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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 6, Pages 977–987 (Mi zvmmf10050)  

This article is cited in 1 scientific paper (total in 1 paper)

Direct and inverse problems of studying the properties of multilayer nanostructures based on a two-dimensional model of $X$-ray reflection and scattering

R. V. Khachaturov

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

Abstract: A mathematical model of $X$-ray reflection and scattering by multilayered nanostructures in the quasi-optical approximation is proposed. $X$-ray propagation and the electric field distribution inside the multilayered structure are considered with allowance for refraction, which is taken into account via the second derivative with respect to the depth of the structure. This model is used to demonstrate the possibility of solving inverse problems in order to determine the characteristics of irregularities not only over the depth (as in the one-dimensional problem) but also over the length of the structure. An approximate combinatorial method for system decomposition and composition is proposed for solving the inverse problems.

Key words: mathematical modeling, multilayered nanostructures, inverse problems, numerical methods, approximate combinatorial method.

DOI: https://doi.org/10.7868/S0044466914060106

Full text: PDF file (474 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:6, 984–993

Bibliographic databases:

UDC: 519.634
MSC: 78A45
Received: 15.05.2013
Revised: 09.12.2013

Citation: R. V. Khachaturov, “Direct and inverse problems of studying the properties of multilayer nanostructures based on a two-dimensional model of $X$-ray reflection and scattering”, Zh. Vychisl. Mat. Mat. Fiz., 54:6 (2014), 977–987; Comput. Math. Math. Phys., 54:6 (2014), 984–993

Citation in format AMSBIB
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\vol 54
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\pages 977--987
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    This publication is cited in the following articles:
    1. R. V. Khachaturov, “Multiobjective optimization in a pseudometric objective space as applied to a general model of business activities”, Comput. Math. Math. Phys., 56:9 (2016), 1580–1590  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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