Study of Dynamics in Metallic MEMS Cantilevers—Pull-In Voltage and Actuation Speed

Round 1

Reviewer 1 Report

Dear authors,

I believe this work is instructing, especially for researcher approaching the topic of MEMS switches and pull-in dynamic. However, I believe the paper should be improved.

- In section 2 and 3 you describe the analytical model for the pull-in. However, there is no clear link between section 2/3 and section 4. The analytical model should have a link to the numerical result. Moreover, the pull-in model of a parallel plate is relevant in case of microstructures with translational motion, like MEMS accelerometers. In the case of cantilever, more adequate models exist in literature.

- analytical model to describe the dynamic behavior of a cantilever under the influence of an electrostatic force has been studied in literature, also taking into account the effect of dumping (which is neglected in this work). For instance: https://asmedigitalcollection.asme.org/vibrationacoustics/article/126/3/332/459620/Pull-in-Dynamics-of-an-Elastic-Beam-Actuated-by

The numerical results should be supported with an analytical model or at least commented having in mind an expected trend. A simple description of the output of simulation does not seem a proper optimization procedure.

- Figure 11, it is not clear how the capacitance change is computed in graph (b). If it is a temporal dependent voltage, what is the time scale of this change? Because the change of voltage vs time is in the fs scale, which is much faster than the cantilever dynamics, while the change of capacitance should depend on the mechanical change of the cantilever.

- Concerning the retardation effect. I would assume that at higher voltages correspond higher peak values of the oscillation and therefore faster reaching of the pull-in voltage. Could this be the explanation? Or the increase of peak-value itself is not sufficient to explain the phenomenon. I see very small changes of the actuation voltage, lead to relevant changes of the pull-in time.

- lien 465, you claim a 1us closing time, but you do not report the pull-in voltage. The closing time should be somehow normalized by the pull-in voltage in order to have a fair comparison with other works from literature.

- finally, your final comment shed light on the issue of this optimization. Real device performance is dominated by stress and non-idealities in the system, or by damping related to the geometry and the working environment. Any consideration, based on literature, on the stress and the type of material used could be helpful for the reader.

 

A few typos:

- line 34, I would use “their” instead of “its” as it is referring to the MEMS cantilevers

Line 178 - 3 versus section 4 is prepended

Line 295 - ot revealing ongioing oxidizing,

Line 421 – Tungesten is reported twice

Author Response

Dear reviewer, we thank you very much for your detailed, useful and pertinent criticism of our manuscript. We have modified the manuscript concerning all the points raised. Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

Authors performed a parametric study to compare the pull-in voltage and actuation range of electro-statically actuated MEMS cantilever beam. Paper can be considered for publication after addressing the following comments.

 

(1)    The introduction section is very weak. Add some recent literature bridging the research gap along with applications.

(2)    The details of the equations governing the dynamics and pull-in should be included. See papers:   https://doi.org/10.1016/j.ijmecsci.2010.12.001  https://doi.org/10.1088/0960-1317/25/11/115028

(3)    Improve the quality of the figures.

(4)    Add schematic of beam model.

(5)    Add following closely related recent articles in the reference list:

https://doi.org/10.1007/s00542-018-4046-4

https://doi.org/10.1007/s00542-020-04850-5

Author Response

Dear reviewer, we thank you very much for your detailed, useful and pertinent criticism of our manuscript. We have modified the manuscript concerning all the points raised. Please see the attachment.

Author Response File: Author Response.docx

Reviewer 3 Report

The manuscript titled " Study of Dynamics in Metallic MEMS Cantilevers - Pull-in Voltage and Actuation Speed" is meaningful and can be useful for a better understanding of Dynamics in Metallic MEMS Cantilevers. I recommend accepting the paper after all the following corrections are incorporated by the author.

1. Please improve the introduction section. Kindly add the following in the appropriate place, (page 1, line 35).

https://doi.org/10.1016/j.mejo.2021.105210

10.1088/1361-6439/ac82f8

2. Please shorten the obvious information present in sections 2 and 3.

3. Please include the details of the meshing of the MEMS cantilever design.

4. Please correct the sentence, (page 12, line 350)” When the voltage is less or equal than 22.195 V, the system reveals a damped oscillation tending to a stable state, finally”.

 

It should be written as “Finally, when the voltage is less or equal to 22.195 V, the system reveals a damped oscillation tending to a stable state”.

Author Response

Dear reviewer, we thank you very much for your detailed, useful and pertinent criticism of our manuscript. We have modified the manuscript concerning all the points raised. Please see the attachment.

Author Response File: Author Response.docx