Bayesian Analysis of Ellipsometry Measurements

1. Bayesian Analysis of Ellipsometry Measurements Udo v. Toussaint and Thomas Schwarz-Selinger • Ellipsometry • Example • Bayesian Analysis • Results and Conclusion

2. shutter 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!

3. Camera analyzer Laser high pressure lamp polarizer monochromator sample stage controller ellipsometer power supplies 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: > 0. 1 Å (1 nm)

4. complex index of refraction: defined by: : extinction coefficient solid sample: Fresnel equations Principles of Ellipsometry: Reflection of light I

5. Snell’s law: Principles of Ellipsometry: Reflection of light II multilayer system:

6. Measured data: detection of the change of polarization of linearly polarized light due to the reflection at the sample surface in fact we measure and (ellipsometric angles):  each measurement delivers only 2 pieces of information but depends on: incident angle  ni and ki and di of each medium i Principles of Ellipsometry  for a single measurement result is ambiguous if neither ni nor kiis known!

7. the plane: Principles of Ellipsometry Use of empirical models:  immer noch komplexer Teilchenzoo!

8. But sometimes… Duoplasmatron (Ivan Bizyukov): a-C:H flux probe (bombardment by 1 keV D+)

9. But sometimes… Duoplasmatron (Ivan Bizyukov): a-C:H flux probe (bombardment by 1 keV D+) ? ?

10. But sometimes… Duoplasmatron (Ivan Bizyukov): a-C:H flux probe (erosion by 1 keV D+) model for the plasma deposited a-C:H film measurement

11. Surface reconstruction from interference images Interference images from ellipsometry: 2 data values (angles) per measurement point

12. Bayesian Model Likelihood: Gaussian likelihood Prior: Bounded, flat : Ill-posedproblem: 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,

13. 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?

14. Surface reconstruction from interference images Virtually indistinguishable solutions: identical Ambigous solutions possible Important: Stay on correct branch of solution

15. Surface reconstruction from interference images Interference images from ellipsometry

16. Surface reconstruction from interference images And what about the edge?

17. 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 Conclusions & Outlook Conclusions:

18. experimental setup ICP

19. 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

20. 12 scans tender spot in general detection of atomic hydrogen in the plasma environment needed: hydrogen sensor erosion of a dense a-C:H-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)

21. 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