To realize flexible and lightweight battery-free systems, we have investigated piezoelectric vibration energy harvesters (PVEHs) composed of piezoelectric thin-film cantilevers with bimorph or unimorph structures. To optimize dimensional parameters of PVEHs, we derived the theoretical equations of output power on the basis of time-resolved equivalent circuit models that are applicable to various types of vibrations with arbitrary waves. In this study, we have calculated the output power of the PVEHs with the shape of trapezoidal stainless-steel cantilevers on which Pb(Zr,Ti)O3 (PZT) thin films are deposited. A theoretical formula of the output power enables the optimization of not only the geometry of the trapezoidal cantilever, but also electrode length and substrate thickness. We fabricated the PVEHs of PZT thin films on stainless steel foils and confirmed that these calculation results were in good agreement with those of the experiments. The theoretical formula indicated that the output power was maximized when the electrode lengths were 66.7% (= 2/3), 76.2%, and 100% of cantilever length with geometries of the cantilever that were rectangular, trapezoidal (V/W = 1/3), and triangular, respectively, while the thickness of piezoelectric film was about 40% of substrate thickness. The output power increases with decreasing substrate thickness, because the reflection loss is reduced owing to the decrease in resonance frequency. The electrode length at which the reflection loss becomes minimum coincides with that at maximum output power, as confirmed by numerical calculation of the output impedance of PVEHs on Smith charts. On the other hand, we also confirmed that the reflection loss decreased to 0 when the piezoelectric coefficient |e31,f| of the piezoelectric thin films was increased to about 30 C/m2, while the output power was increased at the same time. With these electrical optimum solutions, we will be able to determine the optimal design of PVEHs in specific vibration environments.
Read full abstract