Dynamical X-ray scattering from the relaxed structures

High-resolution X-ray diffraction is now widely used analytical tool for investigation of nano scale multilayered structures in semiconductor and optical technologies. The HRXRD method delivers unique information on the crystallographic lattice of the samples, concentration of solid solutions, lattice mismatches, layer thicknesses, defect distribution, and relaxation degree of the epitaxial layers. The evaluation of the experimental results, however, requires a robust and precise theory due to complex dynamical scattering of X-rays from near perfect crystallographic structure of the samples. Usually, the Takagi-Taupin approach [1] or the recurrent matrix methods [2] are used for the simulation of the X-ray diffraction profiles from the epitaxial multilayered structures. The use of these theories, however, becomes essentially difficult, when the lateral lattice mismatches are present in multilayers, for example, in the case of partially or fully relaxed epitaxially grown samples. In the present work, the general solution of this problem is found analytically. The angular divergence of the incident beam is also considered and the algorithm for the diffracted profile mapping in the reciprocal space is developed. The experimental reciprocal space mapping of typical AlGaN/GaN/AlN samples with partially relaxed layers is compared to the simulated maps, which describe well the location and character of the diffraction spots caused by different layers. (author)