Theory of X-ray diffraction on a crystall with surface relief

It is well known that surface diffraction gratings are commonly used in X-ray optics [1], opto- and nanoelectronics [2]. Surface diffraction gratings are an optical component with a periodic structure formed on crystal surface. Thin 0.2 μm surface gratings with period of 10-20 μm were for the first time studied by Aristov et al. [3,4] on a triple-axis diffractometer. Results of X-ray diffraction on InP and GaAs crystals with significantly shorter surface relief period were reported in papers [5-7]. The purpose of the current paper is to provide further development of the coplanar X-ray diffraction theory on surface diffraction gratings. The problem is formulated in general within the framework of two- wave dynamic X-ray diffraction. Stroke profile can be specified in any shape. Since the period and the thickness of the surface relief do not exceed 1 μm, we can study it using the kinematic approximation. New stroke profile models for specific surface reliefs are proposed. These models were used to solve the X-ray diffraction problem analytically in the kinematic approximation. Boundaries of applicability for every solution were indicated. Those solutions may be used to reconstruct profile models from experimental data of high-resolution X-ray diffraction. Results of the current work are applicable to the X-ray and neutron optic studies.