Nonlinear Analytical Model of Two Weakly Coupled MEMS Cantilevers for Mass Sensing Using Electrostatic Actuation

Toky Rabenimanana,Patrice Le Moal,Vincent Walter,Joseph Lardiès,Najib Kacem

doi:10.3390/proceedings2131084

Abstract

This paper presents a nonlinear analytical model of MEMS mass sensor, which is composed of two cantilevers of 98 µm and 100 µm length, 20 µm width and 1.3 µm thick. They are connected by a coupling beam and only the shortest cantilever is actuated by a combined AC-DC voltage. The DC voltage is used to equilibrate the system and the phenomenon of mode localization is investigated when a mass perturbation is applied. The sensor is modeled as a continuous system with beam theory and non-ideal boundary conditions are considered by using flexible supports. With a low AC voltage of 10 mV, a DC voltage of 5.85 V can counterbalance the length difference. This DC voltage decreases at 5.60 V when we increase the AC voltage, due to the effect of electrostatic nonlinearities. For a relative added mass of 0.1%, the amplitude change in the two cantilevers is more important when the coupling is weaker.

Highlights

Mass sensors using coupled resonators have recently been studied in some research, due to the interest that they can bring in chemical and biomedical applications
This DC voltage decreases at 5.60 V when we increase the AC voltage, due to the effect of electrostatic nonlinearities
The use of an electrostatic force to counterbalance the defects of length difference has been already studied in [7] and a Finite Element Model was implemented in COMSOL Multiphysics® to prove its efficiency

Summary

Introduction

Mass sensors using coupled resonators have recently been studied in some research, due to the interest that they can bring in chemical and biomedical applications. Unlike single resonators, which measure the frequency shift, this new generation of sensors uses the phenomenon of mode localization to detect an analyte [1]. When identical resonators are coupled to each other, a small perturbation can lead to a drastic change in the resonant amplitude. This phenomenon has been already investigated in [2], due to its capability of increasing the sensitivity when the coupling is very weak. A small mass is added and the amplitude changes in the two beams are compared when we change the coupling parameter.

Presentation of the Device and the Model

Use of an Electrostatic Force to Equilibrate the System

Effect of the Coupling ratio in Mass Sensing

Conclusions