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Bayesian Analysis of Ellipsometry Measurements
Udo v. Toussaint and Thomas Schwarz-Selinger

• Ellipsometry
• Example
• Bayesian Analysis
• Results and Conclusion

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Principles of Ellipsometry
Detection of the change of polarization of
linearly polarized light due to the reflection at
the sample surface
here single wavelength rotating analyzer
ellipsometer
? immer noch komplexer Teilchenzoo!
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Principles of Ellipsometry
Jobin Yvon PZ 2000 Ellipsometer
wavelength 632 nm (400 -800 nm) spot size 10 x
30 mm (10 mm) motorized xyz sample
stage positioning accuracy 30 mm sample
thickness 2 mm measurement range Å - 30 mm
measurement accuracy gt 0. 1 Å (1 nm)
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Principles of Ellipsometry Reflection of light I
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Principles of Ellipsometry Reflection of light II
multilayer system
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Principles of Ellipsometry
? for a single measurement result is ambiguous if
neither ni nor ki is known!
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Principles of Ellipsometry
Use of empirical models
? immer noch komplexer Teilchenzoo!
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But sometimes
Duoplasmatron (Ivan Bizyukov) a-CH flux probe
(bombardment by 1 keV D)
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But sometimes
Duoplasmatron (Ivan Bizyukov) a-CH flux probe
(bombardment by 1 keV D)
?
?
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But sometimes
Duoplasmatron (Ivan Bizyukov) a-CH flux probe
(erosion by 1 keV D)
model for the plasma deposited a-CH film
measurement
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Surface reconstruction from interference images
Interference images from ellipsometry 2 data
values (angles) per measurement point
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Bayesian Model

• Likelihood Gaussian likelihood

Prior Bounded, flat
Ill-posed problem no. of parameters larger than
no. of data
Use prior-information optical properties vary on
a different length scale
Two-scale approach Nested grids for d and n,?
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Bayesian Model

• Posterior Bayes theorem

• Model specifications 4 layers, 6 unknowns (in
  2 layers)
• domain size inner grid 3x3 -5x5

disappointing

• Optimization with respect to the parameters
  Results were

• Why?

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Surface reconstruction from interference images
Virtually indistinguishable solutions identical
Ambigous solutions possible
Important Stay on correct branch of solution
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Surface reconstruction from interference images
Interference images from ellipsometry
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Surface reconstruction from interference images
And what about the edge?
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Conclusions Outlook
Conclusions

• Ellipsometry is a great non-perturbing surface
  analytical tool - but
• ML - evaluation of data may not be
  straightforward or even misleading ?
• Prior information is essential
• Derived parameter estimation algorithm works
  reliable ?
• Outlook
• Model comparison for number of layers
• Improved consideration of correlations

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experimental setup ICP
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quantification of ellipsometry data
T.Schwarz-Selinger, A. von Keudell, W.Jacob,
J.Appl. Phys. 86, 3988 (1999)
film properties like - hydrogen content -
density - refractive index are closely correlated
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tender spot in general
detection of atomic hydrogen in the plasma
environment
needed hydrogen sensor
erosion of a dense a-CH-film at 650 K
and measuring the erosion depth with
ex-situ-ellipsometry is complicted in the plasma
environment
? T. Schwarz-Selinger, W. Jacob, A. von Keudell,
JVST A. 18 (3), 995 (2000)
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Profilometry versus Ellipsometry/Reflectometry
general take home message
Profilometry mechanical contact with the sample
? topography
Ellipsometry/Reflectometry optical response of
the sample
? thickness x refractive index