Approximating the effect of the Casimir force on the instability of electrostatic nano-cantilevers

Abstract

In this paper, the homotopy perturbation method (HPM) is used to investigate the effect of the Casimir force on the pull-in instability of electrostatic actuators at nano-scale separations. The proposed HPM is employed to solve nonlinear constitutive equations of cantilever beam-type nanoactuators. An analytical solution is obtained in terms of convergent series with easily computable components. Basic design parameters such as critical cantilever tip deflection and pull-in voltage of the nano-cantilevers are computed. As special cases of this work, freestanding nanoactuators and electrostatic micro-actuators are investigated. The analytical HPM results agree well with numerical solutions and those from the literature.

The role of virtual photons in nanoscale photonics

“…In fact it is now recognized that the Casimir effect is the primary cause of stiction or pull‐in instabilities, i.e . the moving parts of the device become to some extent adhesive to the fixed electrode, leading to lose of functionality . Alternatively, exploiting the effect, nanoelectromechanical switches requiring the Casimir force to act as the actuator have been proposed .…”

Untitled

“…In fact it is now recognized that the Casimir effect is the primary cause of stiction or pull-in instabilities, i.e. the moving parts of the device become to some extent adhesive to the fixed electrode, leading to lose of functionality [33][34][35][36][37][38][39][40][41][42][43]. Alternatively, exploiting the effect, nanoelectromechanical switches requiring the Casimir force to act as the actuator have been proposed [44,45].…”

On the design of a robust adaptive tracking control scheme for a nano-cantilever beam

“…For the nonlinear system of the nanobeam as described in Equations (7,8), when the robust adaptive control law (22) and the parameter adaptive law (21) are applied to the tracking control, the output tracking error e 1 satisfies the H ∞ tracking performance if any positive constant ε for any initial condition that satisfies V < ε.…”

“…The resulting energy density difference, gives rise to the attractive Casimir pressure between the plates. The fundamental notion of a force due to to quantum fluctuations is quite general and applies to other geometries [7][8][9]. The force between the interacting bodies is sometimes repulsive, depending on the geometry of the system [10].…”