Strain and shape analysis of multilayer surface gratings by coplanar and by grazing-incidence x-ray diffraction

The surface shape and the spatial distribution of strain in GaInAs/InP multilayer gratings is experimentally determined by combining high-resolution x-ray diffraction and grazing-incidence diffraction. Dramatic deformations of the diffraction patterns in the measured reciprocal space maps of such gratings indicate a strongly nonuniform character of lattice distortions in the layers, caused by elastic strain relaxation. By coupling x-ray diffraction theory and elasticity theory within one single evaluation formalism, an experimental strain and shape analysis could be performed which was not yet available in this form by other methods. The different components of the strain tensor are determined by recording diffraction patterns around different reciprocal lattice points. We study how the strain relaxation of the multilayer grating evolves towards the free surface, and how the local strain distribution is modulated due to the compositional profile of the layered setup. Furthermore, the article describes in detail the effects of the grating shape, the multilayer morphology, and the lattice strain field on the diffraction patterns of multilayered gratings.