X-ray grazing incidence study of inhomogeneous strain relaxation in Si/SiGe wires

The elastic strain relaxation in a series of dry-etched periodic multilayer Si/SiGe wire samples with different etching depths was investigated systematically by means of grazing incidence diffraction (GID). The samples were patterned by holographic lithography and reactive ion etching from a Si/SiGe superlattice grown by molecular beam epitaxy. Scanning electron microscopy and atomic force microscopy were employed to obtain information on the shape of the wires. The inhomogeneous strain distribution in the etched wires and in the non-etched part of the multilayers was derived by means of finite element calculations which were used as an input for simulations of the scattered X-ray intensities in depth dependent GID. The theoretical calculations for the scattered intensities are based on distorted-wave Born approximation. The unperturbed scattering potential was chosen with a reduced optical density corresponding to the ratio of wire width and wire period, in order to reflect the main interaction between the incident X-rays and the patterned samples. The calculations are in good agreement with the experimental data demonstrating the variation of strain relaxation with depth.