Strain investigation of low strained buried gratings by grazing incidence X-ray diffraction and elasticity theory

We investigate the strain evolution in low strained gratings before and aft er embedding in the substrate material by high-resolution grazing incidence X-ray diffraction and elasticity theory. For the experiments, we use a non -coplanar multiple crystal arrangement. A suitable selection of reactions a llows us to characterise the grating shape independently of the strain stat e. Depth selective measurements give evidence for a non-uniform strain rela xation in the surface grating and a complete planarization of the sample su rface by the burying process. In the buried grating a counteraction of the embedding material is found. The counteraction only leads to a partial rest raining of the grating. There remains a laterally periodic strain modulatio n in the grating, which extends into the non-patterned material below and a bove the grating and reaches the free surface of the embedding material. Th e experimental findings are confirmed by calculations of the strain field b ased on elasticity theory. The subsequent simulations of the diffraction pa tterns show a good quantitative agreement with experiment.