Fully Lagrangian Modeling of MEMS With Thin Plates

Abstract

Microelectromechanical systems (MEMS) sometimes use beam or plate shaped conductors that can be very thin-with h=L O(10 02 010 03 ) (in terms of the thickness h and length L of the side of a square pate). Such MEMS devices find applications in microsensors, microactuators, microjets, microspeakers and other systems where the conducting plates or beams oscillate at very high frequencies. Conventional boundary element method (BEM) analysis of the electric field in a region exterior to such thin conductors can become difficult to carry out accurately and efficiently especially since MEMS analysis requires computation of charge densi- ties (and then surface tractions) separately on the top and bottom surfaces of such plates. A new boundary integral equation (BIE)is proposed to handle the computation of charge densities for such high aspect ratio geometries. In the current work, this has been coupled with finite element method (FEM) to obtain the response behavior of devices made of such high aspect ratio structural members. This coupling of electrical and mechanical problem is carried out using a Newton scheme based on a Lagrangian description of both the mechanical and electrical domains.[1603]Index Terms-Aspect ratio, boundary element method (BEM), boundary integral equations, microelectromechanical systems (MEMS), nearly singular integrals, Newton scheme, relaxation scheme, singular integrals, small gap, thin plates, thin shells.

Charge distribution on narrow MEMS beams of nearly square cross‐section

“…This paper complements earlier work on thin plates [19,22] and beams [20]. The 2-D model in [20] is valid for beams of rectangular cross-section with large aspect ratios, while the present work applies to narrow beams of nearly square cross-section.…”

“…Similar work has also been reported recently by Chuyan et al [21] in the context of determining fringing fields and levitating forces for 2-D beam-shaped conductors in MEMS combdrives. A fully coupled BEM/FEM MEMS calculation with very thin plates has been completed recently [22]. See also [23] for an application of the thin plate idea for modelling damping forces on MEMS with thin plates.…”

An investigation of the static and dynamic behavior of electrically actuated rectangular microplates

“…Since in MEMS, structures often undergo large deflection, linear theory becomes inaccurate. Common modeling approaches include lumped mass models and Finite Element Method (FEM) [5,[10][11][12]. Lumped mass models give rough estimate of the response only.…”

“…They compared the results obtained from the FSDT to the results from the linear plate theory and found qualitatively different results. Mukherjee et al [23] and Telukunta et al [12] used a fully Lagrangian approach to analyze the coupled electro-mechanical field of microplate based MEMS. They employed FEM for the analysis of mechanical deformations in the plate and the BEM to obtain the electric field exterior to the plate.…”

Charge distribution on thin semiconducting silicon nanowires

“…Similar work has also been reported recently by Chuyan et al [32] in the context of determining fringing fields and levitating forces for 2-D beam shaped conductors in MEMS combdrives. A fully coupled BEM/FEM MEMS calculation with very thin plates has been completed [33]. See, also, [34] for an application of the thin plate idea for modeling damping forces on MEMS with thin plates.…”