# A Review of MEMS Scale Piezoelectric Energy Harvester
## 3 Analysis and Summaries  
The core of the piezoelectric energy harvester is the piezoelectric material, and recently the common piezoelectric material is piezoelectric ceramics. Piezoelectric ceramics develop towards the lead-free direction while improving the performance. Many researchers have used synthetic materials to optimize and enhance the piezoelectric ceramics. This means that traditional piezoelectric ceramics are composited with some new material with high piezoelectric constant and dielectric permittivity. The piezoelectric material has a promising future because of the diversity of composite materials. Another way to improve the performance of piezoelectric materials is doping. Doping can improve the Curie temperature and the quality of grain growth, but \(d_{33}\) and \(K_{p}\) will be slightly reduced. Furthermore, it will not only affect the dielectric permittivity and piezoelectric constant, but also its lattice constant and phase. The materials are mainly prepared by mixed oxidation, solid-state reaction sintering techniques and SPS. The sintering temperatures of these methods are various. The SPS has many characteristics such as low sintering temperature, low Curie temperature and high cost. By contrast, the traditional method is low cost, but the quality of the prepared material is worse than SPS. The improvement of material properties can directly affect the overall efficiency and stability of the system so the study of piezoelectric materials is a way to enhance the PEH.  
\(d_{31}\) and \(d_{33}\) are two common piezoelectric modes. The \(d_{31}\) polarization direction and stress direction of piezoelectric materials are perpendicular to each other, while the polarization direction and stress direction of piezoelectric materials are parallel to each other for \(d_{33}\). The output power in \(d_{33}\) is generally lower than that in \(d_{31}\) because of \"dead area\" effect. However, by optimizing the electrode width and electrode spacing in \(d_{33}\), the \"dead area\" proportion will be reduced and its output power can be greatly enhanced. Therefore, the output power in \(d_{33}\) mode has larger scope to be enhanced. Moreover, higher output voltage reduces the energy loss in rectifier circuit. Compared to the \(d_{31}\) and \(d_{33}\) modes, PEHs in \(d_{15}\) mode can generate higher output power. However, they are less applied due to the complexity of fabrication.  
To maximize the output power, the resonant frequency of the PEHs needs to be lowered to match the excitation frequency. A commonly used method is to change the shape of cantilever beam. As shown in Table 2, using S-shaped, zigzag or wavy cantilever beam effectively reduces the stiffness coefficient and thus lowers the resonant frequency of the PEHs.  
Frequency up-conversion is a hot method applied in PEHs in recent years. Its basic principle is to apply the external excitation of high amplitude and low frequency on PEHs of high frequency. Current research shows that the frequency up-conversion method can improve the output power of the PEHs. However, it can cause some energy loss because the implementation process of this method involves collisions. Therefore, its conversion efficiency is still a challenge.  
At present, expanding the bandwidth of the PEHs is a popular research method to solve the random changes of external incentive. For the traditional cantilever PEH, the expansion of its bandwidth has the following methods: (1) restricting the displacement of the proof mass; (2) adding the spring force or magnetic force to construct a nonlinear system; and (3) imposing a certain preload to the mass. Although restricting the displacement of the mass or applying a preload to the mass can somewhat expand the operating frequency of the PEH, the maximum output power and output voltage of the PEH are also significantly reduced. The use of nonlinear system can expand the bandwidth of the energy harvester and ensure the output power as well as output voltage.