Electrostatic Field in Terms of Geometric Curvature in Membrane MEMS Devices

In this paper we present, in a framework of 1D-membrane Micro-Electro-Mechanical- Systems (MEMS) theory, a formalization of the problem of existence and uniqueness of a solution related to the membrane deformation u for electrostatic actuation in the steady-state case. In particular, we propose a new model in which the electric eld magnitude E is proportional to the curvature of the membrane and, for it, we obtain results of existence by Schauder-Tychonoff's fixed point application and subsequently we establish conditions of uniqueness. Finally, some numerical tests have been carried out to further support the analytical results.