Mechanics of nanoscale beams in liquid electrolytes: beam deflections, pull-in instability, and stiction

摘要

The pressure between two parallel planar surfaces at equal electric potentials is derivedusing the modified Poisson-Boltzmann (MPB) equation to account for finite ion size.The effects of finite ion size are presented for a z:z symmetric electrolyte and comparedwith the pressure derived by the classical Poisson-Boltzmann (PB) equation. Thepressures predicted by the two models differ more as the bulk ion concentration, surfacepotential, and ion size increase. The ratio of the pressures predicted by the two models ispresented by varying the ion concentration, surface potential, ion size and distance ofseparation. The ratio of pressures is relatively independent of the distance of separationbetween the two surfaces.An elastic beam suspended horizontally over a substrate in liquid electrolyte issubjected to electric, osmotic, and van der Waals forces. The continuous beam structure,not a discrete spring, which is governed by four nondimensional parameters, is solvedusing the finite element method. The effects of ion concentration and electric potentialsto the pull-in instability are especially focused by parametric studies with a carbon nanotube cantilever beam. The pull-in voltage of a double-wall carbon nanotubesuspended over a graphite substrate in liquid can be less than or greater than the pull-involtage in air, depending on the bulk ion concentration. The critical separation betweenthe double-walled carbon nanotube (DWCNT) and the substrate increases with the bulkion concentration. However, for a given bulk ion concentration, the critical separation isindependent of the electric potentials. Furthermore, the critical separation isapproximately equal in liquid and air.Stiction, the most common failure mode of the cantilever-based devices, isstudied in a liquid environment, including elastic energy, electrochemical work done,van der Waals work done and surface adhesion energy. We extend the classical energymethod of the beam peeling for micro-electro-mechanical systems (MEMS) in the air toan energy method for nano-electro-mechanical systems (NEMS) in liquid electrolyte.We demonstrate a useful numerical processing method to find the parameters to free thestiction of the beams and to obtain the detachment length of the beams.