Analysis of electromechanical boundary effects on the pull-in of micromachined fixed–fixed beams

Abstract

Using a commercial finite-element simulation tool, this work considers some of the electromechanical effects commonly neglected during the analysis of electrostatically actuated fixed–fixed beams. These structures are used in many applications of micromechanical systems, from relay switches and RF resonators to thin film characterization tests, but much of the analytical modelling of the device behaviour disregards the effects of electrostatic field fringing, plane-strain conditions and anchor compliance. It is shown that the cumulative total of these errors can be substantial, and may lead to large discrepancies in the expected operational characteristics of the device. We quantify the influence of these effects on the electrostatic pull-in of fixed–fixed beams, and illustrate some of the limitations of ideal pull-in theory. In order to more accurately predict the pull-in voltage for a real structure, a model is developed that combines ideal case theory with anchor compliance correction factors extracted using finite-element analysis. Three common anchor types (ideal, step-up and cup-style) are characterized. The final model takes account of the compliance of the beam anchors, electrostatic field fringing and plane-strain effects, and agrees well with simulated results.

Extending the tuning range of SWIR microspectrometers

“…The difficulty in designing a device with doubly-supported beam actuators is that analytic or empirical equations relating actuator parameters to tuning ranges have not been reported, and reported tuning ranges of this device type are not consistent, with some reports stating that the [4], others suggesting it is fixed at 40% [5], whilst some suggest a 40% minimum but up to 60% [3].…”

“…Details of the initial calculations of this relationship can be found in [4], where a minimization of potential energy is used to determine the equilibrium that exists between the mechanical restorative forces and electrical driving force, assuming a deformed beam profile of w(x) = w 1 cos 2 (πx/L). The analysis for this work differs from [4] by the inclusion of a fringing field term and a previously discounted strain stiffening term, and makes no a priori assumption about the travel range of the actuator. The result is a relationship between applied voltage, displacement, beam dimensions, material parameters and zero-voltage electrode gap;…”

A novel technique for stress gradient measurement of electrostatic MEM switches and non ideal anchor’s effects

“…However, a number of studies [41,42] report that actual boundary conditions such as a pillar support or a step-up anchor have a significant effect on MEM switches performance and that substantial differences exist between the performances of different types of anchors. This is due to the stress absorption and increased compliance of such non-ideal anchors (Fig.…”

Experimental-Numerical Comparison of the Cantilever MEMS Frequency Shift in presence of a Residual Stress Gradient

“…This assumption is possible due to the high ratio between length and width of the beam [24]. Electrostatic field fringing effect was neglected due to the high ratio between width and air-gap [25], so that implementation of 3-D models was not necessary.…”