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 befor and after 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 reflections allows us to characterise the grating shape independently of the strain state. Depth selective measurements give evidence for a non-uniform strain relaxation in the surface grating and a complete planarization of the sample surface by the burying process. In the buried grating a counteraction of the embedding material is found. The counteraction only leads to a partial restraining of the grating. These remains a laterally periodic strain modulation of the grating, which extends into the non-patterned material below and above the grating and reaches the free surface of the embedding material. The experemental findings are confirmed by calculation of the strain field based on elasticity theory . The subsequent simulations of the diffraction patterns show a good quantitative agreement with experiment.