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Advancing X-ray scattering metrology using inverse genetic algorithms.

Adam F Hannon1, Daniel F Sunday1, Donald Windover1

  • 1National Institute of Standards and Technology, Materials Science and Engineering Division, 100 Bureau Drive, Gaithersburg, MD 20899.

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Summary
This summary is machine-generated.

The covariance matrix adaptation evolutionary strategy with a mean-absolute error log objective function is the most effective method for determining nanograting structures from X-ray scattering data.

Keywords:
Markov chain Monte CarloX-ray scatteringcovariance matrix adaptation evolutionary strategydifferential evolutiongenetic algorithmnanostructure metrology

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Area of Science:

  • Materials Science
  • Computational Physics
  • Nanotechnology

Background:

  • Determining the real-space structure of periodic nanogratings is crucial for understanding their properties.
  • Critical dimension small-angle X-ray scattering (CD-SAXS) is a powerful technique for nanostructure analysis.
  • Robust and efficient computational methods are needed to interpret CD-SAXS data.

Purpose of the Study:

  • To compare the robustness and efficiency of genetic optimization algorithms against a Markov chain Monte Carlo (MCMC) algorithm for nanograting structure determination.
  • To identify the optimal combination of algorithm and objective function for analyzing CD-SAXS data.
  • To assess the performance of different optimization strategies when prior structural knowledge is limited.

Main Methods:

  • Implementation and comparison of two genetic optimization algorithms: covariance matrix adaptation evolutionary strategy (CMA-ES) and differential evolution (DE).
  • Utilizing a Markov chain Monte Carlo (MCMC) algorithm as a benchmark for robustness.
  • Employing various objective functions to minimize discrepancies between simulated and measured CD-SAXS diffraction data.
  • Parameterizing simulations with an electron density model approximating nanograting structures.

Main Results:

  • The covariance matrix adaptation evolutionary strategy (CMA-ES) demonstrated superior efficiency compared to differential evolution and MCMC for this specific application.
  • Coupling CMA-ES with a mean-absolute error log objective function proved to be the most effective combination.
  • This optimized approach successfully determined nanograting structures with minimal prior information.

Conclusions:

  • The CMA-ES algorithm, when paired with a mean-absolute error log objective function, is the most efficient and robust method for real-space structure determination from CD-SAXS data.
  • This finding is particularly significant for analyzing nanostructures where detailed prior knowledge is unavailable.
  • The study provides a valuable computational framework for advancing nanostructure characterization using X-ray scattering techniques.