Coplanar and grazing incidence x-ray-diffraction investigation of self-organized SiGe quantum dot multilayers

We report on a formalism for the calculation of diffusely scattered x-ray intensity from spatially inhomogeneous strain fields in Ge rich islands and in the surrounding Si matrix of SiGe/Si multilayers. The data analysis is based on a theory considering the two-dimensional statistical distribution of the dot positions, which allows a common formalism for both coplanar and grazing incidence scattering geometries. The strain fields were simulated based on the approach of the elastic Green function, taking the influence of the elastic strain relaxation at the sample surface into account. From these simulations the degree of relaxation of the islands was obtained, which compared very well with experimental data derived from x-ray reciprocal space maps.