Theoretical analysis of strong-axis bending mode vibrations for resonant microcantilever (bio)chemical sensors in gas or liquid phase

The frequency stability, sensitivity, and limit of detection of a coated-cantilever chemical sensor operating in a dynamic mode are mainly determined by its mechanical quality factor. While a coated-cantilever operating in the gas phase exhibits a large reduction in quality factor, immersion in liquids results in an even greater reduction in the Q-factor due to displaced fluid mass and losses in the surrounding liquid. In this paper, two different bending vibration modes are studied in order to minimize both the losses induced by the surrounding medium and the displaced fluid mass, thus increasing the quality factor and sensitivity and improving (decreasing) the detection limit of the biochemical microsensor. The two particular vibration modes both involve "first mode" flexural vibrations (but in different orthogonal planes), and are referred to herein as "weak-axis bending" (WAB) and "strong-axis bending" (SAB). Using Sader's model, the expressions for both the quality factor and the resonant frequency are analyzed for the case of immersion in a viscous fluid. The results indicate that the strong-axis bending mode has certain advantages over the more conventional weak-axis mode in enhancing the sensor sensitivity and detection limit, even for the case in which the WAB and SAB devices have identical resonant frequencies.