Pull-in instability of multi-phase nanocrystalline silicon beams under distributed electrostatic force

Abstract

The effects of the material structure on the pull-in instability of nano-actuated beams made of nanocrystalline silicon (Nc–Si) and subjected to a distributed electrostatic force are investigated. Nc–Si is represented as a multi-phase material composed of nano-sized grains, nano voids, and an amorphous-like interface to consider the effects of the interface, grain size, porosity, and the inhomogeneities surface energies on the elastic properties of the composite material. To this end, a size-dependent micromechanical model is developed for multi-phase materials considering the inhomogeneities surface energy effects. An atomic lattice model is also proposed to estimate the elastic modulus of the interface of NcMs. Due to the intensive decrease in the beam’s size, the effects of the grain rotations on the beam strain energy and hence on its rigidity are captured and represented using the modified couple stress theory. Considering all these effects and using Euler–Bernoulli beam theory, the governing equation is derived. A finite difference-based solution is used to determine the pull-in voltage of the actuated beams. A parametric study is then performed to reveal the effects of the porosity, interface, surface energy, and grain rotations on the pull-in instability behavior of actuated nano-beams.