X-ray specular scattering from statistically rough surfaces: a novel theoretical approach based on the Green function formalism

X-ray specular scattering from statistically rough surfaces: a novel theoretical approach based on the Green function formalism

Acta Crystallographica Section A 2010, 66, 640-648
F. N. Chukhovskii, A. M. Polyakov

Abstract:

The Green function formalism is applied to the problem of grazing-incidence small-angle X-ray scattering from statistically rough surfaces. Kirchhoff's integral equation is used to describe the X-ray wavefield propagation through a single rough surface separating vacuum and medium. Taking into account multiple diffuse X-ray scattering effects, the reflection R^coh() and transmission T^coh() coefficients of the specular wave are obtained using the Gaussian statistical model of rough surfaces in terms of the two-point height-height correlation function. In the limiting cases when the correlation length is equal to zero or infinity, analytical formulae for the reflection R^coh() and transmission T^coh() coefficients of the specular wave are obtained. It is important that in the case they coincide with the corresponding reflection R^DW() and transmission T^DW() coefficients related to the conventional Debye-Waller approximation for describing the grazing X-ray scattering from a rough surface. In the case of finite values of correlation length the reflection |R^coh()|² and transmission |T^coh()|² scans are numerically calculated.

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