Surface Effects on the Jump-in Instability of Nanomechanical Structures

Surface effects are indispensable for crystalline materials when the characteristic size falls into nanoscale. In this paper, the size-dependent jump-in instability of an ultrathin film, omnipresent in nanoelectromechanical systems, is analyzed by incorporating the effects of surface energies. Based on a nonclassical thin plate theory including surface effects and the thermodynamic energy balance theorem, the jump-in instability mechanism of the film is established to determine the critical separation gap and contact length between the film and the substrate. We found that the dimensionless forms of these two mechanical properties depend on the thickness of the film. When the residual surface stress is ignored, the critical separation gap is affected by the surface elasticity, but the contact length is not. An aluminum film is considered as an illustrative example, for which the effect of residual surface stress is superior to that of surface elasticity.