Influence of surface effects on size-dependent instability of nano-actuators in the presence of quantum vacuum fluctuations

While surface effects often play an important role in the pull-in performance of electromechanical nano-actuators, only a few works have been conducted that take these effects into account. In this paper, the influence of surface effects including residual surface stress and surface elasticity on the pull-in instability of a cantilever nano-actuator is investigated incorporating the influence of quantum vacuum fluctuations through the Casimir attraction. An analytical closed-form solution is obtained in terms of the modified Adomian decomposition (MAD) series and the obtained results are compared with those in the literature as well as the numerical solution. The instability parameters of the actuator are determined. The results demonstrate that surface effects cause the cantilever nano-actuator to behave as a softer structure. It is found that surface effects become more significant for low values of the actuator thickness as well as high values of the initial gap/width ratio. Furthermore, the influence of surface energy on the detachment length and the minimum gap of the freestanding actuator is discussed. Interestingly, the present MAD solution provides reliable results without the shortcomings of the previously proposed homotopy perturbation method.