High-resolution x-ray diffraction is frequently used for the determination of positions, shapes, elastic strains, and indirectly also local chemical composition in semiconductor quantum dots. In these studies the reciprocal space mapping is usually confined to a single scattering plane in reciprocal space (perpendicular or parallel to the sample surface), so that a full characterization of the quantum dots is possible only if a certain dot symmetry is assumed. We present a new diffraction method yielding a full three-dimensional distribution of diffracted intensity in reciprocal space. The method was used for the investigation of a random array of SiGe quantum dots deposited by liquid-phase epitaxy on a Si (001) surface. Three-dimensional distributions of diffracted intensity were measured around various reciprocal lattice points and the measured data were compared with numerical simulations based on continuum elasticity and semikinematical scattering theory. From the comparison we could reconstruct a full three-dimensional image of the shape of an average quantum dot, as well as its local chemical composition, without any a-priori assumption about the dot symmetry.

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