Principles and Applications ofEllipsometry

Modern Techniques for Characterising Dispersions and SurfacesModern Techniques for Characterising Dispersions and Surfaces17 November, 200417 November, 2004

Dr. Joe Keddie University of

Surrey j.keddie@surrey.ac.uk

What Ellipsometry Reveals• Sensitive to the complex refractive index

depth profile (z direction)

n

z

nsub

nfilm

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 0.001.

J.L. Keddie, Curr Opin. Coll. Interf. Sci., 6 (2001) 102-10

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.

kz

2=

i

s

pe

R

R tan==

Ellipsometry parameters

Central Equation of Ellipsometry

Rp and Rs are Fresnel reflection coefficients

p = in the plane of reflection

s = perpendicular to plane of reflection

11

11

cos+coscoscos

=

oo

oop nn

nnR

n1

no

o

1

s

o

Fresnel Reflection Coefficients

11sin=sin nn oo

Snell’s Law:

p

o

n1 = 1.33

11

11

cos+coscoscos

=

nnnn

Roo

oos

51

Vertical Distance (nm)-10 -5 0 5 10

Ref

ract

ive

Inde

x

1.00

1.10

1.20

1.30

1.40

Angle of Incidence (°)51 52 53 54 55

(d

egre

es)

(degrees)

0

1

2

3

4

-50

0

50

100

150

200

Vertical Distance (nm)

Index

Angle of Incidence () 551.0

1.4

-10 10

()

0

4

()

200

0

Ellipsometry Spectra for a Single Sharp Interface

i

s

pe

R

Rtan=

510

n1 = 1.33

B

)(tan= 11

oB n

n

Brewster Angle:

no=1.0

Ellipsometry Spectra for a Single Index Step at an Interface

Vertical Distance (nm)-10 -5 0 5 10 15

Ref

ract

ive

Inde

x

1.00

1.10

1.20

1.30

1.40

1.50

Angle of Incidence (°)51 52 53 54 55

(d

egre

es)

(degrees)

0

1

2

3

4

-50

0

50

100

150

200

Index

Vertical Distance (nm) Angle of Incidence () 55-10 15 0

4 200

() ()

1.0

1.5

i

s

pe

R

R)tan(=

510

= 90° at Brewster angle

High Sensitivity

Types of Polarised Light

EllipticalAp As

p - s 0°• •

•

CircularAp = As

p - s = 90°

LinearAp As

p - s = 0°

i

s

pe

R

R)tan(=

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

is

ip

rs

rp

A

A

A

A

=tan

)()(= is

ip

rs

rp

Exact Solution of Ellipsometry Equations for a Semi- Substrate

i

s

pe

R

R tan==

= ellipticity (complex, except when = 0 or 180°)

21

221 1

41 ]sin

)+([tan=~

onn

no

iknn +=~1

If the ellipsometry parameters, and , are known, then the central equation of ellipsometry can be inverted to determine the complex refractive index, .1n~

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 PolariserLight 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

PhotoresistsOptical Coatings

Printing inks

Fresnel Coefficients for Film on a Substrate

ii

i

r Eerr

errE

•)

+

+(=

21201

21201

1112

cos~=

dn

o

1d

no

1

2

0

1n~

2n~

Polymer Thin Films on Polymer Substrates

20Wavelength (Å)

3000 4000 5000 6000 7000 8000

0

5

10

15

20

25

Model FitExp E 55°Exp E 60°Exp E 65°

Wavelength (Å)3000 4000 5000 6000 7000 8000

0

30

60

90

120

150

180

Model FitExp E 55°Exp E 60°Exp E 65°B. Parbhoo et al., Surf.

Interf. Anal., 29 (2000) 341-5.

648 nm silicone film on

poly(carbonate) substrate

Infrared Ellipsometry of Thick CoatingsGenerated and Experimental

Wave Number (cm -1)1600 1800 2000 2200 2400 2600 2800

in

deg

rees

10

20

30

40

50

60

Model Fit Exp E 65°

Generated and Experimental

Wave Number (cm -1)1600 1800 2000 2200 2400 2600 2800

in

deg

rees

60

80

100

120

140

160

Model Fit Exp E 65°

10 m PDMS coating on Si

Fringe spacings are inversely

related to thickness

1

=hcE

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) 868-75

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. 87-91.

Also, to appear in Phys Rev E.

Thin Film Relaxation

148

149

150

151

152

153

154

155

156

157

0 20 40 60 80

Time (Minutes)

Th

ick

ne

ss

(n

m)

1.465

1.467

1.469

1.471

1.473

1.475

0 10 20 30 40 50 60 70 80

Time (Minutes)

A

Results of Data Analysis:

n

h

t

t

Slow solvent loss over more than 1 hr.

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

0 5 10

Time, min

No

rma

lise

d t

hic

kn

es

s

Swelling of Polymer Thin Film in Solvent

Time (Minutes)0 3 6 9 12 15

in

deg

rees

in degrees

20

22

24

26

28

30

32

60

70

80

90

100

110

120

130

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

ho ~ 100 nm

Tg

Melt

Glass

Keddie et al., Europhys. Lett. 27 (1994) 59-64

H. Richardson et al., Eur. Phys. J. E, 12 (2003) 437-41.

Solvent Loss from Polymer Thin Films

PMMA film spin-cast from toluene

mf ~

Quartz crystal microbalance

Interfaces and Adsorption

Distance from Interface (nm)-20 -10 0 10 20 30 40

Inde

x of

ref

ract

ion

'n'

1.40

1.45

1.50

1.55

1.60

d

n1

no

Sensitivity to Interfacial Layers

PMMAPS

d

)(tan= 11

oB n

n

Brewster Angle:

Wavelength (nm)200 300 400 500 600 700 800

in

deg

rees

33.2

33.4

33.6

33.8

34.0

34.2

34.4

34.6

Wavelength (nm)200 300 400 500 600 700 800

in

deg

rees

0.0

0.2

0.4

0.6

0.8

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 (dlayer) and refractive index (nlayer). Difficult to determine both simultaneously.

• Independent measurements can be made of how n of a solution varies with concentration: dnsoln/dc. The neat liquid has an index of nliq.

• The total amount adsorbed at an interface, , is related to the product of dlayer and nlayer :

dcdn

nnd

so

liqlayerlayer

ln

)(=

Refractive Index of Solutions

A typical value of dn/dc is 0.18 cm3 g-1.

nsoln

c (g cm-3)

1.33

•

•

•

••

•

0.20.1

1.35

1.37

water

C

C

O

O

CH3

CH3

CH2

H3C

N

CH2

CH2

( )y

CH2H2C

+

x)(

CH2

CH2

NH3C

CH2

CH3

CH3

O

O

C

C

Cl

CH2

Permanently hydrophilic block Amphiphilic block

Positively charged De-protonation at high pH

Amphiphilic Poly(Electrolyte)

D. Styrkas et al., Langmuir, 16 (2000) 5980-86

Si substrate

ReflectedPolarisedLight out

Sample Stage of the Ellipsometer

90o90o

Polymer SolutionEntrance Window

Entrance Window

0

40

80

120

160

370 470 570 670

Wavelength, nm

, d

eg

ree

s

0

5

10

15

20

370 420 470 520 570 620 670

Wavelength, nm

, d

egre

es

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) 5980-86

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) 740-48

Penta(ethylene glycol) monododecyl ether [C12E5] adsorbed at the interface

between PMMA and water2 x cmc

1/50 x cmc

varies from 1 to 3.5 x 10-6 mol m-2

= 75°

Protein Adsorption at Polymer/Water Interface

E.F. Murphy et al., Biomaterials 20 (1999) 1501-11

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

hc

E =

2)+(= ikn

Dielectric/Optical Constants of Transparent Dielectric Materials

If transparent: k = 0

21 i+=

UV Near IR2)+(= ikn

Dielectric/Optical Constants of Transparent Dielectric Materials

UV Near IR

Cauchy equation describes the wavelength dependence of n

...+++= 42 CB

An Equation reduces the number of “unknowns” to 2 or 3!

-1

-0.5

0

0.5

1

650 1150 1650 2150 2650 3150 3650 4150

Wavenumber (cm-1)

Cos

(

)

1

45 63

2

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) CH3 deformations, Si-O-Si stretch (4: 1000 – 1100 cm-1), CH3 rock/Si-C stretch (5: 750 - 870 cm-1), asymmetric CH3 stretch (6: 2954 cm-1).

0

0.5

1

1.5

2

2.5

500 1000 1500 2000 2500 3000 3500 4000

Wavenumber (cm-1)

Tan

(

)

Interference fringes

14 m silicone (PDMS) coating on Si

Chemical Sensitivity from IR SE

1

=hcE

T.R.E. Simpson et al., Polymer 44 (2003) 4829-38.

-0.4

-0.3

-0.2

-0.1

0

2100 2120 2140 2160 2180 2200

Wavenumber (cm-1)

Co

s (

)

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) 4829-38.

SiH peak

Chemical Changes

Effective Medium Approximations

Often a material is a blend of two “substances”, such as poly(vinyl alcohol) (nA = 1.50) and water (nB = 1.33) or PMMA (nA = 1.48) and air (nB = 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, nA and nB.

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: nA and nB.

• Usually, nA and nB 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:

)2+

()2+

(= 22

22

22

22

AB

AB

A

AB nn

nn

nn

nn

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, nrough.

Surface Roughness

n=1

nsubst

nrough

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) 136-44.

1.2

1.25

1.3

1.35

1.4

1.45

1.5

5 10 15 20 25 30 35 40 45 50 55

Time After Latex Casting (min)

<n>

(A)

<n>

t

No coalescence -

air voids develop

Gradual particle coalescence

Latex Film Formation

A. Tzitzinou et al., Macromolecules, 32 (1999) 136-44.

Hydrophilic Poly(acrylate)

OC

(CH2CH)1-xPMMA

OR

(CH2CH)x PMMA

C O

OHO

nPMMA PMMA

CH3)3

C

(CH2CH)

OC(

R=CH3(OCH2CH2)m, m=1, 2, or 3

acid catalystROH

W.-L. Chen et al., Macromolecules, 32 (1999) 136-44.

20

40

60

80

100

300 400 500 600 700 800

0 %31 %45 %66 %75 %84 %95 %

Wavelength (nm)

20

40

60

80

100

300 400 500 600 700 800

0 %31 %45 %66 %75 %84 %95 %

Wavelength (nm)

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) 136-44.

Water Sorption in Polymer Thin Films

0%

10%

20%

30%

40%

50%

0% 20% 40% 60% 80% 100%

PMMA-P(MTGA-r-AA)-PMMAPMMA-PAA-PMMAP(MTGA-r-AA)PMMA

Relative Humidity

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) 136-44.

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.