A stationary free boundary problem modeling electrostatic MEMS
Philippe Laurencot (IMT), Christoph Walker (IFAM)
TL;DR
This paper investigates a free boundary problem modeling electrostatic MEMS, establishing stationary solutions for small voltages and connecting the model to the narrow-gap approximation as the aspect ratio diminishes.
Contribution
It proves the existence of stationary solutions for small voltages and justifies the narrow-gap model by showing convergence of solutions as the aspect ratio approaches zero.
Findings
Stationary solutions exist for small voltage values.
Steady states of the free boundary problem converge to those of the narrow-gap model.
The model provides a rigorous mathematical foundation for MEMS device analysis.
Abstract
A free boundary problem describing small deformations in a membrane based model of electrostatically actuated MEMS is investigated. The existence of stationary solutions is established for small voltage values. A justification of the widely studied narrow-gap model is given by showing that steady state solutions of the free boundary problem converge toward stationary solutions of the narrow-gap model when the aspect ratio of the device tends to zero.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.