The chemical structure of rare earth superlattices: A high-resolution x-ray scattering study

The chemical structure of a series of Ho/Lu and Ho/Y superlattices, all grown by MBE, has been investigated using high-resolution x-ray scattering techniques. The detailed functional form of the scattering was determined in scans performed both parallel and perpendicular to the growth direction. For scans of the wave-vector transfer parallel to the growth direction the superlattice satellites broaden as a function of the satellite index. This is shown to be consistent with the presence of discrete cumulative roughness in the superlattices that scales with the thickness of the superlattice period. The transverse width of the superlattice Bragg peaks broadens almost linearly as a function of the component of the reduced wave-vector parallel to the growth direction, while the line shape is invariant, and is described by a Lorentzian raised to the power of ≈5/2. It is shown that this arises from the conformal nature of the interface roughness, and the roughness exponent characterizing the average interface is determined to be α = 0.85 ± 0.05. The dependence of the interface morphology on the growth temperature is also considered, and the limitations of current structural models discussed.