Specular and diffuse scattering from random asperities of any profile using the rigorous method for x-rays and neutrons

 

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 Lewenberg-Markwardt gradient method has turned out an efficient way to the solution of model problems for a Si grating with a trapezoidal profile.. DOI: 10.1117/12.889418.

© 2011 SPIE.

 

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