The X-ray scattering from relaxed hetero-epitaxial layers, with misfit dislocations randomly distributed at the interface between the layer and the substrate, was analyzed theoretically and experimentally. The profiles of the X-ray diffraction peaks, and the reciprocal space maps of the intensity, were measured and simulated for several hetero-epitaxial structures with a wide range of dislocation densities. At high dislocation densities, the peak position was governed by the mean distortions and the peak width was due to the mean-square variation in the distortions. The peak widths that were calculated for an uncorrelated distribution of dislocations exceeded the widths of peaks that were measured in hetero-epitaxial structures with large mismatches. It was shown that spatial correlations of the dislocations reduced the peak width and thus explained the discrepancy. Coherent and diffuse components of the intensity were measured and simulated for low dislocation densities. It was shown that the position of the coherent peak did not parallel the mean distortions. Satellites of the diffuse peak were observed.

X-Ray Diffraction Peaks due to Misfit Dislocations in Hetero-Epitaxial Structures. V.M.Kaganer, R.Köhler, M.Schmidbauer, R.Opitz, B.Jenichen: Physical Review B, 1997, 55[3], 1793-810