# Modeling and Design Enhancement of Electothermal Actuators for Microgripping Applications
## 2 Materials and Methods
### Electrothermal Actuator Design Enhancement
The temperature contour plots show that the hot arm (thinner arm) of the U-shaped actuator undergoes higher temperatures than that of the cold arm (thicker arm) at any applied voltage. To verify the operational reliability and the structural resistance to the electrothermal, we analyze the von-Mises stress generation and present the corresponding results when applying 5 V, as shown in Figure 10. The maximum von-Mises stress occurs at the connection between the arms and the anchor. Of interest, the inclusion of perforations results in lower von-Mises stresses at the hinge where the micro-actuator is connected to the supporting anchors. The maximum von-Mises stress when applying 8 V for the non-perforated actuator 1 is 1.36 GPa, whereas, for the perforated actuator 1, it is found to be equal to 0.89 GPa, \begin{table}
\begin{tabular}{c c c} \hline  & **Actuator 1** & **Actuator 2** \\ \hline Single-row square tip displacement & 7.1388\% & 4.5819\% \\ Single-row circular tip displacement & 7.0831\% & 4.533\% \\ Double-row square tip displacement & 14.9470\% & 9.1521\% \\ Double-row circular tip displacement & 14.6848\% & 8.809\% \\ Single-row square tip temperature & \(-\)11.6684\% & \(-\)12.6766\% \\ Single-row circular tip temperature & \(-\)4.73\% & \(-\)5.36\% \\ Double-row square tip temperature & \(-\)10.4046\% & \(-\)5.5351\% \\ Double-row circular tip temperature & \(-\)10.0923\% & \(-\)11.255\% \\ \hline \end{tabular}
\end{table} 
Table 2: Relative changes in tip displacement and temperature of actuator 1 and 2 after adding different cases of perforations when operating at 8 V.  
Figure 9: Comparison between single-row square-perforated and non-perforated electrothermal actuators: (**a**) actuator 1 displacement contour plot, (**b**) actuator 2 displacement contour plot, (**c**) actuator 1 temperature contour plot, and (**d**) actuator 2 temperature contour plot. The upper and lower frames correspond to non-perforated and perforated arms, respectively. that is, 34.5% lower in magnitude. For actuator 2, the maximum von-Mises stress is found to be equal to 1.35 GPa for the microstructure without perforations. On the other hand, when adding the perforations, the maximum von-Mises stress decreases to 1.21 GPa. For both actuators 1 and 2, the maximum von-Mises stresses do not exceed 4 GPa, which is the approximate ultimate tensile strength of polysilicon [48]. The results indicate the safe operation of actuators 1 and 2 without potential mechanical failures. The response time is an essential design consideration, especially for an application requiring an immediate response. To investigate this aspect, we examine the time response characteristics of the electrothermal actuator when subjected to an applied DC voltage. We plot in Figure 10(a),b the time responses of actuators 1 and 2, respectively. We present in Table 3 the characteristics of the time response of both actuators at 8 V. Of interest, the introduction of the single-row square perforations on the surface of the hot arm is observed to speed up the mechanical response. Indeed, the displacement-perforated actuator takes less time to reach the steady-state response. Figure 10: von-Mises stress distribution obtained for: (**a**) non-perforated actuator 1, (**b**) single-row square-perforated actuator 1, (**c**) non-perforated actuator 2, (**d**) single-row square-perforated actuator 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Rise Time (ms)** & **Settling Time (ms)** & **Overshoot** & **Peak** & **Peak Time (ms)** \\ \hline Non-Perforated actuator 1 & 0.6929 & 5.8266 & 0 & 1.7913 & 15 \\ Single-row perforated actuator 1 & 0.5107 & 0.8769 & 0.0366 & 1.9217 & 1.6 \\ Non-Perforated actuator 2 & 0.6277 & 3.6230 & 0.0018 & 3.0901 & 45 \\ Single-row perforated actuator 2 & 0.5530 & 0.9925 & 0.4759 & 3.2464 & 1.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Time response characteristics of single-row square-perforated and non-perforated actuators 1 and 2.