# Modeling and Design Enhancement of Electothermal Actuators for Microgripping Applications
## 2 Materials and Methods
### Electrothermal Actuator Model Validation  
To validate the computational model implemented using the COMSOL Multiphysics FEA tool, the results obtained are compared against the previously published numerical and experimental results reported in [12]. Figure 5 shows the variations of the tip displacement and temperature with the applied DC voltage obtained for actuators 1 and 2, respectively. The simulation results for actuator 1 agree with the simulation results shown in the literature [12]. Figure 5a reveals the relationship between the voltage, tip displacement, and temperature of the actuator 1. In Figure 5a, the tip displacement is approximately zero at 1 V. On the other hand, the tip displacement and temperature increase with the applied voltage following a nonlinear trend. At 9 V, the tip temperature observed was 1255.65 \({}^{\circ}\)C, which is close to the approximate value of 1256.73 \({}^{\circ}\)C reported in the literature for actuator 1 subjected to the same voltage. The tip displacement obtained when setting the voltage at 9 V was 2.269 \(\upmu\)m, whereas the work in the literature reported an approximate value of 2.443 \(\upmu\)m. This slight deviation in results is mostly associated with the difference in the boundary conditions. Regardless, the present model demonstrates a great capability to predict the thermal and mechanical responses of the actuator. In Figure 5b, the variations of the temperature and the tip displacement of actuator 2 are plotted with the applied voltage and compared to their numerical counterparts reported in the literature [12]. Similar to the previous case, the two sets of data show good agreement. At 9 V, the temperature and tip displacement values obtained from the present simulations were 1353.77 \({}^{\circ}\)C and 3.911 \(\upmu\)m, respectively, which slightly differ from the values of 1249.66 \({}^{\circ}\)C and 3.62 \(\upmu\)m, obtained in [12]. The slight discrepancy observed in the tip displacement can be associated with the boundary conditions imposed in the simulations. Fixed constraints are considered. However, the actual actuator may have imperfect clamping. Figure 4: Variations of the tip displacement and temperature with the number of mesh elements at 5 V: (**a**) actuator 1 and (**b**) actuator 2. To further verify the present computational model, the simulation results are compared against their experimental counterparts obtained by [PERSON] and [PERSON] [12]. The actuator is fabricated using three-level Silicon-on-Insulator (SOI) mask patterning. The top surface of the silicon layer is annealed with Phosphosilicate Glass (PSG) material for 1 h in Argon. Next, a stack of 25 nm chrome and 500 nm Gold are patterned on the structure. Finally, Deep Reactive Ion Etching (DRIE) is used to etch the front surface of the actuator [12]. The material selected for the microgripper is polysilicon due to its physical and chemical properties, which make it a versatile material in accomplishing structural, mechanical, and electrical tasks in the fabrication of a microgripper [12]. It also gives a similar performance as the material used in the previous experimental work [12]. Figure 5(a),b shows a comparison between the numerical (FEM model), analytical (as given by Equation (11)), and experimental results for actuator 1 and actuator 2, respectively. A good agreement is obtained when comparing the analytical solution to the experimental and simulation results for actuator 1. However, the analytical solution for actuator 2 largely deviates from the experimental and simulation results. This discrepancy is mostly due to the change in the mechanical and electrical properties of the polysilicon at the micro scale which is caused by the dimensional change of the cold arm of the electrothermal actuator. We recall that actuator 2 has a thicker arm (larger \(W_{c}\)) in comparison to actuator 1. Any impurity in the constituent material (assumed perfectly homogeneous) will be magnified when enlarging the system.