Influence of residual stress on diffusion-induced bending in bilayered microcantilever sensors

The influence of residual stress on diffusion-induced bending in bilayered microcantilever sensors has been analyzed under the framework of thermodynamic theory and Fick's second law. A self-consistent diffusion equation involving the coupling effects of residual stress and diffusion-induced stress is developed. Effects of thickness ratio, modulus ratio, diffusivity ratio and residual stress gradient of film and substrate on the curvature of bilayered cantilever are then discussed with the help of finite difference method. Results reveal that the curvature of bilayered cantilever increases with decreasing the diffusivity ratio and modulus ratio of substrate to film at a given time. Case study of the polysilicon/palladium hydrogen sensor has been finally carried out using the above developed bending theory.