Analytical modeling of static behavior of electrostatically actuated nano/micromirrors considering van der Waals forces

In this paper, the effect of van der Waals (vdW) force on the pull-in behavior of electrostatically actuated nano/micromirrors is investigated. First, the minimum potential energy principle is utilized to find the equation governing the static behavior of nano/micromirror under electrostatic and vdW forces. Then, the stability of static equilibrium points is analyzed using the energy method. It is found that when there exist two equilibrium points, the smaller one is stable and the larger one is unstable. The effects of different design parameters on the mirror’s pull-in angle and pull-in voltage are studied and it is found that vdW force can considerably reduce the stability limit of the mirror. At the end, the nonlinear equilibrium equation is solved numerically and analytically using homotopy perturbation method (HPM). It is observed that a sixth order perturbation approximation can precisely model the mirror’s behavior. The results of this paper can be used for stable operation design and safe fabrication of torsional nano/micro actuators.