A first-principles study on the electromechanical effect of graphene nanoribbon

doi:10.1016/j.cpc.2010.07.019

Computer Physics Communications

Volume 182, Issue 1, January 2011, Pages 99-102

https://doi.org/10.1016/j.cpc.2010.07.019 Get rights and content

Abstract

The electromechanical effect of graphene nanoribbons (GNRs) is investigated via a first-principles method. The deformations of GNRs with zigzag shaped edges (ZGNR) and armchair shaped edges (AGNR) are considered. The nonlinear stress–strain relations are found for both of the AGNRs and the ZGNRs. The AGNRs seem to be stiffer than the ZGNRs as concluded from inspecting the Young's modulus and the ideal strength of GNRs. It is found that a mechanical deformation will affect the electronic structures of GNRs. The band gap of AGNRs exhibits sawtooth oscillations under strains and the oscillating strength is up to 1 eV. On the contrary, the band gap of ZGNRs is insensitive to strain. However, the band gap of ZGNRs will be reduced dramatically to zero as the compressive strain is greater than 0.17. The large variation of the band gap of AGNRs under strain indicates that deformation can provide an opportunity for tuning the band gap of an AGNR.

Introduction

A graphene nanoribbon (GNR) is essentially a strip of graphene with finite width in nanometer size. The study of GNR is motivated by the fundamental physics interests for the low-dimensional materials and the potentials of versatile applications of the novel structures [1], [2], [3]. Owing to the structure being similar to carbon nanotubes (CNTs), GNRs are expected to have various unique properties and capabilities for the next generation devices [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14]. As CNTs are predicted to have high stiffness and axial strength, the mechanical properties of CNTs have been a focus of extensive studies. As well as the interesting mechanical characteristics, the electromechanical properties of CNTs have also attracted much attention and have been studied both experimentally and theoretically [15], [16], [17], [18], [19]. The mechanical deformation will affect the electrical properties of CNTs and could be applied in electromechanical devices. The effects of mechanical deformations of planar graphene sheets have been extensive studied [20], [21], [22], [23] in the few years. Recently, CNRs have been attracted enormous interest on their electronic and transport properties [3], [4], [5], [11], [12], [13], but little attention has been paid to mechanical properties of GNRs. However, the mechanical deformations have been predicted to affect the band structure of GNRs [5], [24]. In this paper, we will present the mechanical properties of GNRs and the electromechanical effect on GNRs including the GNRs with the armchair shaped edges (AGNRs) and with the zigzag shaped edges (ZGNRs). The arrangement of this paper is as follows: The calculation details are described in Section 2. Section 3 is the results and discussions. Section 4 is the conclusions.

Section snippets

Calculation details

This work is performed within the density functional theory (DFT) [25] and the local (spin) density approximation [L(S)DA] [26] via the Vienna ab initio simulation package (VASP) [27], [28], [29]. The exchange–correlation energy is in the Ceperley–Alder form [30] and the ultrasoft pseudopotentials [28] are used. The $1 \times 80 \times 1$ k-points sampling in the first BZ and plane-wave the cutoff up to 358.2 eV have been carried out. The total energies are converged to within 1 meV. The ZGNRs and AGNRs with

Mechanical properties

Table 1 displays the Young's modulus and the ideal strength of GNRs and those of graphene and CNTs are also listed for comparison. Though AGNRs own slightly smaller $Y_{0}$ than ZGNRs, the $Y_{0}$ of both of the AGNRs and the ZGNRs are around 1 TPa. It demonstrates that GNRs exhibit extraordinary stiffness as well as CNTs and graphene. The $Y_{0}$ of a ZGNR increases and tends to approach that of graphene as the ribbon is growing wider. The stress–strain relations of the GNRs under tensile strains are

Conclusions

We have carried out the first-principles calculations for the mechanical properties and the electromechanical effect of GNRs. The Young's modulus and the ideal strength reveal that the ZGNRs seem to be stiffer than the AGNRs. The band gap of AGNRs exhibits sawtooth shaped oscillations under strain. On the contrary, the band gap of ZGNRs is insensitive to the strain. The insensitive of the band gap of ZGNRs can be referred to the origin of the band gap. The large variation of the band gap of

Acknowledgements

We would like to acknowledge NCTS and National Center for high-performance computing, Hsin-Chu, Taiwan for computing facilities and the financial support from NSC of Taiwan under Grant Nos. NSC 97-2112-M-182-003, NSC-98-2811-M-165-001 (W.S.S.) and CGU under Grant No. UMRPD580201. W.S.S. also thanks for the supporting by the Department of Physics, National Cheng Kung University.

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A first-principles study on the electromechanical effect of graphene nanoribbon

Abstract

Introduction

Section snippets

Calculation details

Mechanical properties

Conclusions

Acknowledgements

Nature (London)

Synth. Met.

Comput. Mater. Sci.

Nature

Science

Phys. Rev. B

J. Appl. Phys.

Nano Lett.

Phys. Rev. Lett.

Phys. Rev. B

J. Phys. Soc. Jpn.

Phys. Rev. Lett.

Nature

Nature

Nano Lett.