Polarization-dependence of the Raman response of free-standing strained Ce_0.8Gd_0.2O₂ membranes

Square-shaped Ce_0.8Gd_0.2O₂ (GDC) membranes are prepared by microstructuring techniques from (111)-oriented, polycrystalline GDC thin films. The strain state of the membranes is investigated by micro-Raman mapping using polarized excitation light. Using circularly polarized excitation, the maps of the Raman shifts reveal circular contour lines in concordance with the quadratic shape of the membrane and with optical investigations of the residual strain distribution. In contrast, asymmetric contours of the maps of the Raman shifts exhibiting a two-fold symmetry are found when using linearly polarized excitation. The contour plots for a linear polarization perpendicular or parallel to the local curvature are rotated by 90°. This behavior is caused by the polarization dependence of three overlapping Raman modes arising from the splitting of the triply degenerate F_2g mode due to strain. The contribution of their Raman intensity to the overall Raman signal depends on the measurement geometry and the polarization of the incoming and scattered light. Varying the polarization of the incoming excitation light results in different averaging of the Raman-active modes contributing to the broad Raman signal observed. These results clearly demonstrate that polarization-dependent Raman measurements have the potential to yield additional insight into the local strain distribution in free-standing oxide membranes.