Principles and Applications of Ellipsometry Modern Techniques for Characterising Dispersions and Surfaces 17 November, 2004 Dr. Joe Keddie University of Surrey

What Ellipsometry Reveals Sensitive to the complex refractive index depth profile (z direction) n z n sub n film z

Principle of Ellipsometry

Wavelength range: 200 nm to 1200 nm Angular control polariseranalyser Spectroscopic Ellipsometer at the University of Surrey

Advantages of Ellipsometry Fast (measurements in seconds) and non-invasive. Applicable to any interface: solid/liquid; liquid/air; solid/solid, etc. (but must be able to obtain specular reflection). Measures the changes in both the amplitude (intensity) and the phase of polarised light after reflection. Hence, it is highly sensitive. Detects changes in thickness of 0.1 nm and in index of J.L. Keddie, Curr Opin. Coll. Interf. Sci., 6 (2001)

Applications of Ellipsometry Thin films : Thickness, thermal expansivity, solvent loss and relaxation, swelling, crosslink density. Adsorption : any small molecule, e.g. proteins, surfactants, and amphiphilic polymers, at any interface (solid/liquid; air/liquid; liquid/liquid). Bulk : complex refractive index (n + ik), void content, surface roughness, composition, density, and structure, e.g. crystalline vs. glassy and solid vs. liquid.

System Requirements Planar across the footprint of the light beam, typically a few mm. Smooth enough to achieve specular reflection. Reflective : a higher contrast in refractive index leads to greater reflectivity. Not too thick: non-transparent films must be less than the penetration depth of light, z: Key point : There must be specular reflection from the interface(s) of interest.

Ellipsometry parameters Central Equation of Ellipsometry R p and R s are Fresnel reflection coefficients p = in the plane of reflection s = perpendicular to plane of reflection

n1n1 nono o 1 s o Fresnel Reflection Coefficients Snells Law: p o n 1 = 1.33

51 Vertical Distance (nm) IndexIndex Angle of Incidence ( ) ( ) Ellipsometry Spectra for a Single Sharp Interface 51 0 n 1 = 1.33 B Brewster Angle: n o =1.0

Ellipsometry Spectra for a Single Index Step at an Interface IndexIndex Vertical Distance (nm) Angle of Incidence ( ) ( ) = 90° at Brewster angle High Sensitivity

Types of Polarised Light Elliptical A p A s p - s 0° Circular A p = A s p - s = 90° Linear A p A s p - s = 0°

Ellipsometry parameters Definition of Ellipsometry Parameters Physical Meaning of Parameters: = ratio of the amplitudes (A) before and after reflection = change in the phase difference ( ) caused by reflection i = initial amplitude ; r = reflected amplitude

Exact Solution of Ellipsometry Equations for a Semi- Substrate = ellipticity (complex, except when = 0 or 180°) nono If the ellipsometry parameters, and, are known, then the central equation of ellipsometry can be inverted to determine the complex refractive index,.

Types of Ellipsometer Null Ellipsometer (uses circularly polarised light) Rotating Element (uses linearly polarised light) Rotating Analyser Light Source Polariser Sample Rotating Analyser Detector Rotating Polariser Light Source Rotating Polariser Sample Analyser Detector Light Source Linear Polariser Compensator Sample Analyser Detector

Approach to Data Analysis In most cases, the data cannot be inverted to determine all of the unknown parameters, and therefore this approach is used: Measure and for various and/or Predict and using a physical model and calculating Fresnel coefficients. Compare Adjust model to improve the fit

Thin Film Analysis Flexible displays Photoresists Optical Coatings Printing inks

Fresnel Coefficients for Film on a Substrate o 1 d nono 1 2 0

Polymer Thin Films on Polymer Substrates 20 B. Parbhoo et al., Surf. Interf. Anal., 29 (2000) nm silicone film on poly(carbonate) substrate

Infrared Ellipsometry of Thick Coatings 10 m PDMS coating on Si Fringe spacings are inversely related to thickness

h Monolayers of OTS (Octadecyl trichlorosilane) Data analysis reveals that the OTS layer thickness is 2.5 nm. Sensitivity of Ellipsometry D.A. Styrkas et al, J. Appl. Phys., 85 (1999) Bare Si OTS layer 80° 75° 70° Si

Ellipsometry scans of a PMMA thin film immediately after spin-casting Data obtained at four different wavelengths H. Richardson et al., Eur. Phys. J. E Suppl. 1, 12 (2003) p Also, to appear in Phys Rev E. Thin Film Relaxation

Results of Data Analysis: n h t t Slow solvent loss over more than 1 hr.

Swelling of Polymer Thin Film in Solvent 39 nm PS thin film on Si exposed to MEK in water. Data obtained every 2 sec. = 450 nm; = 72 Solvent added

Determining the Glass Transition Temperature PS on Si h o ~ 100 nm TgTg Melt Glass Keddie et al., Europhys. Lett. 27 (1994) 59-64

H. Richardson et al., Eur. Phys. J. E, 12 (2003) Solvent Loss from Polymer Thin Films PMMA film spin- cast from toluene Quartz crystal microbalance

Interfaces and Adsorption

d n1n1 nono Sensitivity to Interfacial Layers PMMAPS d Brewster Angle:

Away from the Brewster Angle Poor Sensitivity! = 70 ° d = 10 nm d = 0 nm = 633 nm

Excellent Sensitivity! Near the Brewster Angle = 633 nm = B = 46.8 ° d = 0 nm d = 10 nm

Adsorption at Solid/Liquid Interfaces For thin films < ~20 nm, there is strong correlation between thickness (d layer ) and refractive index (n layer ). Difficult to determine both simultaneously. Independent measurements can be made of how n of a solution varies with concentration: dn soln /dc. The neat liquid has an index of n liq. The total amount adsorbed at an interface,, is related to the product of d layer and n layer :

Refractive Index of Solutions A typical value of dn/dc is 0.18 cm 3 g -1. n soln c (g cm -3 ) water

Permanently hydrophilic block Amphiphilic block Positively charged De-protonation at high pH Amphiphilic Poly(Electrolyte) D. Styrkas et al., Langmuir, 16 (2000)

Low ( ; pH = 2.7) and high ( ; pH = 9.2) values of pH. Adsorbed amount varies from ~1 to ~4 mg m -2. Ellipsometry Liquid Cell = 72°

Amphiphilic Poly(Electrolyte) Adsorption at Solid/Liquid Interfaces D. Styrkas et al., Langmuir, 16 (2000) Adsorption is tuneable with pH Evidence for unimer vs. micellar adsorption Copolymer composition, charge and molecular architecture can be correlated with the total adsorbed amount.

Surfactant Adsorption at Polymer/Water Interface V.A. Gilchrist et al., Langmuir 16 (2000) Penta(ethylene glycol) monododecyl ether [C 12 E 5 ] adsorbed at the interface between PMMA and water 2 x cmc 1/50 x cmc varies from 1 to 3.5 x mol m -2 = 75°

Protein Adsorption at Polymer/Water Interface E.F. Murphy et al., Biomaterials 20 (1999) Lysozyme adsorbed onto a phosphorylcholine polymer thin film on Si 1 g dm -3 aq. soln. water = 75° pH = 7

Bulk Characteristics

Optical Constants of Silicon

Dielectric/Optical Constants of Transparent Dielectric Materials If transparent: k = 0 UV Near IR

Dielectric/Optical Constants of Transparent Dielectric Materials UV Near IR Cauchy equation describes the wavelength dependence of n Equation reduces the number of unknowns to 2 or 3!

The SiH stretching mode (1) is apparent in the spectrum at about 2150 cm -1 as indicated with the heavy red line. The other bands are the asymmetric (2: 1400 cm -1 ) and symmetric (3: 1250 cm -1 ) CH 3 deformations, Si-O-Si stretch (4: 1000 – 1100 cm -1 ), CH 3 rock/Si-C stretch (5: cm -1 ), asymmetric CH 3 stretch (6: 2954 cm -1 ). Interference fringes 14 m silicone (PDMS) coating on Si Chemical Sensitivity from IR SE T.R.E. Simpson et al., Polymer 44 (2003)

The times shown are 0 ( ), 1.2 ( ), 3.7 ( ), 4.9 ( ), 13.7 ( ), and 182 min. ( ). The lines show the best fit to the data using an EMA model, corresponding to 0%, 19%, 29%, 42%, 64% and 100% completion (in chronological order). Crosslinking reaction over time at 80 °C T.R.E. Simpson et al., Polymer 44 (2003) SiH peak Chemical Changes

Effective Medium Approximations Often a material is a blend of two substances, such as poly(vinyl alcohol) (n A = 1.50) and water (n B = 1.33) or PMMA (n A = 1.48) and air (n B = 1.0). An effective medium approximation enables us to calculate the refractive index of a composite based on the volume fractions and refractive indices of its components, n A and n B. A B

Effective Medium Approximation (EMA) For a composite consisting of substances B dispersed in substance A, the refractive index, n, is not a simple average of the indices of A and B: n A and n B. Usually, n A and n B can be measured separately or determined from the literature. Ellipsometry measurement of n can be used to find the volume fraction of component B, B :

Surface roughness can be described as being a layer that consists of 50 vol.% air and 50 vol.% of the substrate. An EMA model can be applied to calculate the refractive index of the rough surface layer, n rough. Surface Roughness n=1 n subst n rough

Structure of Latex Films 5 m x 5 m Interparticle voids Surface roughness The concentration of air voids and the surface roughness of a latex film can be independently determined.

Scans made near the Brewster angle to obtain best sensitivity Fresh film: 7.5 vol.% voids and 20 nm surface roughness 36 hr. old film with 4.2 vol.% voids and 10 nm roughness Levelling and Coalescence A. Tzitzinou et al., Macromolecules, 32 (1999)

<n><n> t No coalescence - air voids develop Gradual particle coalescence Latex Film Formation A. Tzitzinou et al., Macromolecules, 32 (1999)

Hydrophilic Poly(acrylate) W.-L. Chen et al., Macromolecules, 32 (1999)

Shifts in data with varying humidity are caused by changes in the film thickness and refractive index. W.-L. Chen et al., Macromolecules, 32 (1999) Water Sorption in Polymer Thin Films

Volume fraction of water is determined from the refractive index of the film via an EMA model. W.-L. Chen et al., Macromolecules, 32 (1999)

Summary Ellipsometry is an ideal, non-destructive technique for probing optically-reflective interfaces. It is sensitive to refractive index steps or gradients caused by variations in composition, structure or density. Applications include measurements of: thin film thickness, adsorption, phase transitions (e.g. melting), swelling and de-swelling, surface roughness, etc.