Nonlinear Modeling of MEMS Fixed-Fixed beams

TL;DR

This paper introduces a coupled hyperbolic nonlinear model for MEMS fixed-fixed beams that improves accuracy over classical methods, validated against simulations and experiments, and aids in device design.

Contribution

It presents a novel nonlinear electro-mechanical model using hyperbolic functions, surpassing the classical parallel-plate approximation for MEMS beams.

Findings

Model accurately predicts deflection and capacitance-voltage characteristics.

Nonlinear stretching significantly increases pull-in voltage.

Excellent agreement with experimental data for graphene NEMS resonator.

Abstract

This dissertation presents a new coupled electro-mechanical model that is an improvement on the classical parallel-plate approximation. The model employs a hyperbolic function to account for the beam deformed shape and electrostatic field. Based on this, the model can accurately calculate the deflection of a fixed-fixed beam subjected to an applied voltage and the switch capacitance-voltage characteristics without using parallel-plate assumption. For model validation, the model solutions are compared with ANSYS finite element results and experimental data. It is found that the model works especially well in residual stress dominant and stretching dominant cases. The model shows that the nonlinear stretching can significantly increase the pull-in voltage and extend the beam maximum travel range. Based on the model, a graphene nanoelectromechanical systems (NEMS) resonator is simulated and the agreement with the experimental data is excellent. The proposed coupled hyperbolic model demonstrates its capacity to guide the design and optimization of both RF microelectromechanical system (MEMS) capacitive switches and NEMS devices.