MEMS resonator mass loading noise model: The case of bimodal adsorbing surface and finite adsorbate amount

Abstract

Modeling of adsorption and desorption in microelectromechanical systems (MEMS) generally is crucial for their optimization and control, whether it is necessary to decrease the adsorption-desorption influence (thus ensuring stable operation of ultra-precise micro and nanoresonators) or to increase it (and enhancing in this manner the sensitivity of chemical and biological resonant sensors). In this work we derive and use analytical mathematical expressions to model stochastic fluctuations of the mass adsorbed on the MEMS resonator (mass loading noise). We consider the case where the resonator surface incorporates two different types of binding sites and where non-negligible depletion of the adsorbate occurs in a closed resonator chamber. We arrive at a novel expression for the power spectral density of mass loading noise in resonators and prove the necessity of its application in cases when resonators are exposed to low adsorbate concentrations. We use the novel approach presented here to calculate the resonator performance. In this way we ensure optimization of these MEMS devices and consequentially abatement of adsorption-desorption noise-caused degradation of their operation, both in the case of micro/nanoresonators and resonant sensors. This work is intended for a general use in the design, development and optimization of different MEMS systems based on mechanical resonators, ranging from the RF components to chemical and biological sensors.