Nonlinear Modeling of MEMS Fixed-Fixed beams

This dissertation studies critical topics associated with MEMS fixed-fixed beams. One of the typical devices of fixed-fixed beams is radio frequency microelectromechanical system (MEMS) capacitive switches. The interesting topic for this device includes the instability at the pull-in voltage; the switches' deformation characteristics when subject to an electrostatic force; nonlinear stretching effects, and the capacitance calculation in small scale. Specifically, the accuracy of parallel-plate theory in calculating the pull-in voltage and capacitance is investigated. The study shows that applying average displacement rather than maximum displacement into parallel-plate theory demonstrates better accuracy. The improvement increases with the bottom stationary electrode to moveable electrode ratio and it reaches 50% when the ratio is equal to 1. Besides average displacement, the nonlinear stretching effect and empirical linear correction coefficients are also added to the parallel-plate model to extend model's validity range. In order to improve the lifetime of RF MEMS capacitive switch, a relationship between switches' geometry and membrane strain is derived, which helps avoid switches operating beyond the elastic region.Furthermore, this dissertation presents a new coupled hyperbolic electro-mechanical model that is an improvement on the classical parallel-plate approximation. The model employs a hyperbolic function to account for the beam's deformed shape and electrostatic field. Based on this, the model accurately calculates the deflection of a fixed-fixed beam subjected to an applied voltage and the switch's 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 significantly increases the pull-in voltage and extend the beam's maximum travel range. Based on the model, a graphene nanoelectromechanical systems (NEMS) resonator is designed and the performance agrees very well with the experimental data. The proposed coupled hyperbolic model demonstrates its capacity to guide the design and optimization of both RF MEMS capacitive switches and NEMS devices.