Tomographic nanometer-scale images of self-assembled InAs͞GaAs quantum dots have been obtained from surface-sensitive x-ray diffraction. Based on the three-dimensional intensity mapping of selected regions in reciprocal space, the method yields the shape of the dots along with the lattice parameter distribution and the vertical interdiffusion profile on a subnanometer scale. The material composition is found to vary continuously from GaAs at the base of the dot to InAs at the top.

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. A. Spatial distinctionIn reciprocal space, the distance between two crystals is equivalent to the reciprocal difference of their lattice param-

Self-assembled coherent InAs islands on GaAs (100) have been investigated by a novel version of grazing-incidence diffraction ("iso-strain scattering"). This method permits the determination of the interdependence of strain and shape, as well as the relaxation gradient within the InAs dots. The relaxation in the islands ranges from fully strained at the bottom to completely relaxed at the top of the islands. The radius of the dots at a given height depends linearly on the local elastic lattice relaxation, with a rapidly increasing relaxation gradient when approaching the top of the islands.

We have investigated the strain and composition distribution in uncapped SiGe islands grown on Si (001) by x-ray diffraction. In order to be sensitive to the dot layer on the sample surface, and at the same time being able to measure in-plane strain and strain in growth direction, we utilized a scattering geometry at grazing incidence angles, but with high exit angles. The measured intensity distribution is compared to simulations based on the strain distribution calculated by a finite element method. Although pure Ge has been deposited during island growth by molecular beam epitaxy, the Ge composition varies from 0.5 at the island base to 1.0 at the top of the islands. Even at this top, the elastic relaxation reaches only about 50%.

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