Transcript Ellipsometry.pps - University of Surrey

Principles and Applications of
Ellipsometry
Dr. Joe Keddie
University of Surrey
[email protected]
Modern Techniques for Characterising Dispersions and Surfaces
17 November, 2004
What Ellipsometry Reveals
• Sensitive to the complex refractive index
depth profile (z direction)
z
nfilm
n
nsub
z
Principle of Ellipsometry
Spectroscopic Ellipsometer
at the University of Surrey
analyser
q
polariser
 Wavelength range: 200 nm to 1200 nm
 Angular control
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
Key point: There must be specular reflection
from the interface(s) of interest.
• 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:

z=
2k
Central Equation of Ellipsometry
=
Rp
Rs
= tane
i
Ellipsometry
parameters
Rp and Rs are Fresnel reflection coefficients
p = in the plane of reflection
s = perpendicular to plane of reflection
Fresnel Reflection Coefficients
n1 cos qo no cos q1
Rp =
n1 cos qo + no cos q1
qo
p
n1 = 1.33
no
q1
n1
qo
s
no cos qo n1 cos q1
Rs =
no cos qo + n1 cos q1
Snell’s Law:
no sinqo = n1 sinq1
qo
Ellipsometry Spectra for a
Single Sharp Interface
1.40
1.4
200
150
3
(degrees)
n1 = 1.33

()
1.20
100
()
2
50
Y
Refractive Index
1.30
200
1
51
1.10
1.00
1.0
-10
-10
no=1.0
-5
00
5
Vertical Distance (nm)
Vertical
Distance (nm)
Rp
Rs
00
51
51
1010
= tane
0
0
52
53
54
Angle of Incidence (°)
Angle
of Incidence ()
qB
i
 (degrees)
I
n
d
e
x
4
4
Brewster Angle:
n
qB = tan 1( 1 n )
o
55
-50
55
Ellipsometry Spectra for a Single
Index Step at an Interface
1.50
1.5
150
(degrees)
3

()
1.30
1.20
100
()
2
50
Y
Refractive Index
1.40
200
200
1
1.10
1.0
1.00
-10
-10
Rp
Rs
-5
00
5
10
Vertical Distance (nm)
Vertical
Distance (nm)
= tan( )e
i
1515
 (degrees)
I
n
d
e
x
44
0
00
51
51
52
53
54
Angleof
of Incidence
(°)
Angle
Incidence
()
 = 90° at Brewster angle
High Sensitivity
-50
55
55
Types of Polarised Light
Elliptical
Ap  As
dp - ds  0°
•
Circular
Ap = As
dp - ds = 90°
Linear
Ap  As
dp - ds = 0°
•
•
Definition of Ellipsometry Parameters
Rp
Rs
= tan( )e
i
Ellipsometry parameters
Physical Meaning of Parameters:
 = ratio of the amplitudes (A) before
and after reflection
tan =
i = initial amplitude; r = reflected amplitude
Apr
Asr
Api
Asi
 = change in the phase difference (d) caused by reflection
 = (d pr d sr ) (d pi d si )
Exact Solution of Ellipsometry
Equations for a Semi- Substrate
q
no
~ = n + ik
n
1
If the ellipsometry parameters,  and , are known,
then the central equation of ellipsometry can be
~.
inverted to determine the complex refractive index, n
1
=
Rp
Rs
= tane
i
n~1 = no tan q [1
4
(1 +  )2
sin q ]
 = ellipticity (complex, except
when  = 0 or 180°)
2
1
2
Types of Ellipsometer
Null Ellipsometer (uses circularly polarised light)
• Light Source Linear Polariser  Compensator 
Sample  Analyser  Detector
Rotating Element (uses linearly polarised light)
• Rotating Polariser
Light Source  Rotating Polariser  Sample 
Analyser  Detector
• Rotating Analyser
Light Source  Polariser  Sample  Rotating
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:
Adjust model
to improve
the fit
Measure  and  for
various q and/or 
Compare
Predict  and  using a
physical model and
calculating Fresnel
coefficients.
Thin Film Analysis
Flexible displays
Optical Coatings
Printing inks
Photoresists
Fresnel Coefficients for Film on a
Substrate
qo
q1
d

r01 + r12e
Er = (
1 + r01r12e
i 2

i 2  ) • Ei
0
no
1
n~1
2
~
n
2
d
~
 = 2n1 cos q1

Polymer Thin Films on Polymer Substrates
25
Model Fit
Exp E 55°
Exp E 60°
Exp E 65°
20
15
648 nm silicone
film on
poly(carbonate)
substrate
Y
10
5
0
3000
4000
5000
6000
7000
8000
Wavelength (Å)
20
180
150
120
Model Fit
Exp E 55°
Exp E 60°
Exp E 65°
90
B. Parbhoo et al., Surf.
Interf. Anal., 29 (2000)
341-5.

60
30
0
3000
4000
5000
6000
Wavelength (Å)
7000
8000
Infrared Ellipsometry of Thick Coatings
Generated and Experimental
60
Model Fit
Exp E 65°
Y in degrees
50
10 mm PDMS
coating on Si
40
30
20
10
1600
1800
2000
2200
2400
2600
Generated
andNumber
Experimental
Wave
(cm -1)
2800
Fringe spacings
are inversely
related to thickness
160
Model Fit
Exp E 65°
 in degrees
140
120
E 1
=
hc 
100
80
60
1600
1800
2000
2200
Wave Number (cm
2400
)
-1
2600
2800
Monolayers of “OTS”
35
30
Y in degrees
Sensitivity of
Ellipsometry
Bare Si
25
OTS layer
20
15
10
5
(Octadecyl trichlorosilane)
0
300
400
500
600
700
Wavelength (nm)
Si
Data analysis reveals
that the OTS layer
400
500
600
thickness
is
2.5
nm.
Wavelength (nm)
Figure 3. A comparison of spectroscopic elli
150
block (solid lines) and the same block70°
coated
120
obtained
at angles-of- incidence of 70, 75 and
 in degrees
h
180
90
75°
60
30
80°
700
0
300
400
500
600
Wavelength (nm)
D.A. Styrkas et al, J. Appl. Phys., 85 (1999) 868-75
e 3. A comparison of spectroscopic ellipsometry measurements on clean silicon
700
76
74
Y (degrees)
Thin Film
Relaxation
78

Ellipsometry scans of a
PMMA thin film immediately
after spin-casting
72
70
68
66
650nm
64
660nm
62
680nm
670nm
60
0
20
40
60
80
Time (Minutes)
70
65
H. Richardson et al., Eur. Phys. J.
E Suppl. 1, 12 (2003) p. 87-91.
 60
 (degrees)
Data obtained at four
different wavelengths
55
650nm
660nm
50
670nm
680nm
45
0
Also, to appear in Phys Rev E.
20
40
Time (Minutes)
60
80
157
Thickness (nm)
h
Results of
Data Analysis:
156
155
154
153
152
151
150
149
148
0
20
40
60
Time (Minutes)
t
80
1.475
Slow solvent loss
over more than 1 hr.
1.473
A
n
1.471
1.469
1.467
1.465
0
10
20
30
40
50
Time (Minutes)
60
70
t
80
32
130
30
120
110
28
100
26
 = 450 nm; q = 72
24
90
80
22
39 nm PS thin film on
Si exposed to MEK in
water. Data obtained
every 2 sec.
70
3
Solvent added
6
9
Time (Minutes)
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1
0
60
15
12
Normalised thickness
20
0
 in degrees
Y in degrees
Swelling of Polymer Thin Film in Solvent
5
Time, min
10
Determining the Glass Transition Temperature
PS on Si
ho ~ 100 nm
Glass
Melt
Tg
Keddie et al., Europhys. Lett. 27 (1994) 59-64
Solvent Loss from Polymer Thin Films
PMMA film spincast from toluene
Quartz crystal
microbalance
f ~ m
H. Richardson et al., Eur. Phys. J. E, 12 (2003) 437-41.
Interfaces and Adsorption
Sensitivity to Interfacial Layers
PS
PMMA
Brewster Angle:
d
Index of refraction ' n'
1.60
n
qB = tan 1( 1 n )
o
n1
1.55
1.50
no
1.45
d
1.40
-20
-10
0
10
20
Distance from Interface (nm)
30
40
Away from the Brewster Angle
34.6
Y in degrees
34.4
34.2
q = 70°
34.0
33.8
33.6
= 633 nm
33.4
33.2
200
300
400
500
600
700
800
Wavelength (nm)
Poor
Sensitivity!
0.8
d = 10 nm
 in degrees
0.6
0.4
d = 0 nm
0.2
0.0
200
300
400
500
600
Wavelength (nm)
700
800
Near the Brewster Angle
1.0
Y in degrees
0.8
0.6
q =qB = 46.8°
0.4
0.2
0.0
200
= 633 nm
300
400
500
600
700
800
Wavelength (nm)
200
 in degrees
Excellent
Sensitivity!
d = 10 nm
150
100
d = 0 nm
50
0
200
300
400
500
Wavelength (nm)
600
700
800
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, G, is related
to the product of dlayer and nlayer :
d layer (nlayer nliq )
G=
dnso ln
dc
Refractive Index of Solutions
nsoln
A typical value of dn/dc is 0.18 cm3 g-1.
1.37
•
1.35
•
•
•
•
1.33
water
•
0.1
0.2
c (g cm-3)
Amphiphilic Poly(Electrolyte)
Permanently hydrophilic block
Amphiphilic block
CH3
CH3
Positively charged
( CH2
C
)x
C
( CH2
O
C
)y
C
O
O
O
CH2
CH2
CH2
CH2
Cl
+
H3 C N
CH2
De-protonation at high pH
N
CH3
H 2C
CH2
H 3C
CH3
D. Styrkas et al., Langmuir, 16 (2000) 5980-86
Ellipsometry Liquid Cell
Reflected
Polarised
Light out
90o
q = 72°
90o
Polymer Solution
Entrance Window
Entrance Window
Si substrate
Sample Stage of the Ellipsometer

20

 , degrees
Y , degrees
15
10
5
160
120
80
40
0
370
420
470
520
570
Wavelength, nm
620
670

0
370
470
570
Wavelength, nm
Low (; pH = 2.7) and high (; pH = 9.2) values of pH.
Adsorbed amount varies from ~1 to ~4 mg m-2.

670
Amphiphilic Poly(Electrolyte) Adsorption
at Solid/Liquid Interfaces
 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.
D. Styrkas et al., Langmuir, 16 (2000) 5980-86
Surfactant Adsorption at Polymer/Water Interface
Penta(ethylene glycol)
monododecyl ether [C12E5]
adsorbed at the interface
between PMMA and water
2 x cmc
1/50 x cmc
q = 75°
G varies from 1 to
3.5 x 10-6 mol m-2
V.A. Gilchrist et al., Langmuir 16 (2000) 740-48
Protein Adsorption at Polymer/Water Interface
Lysozyme adsorbed onto
a phosphorylcholine
polymer thin film on Si
1 g dm-3 aq. soln.
water
q = 75°
E.F. Murphy et al., Biomaterials 20 (1999) 1501-11
pH = 7
“Bulk” Characteristics
Optical Constants of Silicon
E=
hc

 = (n + ik )
2
Dielectric/Optical Constants of
Transparent Dielectric Materials
 = 1 + i 2
UV
 = (n + ik )
2
If transparent: k = 0
Near IR
Dielectric/Optical Constants of
Transparent Dielectric Materials
Cauchy equation describes the
wavelength dependence of n
UV
n = A+
Near IR
B
C


2+
4 + ...
Equation reduces the number
of “unknowns” to 2 or 3!
Chemical Sensitivity from IR SE
2
Interference
fringes
1
Cos ( )
Tan (Y )
2.5
1.5
1
0.5
0
500 1000 1500 2000 2500 3000 3500 4000
-1
Wavenumber (cm )
0.5
5 4 3
6
2
1
0
-0.5
-1
650 1150 1650 2150 2650 3150 3650 4150
E 1
=
hc 
Wavenumber (cm-1)
14 mm silicone (PDMS) coating on Si
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).
T.R.E. Simpson et al., Polymer 44 (2003) 4829-38.
Chemical
Changes
0
Cos (  )
-0.1
Crosslinking
reaction over
time at 80 °C
-0.2
-0.3
SiH peak
-0.4
2100
2120
2140
2160
2180
Wavenumber (cm-1)
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).
T.R.E. Simpson et al., Polymer 44 (2003) 4829-38.
2200
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).
A
B
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.
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, fB:
2
nB 2 + 2nA 2
fB = ( 2
) ( 2
2 )
2
nB nA
n + 2nA
n
nA2
Surface Roughness
Surface roughness can be described as being a
layer that consists of 50 vol.% air and 50 vol.% of
the substrate.
n=1
nrough
nsubst
An EMA model can be applied to calculate the
refractive index of the rough surface layer, nrough.
Structure of Latex Films
5 mm x 5 mm
Surface roughness
Interparticle voids
The concentration of air voids and the surface roughness
of a latex film can be independently determined.
Levelling and Coalescence
200
Delta (degrees)
Psi (degrees)
15
10
5
0
50
55
60
65
Angle of Incidence (degrees)
150
100
50
0
50
55
60
65
Angle of Incidence (degrees)
 Fresh film: 7.5 vol.% voids and 20 nm surface roughness
 36 hr. old film with 4.2 vol.% voids and 10 nm roughness
Scans made near the Brewster angle to obtain
best sensitivity
A. Tzitzinou et al., Macromolecules, 32 (1999) 136-44.
Latex Film Formation
1.5
(A)
Gradual particle coalescence
1.45
<n>
1.4
<n>
1.35
1.3
No coalescence air voids develop
1.25
1.2
5
10
15
20
25
30
35
40
45
Time After Latex Casting (min)
A. Tzitzinou et al., Macromolecules, 32 (1999) 136-44.
50
t
55
Hydrophilic Poly(acrylate)
PMMA (CH2CH)n PMMA
C O
OC(CH3)3
PMMA (CH2CH)1-x (CH2CH)x PMMA
ROH
C O
C O
acid catalyst
OH
OR
R=CH3(OCH2CH2)m, m=1, 2, or 3
W.-L. Chen et al., Macromolecules, 32 (1999) 136-44.
Water Sorption in Polymer Thin Films
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
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.