Unified formula for elastic bending of ultrathin bilayer nanofilms

Abstract This study develops a universal formula for predicting the bending and curling of ultrathin nanofilms. The universal formula is derived using a uniform curvature approximation. The proposed formula includes surface elastic and size-dependent surface stress effects. It is valid for anisotropic misfit strain and any type of surface stress configuration and consists of two parts: Timoshenko and Stoney terms. The Timoshenko term is the bending of bilayer films due to lattice mismatch, prestress, or magnetostriction. The Stoney term is due to a surface stress imbalance. Calculations for the prestressed Si/Si and InAs/GaAs bilayer thin films proved the validity of the proposed formula. More importantly, material parameters such as the surface Young’s modulus and size-dependent surface stress are physically reasonable and they fit well with the available experiment. Therefore, the proposed formula can predict the bending of ultrathin nanofilms (a few monolayers) under arbitrary stress loads or misfit strains.