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We studied the feasibility to create a Bragg-Fresnel optical element through the use of silicon dioxide films grown on the silicon perfect crystal surface. In our case the Bragg-Fresnel lens structure consists of a set of silicon dioxide rectangular shape etched zones arranged by the Fresnel zone law. The stress within coated and uncoated crystal regions is opposite in sign, whether tensile or compressive. The strain in the substrate crystal lattice directly underneath discontinuities in the deposited film give rise to phase difference between waves diffracted from coated and uncoated crystal regions. This phase difference is known to be dependent on the thickness and composition of film and substrate. In this paper the focusing properties of Si/SiO2 Bragg-Fresnel lenses with 107 zones and 0.3 micrometer outermost zone width were experimentally studied as a function of the silicon oxide thickness in the range of 100 - 400 nanometers. The efficiency of the focusing of hard X-rays was found to be about 16% at energy 10 keV.
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Vitaly V. Aristov, Michael Drakopoulos, Serguei Kuznetsov, Anatoly A. Snigirev, Irina Snigireva, Vecheslav Yunkin, "Deformation Bragg-Fresnel lens with SiO² surface structure," Proc. SPIE 4783, Design and Microfabrication of Novel X-Ray Optics, (21 November 2002); https://doi.org/10.1117/12.451016