Reconstruction of periodic structures from optical scattering measurements using adjoint equations

Gonzalo R. Feijóo

doi:10.1364/JOSAA.25.001906

Reconstruction of periodic structures from optical scattering measurements using adjoint equations

Gonzalo R. Feijóo

Journal of the Optical Society of America A
Vol. 25,
Issue 8,
pp. 1906-1920
(2008)
•https://doi.org/10.1364/JOSAA.25.001906

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Gonzalo R. Feijóo, "Reconstruction of periodic structures from optical scattering measurements using adjoint equations," J. Opt. Soc. Am. A 25, 1906-1920 (2008)

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Related Topics
Table of Contents Category
- Scattering
Optics & Photonics Topics
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The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Diffraction and gratings (050.0050)
- Numerical approximation and analysis (000.4430)
- Instrumentation, measurement, and metrology (120.0120)
- Inverse scattering (290.3200)

About this Article
History
- Original Manuscript: August 24, 2007
- Revised Manuscript: April 7, 2008
- Manuscript Accepted: April 25, 2008
- Published: July 8, 2008

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Abstract

A new numerical approach to efficiently reconstruct the profile of a grating from measurements of reflection coefficients is demonstrated. The problem is posed in the mathematical framework of an inverse scattering problem and solved using gradient-based algorithms. The gradient is computed efficiently using adjoint equations, which amounts to an extra scattering computation per iteration. For symmetric profiles it is shown that only knowledge of the scattered field is sufficient to compute the gradient. As a result, complex profiles can be reconstructed rapidly, and the method can be potentially used in metrology applications in semiconductors. The technique is demonstrated for the case of TE polarization.

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	$λ_{0} = 300 nm$			$λ_{0} = 600 nm$
Layer #	adj $(\times 10^{5})$	fd $(\times 10^{5})$	$∣ (adj - fd) ∕ fd ∣$	adj $(\times 10^{4})$	fd $(\times 10^{4})$	$∣ (adj - fd) ∕ fd ∣$
1	$- 1.659236$	$- 1.659245$	$5.236749 \times 10^{- 6}$	$- 1.167154$	$- 1.167143$	$9.379807 \times 10^{- 6}$
2	$- 4.944221$	$- 4.944314$	$1.893959 \times 10^{- 5}$	$- 2.913201$	$- 2.913266$	$2.247633 \times 10^{- 5}$
3	$- 6.843224$	$- 6.843347$	$1.794846 \times 10^{- 5}$	$- 4.199008$	$- 4.199120$	$2.682196 \times 10^{- 5}$
4	$- 6.056257$	$- 6.056184$	$1.207015 \times 10^{- 5}$	$- 4.868901$	$- 4.868922$	$4.175935 \times 10^{- 6}$
5	$- 3.641104$	$- 3.640908$	$5.381425 \times 10^{- 5}$	$- 4.763485$	$- 4.763283$	$4.244237 \times 10^{- 5}$
6	$- 1.649989$	$- 1.649941$	$2.929343 \times 10^{- 5}$	$- 3.758022$	$- 3.758099$	$2.058973 \times 10^{- 5}$
7	$- 1.344967$	$- 1.345055$	$6.592388 \times 10^{- 5}$	$- 1.833276$	$- 1.832837$	$2.399876 \times 10^{- 4}$
8	$- 2.641041$	$- 2.641350$	$1.172786 \times 10^{- 4}$	$0.859225$	$0.858974$	$2.922627 \times 10^{- 4}$

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