Concurrent evaluation of strain in heteroepitaxial thin films with continuous lattice mismatch spread

We have developed a way to map out concurrently the in-plane lattice constant of a heteroepitaxial thin film with a spatial resolution of 0.1 mm by using concurrent x-ray diffractometer equipped with a convergent x-ray source and two-dimensional detector. Spatial distribution of heteroepitaxial strain is analyzed for a (Ba_xSr_1-x)TiO₃ composition-spread thin film grown on a SrTiO₃ substrate. As x increases, elastic deformation caused by compressive stress due to the lattice mismatch forces the lattice of the film to be coherent with that of the substrate until a critical point of x=0.6, above which the film lattice relaxes. By just taking three snap shots of x-ray diffraction image at a symmetric and two asymmetric diffraction configurations, such useful information inherent in heteroepitaxy can be revealed.