X-Ray Diffraction in a Uniformly Bent Crystal in Reflection Geometry

The features of the intensity distribution over the exit surface of a uniformly bent crystal have been investigated in reflection geometry. Experiments have been performed using thin-layer heterostructures Si(1-x)Gex/Si. For heterosystems, internal stresses induced in the film and substrate lead to an elastic bending of the whole system. The section topographs exhibit deformation interference fringes. It is important that the contrast of this interference pattern is almost one order of magnitude higher than the contrast in the case of Bragg scattering in a perfect crystal. The observed interference pattern depends on the radius of bending of the crystal. As the bending radius increases, all maxima shift toward the basic Bragg peak. Correspondingly, all distances between the interference fringes decrease. It has been shown that the positions of intensity maxima do not depend on the sign of the crystal bending. For a negative sign of the radius of the crystal bending (positive strain gradient), the integrated intensity increases. The results of the numerical simulation of the diffraction images agree well with the experimental topographs. A comparison of the numerical simulation of the interference pattern with the experimental topographs makes it possible to exactly determine the radius of the crystal bending (4%). The formulas describing the positions of interference maxima as a function of the bending radius of the sample have been obtained using the results of the numerical simulation of the experiment.