Exploiting nonlinearity to enhance the sensitivity of mode-localized mass sensor based on electrostatically coupled MEMS resonators

An ultrasensitive mass sensor is proposed by combining the benefits of mode localization and nonlinear dynamics in two clamped-clamped microbeams of different lengths. The coupling electrostatic stiffness between the two resonators can be tuned for modulating sensitivity, and the actuation voltage applied to the shorter beam can be adjusted in order to overcome mechanical defects such as geometric asymmetry. The analytical dynamic model considering the quadratic and cubic nonlinearities is established and solved by the asymptotic numerical method (ANM) combined with harmonic balance method (HBM), as well as validated by the long-time integration (LTI) method. A parametric study is performed in order to investigate the effects of the coupling voltage, gap ratio, position of added mass and length ratio on the device sensitivity. Beyond the critical Duffing amplitude and while taking advantage of mode localization, it is shown that the device sensitivity in terms of amplitude ratio is significantly enhanced with up to three orders of magnitude higher than the relative shift in resonance frequencies. The proposed model can be used as a design tool to tune the nonlinearity level enabling the performance improvement of multimodal MEMS mass sensors.