Influence of miscut on crystal truncation rod scattering

X-rays can be used to measure the roughness of a surface by the study of crystal truncation rod scattering. It is shown that for a simple cubic lattice the presence of a miscut surface with a regular step array has no effect on the scattered intensity of a single rod and that a distribution of terrace widths on the surface is shown to have the same effect as adding roughness to the surface. For a perfect crystal without miscut, the scattered intensity is the sum of the intensity from all the rods with the same in-plane momentum transfer. For all real crystals, the scattered intensity is better described as that from a single rod. It is shown that data-collection strategies must correctly account for the sample miscut or there is a potential for improperly measuring the rod intensity. This can result in an asymmetry in the rod intensity above and below the Bragg peak, which can be misinterpreted as being due to a relaxation of the surface. The calculations presented here are compared with data for silicon (001) wafers with 0.1 and 4° miscuts.