Principles and Applications of Ellipsometry Modern Techniques for Characterising Dispersions and...
-
Upload
martin-tinkham -
Category
Documents
-
view
224 -
download
7
Transcript of Principles and Applications of Ellipsometry Modern Techniques for Characterising Dispersions and...
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 [email protected]
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.