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©2014 J.A. Woollam Co., Inc. www.jawoollam.com 1
Nina Hong
3B: Review
U Penn, February 2014
©2014 J.A. Woollam Co., Inc. www.jawoollam.com 2
Review
1A: Introduction to WVASE: Fun Quiz!
1B: Cauchy
2A: Pt-by-Pt and GenOsc
2B: Advanced GenOsc
3A: Non-Idealities
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If the left column shows the Psi and Delta for an
ideal glass substrate, can you identify the
complexity of the right column data?
Q1
Ideal Surface Roughness
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If the left column shows the Psi and Delta for an
ideal glass substrate, can you identify the
complexity of the right column data?
Q2
Ideal Backside Reflection
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If the left column shows the Psi and Delta for a
Si substrate, can you identify the complexity of
the right column data?
Q3
Ideal Backside Reflection
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What is the substrate type of the following
ellipsometric data?
①Transparent substrate (dielectric)② Semi-absorbing substrate (semiconductor)③ Absorbing substrate (Metal)
Q4
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What does ellipsometric measurement probe?
① Size of electric field② Shape of electric field
Q5
X
Y
ELess
Intense
X
Y EMore
IntenseDifferent Size
(Intensity).
Same Shape!
(Polarization)
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Q6Pseudo Optical Constants <n>, <k>Which one is corresponding to a single reflection on surface?
① ②
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Q7Unknown Film on GlassWhich spectral range does the film look transparent?
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Data Analysis Strategies
Substrates
S-1: Opaque Substrates
S-2: Semiconductor substrates
S-3: Transparent substrates
Films
F-1: Transparent films
F-2: Semi-Absorbing films
F-3: Absorbing films
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Psi stays near 45°
Delta away from 0°or 180°
Wavelength (nm)
200 400 600 800 1000 1200
Psi in
de
gre
es
36
38
40
42
44
46
65°75°85°
Wavelength (nm)
200 400 600 800 1000 1200
Delta
in d
egre
es
0
30
60
90
120
150
180
65°75°85°
S-1 Opaque Substrates
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S-1 Opaque Substrates
Two Categories
“Bulk” Samples No overlayers.
– Polished metal.
Optically thick films.
Fit Strategy“Invert” psi and delta for n and k.
Normal fit from reference values
2 Known: Ψ, Δ
2 Unknowns: n, k
Example 1 Optically Thick Cr Film
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Psi follows shape of absorption
Delta away from 0°or 180° when absorbing
Wavelength (nm)
200 400 600 800 1000 1200
Yin
de
gre
es
0
10
20
30
40
50
55°65°75°
Din
de
gre
es
1200
Wavelength (nm)
200 400 600 800 10000
50
100
150
200
55°65°75°
S-2 Semiconductor Substrates
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S-2 Semiconductor Substrates
Bulk semiconductor n&k are well known– Crystalline structure insures repeatable
optical/electrical properties.
Doping NOT important at VIS wavelengths– Doping Is important in the MID-IR, however (5
micron or longer).
Fit Strategy
– Use published index values.
– Fit for oxide thickness.
Example 2 Bare Si Wafer
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Psi flat and smooth- follows shape of index
Delta = 0°,180° - except for surface films
Wavelength (nm)
0 300 600 900 1200 1500 1800
Yin
de
gre
es
0
5
10
15
20
25
30
45°55°65°75°
Wavelength (nm)
0 300 600 900 1200 1500 1800
Din
de
gre
es
0
30
60
90
120
150
180
45°55°65°75°
0.5nm roughness
S-3 Transparent Substrates
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S-3 Transparent Substrates
Fit Strategy– Cauchy
Complexities– Surface roughness (Add srough)
– Backside reflection (Suppress or Model correction)
How to obtain small k-values
– Add Transmission data and fit k only.
Example 3 10mm bk7 (Two dat files: SE and T)Experimental Data
Wavelength (nm)
0 300 600 900 1200 1500 1800
Y in
de
gre
es
0
5
10
15
20
25
Exp E 55°Exp E 57.5°Exp E 60°Exp E 62.5°Exp E 65°Exp E 67.5°Exp E 70°
Experimental Data
Wavelength (nm)
0 300 600 900 1200 1500 1800
D in
de
gre
es
-50
0
50
100
150
200
Exp E 55°Exp E 57.5°Exp E 60°Exp E 62.5°Exp E 65°Exp E 67.5°Exp E 70°
Experimental Data
Wavelength (nm)
200 400 600 800 1000
Tra
nsm
issio
n
0.0
0.2
0.4
0.6
0.8
1.0
Exp pT 0°
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Each reflected wave will have a different
phase and amplitude.
0~n
1~n
2~n
Delay caused
by both index
and thickness
F-1 Transparent Films
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Interference shifts toward red as film grows.
More Interference oscillations as film grows.
Wavelength (nm)
0 300 600 900 1200 1500 1800
Yin
degre
es
0
20
40
60
80
100
25nm50nm
100nm
200nm
300nm
400nm500nm
0nm
75nm
F-1 Thickness Effects
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Index difference affects Interference
oscillations (Mostly Psi amplitude).
Wavelength (nm)
0 300 600 900 1200 1500 1800
Yin
degre
es
0
20
40
60
80
100n=1.5
n=1.75n=2.0
n=2.25
n=2.5
n=2.75
n=3.5
n=3.0
n=3.75
n=3.25
n=4.0
F-1 Effect of Film Index
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Adjust Index to match Psi peak height.
Adjust Thickness to match oscillation period.
Experimental Data
Wavelength (nm)
600 700 800 900 1000 1100
Yin
de
gre
es
0
15
30
45
60
75
90
Exp E 75°
n=1.5
n=2
n=2.5
n=3
Generated and Experimental
Wavelength (nm)
600 700 800 900 1000 1100
Y in d
egre
es
0
5
10
15
20
25
30
Model Fit Exp E 75°
F-1 Using This Information
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1. Adjust An parameter to approximate index.
– Psi amplitude can help estimate.
2. Adjust thickness to match # of oscillations.
3. Fit Thickness, An and Bn.
4. Add Cn. Does it improve the MSE?
5. Normal dispersion???
Normal Fit IF Model is Close to Answer!
RESET if fit fails!!!
F-1 Cauchy Procedure
Example 4 Al2O3 on Si
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If light is absorbed before returning to surface, only top
reflection is ‘seen’ (Film appears as Substrate)
Wavelength (nm)
120 150 180 210 240 270 300
Din
degre
es
-50
0
50
100
150
200
250
300
F-2 Semi-Absorbing Films
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Fit Cauchy to Transparent region
– determine thickness.
Fix thickness and fit “n,k” at all wavelengths
using point-by-point fit.
When in doubt, convert to Genosc to insure
Kramers-Kronig consistency.
Surface roughness, grading, and anisotropy can
be added if they improve MSE.
F-2 Choosing a Model
Example 5 Semi Absorbing Film on Si
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Roughness sensitivity when material is
absorbing or has high index.
Grading and roughness often correlated when
both lower index toward surface.
When grading increases index toward surface,
may also be sensitive to roughness.
F-2 Surface Roughness / Index Grading
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Most metal films are opaque above 50-
100nm thickness.
Absorption at all wavelengths prevents
periodic oscillations from thickness.
Data will appear similar to absorbing
substrates:
– Psi large and never close to zero.
– Delta between 0 and 180.
– Pseudos from different angles the same.
F-3 Absorbing Films
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No new information!
Wavelength (nm)
200 400 600 800 1000 1200
Y in d
egre
es
15
20
25
30
35
40
Exp E 45°Exp E 55°Exp E 65°Exp E 75°
Wavelength (nm)
200 400 600 800 1000 1200
D in d
egre
es
40
60
80
100
120
140
160
180
Exp E 45°Exp E 55°Exp E 65°Exp E 75°
Wavelength (nm)
200 400 600 800 1000 1200<
1>
<
2 >
-5.0
-2.5
0.0
2.5
5.0
0
5
10
15
20
25
30
Exp <1>-E 65°Exp <1>-E 75°Exp <2>-E 65°Exp <2>-E 75°
F-3 Multiple angles
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Challenge:
More unknown
sample properties
than measured
values.
Solution:
Measure additional
information or
reduce number of
unknown properties.
Known Substrate
n(l), k(l) d
Y(l), D(l)
F-3 Modeling?
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Opaque Layer
Transparent Region
Optical Constant Parameterization
Multiple Angles
Interference Enhancement
SE + Intensity
Multiple-Sample
In-Situ
Multiple-Ambient
J. Hilfiker, “Survey of methods to characterize thin absorbing
films with Spectroscopic Ellipsometry” Thin Solid Films 516 (2008) 7979-7989.
F-3 Methods for Absorbing Films
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Preferred Method #1
– Measure n,k from single-layers: use dispersion models.
– Fit thickness only.
– If poor fit, add dispersion parms. for least stable film.
Substrate
Film A
Substrate
Film B
Substrate
Film C
Substrate
Film A
Film B
Film C
Multi-Layer Strategies
©2014 J.A. Woollam Co., Inc. www.jawoollam.com 30
Preferred Method #2
– Measure n,k for each “new” layer with previous layers
fixed: use dispersion models.
– If poor fit, add thickness and then dispersion
parameters for previous layers.
Substrate
Film A
Film B
Film C
Substrate
Film A
Substrate
Film A
Film B
Multi-Layer Strategies
©2014 J.A. Woollam Co., Inc. www.jawoollam.com 31
6 Example 6-poly Si on 100nm TOx on Si
Two Film layers
– Unknown thickness poly Si
– ~100nm Thermal Oxide
Build your own method to fit the
data.
©2014 J.A. Woollam Co., Inc. www.jawoollam.com 32
Thank You & Good Luck!
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