Elastic-strain tensor and inhomogeneous strain in thin films by X-ray diffraction

Elastic residual and inhomogeneous defect-related strains are very important parameters when considering thin-film and microelectronics device properties and operation. In regard to the residual strain/stress modeling, we describe a novel approach to model diffraction line shifts caused by elastic residual or applied stresses in textured polycrystals. The model yields the complete texture-weighted strain and stress tensors as a function of crystallite orientations, the so-called weighted strain orientation distribution function. In the second part, we present an extension to the phenomenological thermodynamic theory for ferroelectrics. It includes the contribution of both residual-elastic lattice-misfit strain and inhomogeneous strain caused by lattice defects. The model yields correction terms for dielectric and ferroelectric quantities in terms of both elastic misfit strain and defect-related strain that was successfully applied to the pristine, W and Mn 1% doped Ba_0.6Sr_0.4TiO₃ epitaxial thin films grown on the LaAlO₃ substrate.