Unified Formula for Elastic Bending of Ultrathin Bilayer Nanofilms

A universal formula for bending/curling of ultra-thin nanofilm is derived within the uniform curvature approximation. Current model includes the surface elastic effect and the size dependent surface stress effect reasonably. The derived formula is valid for anisotropic misfit strain and any types of surface stress configuration, and this formula consist of two terms, respectively, the Timoshenko term and the Stoney term. The Timoshenko term is bending of bilayer films due to the lattice mismatch, prestress or magnetostriction etc., and the Stoney term is due to the surface stress imbalance. Therefore, current model can be used to describe the bending or curling characteristics of free standing single layer and bilayer thin films. The model calculations for prestressed Si/Si and InAs/GaAs bilayer thin films proved the validity of current model. More importantly, the materials parameters such as surface Young’s modulus, size dependent surface stress are physically reasonable and fit well with available experiment. Therefore, current model can make good prediction to bending of ultrathin nanofilms (a few monolayers) with arbitrary stress load or misfit strains.