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Proceedings Paper

Solution of the inverse problem of diffraction from low-dimensional periodically arranged nanocrystals
Author(s): Leonid I. Goray
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Paper Abstract

The paper reports on development of an integral and nondestructive technique of characterization of low-dimensional periodically arranged nanocrystals (LDPAN) by spectroscopic scatterometry in the UV-IR ranges. Some approaches to the solution of direct and inverse problems in scatterometry are addressed. For the solution of the direct problem, the author has chosen the universal method of boundary integral equations, which has demonstrated a broad range of applicability and a high accuracy. Cases are analyzed in which a complicated three-dimensional diffraction problem involving 2D gratings can be reduced to a two-dimensional one with 1D gratings, or multilayer mirrors with plane boundaries. An algorithm is proposed for the solution of a system of nonlinear operator equations with an arbitrary, but limited set of unknown LDPAN structural parameters, and a given set of measured values of diffraction efficiency. The functional to be minimized in the course of solution of the inverse problem is identified, and methods of its regularization and for monitoring the accuracy of the solution are proposed. A Fortran code written with the use of the Löwenberg-Markwardt gradient method has turned out an efficient way to the solution of model problems for a Si grating with a trapezoidal profile.

Paper Details

Date Published: 23 May 2011
PDF: 12 pages
Proc. SPIE 8083, Modeling Aspects in Optical Metrology III, 80830L (23 May 2011); doi: 10.1117/12.889418
Show Author Affiliations
Leonid I. Goray, Saint Petersburg Academic Univ. (Russian Federation)
Institute for Analytical Instrumentation (Russian Federation)
I.I.G., Inc. (United States)

Published in SPIE Proceedings Vol. 8083:
Modeling Aspects in Optical Metrology III
Bernd Bodermann, Editor(s)

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