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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 12 — Jun. 4, 2012
  • pp: 12771–12786

A maximum likelihood approach to the inverse problem of scatterometry

Mark-Alexander Henn, Hermann Gross, Frank Scholze, Matthias Wurm, Clemens Elster, and Markus Bär  »View Author Affiliations

Optics Express, Vol. 20, Issue 12, pp. 12771-12786 (2012)

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Scatterometry is frequently used as a non-imaging indirect optical method to reconstruct the critical dimensions (CD) of periodic nanostructures. A particular promising direction is EUV scatterometry with wavelengths in the range of 13 – 14 nm. The conventional approach to determine CDs is the minimization of a least squares function (LSQ). In this paper, we introduce an alternative method based on the maximum likelihood estimation (MLE) that determines the statistical error model parameters directly from measurement data. By using simulation data, we show that the MLE method is able to correct the systematic errors present in LSQ results and improves the accuracy of scatterometry. In a second step, the MLE approach is applied to measurement data from both extreme ultraviolet (EUV) and deep ultraviolet (DUV) scatterometry. Using MLE removes the systematic disagreement of EUV with other methods such as scanning electron microscopy and gives consistent results for DUV.

© 2012 OSA

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(120.3940) Instrumentation, measurement, and metrology : Metrology

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: February 8, 2012
Revised Manuscript: March 16, 2012
Manuscript Accepted: April 1, 2012
Published: May 23, 2012

Mark-Alexander Henn, Hermann Gross, Frank Scholze, Matthias Wurm, Clemens Elster, and Markus Bär, "A maximum likelihood approach to the inverse problem of scatterometry," Opt. Express 20, 12771-12786 (2012)

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