Finite Element Analysis on Nonlinear Oscillation Behavior of NEMS Resonators for Atomic–Scale Mass Detection

Abstract

Nanoelectromechanical system (NEMS) has been studied in various fields, especially in high sensing applications such as mass detection. The principle of mass detection with NEMS resonators is a shift of resonance frequency according to increasing of the system mass due to attached material. The mass detection sensitivity can be improved using resonators with smaller size and high specific stiffness. Thus, carbon nanotube (CNT) and graphene have been employed as suitable materials in NEMS resonators for mass sensing because of their small sizes and remarkable properties. CNT and graphene-based resonators can easily exhibit the geometrically nonlinear behavior due to its large aspect ratio, and this nonlinearity affects the mass detection sensitivity. However, most studies have been limited to the linear dynamic behavior of NEMS resonators. Also, some studies with nonlinear behaviors have utilized molecular dynamics (MD) simulations and analytical solution models with an assumed eigenmode. The MD simulations have a restriction on the length scale of resonators due to limitation of the computation time and cost, and the analytical methods have a difficulty which the assumed eigenmode varies according to the shape and boundary conditions of resonator. Thus, it is the current lack of study on the general-purpose analysis model including nonlinear dynamic behaviors for the NEMS resonator which can handle effectively shape and boundary conditions, especially can be helpful in design of NEMS resonator for mass sensing. This study aims to propose a finite element analysis model for CNT and graphene-based NEMS resonators, and to analyze their oscillatory behaviors for atomic-scale mass sensing. To this end, nonlinear oscillation behaviors of the CNT and graphene are studied using the finite element method (FEM) based on continuum mechanics. The study contains two major parts, the first part is numerical modeling of CNT and graphene with nonlinear dynamic behaviors, and the second part is parametric studies for enhancement of the mass detection sensitivity. At first, the continuum mechanics approach has been employed to analyze the nonlinear dynamic behavior of a CNT and graphene resonator actuated with electrostatic force, wherein beam (for CNT) and plate (for graphene) elements are also utilized within FEM. The proposed nonlinear FE model is verified through direct comparisons with the experimental results and the previous analytical model. Then, the analysis for the resonance behaviors of CNT and graphene resonator is carried out, and in order to investigate the effect on the mass detection sensitivity which is defined a shift of the resonance frequency due to an attached, parametric studies are conducted with respect to the amount of attached mass, a size of the resonator, and the amplitude of electrostatic force. Moreover, thermal effects due to temperature changes of the CNT resonator are examined on the nonlinear behavior and the mass detection sensitivity. As a result, nonlinear oscillatory behaviors of NEMS resonator can be predicted successfully by the proposed FE analysis model, and correlations on the mass detection sensitivity are elucidated with respect to the design parameters and linear/nonlinear oscillatory behaviors. It is expected that the proposed nonlinear FE analysis model and the results of parametric studies will be effectively utilized in design of NEMS resonator for atomic-scale mass sensing.