Leveraging size effects in flexoelectric-piezoelectric vibration energy harvesting

Abstract This chapter explores the potential of vibration energy harvesting from structures leveraging flexoelectricity (i.e., strain gradient-induced polarization) and presents analytical modeling and analysis results for next-generation submicron scale energy harvesters. At such small geometric scales, flexoelectricity, as a gradient effect, enables significant electromechanical behavior even in nonpiezoelectric dielectric materials, while it enhances the electromechanical coupling in piezoelectric ones. In particular, energy harvesting is a potential future application area of flexoelectricity to enable ultra-low-power nanoscale devices by converting vibrations into electricity. The focus of this chapter is first placed on bending vibration of centrosymmetric cantilevers, such as a monolayer STO (Strontium Titanate) cantilever. An electroelastodynamic framework is presented and analyzed for flexoelectric power generation from strain gradient fluctuations in centrosymmetric dielectrics, by accounting for the presence of a finite electrical load across the surface electrodes as well as two-way electromechanical coupling, and capturing the size effect. Following recent efforts on the converse flexoelectric effect in finite samples, the proposed model properly accounts for a thermodynamically consistent, symmetric two-way coupling, i.e., the direct and converse effects. In addition to the electromechanical frequency response functions, the transverse mode flexoelectric coupling coefficient (a direct measure of energy conversion) is obtained analytically; its dependence on the cantilever thickness and a material figure of merit is shown. The modeling framework is then extended to noncentrosymmetric configurations, such as bimorph cantilevers made from Barium Titanate (BTO), to understand the interaction between flexoelectricity and piezoelectricity for different thickness levels from mm-scale to nm-scale, with a focus on resonant energy harvesting. The level of enhancement in the overall electromechanical coupling due to flexoelectricity with reduced thickness is quantified.