## 6 Conclusions  
The influences of material and geometrical properties on pull-in voltage and actuation speed have been studied. Comparing results obtained by numerical simulations with trends predicted from simple analytical formula, a similar tendency can be observed qualitatively. The formula can provide a qualitative tendency, even if only a simple parallel plate actuator is considered and compared to a more complex cantilever actuator. However, for quantitative statements, numerical simulations are required. Based on COMSOL Multiphysics(r) simulations, various results have been obtained for metallic cantilever actuators. If a short actuation time is the goal, the most important dependencies are:  
* Thicker cantilevers are acting faster;
* Shorter cantilevers are acting faster;
* Cantilevers with larger \(E\) are acting faster;
* Cantilevers with smaller \(\rho\) ratio are acting faster; and
* Higher step function voltages make the actuation faster.  
However, if the cantilever thickness is increased, higher actuation voltages are also required, which could be contra-productive, since electrical switching becomes slower with larger actuation voltages.  
Our simulations reveal that reducing actuation time and actuation voltage cannot be obtained at the same time. However, optimizing the material is found to be efficient. Different metals such as Au, Ag, Cu, Ti, Ni, Al, W, Cr, Ta, and Mo as well as artificial metals are studied and compared. Aluminum is found to be an ideal material concerning the improvement with respect to smaller pull-in voltages and shorter actuation times.  
The calculated actuation times are found to be in the same order of magnitude as experimental data from the literature. The trends obtained from numerical simulations are also in agreement with the trends from analytical formula for MEMS cantilevers and MEMS parallel plate actuators.  
Conceptualization, H.H., Q.L. and X.Y.; Methodology, H.H., P.K. and X.Y.; Validation, X.Y., P.K., E.K. and H.H.; Formal Analysis, X.Y., P.K., E.K. and H.H.; Investigation, X.Y. M.S. and S.L.; Writing--Original Draft Preparation, X.Y., H.H.; Writing--Review and Editing, all authors; Visualization, X.Y. and H.H.; Funding Acquisition, H.H. and Q.L. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Deutscher Akademischer Austauschdienst (DAAD): DAAD STIBET Degree Completion Support 2022 (using corresponding author's name but no number); Deutsche Forschungsgemeinschaft (DFG):(grant number: Nos Hi 763/21-1 and Hi 763/19-1); Deutsche Bundesstiftung Umwelt (DBU):(grant number: Nos. AZ23717, AZ20012/189, and AZ35501); and Bundesministerium fur Bildung und Forschung (BMBF):(grant number: Nos. 13N14517 and 13N15740).  
Not applicable.  
The authors would like to thank [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON] for fruitful discussions and technological support; as well as DAAD STIBET Degree Completion Support 2022, DFG (Nos Hi 763/21-1 and Hi 763/19-1), DBU (Nos. AZ23717, AZ20012/189, and AZ35501), and BMBF (Nos. 13N14517 and 13N15740) for financial support. The author [PERSON] acknowledges gratefully the support by the Ph.D. scholarship of DAAD and University of Kassel.  
The authors declare no conflict of interest.