Size-dependent effects of surface stress on resonance behavior of microcantilever-based sensors

The mass and surface stress loadings in microcantilever-based sensors, caused by surface adsorption of target analytes/biomolecules, change their resonance behavior. Despite numerous efforts, the mechanisms of surface stress impact on the resonance behavior of microcantilevers are not fully understood. This results in substantial discrepancies between theoretically predicted and experimentally measured resonance frequency shifts in wide microcantilevers with aspect ratios (width-to-thickness) larger than 10, commonly found in chemical and biological sensing applications. This also impedes the proper decoupling of the effects of mass and surface stress loading and hinders the development of accurate microcantilever-based sensors. In this work, we attempt to decrease the discrepancy found between theoretical models and experiments by introducing a new mechanism that correlates the nonlinear geometric effects associated with surface stress-induced variation of microcantilever biaxial curvature to its frequency and modal responses, with a correlation intensity that strongly depends on the microcantilever aspect ratio. A new comprehensive analytical model combining the new mechanism with currently available theoretical models is proposed and used to study the resonance behavior of microcantilevers with different deformations and sizes. Using the new model, it is shown that in wide microcantilevers, the theoretically predicted resonance frequency shifts agree with experimental and finite element simulations results within 30% whereas the predictions by other currently available theoretical models are off by more than one order of magnitude. The new model is also used to investigate the modal response of microcantilevers where it anticipates the bending-extensional mode coupling associated with the flexural vibration modes of microcantilevers with a coupling strength that depends on the microcantilever curvature. The presented model is expected to provide a new tool to decouple the effects of mass and surface stress loadings on the resonance behavior of microcantilevers used in chemical and biological sensors.