Strain Determination in Epitaxic Films of Materials of Orthorhombic Symmetry by High-Resolution X-ray Diffraction

In this paper, we derive the most general expression of the X-ray incidence parameter. The new expression of the incidence parameter allows us to determine the lattice deformation of strained epitaxic films of materials of orthorhombic symmetry by high-resolution X-ray diffraction. The strain status of epilayers can be evaluated by using layer and substrate peaks of different reflections. In particular, the lattice mismatch (strain fields) between substrate and epilayers can be determined even if the heterostructure is made of materials of different crystallographic symmetry, e.g. high-T_c perov-skite superconductor thin films deposited on SrTiO₃. In addition, the new expression of the incidence parameter takes into account the most general uniform lattice deformation of the epilayer crystal unit cell. Furthermore, it should be noted that the new expression is particularly useful if the angular separation Δθ between layer and substrate Bragg peaks is so large that the more conventional first- or second-order approximations in Δθ of the incidence parameter are not valid.