Design and optimization of laminated piezoresistive microcantilever sensors

Microcantilevers-based sensors (MCSs) are a new approach to detecting and measuring physical, chemical, and biological signals in the nano- to femto-range level. Piezoresistive readout systems for MCSs have the advantages of full integration, low cost, ease of use, and the capability of manipulating large arrays. This paper presents a design method for laminated piezoresistive MCSs to obtain optimal performance by optimizing the dimensions of the microcantilevers and the doping concentration of the piezoresistors. Laminated theory was employed to deduce the closed-form solutions to static stress and natural frequency. Expressions for predicting sensitivity and resolution were derived by combining stress distribution with power densities of 1/f noise and Johnson noise. Finite element method (FEM) was performed to verify the theoretical results. The thickness of the laminated MCSs and the doping concentration were optimized by using static analyses and power densities of noise to generate the best sensitivity and resolution. A method based on non-linear programming is given to facilitate the solving process. These methods and some conclusions are also applicable to developing other types of piezoresistive sensors that use laminated structures.