEt -0°Exp Apst -0°Exp Aspt -0°

Generated and Experimental

Wavelength (nm)800 1000 1200 1400 1600

in

deg

rees

-100

0

100

200

300

Model Fit Exp AnEt -0°Exp Apst -0°Exp Aspt -0°Exp AnEt -0°Exp Apst -0°Exp Aspt -0°

25 30 35 40 45 50 55 60 65 70

0.00704

0.00706

0.00708

0.00710

0.00712

0.00714

Temperature (°C)

Bir

efr

ing

en

ce

976 nm 1550 nm

antigone@na.infn.it

Angular Dependence of and @976nm

Angle of Incidence (°)48 51 54 57 60 63 66

in

deg

rees

in degrees

0

30

60

90

120

150

180

0

2

4

6

8

10

12

Model FitExp Exp

Angular Dependence of and @1550nm

Angle of Incidence (°)48 51 54 57 60 63 66

in

deg

rees

in degrees

0

30

60

90

120

150

180

0

2

4

6

8

10

12

Model FitExp Exp

Esempio: Fluoruro di Lantanio

antigone@na.infn.it

In futuro, l’ellissometria nel Terahertz

Bal. Ph-diodes

Si

Si

Ti:Salaser

800 mW @ 80 MHz

10 fs100 nm BW

800 mW @ 80 MHz

10 fs100 nm BW