Piezoelectric Film Response Studied with Finite Element Method

It is difficult to measure accurately the piezoelectric constant, d ₃₃, of either a thin or thick film on a substrate, because piezoelectric deformation of a film is small. The measured value of d ₃₃ for the film is often smaller than the value of d ₃₃ for the bulk material. This is partly because of bending of the sample and side clamping of the film. However, we used finite element method (FEM) to simulate common experimental conditions and show that inner local deformation was more significant than either bending or side clamping. Using our FEM results, we propose optimum conditions for making unbiased d ₃₃ measurements.