Influence of substrate deformation on piezoelectric displacement measurement of piezoelectric film

In this work, effect of the substrate deformation on the measured displacement of piezoelectric films by laser interferometer was simulated using finite element analysis (FEA). The piezoelectric displacements measured by single-beam laser interferometer, laser scanning interferometer and double-beam interferometer were simulated. The results suggest that the substrate deformation may easily result in a large measurement error of effective piezoelectric coefficients if only calculating a ratio of the film thickness change obtained from the laser interferometer method over the applied voltage across the film. In order to measure exactly the piezoelectric responses of piezoelectric films, the size of the top electrode on the film should be larger than a critical electrode size and the bottom surface of the substrate should be perfectly clamped on a sample holder to inhabit the substrate bending and substrate deformation.