Clamping of piezoelectric thin films on metallic substrates: influence on the effective piezoelectric modulus d33

The piezoelectric properties of ferroelectric thin films can strongly be influenced by mechanical clamping on the surrounding media, i.e. the substrate, the electrode as well as the surrounding unpoled film. The influence of these effects on the measurement of the piezoelectric modulus d₃₃ is investigated. A Finite Element Method (FEM) modeling using coefficients of bulk materials for PZT at the morphotropic phase boundary shows that for common film and substrate dimensions the measurable piezoelectric modulus d_33,m can reach only 50% of the value under free conditions. The films can be regarded as perfectly laterally clamped. This is caused mainly by the clamping on the substrate. The contribution of the substrate to the total change of sample thickness is calculated. The calculations are compared to experimental results from PZT (53/47) films prepared on metallic substrates