General Theory of Nano Trilayer Film Bending

Abstract

Multilayer sheets or films have many potential applications in micro-nanoelectromechanical systems. When surface and scale effects are not considered, the bending of multilayer film systems can theoretically be discussed by the classical Stoney formula or Timoshenko formula. When the system has anisotropic surface stress or mismatch strain, the four-parameter bending model proposed by Narsu et al. can be used. However, if the thickness of the film is several nanometers and the bending radius of curvature is less than 1micron, the existing theoretical model is no longer applicable. For this reason, a bending formulation for the nanomulti-layer film system is derived and the structure of the multilayer film is optimized in this paper.