Strain and x-ray diffraction from axial nanowire heterostructures

Lattice distortions in a cylindrical nanowire with nonuniform intrinsic strains arbitrarily varying along its axis are analyzed, with a special emphasis on heterostructures. We find that, as a result of the elastic relaxation on the side surface, the lateral mismatch does not change the average longitudinal lattice period of the whole cylinder, but effects the average period of heterostructure. As a consequence, the positions of the x-ray diffraction peaks due to a periodic axial heterostructure depend on the ratio of the total height of the whole heterostructure to the cylinder diameter. The peaks attain the positions of the planar heterostructure peaks only when the diameter becomes orders of magnitude larger than the heterostructure height. The typical nanowire heterostructure parameters correspond to the opposite limit of full lateral relaxation.