A theoretical model for surface-stress piezoresistive microcantilever biosensors with discontinuous layers

A theoretical model for laminated piezoresistive microcantilevers with discontinuous layers is developed for surface stress sensitive biosensors. The microcantilever consists of two supporting layers of silicon dioxide and two silicon piezoresistor strips sandwiched in-between. To address the issue of discontinuity of the piezoresistive layer, the microcantilever is segmented and a closed-form equation is developed for each segment using classical laminated plate theory. A two-dimensional theoretical model for the discontinuous microcantilever is deduced by integrating all the segments and is validated using finite-element-method (FEM) simulation. The model allows the predication of the deflection and the sensitivity of piezoresistive microcantilever biosensors with discontinuous layers and surface stress. The effects of the dimension of the discontinuous piezoresistors on the performance of the microcantilevers are obtained using the segment model. Based on the model, guidelines for design and optimization of surface stress sensitive microcantilever biosensors are given.