Mathematical Modeling of Microcantilever-Based Biosensor as a Nonuniform Rectangular Plate for Detection of Ultrasmall Adsorbed Mass

Development of label-free, highly sensitive biological sensors has been enabled due to nanomechanical advancements. Ultrasmall adsorbed biological species could be detected by means of transducing molecular recognition into some physical property. Microcantilever (MC) biosensors have received tremendous attention for offering cost-benefit, label-free and highly sensitive detection tool. Although there are a lot of studies investigating microcantilever-based sensors and their biological applications, a comprehensive mathematical modeling and validated experimentally of such devices providing a closed form mathematical framework is still lacking. In almost all of the studies a simple lumped-parameters model has been proposed. Other than that, MCs have been treated as Euler Bernouli beam. However, in order to have a precise biomechanical sensor, derivation of a comprehensive model is required in an effort to describe all the phenomena and dynamics of the biosensor which can lead to better design of MC. Therefore, in this study, extensive distributed-parameters modeling framework is proposed for piezoelectric microcantilever-based biosensor treating the MC as a non-uniform rectangular plate. Free vibration and force vibration studies were performed and simulated for the purpose of detection of ultrasmall mass. It was shown that plate modeling predicts the real situation with a degree of precision of 99.99%.