Frequency Tuning of Graphene Nanoelectromechanical Resonators via Electrostatic Gating

Abstract

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.

Ultrawide Frequency Tuning of Atomic Layer van der Waals Heterostructure Electromechanical Resonators

“…Here r is the total strain level of the vdW heterostructure membrane, which is expressed as [28]  …”

“…Therefore, k eff is given as the sum of the second-order differentiation of electrostatic energy and the second-order differentiation of elastic energy , where δ U elastic is the elastic energy for the fundamental mode and δz is the vibration amplitude of the device. The resonance frequency under applied voltage is given as Here ε r is the total strain level of the vdW heterostructure membrane, which is expressed as where z is the static deflection displacement of the vdW heterostructure membrane under applied V G , which is obtained by iteratively computing eqs S3, S5, and S13 of the Supporting Information until convergence. (See the Supporting Information for details of analytical model #2.)…”

Stopping and reversing sound via dynamic dispersion tuning in a phononic metamaterial

“…Prestress modulation of phonon bands via electrostatic backgating has been demonstrated in SiN resonator arrays with Q ≈ 1, 700 [8], and Q-factors as high as 10 8 have been reported for individual SiN resonators [39]. Graphene-based resonator arrays [40] can be tuned via electrostatic [41] or thermally-induced [27] prestresses; Q-factors of order 10 5 have been reported [42,43] in non-tunable systems.…”

A Review on Graphene-Based Nano-Electromechanical Resonators: Fabrication, Performance, and Applications

“…The competition between the two effects may result in a 'W' tuning curve, as shown in Figure 5c [52]. So far, many theoretical models have been investigated to describe and understand the experimentally observed complex tuning behaviors of graphene resonators, but an accurate and universal electrostatic tuning model still needs to be developed [23,33,[53][54][55].…”