Elsevier

Current Applied Physics

Volume 23, March 2021, Pages 30-35
Current Applied Physics

Mechanical resonance properties of porous graphene membrane; simulation study and proof of concept experiment

https://doi.org/10.1016/j.cap.2020.12.011Get rights and content

Abstract

Mechanical resonance properties of porous graphene resonators were investigated by simulation studies. The finite element method was utilized to design the porous graphene membrane pattern and to calculate the mechanical resonance frequency and quality factor. The changes in the resonance frequency and quality factor were systematically studied by changing the size, number, and relative location of pores on the graphene membrane. Mass loss and carbon-carbon bond break were found to be the main competing parameters for determining its mechanical resonance properties. The correlation between the geometry and the damping effect on the mechanical resonance of graphene was considered by suggesting a model on the damping factor and by calculating the membrane deflections according to the pore location. Based on the simulation results, an optimal porosity and porous geometry were found that gives the maximum resonance frequency and quality factor. Suspended graphene with various number pore structures was experimentally realized, and their mechanical resonance behaviors were measured. The trend of changes in resonance frequency and quality factor according to the number of pores in the experiment was qualitatively agreed with simulation results.

Introduction

Since graphene was exfoliated from graphite flakes [1], an enormous amount of studies have been reported on the physical properties and applications [[2], [3], [4]]. Its two-dimensional nature offers a lot of interesting quantum mechanical phenomena, such as the quantum Hall effect [5], valley states [6], quantum electron optics [7], and so on. Graphene receives anew spotlights as it recently showed superconductivity and Mott insulator states [8], which are unexpected and emerging phenomena, from bilayer graphene with a specific twisted angle. Besides the aforementioned phenomena, which mainly originate from electrical properties, graphene also has superior mechanical properties with high strength, high flexibility, and light mass [9]. However, the research on graphene-based mechanical or electromechanical systems has been relatively less investigated than electrical studies.

Nanoelectromechanical systems (NEMS) combine mechanical and electrical degrees of freedom with nanoscale, which enables higher sensitivity than other electrical devices as they utilize two orthogonal information, that is, mechanical and electrical information [10]. Graphene can be one of the best candidate materials for NEMS since it has good electrical conductivity as well as high mechanical strength [11]. Recent reports showed that it was possible to achieve a ‘quantum mechanical’ phenomena [12] and an ultra-sensitive mechanical measurement [13] using graphene-based nanoelectromechanical devices. To improve the device performance of graphene NEMS, it is necessary to increase the mechanical resonance frequency and quality (Q) factor. However, it was found from the previously reported works that the resonance frequency and Q factor of graphene nanomechanical resonator, realized in experiments, were much less than theoretically estimated values [14].

We have especially focused on the effect of damping on the graphene resonator, which is a crucial factor in degrading the mechanical performances of devices. In the case of the microelectromechanical system (MEMS), there have been many trials to solve this issue. One of the most suitable methods is defining a porous structure on the MEMS resonator [[15], [16], [17]]. The hole patterns on the resonator material help the Q factor increase by reducing the damping parameter, and the resonance frequency increases by reducing the effective mass. In this work, we adapted the above-mentioned idea of MEMS to the graphene nanomechanical resonator. Graphene resonators with various porous patterns were designed, and their mechanical resonance properties were studied by the finite element method. Based on the modeling and simulation work, the optimal geometry of the graphene resonator could be suggested. The graphene resonator with hole structures was realized by nanofabrication. The measured mechanical properties of graphene resonators in experiments were qualitatively consistent with the simulation results.

Section snippets

Simulation method and result

COMSOL Multiphysics with finite element analysis is used for simulating porous graphene geometry. This method assumes that the structure under test consists of small pieces, and the equations of motion on each piece are integrated and formulates into one equation. Then, a numerical analysis of the equation is conducted for determining the significant features of mechanical behavior on the entire structure. To study the resonance behaviors of porous graphene resonators, we used the structural

Experimental

The mechanical properties of suspended graphene resonator devices were investigated to compare the simulation results. Graphene flakes for the resonator device were produced by a mechanical exfoliation method. The nanoscale pore structures were defined on top of the pre-deposited graphene flakes using electron beam lithography followed by oxygen plasma etching. Fig. 5(a) shows an optical microscope image of an exfoliated graphene with porous hole patterns. The graphene flake with pore structure

Summary

In summary, the mechanical resonance properties of the porous graphene membrane were studied by the finite element method, and the simulated results were compared with experimental test devices. The mechanical resonance frequency of the membrane was calculated by varying the porosity of the graphene membrane, the number of pores, and the geometry of pore patterns. Mass loss and carbon-carbon bond break are two main competing parameters for determining resonance frequency values. The Q factor of

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was supported by the Basic Research Program (NRF-2019R1A2C1085641, NRF-2019R1A4A1029052, and NRF-2017R1D1A1B03035727), by the International Collaboration Program (NRF-2016K2A9A1A03905001), and by Global Research and Development Center Program (2018K1A4A3A01064272) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education. This research was also supported by Human Frontier Science Program (RGP00026/2019). DHS acknowledges the support by RP-Grant

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Current address: Institute of Sensor and Actuator Systems, TU Wien, Gußhausstraße 27–29, Vienna 1040, Austria.

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