This article is cited in 10 papers

Direct and inverse problems of determining the parameters of multilayer nanostructures from the angular spectrum of the intensity of reflected X-rays

R. V. Khachaturov

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

Abstract: Mathematical models and methods for determining the degree of roughness and other parameters of multilayer nanostructures from the angular spectrum of the intensity of the reflected X-rays are studied. The proposed mathematical model for solving the direct problem of x-ray propagation and the distribution of their electromagnetic field within a multilayer nanostructure takes into account the refraction effect due to the inclusion of the second derivative with respect to the structure depth. A numerical method for solving the resulting problem is developed, and the numerical results are analyzed. The approximation-combinatorial method of the decomposition and composition of systems is used to solve the inverse problem.

Key words: methods for determining parameters of multilayer nanostructures, mathematical modeling, finite difference method, approximation-combinatorial method.

UDC: 519.677

Received: 03.07.2008
Revised: 29.04.2009

 English version: Computational Mathematics and Mathematical Physics, 2009, 49:10, 1781–1788

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