Determination of residual stresses in Pb(Zr_0.53Ti_0.47)O₃ thin films with Raman spectroscopy

The present work uses Raman spectra to measure residual stresses in Pb(Zr_0.53Ti_0.47)O₃ thin films. Based on thermodynamic analysis, a linear relationship is found between the stress and the square of the Raman frequency in the A₁ [transverse optical₃ (TO₃)] and E [longitudinal optical₃ (LO₃)] modes. We calibrate the linear relationship by measuring the Raman spectra of stressed bulk Pb(Zr_0.53Ti_0.47)O₃ samples. Then, we assess residual stresses in the lead zirconate titanate thin films at different thicknesses and different annealing temperatures. The residual stresses extracted from the A₁(TO₃) mode are consistent with those from the E(LO₃) mode, which are more or less the same as those measured by the x-ray diffraction sin² ψ method.