Dynamical Theory of X-Ray Diffraction in a Crystal with a Surface Grating of Another Material
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Dynamical Theory of X-Ray Diffraction in a Crystal with a Surface Grating of Another Material V. I. Punegov Institute of Physics and Mathematics, Komi Research Center, Ural Branch, Russian Academy of Sciences, Syktyvkar, 167982 Russia e-mail: [email protected] Received February 1, 2019; revised February 1, 2019; accepted March 12, 2019
Abstract—A general theory is developed for dynamical X-ray diffraction in a crystal on the surface of which a lateral periodic structure of thin-film lines (strips) of another material is formed. On the basis of the model of edge forces, the fields of elastic lattice displacements in the substrate are calculated that arise as a result of formation of a lateral surface grating (SG). With the use of the formalism of diffraction of spatially restricted X-ray beams, solutions are obtained for the amplitudes of X-ray waves reflected from a crystal with an SG whose chemical composition differs from the composition of the substrate. A numerical simulation is carried out of X-ray diffraction in a silicon substrate with SGs of tungsten and SiO2 oxide. It is shown that the angular distributions of the scattering intensity by a silicon crystal with tungsten and oxide lines of identical size differ significantly, and the physical nature of such difference is established. DOI: 10.1134/S1063776119070185
1. INTRODUCTION The first experiments using triple-axis X-ray diffractometry [1] on silicon crystals with a rectangular surface relief [2, 3] and on structures modulated by a surface acoustic wave [4, 5] have shown that, in addition to the main diffraction peak, there arise lateral diffraction orders (satellites). Lateral orders also arise in the case of X-ray scattering by silicon crystals with periodically repeated thin-film lines (strips) of SiO2 [6, 7]. Oxide film lines are produced by thermal oxidation of the surface or by chemical vapor deposition of SiO2 oxide, where a part of the oxide film is removed by the lithography technique followed by chemical etching, so that the surface of the Si substrate is covered by a surface grating (SG) of oxide material [6, 7]. In [8, 9], the authors investigated X-ray diffraction in silicon crystals on the surface of which a grating was produced by the lithography technique in the form of periodically arranged gold and tungsten lines. In this case, in contrast to known lateral gratings [2–7], satellites arose on reciprocal space maps (RSMs) not only in the horizontal direction of the reciprocal space but also along the lines of pseudo-peaks of monochromator and analyzer. Note that, earlier [10], the authors obtained a two-dimensional map of X-ray scattering intensity distribution on an Au/Si(111) system in which an SG of alternating gold lines had a period of
2 μm [10]. Due to the poor angular resolution and the relatively large period of metal strips, the diffraction orders were blurred, and the results were not analyzed in detail. To explain the abnormal appearance of diagonal satellites along the directions of pseudo-peaks of the
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