The problem of pullin instability of a cantilever micro or nanoswitch under electrostatic forces has attracted considerable attention in the literature, given its importance in designing micro and nanoelectromechanical systems (MEMS and NEMS). The nonlinear nature of the problem supports the typical approach that relies on numerical or semianalytical tools to approximate the solution. By contrast, we determine fully analytical upper and lower bounds to the pullin instability phenomenon for a cantilever beam under the action of electrostatic, van der Waals or Casimir forces. In particular, the novel contribution of this works consists in accounting for size effects analytically, in the spirit of surface elasticity, which adds considerable complication to the problem, allowing for a nonconvex beam deflection. Surface energy effects are generally ignored in classical elasticity. However they become relevant for nanoscale structures due to their high surface/volume ratio. Closed form lower and upper bounds are given for the pullin characteristics, that allow to discuss the role of several tuneable parameters. Indeed, the evolution of the cantilever tip deflection is presented as a function of the applied voltage up to the occurrence of pullin and the contribution of van der Waals and Casimir intermolecular interactions is discussed. It is found that intermolecular forces strongly decrease the pullin voltage, while surface elasticity works in the opposite direction and stabilizes the system. The accuracy of the bounding solutions is generally very good, given that upper and lower analytical bounds are very close to each other, although it decreases as the effect of surface elasticity becomes more pronounced. Finally, approximated closedform relations are developed to yield simple and accurate design formulae: in particular, they provide estimates for the minimum theoretical gap and for the maximum operable length for a freestanding cantilever in the presence of the effects of surface elasticity and intermolecular interactions. Results may be especially useful for designing and optimizing NEMS switches.
Bounds to the pullin voltage of a mems/nems beam with surface elasticity / Radi, E.; Bianchi, G.; Nobili, A..  In: APPLIED MATHEMATICAL MODELLING.  ISSN 0307904X.  91:(2021), pp. 12111226. [10.1016/j.apm.2020.10.031]
Bounds to the pullin voltage of a mems/nems beam with surface elasticity
Radi E.;Bianchi G.;Nobili A.^{}
2021
Abstract
The problem of pullin instability of a cantilever micro or nanoswitch under electrostatic forces has attracted considerable attention in the literature, given its importance in designing micro and nanoelectromechanical systems (MEMS and NEMS). The nonlinear nature of the problem supports the typical approach that relies on numerical or semianalytical tools to approximate the solution. By contrast, we determine fully analytical upper and lower bounds to the pullin instability phenomenon for a cantilever beam under the action of electrostatic, van der Waals or Casimir forces. In particular, the novel contribution of this works consists in accounting for size effects analytically, in the spirit of surface elasticity, which adds considerable complication to the problem, allowing for a nonconvex beam deflection. Surface energy effects are generally ignored in classical elasticity. However they become relevant for nanoscale structures due to their high surface/volume ratio. Closed form lower and upper bounds are given for the pullin characteristics, that allow to discuss the role of several tuneable parameters. Indeed, the evolution of the cantilever tip deflection is presented as a function of the applied voltage up to the occurrence of pullin and the contribution of van der Waals and Casimir intermolecular interactions is discussed. It is found that intermolecular forces strongly decrease the pullin voltage, while surface elasticity works in the opposite direction and stabilizes the system. The accuracy of the bounding solutions is generally very good, given that upper and lower analytical bounds are very close to each other, although it decreases as the effect of surface elasticity becomes more pronounced. Finally, approximated closedform relations are developed to yield simple and accurate design formulae: in particular, they provide estimates for the minimum theoretical gap and for the maximum operable length for a freestanding cantilever in the presence of the effects of surface elasticity and intermolecular interactions. Results may be especially useful for designing and optimizing NEMS switches.File  Dimensione  Formato  

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