# A Review of MEMS Scale Piezoelectric Energy Harvester
## 2 Research Progress of PEH
### Research Progress of Piezolectric Materials  
Piezoelectric material is a class of solid materials that can accumulate electric charge in response to applied mechanical stress. In 1880, [PERSON] and [PERSON] [26] discovered the piezoelectric effect of quartz crystals. Since then, more piezoelectric materials have been found. These crystals have the characteristic of low crystal symmetry. The crystal is also prone to polarization. Usually at elevated temperatures, polycrystalline ferroelectric materials may be brought into a polar state by applying a strong electric field [27], as shown in Figure 2. For a single crystal, it does not contain domains and is said to be in a single-domain or monodomain state. The constitutive equations for piezoelectric material, which describe the direct piezoelectric effect, are shown in Equations (5) and (6):  
\[\delta=\sigma/Y+dE \tag{5}\]  
\[D=\varepsilon E+d\sigma \tag{6}\]  
where \(\delta\) represents the mechanical strain, \(\sigma\) the mechanical stress, \(Y\) the Young's modulus, \(D\) the charge density, \(E\) the electric field, \(\varepsilon\) the dielectric constant, and \(d\) the piezoelectric constant. Figure 1: Schematic of spring–mass–damping system. Figure 2: A polycrystalline ferroelectric is before and after poling. Reprinted by permission from [PERSON]. Equations (5) and (6) are coupled together via the piezoelectric coupling term \(d\). They provide the mechanism for power generation from vibrations. The voltage generated by the piezoelectric material is proportional to the distance between electrodes \(L\), voltage constant \(g_{ij}\) and stress \(\sigma_{xx}\) as shown in Equation (7) [28]. The voltage constant \(g_{ij}\) can be derived from Equation (8), where \(d_{ij}\) is the piezoelectric constant, \(\varepsilon_{r}\) is the relative dielectric constant and \(\varepsilon_{0}\) is the permittivity of vacuum [29]. \[V_{oc}=\sigma_{xx}g_{ij}L \tag{7}\]  
\[g_{ij}=\frac{d_{ij}}{\varepsilon_{r}\varepsilon_{0}} \tag{8}\]  
From Equations (7) and (8), output power is affected by piezoelectric material parameters, the voltage constant \(g_{ij}\) and the piezoelectric constant \(d_{ij}\). Therefore, the \(d\)-\(g\) product is an important characteristic of piezoelectric materials. Piezoelectric materials are roughly divided into inorganic and organic matters. At present, the common inorganic piezoelectric materials are piezoelectric single crystals and piezoelectric ceramics (polycrystalline). Organic piezoelectric materials generally refer to piezoelectric polymers such as polyvinylidene fluoride (PVDF) [30]. In recent years, some organic nanostructures through special processing, such as nanotubes [15], nanowires [16], and nanoparticles [17], are also found to have piezoelectric activity. Among these materials, nanostructures with high effective piezoelectric constant are used for energy harvesting in nanoscale PEHs. Recent reports have shown high conversion efficiency in nanoscale PEHs. Besides, nanostructures are lead-free and environment friendly. For larger scale PEHs, piezoelectric ceramics is the largest material group for piezoelectric devices, while piezoelectric polymer demonstrates fastest growth due to its light weight and small size. In addition, the piezoelectricity and dielectric constant of the piezoelectric single crystal are lower than that of piezoelectric ceramics. By contrast, although the piezoelectric polymer has low density, low impedance, the strain constant and the piezoelectric constant is relatively low. At present, some people are trying to apply piezoelectric polymer to nanoscale PEHs [31; 32]. Comparing the above two materials, piezoelectric ceramics have some advantages: (1) the piezoelectric constant and dielectric constant are higher; (2) higher plasticity of the shape; and (3) material composition is easy to be controlled, thereby improving its prospects. However, it should be noted that the stability and energy consumption of the piezoelectric materials still need to be further studied.