Determination of residual stresses in Pb(Zr0.53Ti0.47)O3 thin films with Raman spectroscopy

The present work uses Raman spectra to measure residual stresses in Pb(Zr0.53Ti0.47)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(Zr0.53Ti0.47)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.