Diffuse scattering from interface roughness in grazing-incidence x-ray diffraction.

Abstract

A theory of x-ray diffuse scattering from interface roughness in grazing-incidence diffraction ~GID! is presented. The theory assumes dynamical diffraction of x rays from perfect multilayers with the diffuse scattering from roughness calculated in the distorted-wave Born approximation. This permits the calculation of scattering due to roughness at all points on the diffraction curves, including the vicinity of the Bragg peaks. It is shown that the measurements of diffuse scattering in GID can provide information on atomic ordering at crystal interfaces which is not accessible by usual x-ray specular reflection and nonspecular x-ray scattering. The theory is found to be in good agreement to the two GID experiments carried out with an etched Ge surface and an AlAs/GaAs superlattice at the Cornell High-Energy Synchrotron Source and European Synchrotron Radiation Facility, respectively. In the case of the etched Ge surface, an anti-Yoneda dip in the diffuse scattering pattern at the Bragg peak and two symmetrical shoulders on the Bragg curve wings have been found and explained. In the case of the AlAs/GaAs superlattice, the diffuse scattering has been separated from GID by means of high-resolution measurements. A comparison between diffuse scattering in GID and diffuse scattering in grazing incidence far from the diffraction conditions has shown that the atomic ordering was preserved in the interface roughness, while it was partially destroyed in the surface roughness.