In this article, we report on a comprehensive modeling study of frequency tuning of graphene resonant nanoelectromechanical systems (NEMS) via electrostatic coupling forces induced by controlling the voltage of a capacitive gate. The model applies to both doubly clamped graphene membranes and circumference-clamped circular drumhead device structures. Frequency tuning of these devices can be predicted by considering both capacitive softening and elastic stiffening. It is shown that the built-in strain in the device strongly dictates the frequency tuning behavior and tuning range. We also find that doubly clamped graphene resonators can have a wider frequency tuning range, while circular drumhead devices have higher initial resonance frequency with same device characteristic parameters. Further, the parametric study in this work clearly shows that a smaller built-in strain, smaller depth of air gap or cavity, and larger device size or characteristic length (e.g., length for doubly clamped devices, and diameter for circular drumheads) help achieve a wider range of electrostatic frequency tunability. This study builds a solid foundation that can offer important device fabrication and design guidelines for achieving radio frequency components (e.g., voltage controlled oscillators and filters) with the desired frequencies and tuning ranges.
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