# A Review of MEMS Scale Piezoelectric Energy Harvester
## 2 Research Progress of PEH
### Research and Improvement of Piezoelectric Modes
#### 2.3.1 Piezoelectric Energy Harvesters in \(d_{31}\) and \(d_{33}\) Mode
The experiments showed that the maximum output power was 2.15 \(\upmu\)W for the PEH in \(d_{31}\) mode, while it reached 1.71 \(\upmu\)W in \(d_{33}\) mode. The reason the \(d_{31}\) mode device has higher output power than the \(d_{33}\) mode device is that the matching impedance in the \(d_{31}\) mode device is lower relatively. Besides, there exists a \"dead area\" under the electrode in the \(d_{33}\) device, which causes it a lower efficiency [51]. However, the proportion of \"dead area\" under the electrode can be reduced by altering the electrode width and spacing. The simulation result showed that, when the interdigital electrode width of the \(d_{33}\) mode PEH was lower than 2 \(\upmu\)m and the interdigital electrode spacing was 8-20 \(\upmu\)m, its output power was higher than that of \(d_{31}\) mode. Considering that the output voltage of the \(d_{33}\) mode device was higher, the generated electricity through the rectifier circuit had less loss. In 2013, [PERSON] [52] mentioned two models to calculate the relative permittivity (\(\varepsilon_{r}\)) of the PEH film in \(d_{33}\) mode in his research. One calculated an approximation of the permittivity (\(\varepsilon_{rIDE(approx. )}\)) without considering the \"dead area\" effect. The other calculated a more accurate solution  
Figure 4: Poling direction of: (**a**) \(d_{31}\) mode; and (**b**) \(d_{33}\) mode devices in cross section. Figure 3: Schematic of the PEHs for: (**a**) a parallel plate electrode system; and (**b**) an interdigital electrode system. Reprinted by permission from [PERSON] et al., IEEE Trans. Ultrason. Eng. 59, 1624 (2012). Copyright 2012 IEEE. (\(\varepsilon_{r,IDE}(Georgian)\)) by using conformal mapping method with Schwarz-Christoffel transformation [53], \(\varepsilon_{r,IDE}(Georgian)\) could be derived by multiplying \(\varepsilon_{r,IDE}(approx. )\) and the factor \(\alpha\), which was decided by the thickness of the piezoelectric material, the finger width and gap of the interdigital electrodes. As the thickness of the piezoelectric material decreased and the finger gap of the interdigital electrodes increased, \(\alpha\) was close to 1, which indicated that the proportion of the \"dead area\" in piezoelectric material reduced. In addition, the finger width had little impact on \(\alpha\). If taking no account of \"dead area\" effect, the PEHs in \(d_{33}\) mode could generate 23% more electrical energy, with an order of magnitude higher voltage. Besides, the \(d_{33}\) mode device had about four orders of magnitude lower leakage currents compared with the \(d_{31}\) mode device, indicating lower power loss inside the piezoelectric material for this kind of electrodes. Aiming at solving the problem that the piezoelectric material of the PEHs in \(d_{33}\) mode is not completely polarized, [PERSON] et al. [54] proposed a kind of interdigital electrode running through piezoelectric layer rather than on surface for PEHs in 2015. The output power of the newly-designed energy harvester and the common \(d_{33}\) mode PEH were calculated under the same conditions. The result showed that when the electrode spacing was 8-16 \(\upmu\)m, the common \(d_{33}\) mode PEHs generated more power. However, when the electrode spacing exceeded 16 \(\upmu\)m, the output power of the newly-designed energy harvester was ideal. As the thickness of the piezoelectric material has a great influence on the PEH's performance in \(d_{33}\) mode, the technology of fabricating the cantilever beam of the PEH worth exploring. In 2017, [PERSON] et al. [55] presented a micro-fabricated flexible and curled cantilever. By replacing ceramic cantilever with thin polyimide film, the energy harvester had a lower resonant frequency. In addition, the PZT/PbTiO\({}_{3}\) thin film was deposited by using sol-gel spin-coating method, which reduced the thickness of piezoelectric material.