Lattice relaxation of nanostructured semiconductor pillars observed by high-resolution x-ray diffraction

Abstract
High resolution x-ray diffraction is used to obtain two-dimensional reciprocal space maps from two-dimensional periodic arrays of small (<250 nm) semiconductor pillars. The pillars were made by etching an (001) oriented Si wafer that was epitaxially overgrown with Si1−xGex. The pillars were etched to such a depth that they have a Si bottom and a Si1−xGex top. The shape of the pillars and the lattice parameters in the pillars are determined by comparison of the measured maps with kinematical diffraction model calculations using separate Fourier transformation of the shape of the Si and Si1−xGex parts of the grating. It was found that in the pillars the Si1−xGex lattice was totally relaxed, whereas it was compressively strained prior to etching.