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Quantitative nondestructive imaging of structural properties of semiconductor layer stacks at the nanoscale is essential for tailoring the device characteristics of many low-dimensional quantum structures, such as ultrafast transistors, solid state lasers and detectors. Here it is shown that scanning nanodiffraction of synchrotron X-ray radiation can unravel the three-dimensional structure of epitaxial crystals containing a periodic superlattice underneath their faceted surface. By mapping reciprocal space in all three dimensions, the superlattice period is determined across the various crystal facets and the very high crystalline quality of the structures is demonstrated. It is shown that the presence of the superlattice allows the reconstruction of the crystal shape without the need of any structural model.

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