17 June 2009 Specular and diffuse scattering from random asperities of any profile using the rigorous method for x-rays and neutrons
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The present work deals with a comprehensive numerical analysis of x-ray grazing-incidence scattering from single- and double-boundary, finite-conducting rough surfaces with asperities of different statistics, performed with the use of a mid-end workstation in a reasonable computation time. Multiple and multi-wave diffraction, refraction, absorption, and resonances influence significantly x-ray and neutron scattering. These are pure dynamic effects, which require application of a rigorous theory to correctly describe the power change in the specular order and to describe nonspecular distribution. Despite the impressive progress attained in developing a rigorous theory with account for random roughness, the author is aware only of approximate and asymptotic approaches in the case of neutron and x-ray scattering even by 1D surfaces, such as the Born approximation, the distorted-wave Born approximation, parabolic equation methods, etc. The PCGrate®-SX v.6.3 software developed on the basis of a modified boundary integral equation method and the Separating solver allows one to operate with exact models, e.g., those involving Maxwell's equations and rigorous boundary conditions, and appropriate radiation conditions. In order to compute the scattering properties of a rough surface using the forward electromagnetic solver, Monte Carlo simulation is employed to average the deterministic scattered power due to individual surfaces over an ensemble of realizations. The difference between approximate and rigorous approaches can be clearly seen in cases where grazing incidence occurs at close to or larger than the critical angle. This difference may give rise to wrong estimates of rms roughness and correlation length if they are determined by comparing experimental data with calculations. Besides, the rigorous approach permits taking into account any known roughness statistics, including quasi-periodicity of quantum dot ensembles.
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Leonid I. Goray, "Specular and diffuse scattering from random asperities of any profile using the rigorous method for x-rays and neutrons", Proc. SPIE 7390, Modeling Aspects in Optical Metrology II, 73900V (17 June 2009); doi: 10.1117/12.827444; https://doi.org/10.1117/12.827444

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