Thickness ratio and d33 effects on flexible piezoelectric unimorph energy conversion

Piezoelectric unimorphs are bilayer structures where a blanket piezoelectric film (with top and bottom electrodes) is uniformly laminated on an inactive but flexible substrate. Because of their simple construction and flexibility, unimorphs are widely used as a key element in flexible sensors and actuators. The response of a unimorph is governed by the material properties of the film and the substrate as well as their geometric parameters. For low frequency biological energy harvesting, structural optimization is critical due to the dimensional confinement imposed by curvilinear and deformable bio-tissues. Here we report a comprehensive theoretical framework to investigate the effects of the film-to-substrate thickness ratio on voltage, charge, and energy outputs when the unimorph is subjected to eight different boundary/loading conditions. A broad class of power generators can be designed using such a framework under the assumption that the unimorph length is very large compared to its thickness, where the only dimensionless variable is the film-to-substrate thickness ratio. We show that the analytical and finite element modeling results are in excellent agreement. For not so thin unimorphs, there is non-zero normal stress in the thickness direction (σ3) and d33 can play a significant role in this case. Non-monotonic dependence of voltage and energy generation on thickness ratio has been found in some cases and optimum thickness ratio for unimorph generator can be predicted. When the unimorph is actuated by voltage applied across the piezo-film thickness, non-monotonic maximum deflection versus thickness ratio is also found. This work provides new physical insights on unimorphs and analytical solutions that can be used for the structural design and optimization of unimorphs under different boundary/loading conditions.