Lateral correlation of SiGe Stranski-Krastanow islands on silicon as probed by high resolution x-ray diffraction

We describe a procedure to consider the impact of lateral positional correlation of SiGe nanoscale islands onto the diffuse scattering within a high resolution x-ray diffraction experiment. The samples have been grown by means of liquid phase epitaxy which provides monodisperse island ensembles containing up to 10(9) equivalent objects. It is shown that a proper numerical simulation of the x-ray diffuse scattering pattern requires careful consideration of the partial coherence of x rays. An appropriate numerical procedure consists of coherent summation over sample areas with lateral dimensions as given by the coherence properties of the radiation and subsequent incoherent summation over a large enough number of such areas. For the given case an effective lateral coherence length of approximate to1 mum has been used, which is derived taking into account also the detector resolution. The according simulation is in good agreement with the experimentally observed x-ray diffuse intensity pattern. (C) 2004 American Institute of Physics.