The optimal planform of a cantilever unimorph piezoelectric vibrating energy harvester (PVEH) with a device-layer edge block

The study considers the optimal planform of a cantilever piezoelectric vibrating energy harvester (PVEH) with an edge block that is patterned only in the device layer. The optimal response of a PVEH is achieved when the strain in the piezoelectric layer is uniform. It is possible to design the planform of the PVEH such that when it vibrates at a given frequency of excitation vibrations, the mode shape results in a uniform strain in the piezoelectric layer. Another design choice is the size of the edge block. The size of the edge block affects the natural frequency of the structure and hence may be adjusted such that the natural frequency of the PVEH matches the frequency of the excitation vibrations. Previous studies considered the optimal planform of a PVEH with a massive edge block that is patterned in both the device and handle layers of the wafer. For this case, it was found that the optimal planform of such a device is trapezoidal. However, there is another class of PVEH devices in which the edge block is patterned only in the device layer (i.e., a device-layer edge block). In the present study, we show that the optimal planform for such a PVEH is defined by Bessel functions, and we demonstrate the predictive capabilities of our analytic model by comparison to results of finite-element simulations.