![]() 35 ∘ for In 0.6 Ga 0.4 As QDs and a GaAs substrate. (b) An experimental GID RSM of the 220 Bragg reflection in GID geometry at incidence angle α i = 0. The label “3 Ch” indicates the energy losses in the specular beam due to the dynamical rescattering of the x rays according to channel 3 in Fig. (a) A single detector frame with dynamical effects. 8ANKA, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, 76344 D-Eggenstein-Leopoldshafen, GermanyĮxperimental GID reciprocal-space map and observation of dynamical effects.7Clausthal University of Technology, Energy Research Center of Lower Saxony and Institute for Energy Research and Physical Technologies, Am Stollen 19B, D-38640 Goslar, Germany.6Institute for Applied Physics, University of Hamburg, Jungiusstraße 11, D-20355 Hamburg, Germany.5Laboratory for Application of Synchrotron Radiation, Karlsruhe Institute of Technology, Kaiserstraße 12, D-76131 Karlsruhe, Germany.4University of Siegen, Solid State Physics, Emmy-Noether Campus, Walter-Flex Straße 3, D-57068 Siegen, Germany.3Institute for Photon Science and Synchrotron Radiation, Karlsruhe Institute of Technology, Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany.2National Research Tomsk Polytechnic University (TPU), pr.1Deutsches Elektronen-Synchrotron DESY, Notkestraße 85, D-22607 Hamburg, Germany.Finally, the substrate contribution itself may yield information sufficient for a novel and fast approach for the structural characterization of strained semiconductor heteronanostructures. We show that neglecting the substrate contribution to the x-ray scattering causes errors in the standard isostrain approach. The advantages of our approach are demonstrated by comparison with the standard isostrain approach that is commonly used for strain analysis of the nanostructures. Further, analyzing the experimental and simulated x-ray diffraction patterns in x-ray grazing incidence diffraction, we demonstrate the importance of accounting for strain in the substrate and interference effects between the surface and the QDs for strain analysis of the nano-objects. Employing the finite-element method, we give a detailed analysis of the strain distribution inside the nanostructure and the substrate. In the frame of the distorted wave Born approximation, we take into account multiple scattering and coherent interactions of the x-ray beams involved in the diffraction process. By the example of free-standing In 0.6 Ga 0.4 As quantum dots (QDs), we discuss the contributions of the strained epitaxial surface nanostructures and the substrate to the scattered x-ray intensity under grazing incidence conditions. Fast and reliable characterization of their structural properties is of high importance for industry and science. Semiconductor heteronanostructures are of interest for a vast field of applications in optoelectronics.
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