Determination of strain fields and composition of self-organized quantum dots using x-ray diffraction

We give a detailed account of an x-ray diffraction technique which allows us to determine shape, strain fields, and interdiffusion in semiconductor quantum dots grown in the Stranski--Krastanov mode. A scattering theory for grazing incidence diffraction is derived for the case of highly strained, uncapped nanostructures. It is shown that strain resolution can be achieved by ``decomposing'' the dots in their iso-strain areas. For a selected iso-strain area, it is explained how lateral extent, height above the substrate and radius of curvature can be determined from the intensity distribution around a surface Bragg reflection. The comparison of intensities from strong and weak reflections reveals the mean material composition for each strain state. The combination of all these strain resolved functional dependences yields tomographic images of the dots showing strain field and material composition.