Surface stress-induced change in overall elastic behavior and self-bending of ultrathin cantilever plates

Abstract

In this letter, the dominant role of surface stress and surface elasticity on the overall elastic behavior of ultrathin cantilever plates is studied. A general framework based on two-dimensional plane-stress analysis is presented. Because of either surface reconstruction or molecular adsorption, there exists a surface stress and a surface elasticity imbalance between top and bottom surface of the cantilever. The surface elasticity imbalance creates an extra bending-extensional coupling which has not been taken into account previously. This leads to a modified extensional stiffness, bending stiffness and bending-extensional coupling stiffness. Due to the surface stress imbalance, an extended Stoney's formula for self-bending of ultrathin cantilevers is derived.