The piezoelectric properties of lead zirconate titanate (PZT) thin films deposited on thick silicon substrates and thin silicon membranes were investigated using optical interferometry. The effect of the geometrical constraints and clamping effects on the piezoelectric response is discussed. The study of the dielectric permittivity and the loss as a function of the amplitude of the alternating electric field reveals that extrinsic contributions to the dielectric permittivity become active at large fields. The DC electric field has the effect of freezing out the extrinsic contributions. The influence of the dielectric loss on the piezoelectric properties is discussed.