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 mult ilayer gratings is experimentally determined by combining high-resolution x -ray diffraction and grazing-incidence diffraction. Dramatic deformations o f the diffraction patterns in the measured reciprocal space maps of such gr atings indicate a strongly nonuniform character of lattice distortions in t he layers, caused by elastic strain relaxation. By coupling x-ray diffracti on 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 s train tensor are determined by recording diffraction patterns around differ ent reciprocal lattice points. We study how the strain relaxation of the mu ltilayer 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 grat ing shape, the multilayer morphology, and the lattice strain field on the d iffraction patterns of multilayered gratings. (C) 2000 American Institute o f Physics. [S0021-8979(00)00708-8].