Solution of the inverse problem of diffraction from low-dimensional periodically arranged nanocrystals

Leonid I. Goray

doi:10.1117/12.889418

23 May 2011 Solution of the inverse problem of diffraction from low-dimensional periodically arranged nanocrystals

Leonid I. Goray

Proceedings Volume 8083, Modeling Aspects in Optical Metrology III; 80830L (2011) https://doi.org/10.1117/12.889418
Event: SPIE Optical Metrology, 2011, Munich, Germany

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.

Citation Download Citation

Leonid I. Goray "Solution of the inverse problem of diffraction from low-dimensional periodically arranged nanocrystals", Proc. SPIE 8083, Modeling Aspects in Optical Metrology III, 80830L (23 May 2011); https://doi.org/10.1117/12.889418

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