Grazing incidence diffraction by laterally patterned semiconductor nanostructures

A theoretical study of grazing incidence diffraction by laterally patterned epitaxial nanostructures is presented and successfully applied to experimental findings of pseudomorphic multilayer gratings. Numerical results from a distorted wave Born approximation are given. The grating structure generates a fine structure around the reciprocal lattice points consisting of grating truncation rods, which are similar to the crystal truncation rod of a planar crystal surface. We show the influence of the grating shape, the compositional profile and the lattice strain on the intensity pattern along the grating truncation rods. The effect of lattice strain will be discussed by comparing the fully strained state (tetragonal lattice distortion), uniform strain relaxation and graduated strain relaxation in the surface grating. Our theoretical treatment allows us to interpret grazing incidence diffraction measurements obtained from strained layer gratings and superlattice gratings.