Grazing-incidence dynamic X-ray diffraction from a crystal with a shaped surface
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he 100th anniversary of the discovery of Xray diffraction
GrazingIncidence Dynamic XRay Diffraction from a Crystal with a Shaped Surface A. Yu. Gaevskiia, b, I. E. Golentusa, and V. B. Molodkina a
Institute of Metal Physics, National Academy of Sciences of Ukraine, Kiev, 03142 Ukraine b National Technical University of Ukraine “Kiev Polytechnical Institute,” Kiev, Ukraine email: [email protected] Received August 29, 2011
Abstract—The dynamic grazingincidence Xray diffraction from a crystal with a shaped surface in the form of onedimensional submicron grating has been investigated. The interaction between the specularly reflected and diffracted waves and grating harmonics is taken into account for noncoplanar diffraction under the conditions of total external reflection. It is shown that this approximation exhibits good convergence in the number of harmonics taken into account. The influence of the angular divergence of the incident beam on the rockingcurve shape is shown. DOI: 10.1134/S1063774512050045
Crystals with surfaces in the shape of one or two dimensional submicron gratings are basic elements for many devices of optoelectronics and Xray optics. The structure of such surface gratings is most often investi gated by Xray methods under grazingincidence dif fraction (GID) conditions [1, 2] and, theoretically, based on the kinematic approximation of the dis tortedwave Born approximation (DWBA) type [3–5] or within some version of dynamic theory [6–9]. However, the dynamic theory of grazingincidence diffraction from surface gratings generally disregards the crystalline structure of the scatterer [10, 11]. The purpose of this study was to analyze the joint dynamic diffraction from the crystal lattice and surface grating in the grazing geometry. FIELD EQUATIONS FOR A CRYSTAL WITH A SHAPED SURFACE Let a plane transversely polarized electromagnetic wave with a wave vector K = (K ||, K z ) and a frequency ω be incident from vacuum on a crystal. A onedimen sional grating with a period of ~(103–104)a (a is the crystal lattice period) is formed on the crystal. Scatter ing processes include diffraction from both the crystal lattice and surface grating. The surface periodicity leads to the following: a fine structure of grating trun cation rods (GTRs) manifests itself in the reciprocal space near Bragg rods (crystal truncation rods (CTRs) in the lateral direction of the surface grating). This complex structure of points in the reciprocal space can be investigated using highresolution Xray diffrac tion. Cases of coplanar and noncoplanar diffraction are distinguished, depending on the orientation of the dif
fraction vector, which, respectively, lies or does not lie in the plane of incidence [1, 6]. In the case of small angles of incidence, only the vectors K + H with vec tors H lying in the plane oriented perpendicularly to the plane of incidence can be found near the Ewald sphere; i.e., the neighborhood of Bragg rods (hk0) is investigated in the case of grazingincidence diffrac tion. Let us int
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