Nonlinear Behavior of a Parametric Resonance-Based Mass Sensor

Abstract

The ability to detect mass change of the order of femtograms (10e-15g) opens up implementations of various precise chemical and biological sensors. Micro-scale oscillator based mass sensors are promising due to their small mass and high sensitivity. Many such sensors detect mass change by measuring the shift of natural frequency. We have reported previous work introducing the idea of using parametric resonance to detect mass change. This method utilizes stability behavior with mass variation as the detection criterion and high sensitivity is expected. This paper presents theoretical and experimental research on nonlinearity effects on the dynamic behavior of a MEMS oscillator, which is the prototype of such a mass sensor. A Duffing equation and a nonlinear Mathieu equation are used to model the behavior of nonlinear harmonic resonance and parametric resonance. Experimental results agree with the theoretical analysis very well. Some bulk equivalent parameters, such as Q factor, cubic stiffness and linear electrostatic stiffness can be estimated by studying the nonlinear behavior. The estimation of the parameters is important for design of the optimal mass sensor. The potential effects of nonlinearity on mass sensor application are discussed.