Influence of miscut on crystal truncation rod scattering

X-rays can be used to measure the roughness of a surface by the study of cr ystal truncation rod scattering. It is shown that for a simple cubic lattic e 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 terra ce widths on the surface is shown to have the same effect as adding roughne ss to the surface. For a perfect crystal without miscut, the scattered inte nsity 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 stra tegies must correctly account for the sample miscut or there is a potential for improperly measuring the rod intensity. This can result in an asymmetr y in the rod intensity above and below the Bragg peak, which can be misinte rpreted as being due to a relaxation of the surface. The calculations prese nted here are compared with data for silicon (001) wafers with 0.1 and 4 de grees miscuts.