Cantilever beam electrostatic MEMS actuators beyond pull-in

Abstract

The operational range of electrostatic MEMS parallel plate actuators can be extended beyond pull-in in the presence of an intermediate dielectric layer, which has a significant effect on the behavior of such actuators. Here, we study the behavior of cantilever beam electrostatic actuators beyond pull-in using a beam model along with a dielectric layer. The results from the simple beam model are validated with 3D simulations performed in CoventorWare TM . Three possible static configurations of the beam are identified over the operational voltage range. We call them floating, pinned and flat; the latter two are also called arc-type and S-type in the literature. We compute the voltage ranges over which the three configurations can exist and the points where transitions occur between these configurations. Voltage ranges are identified where bi-stable and tri-stable states exist. A classification of all possible transitions (pull-in and pull-out as well as transitions we term pull-down and pull-up) is presented based on the dielectric layer parameters. Dynamic stability analyses are presented for the floating and pinned configurations. For high dielectric layer thickness, discontinuous transitions between configurations disappear and the actuator has smooth predictable behavior, but at the expense of lower overall tunability.

Modelling of a charge control method for capacitive MEMS

“…The time required to reach it is very fast Let us use the following normalized quantities [10]:ŷ = y/g,…”

“…For the clamped-clamped beam shown in fig. 2a, both ends are fixed and the boundary conditions are [10]:…”

“…For the cantilever beam, at the clamped end, the boundary conditions are the same as in previous case. For the free end, there are three cases described in [10]. The following one is used in this paper (a flat configuration):…”

“…If n p,0 is computed for a given voltage V 0 , the value of n p can then be calculated for any voltage V using the function f (V ) = n po · p Vo p V [10]. This function will give real values for n p , so these values must be rounded up and n p = round(n po · p Vo p V ) 2 Integers.…”

Robust LMI-Based PID Controller Architecture for a Micro Cantilever Beam

“…In addition, there exist more effects that play a dominant role especially in systems of narrow micro cantilever beams undergoing large deflections (Rottenberg et al, 2007). In such structures, the effects of the fringing fields on the electrostatic force are not negligible because of the non zero thickness and finite width of the beam (Gorthi et al, 2004;Younis et al, 2003). Thus, the incorporation of the fringing field capacitance, while modeling EµCbs is mandatory.…”