Frequency and displacement analysis of electrostatic cantilever-based MEMS sensor

In this work we present behavior level modeling to predict the frequency and displacement of electrostatic cantilever based microelectromechanical system sensor for mass detection. Linear time invariant (LTI) technique is used to study the linear and nonlinear behavior of the device. The shift in resonance frequency in damped and undamped medium is formulated by using the conception of dynamic mass and law of identity. First a complete analytical model is developed by coupling electrostatic force with the bending moment of cantilever to produce vertical actuation at a resonance frequency. Then displacement of the cantilever is correlated with piezoresistive mechanism for mass sensing. We assumed mass of blood cells as the external load on cantilever tip which results in shift in resonance frequency. Simulink tool is used to develop the LTI model that is based on electromechanical coupling of linear and nonlinear equations. The same device is then designed using COMSOL tool and FEM analysis is performed. For validation, the analytical results are compared with the FEM simulations.