Anisotropic Strain in Rare-Earth Substituted Ceria Thin Films Probed by Polarized Raman Spectroscopy and First-Principles Calculations

Lattice strain in oxygen ion conductors can be used to tune their functional properties for applications in fuel cells, sensors, or catalysis. However, experimental measurements of thin film strain in both in- and out-of-plane directions can be experimentally challenging. We propose a method for measuring strain in rare-earth doped ceria thin films by polarized Raman spectroscopy. We study epitaxial CeO₂ films substituted by La, Gd, and Yb grown on MgO substrates with BaZrO₃ and SrTiO₃ interlayers, where different levels of strain are generated by annealing at distinct temperatures. The films show in-plane compression and out-of-plane expansion, resulting in a lowering from the bulk cubic to tetragonal lattice symmetry. This leads to the splitting of the F_2g Raman mode in the cubic phase to B_2g and E_g modes in the tetragonal lattice. The symmetry and frequency of these modes are determined by polarized Raman in the backscattering and right-angle scattering geometries as well as by first-principal calculations. The frequency splitting of the two modes is proportional to the strain measured by X-ray diffraction and its magnitude agrees with first-principles calculations. The results offer a fast, nondestructive, and precise method for measuring both in- and out-of-plane strain in ceria and can be readily applied to other ionic conductors.