Molecular dynamics modeling and simulation of a graphene-based nanoelectromechanical resonator
Highlights
► Tunable graphene-resonator investigated using molecular dynamics simulations. ► Tunable range above several hundred gigahertz at very small initial axial-strains. ► Tunability and tunable range decreased with increasing initial axial-strain.
Introduction
The electronic and mechanical properties of graphene have been studied extensively [1], [2], [3], [4], [5], [6], [7], [8], [9]. The quantum Hall effect has been probed in experiments [3], [4] and other remarkable mechanical properties have been uncovered, including a high in-plane Young's modulus of ∼1 TPa probed using nanoindentation of suspended graphene [5], force extension measurements [6] and electromechanical resonators [7], [8], [9]. Nanoelectromechanical systems (NEMS) devices using nanostructures like carbon nanotubes [10], [11], [12], [13], [14], [15], [16], nanowires [17], [18] and micromachined structures [19], [20], [21] offer the promise of new applications in fundamental science and engineering and allow us to probe fundamental properties at the nanoscale, such as sensing, studies of fundamental physics and high-frequency signal processing.
Of special interest is the high frequency NEMS resonator [22], [23], [24], [25], [26], [27], [28], [29], [30], which not only offers the potential for extreme mass and force sensitivity [25] but also provides a unique way to observe the imprint of quantum phenomena directly [22], including uncertainty principle limits on position detection [24]. So graphenes have been considered as ideal candidates for NEMS devices because of their unique mechanical properties [25]. Materials with a high young's modulus can bring more resolution to these systems. Graphene has a high elasticity compared to other materials being applied to NEMSs. A large surface with the atomic thickness of graphene provides a special advantage over other nanostructures for ultra-sensitive resonators. Atalaya et al. [27] showed the relationship between the out-of-plane deflection (w) and the driving force (FD) to be w ∼ FD0.333 and discussed the tunability of graphene oscillators by changing the dc bias. Graphene resonators have shown the potential to be very sensitive detectors of mass, charge and chemicals while improving the quality factor [7], [8], [28]. In order to better understand the potential of graphene-based electrically actuated and detected resonators [8] and the challenges in realizing strain-engineered graphene devices [29], [30], these systems vibrational properties should be investigated. Computational simulation works have advanced this field and helped reveal the potential of graphene devices in future technologies [31], [32], [33], [34], [35], [36], [37], [38], [39], [40].
In this paper, the fundamental resonance frequency variation of a defect-free graphene resonator at constant temperature is investigated by classical molecular dynamics (MD) simulations. In order to explore graphene resonators as ultra-sensitive sensors, the resonance frequency of the suspended graphene ribbon is modeled using the average tension induced by the axial strain and gate force. Strain engineering of graphene is achieved from the mismatch between the negative thermal expansion coefficient of the graphene and the positive thermal expansion of the substrate. Schematics and methods are addressed in Sections 2 Schematics, 3 Simulation methods, respectively, the simulation results are presented and discussed in Section 4, and lastly we summarize in Section 5.
Section snippets
Schematics
Schematics of graphene-resonator are composed of a suspended graphene-ribbon placed on the bottom gate with spacing and clamps on both ends, as shown in Fig. 1. In classical continuum theory, the resonance frequencies (f) of strings are basically tuned by the tension (T) in such a way that f ∼ T0.5 [8]. This tension can be controlled by adjusting the axial strain of the string or deflecting the string. So firstly, engineering the axial strain of the graphene can be achieved from a temperature
Simulation methods
We performed MD simulations to obtain the resonance frequencies of the graphene-resonator as functions of the strain and the gate force. Both sides of the GRNs were clamped, and this condition is described as both sides being fixed as seen in Fig. 1. Armchair-edge graphene with a width of 0.7 nm and length of 14.1 nm composed of 424 atoms was considered. First the graphene was initially relaxed without external force. After that, an external gate-forces (FA), which can be induced by an
Results and discussion
First we calculated the tension as a function of the strain for the graphene ribbon as shown in Fig. 2. Optimal atomic configurations of graphene under each axial strain were obtained using a steepest descent (SD) method, which is the simplest of the gradient methods [59], from the atomic configurations of graphene with a C–C bond length 1.42 Å. The choice of direction was determined by where the force exerted by the interatomic interaction decreased fastest, which was in the opposite direction
Concluding remarks
We performed modeling and simulations of a tunable graphene-resonator using classical MD simulations. The resonance frequencies as a function of the gate force and the axial-strain were in good agreement with previous experiments. The resonance frequency of the graphene resonator was very closely related to the average tension. The initial strain-induced tension could be adjusted by the mismatch of thermal expansion coefficients and the deflection-induced tension could be controlled by the
Acknowledgment
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2012R1A1A1042640).
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