Buckling Electrothermal NEMS Actuators: Analytic Design for Very Slender Beams

Dixi Liu,Richard Syms

doi:10.3390/micro2010003

Abstract

Analytic approximations are presented for the response of buckling-mode electrothermal actuators with very slender beams with a width-to-length ratio of W/L≤0.001 of the type found in nanoelectromechanical systems (NEMS). The results are found as closed-form solutions to the Euler beam bending theory rather than by an iterative numerical solution or a time-consuming finite element analysis. Expressions for transverse deflections and stiffness are presented for actuators with the common raised cosine and chevron pre-buckled shapes. The approximations are valid when the effects of bending dominate over those of axial compression. A few higher-order approximations are also presented for less slender beams with 0.001≤W/L≤0.01.

Highlights

IntroductionElectrothermal actuators are widely used in microelectromechanical systems Electrothermal actuators widely used in microelectromechanical (MEMS)because a device withare in-plane motion may be constructed simplysystems by etching and because a device with in-plane motion may be constructed by etching and undercutundercutting a mechanical layer to form a suspended structure that is heated by passing a mechanical to form[1].a suspended structure arrangements that is heated by a current ating current between layer the anchorsThe most common arepassing shape bimorph between the anchors [1].actuators.The mostHere, common arrangements are shape and [2,3]and buckling [4,5,6]we focus on the latter, whichbimorph have the[2,3]general buckling [4,5,6]asactuators. we1a.focus onan thearray latter,ofwhich have the generalonarrangement arrangement shown inHere, Figure
We considered alternative approximations for a raised cosine actuator that could be viable for less slender beams when the axial compression term in Equation (8) could not be neglected
We considered the transverse stiffness of a buckling actuator and showed how the slender beam approximation could be used to evaluate this quantity for the raised cosine type

Summary

Introduction

Electrothermal actuators are widely used in microelectromechanical systems Electrothermal actuators widely used in microelectromechanical (MEMS)because a device withare in-plane motion may be constructed simplysystems by etching and because a device with in-plane motion may be constructed by etching and undercutundercutting a mechanical layer to form a suspended structure that is heated by passing a mechanical to form[1].a suspended structure arrangements that is heated by a current ating current between layer the anchorsThe most common arepassing shape bimorph between the anchors [1].actuators.The mostHere, common arrangements are shape and [2,3]and buckling [4,5,6]we focus on the latter, whichbimorph have the[2,3]general buckling [4,5,6]asactuators. we1a.focus onan thearray latter,ofwhich have the generalonarrangement arrangement shown inHere, Figure. Because a device withare in-plane motion may be constructed simplysystems by etching and because a device with in-plane motion may be constructed by etching and undercutundercutting a mechanical layer to form a suspended structure that is heated by passing a mechanical to form[1]. A suspended structure arrangements that is heated by a current ating current between layer the anchors. The most common arepassing shape bimorph between the anchors [1].actuators. The mostHere, common arrangements are shape and [2,3]. Buckling [4,5,6]. We focus on the latter, whichbimorph have the[2,3]. General buckling [4,5,6]asactuators. Focus onan thearray latter,ofwhich have the generalonarrangement arrangement shown inHere, Figure

Objectives

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Results

Conclusion