Lattice tilt and strain mapped by X-ray scanning nanodiffraction in compositionally graded SiGe/Si microcrystals

The scanning X-ray nanodiffraction technique is used to reconstruct the three-dimensional distribution of lattice strain and Ge concentration in compositionally graded Si_1−xGe_x microcrystals grown epitaxially on Si pillars. The reconstructed crystal shape qualitatively agrees with scanning electron micrographs and the calculated three-dimensional distribution of lattice tilt quantitatively matches finite-element method simulations. The grading of the Ge content obtained from reciprocal-space maps corresponds to the nominal grading of the epitaxial growth recipe. The X-ray measurements confirm strain calculations, according to which the lattice curvature of the microcrystals is dominated by the misfit strain, while the thermal strain contributes negligibly. The nanodiffraction experiments also indicate that the strain in narrow microcrystals on 2 × 2 µm Si pillars is relaxed purely elastically, while in wider microcrystals on 5 × 5 µm Si pillars, plastic relaxation by means of dislocations sets in. This confirms previous work on these structures using transmission electron microscopy and defect etching.