Quantification of the surface stress in microcantilever biosensors: revisiting Stoney's equation

Microcantilever biosensors in the static operation mode translate molecular recognition into a surface stress signal. Surface stress is derived from the nanomechanical cantilever bending by applying Stoney's equation, derived more than 100 years ago. This equation ignores the clamping effect on the cantilever deformation, which induces significant errors in the quantification of the biosensing response. This leads to discrepancies in the surface stress induced by biomolecular interactions in measurements with cantilevers with different sizes and geometries. So far, more accurate solutions have been precluded by the formidable complexity of the theoretical problem that involves solving the two-dimensional biharmonic equation. In this paper, we present an accurate and simple analytical expression to quantify the response of microcantilever biosensors. The equation exhibits an excellent agreement with finite element simulations and DNA immobilization experiments on gold-coated microcantilevers.