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Related Experiment Videos

Bayesian inference analysis of ellipsometry data.

N P Barradas1, J L Keddie, R Sackin

  • 1School of Electronic Engineering, Information Technology and Mathematics, University of Surrey, Guildford, Surrey GU2 5XH, United Kingdom.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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Variable angle spectroscopic ellipsometry (VASE) can determine thin film properties. This study uses simulated annealing and Bayesian inference to analyze VASE data, revealing ambiguities in bilayer models, such as polystyrene on silicon dioxide.

Area of Science:

  • Materials Science
  • Optical Physics
  • Data Analysis

Background:

  • Variable angle spectroscopic ellipsometry (VASE) is a powerful, non-destructive method for characterizing thin films.
  • Traditional VASE data analysis often relies on predefined models or approximations, limiting its application to complex or unknown structures.
  • Accurate determination of film thickness and refractive index is crucial for material performance and device fabrication.

Purpose of the Study:

  • To apply a model-free approach using simulated annealing and Bayesian inference for analyzing VASE data.
  • To assess the inherent ambiguities in VASE data for complex thin film structures, specifically bilayers.
  • To provide a robust method for quantifying uncertainties and exploring all plausible models that fit experimental data.

Main Methods:

Related Experiment Videos

  • Utilized simulated annealing for least-squares fitting of VASE data (simulated and experimental) in a model-free manner.
  • Employed Bayesian inference with the Markov chain Monte Carlo algorithm to assess solution ambiguity and incorporate prior knowledge.
  • Validated results using Rutherford backscattering spectrometry for accuracy assessment.

Main Results:

  • Successfully applied simulated annealing and Bayesian inference to determine unknown thicknesses and refractive indices of single and bilayer films.
  • Demonstrated that VASE data for a bilayer system (polystyrene on silicon dioxide on silicon) can be ambiguous.
  • Identified multiple distinct models that adequately explain the same experimental ellipsometry data for the ambiguous bilayer case.

Conclusions:

  • The combination of simulated annealing and Bayesian inference offers a comprehensive approach to VASE data analysis, especially for unknown structures.
  • Ambiguities in VASE data analysis are inherent, particularly for multilayer systems, and must be rigorously assessed.
  • This methodology provides a more complete understanding of thin film characterization by revealing all acceptable models and their uncertainties.