Strain relaxation in surface nano-structures studied by X-ray diffraction methods

We study the lattice strain relaxation in pseudomorphic surface gratings us ing high resolution X-ray diffraction (XRD), grazing incidence diffraction and elasticity theory. By means of grazing incidence diffraction we determi ne the grating shape and detect a depth dependent lattice strain relaxation in the grating. Symmetrical and asymmetrical XRD gives evidence of a non-u niform strain relaxation in the etched structures and the creation of a per iodic strain field deep in the substrate. The experimental findings are con firmed by an elasticity model which describes the interaction of the differ ent crystalline media. Comparing the measured diffraction maps with calcula ted ones, we determine the actual strain distribution in the trapezoidal gr ating and in the substrate.