A model of electrostatically actuated mems and carbon nanotubes resonators for biological mass detection

Abstract

We investigate the dynamics of electrically actuated Micro and Nano (Carbon nanotube (CNT)) cantilever beams implemented as resonant sensors for mass detection of biological elements. The beams are modeled using an Euler-Bernoulli beam theory including the nonlinear electrostatic forces and the added biological elements, which are modeled as a discrete point mass. A multi-mode Galerkin procedure is utilized to derive a reduced-order model, which is used for the dynamic simulations. The frequency shifts due to added mass of Escherichia coli (E. coli) and Prostate Specific Antigen (PSA) are calculated for the primary and higher order modes of vibrations. Also, analytical expressions of the natural frequency shift under dc voltage and added mass have been developed. We found that using higher-order modes of vibration of MEMS beams or miniaturizing the size of the beam to Nano scale leads to significant improved sensitivity.