High-resolution x-ray-scattering study of the structure of niobium thin films on sapphire

The structure of two thin films of Nb grown epitaxially on sapphire has been studied using high-resolution x-ray-scattering techniques. The films, of nominal thickness 400 and 150 Å, were grown using molecular-beam epitaxy on a (112¯0) sapphire substrate. They were of exceptionally high quality, with rocking curves of ≊0.004° for the (110${)}_{\mathrm{Nb}}$ Bragg peak. The x-ray scattering observed in transverse scans of the wave-vector transfer through the (110${)}_{\mathrm{Nb}}$ Bragg peak exhibits two other unusual features. First, weak satellite Bragg peaks are observed. These are shown to arise from a regular sinusoidal distortion of the Nb thin film. Using a frozen phonon model for this distortion, we relate the position of the satellites to the length of a terrace on the vicinal sapphire surface, and the intensity of the satellites to the lattice mismatch between the two materials in the surface normal direction. Second, in addition to the sharp Bragg peaks, there is a broader, diffuse component. This is isotropic in the plane of the film and has a Lorentzian-squared line shape. The diffuse component is shown to arise from a random network of two-dimensional Nb domains, with the size of domain related to the in-plane lattice mismatch. By combining these results with x-ray-reflectivity measurements from the thin films, and x-ray-reflectivity and crystal-truncation-rod measurements from the bare substrates, we develop a detailed model of the structure of Nb films on sapphire.