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Solid State Sciences 14 (2012) 711e714

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Solid State Sciences

journal homepage: www.elsevier .com/locate/ssscie

Zigzag graphene nanoribbons: Flexible and robust transparent conductors

H.P. Xiao, Zhizhou Yu, M.L. Hu, X.Y. Peng, L.Z. Sun*, Jianxin Zhong*

Laboratory for Quantum Engineering and Micro-Nano Energy Technology, Xiangtan University, Xiangtan, Hunan 411105, People’s Republic of China

a r t i c l e i n f o

Article history:Received 16 December 2011Received in revised form20 March 2012Accepted 30 March 2012Available online 7 April 2012

Keywords:Graphene nanoribbonBending deformationOptical propertyTransport property

* Corresponding authors.E-mail addresses: lzsun@xtu.edu.cn (L.Z. Sun), jxzh

1293-2558/$ e see front matter � 2012 Elsevier Masdoi:10.1016/j.solidstatesciences.2012.03.027

a b s t r a c t

We report the effect of bending deformation on the optical and transport properties of zigzag graphenenanoribbons (ZGNRs) induced by the uniaxial strain using the first-principles method combined withnon-equilibrium Green’s function. The optical properties of ZGNRs in the region of visible light arealmost unchanged under the uniaxial strain, whereas an absorption peak occurs at the infrared region forthe bent ZGNRs under the transverses strain. The transport properties of ZGNRs under the transversesstrain with the bending angle up to 65� remain almost the same as those of the flat one. The transmissioncoefficients around the Fermi level only slightly decrease when the bending angle further increases to72.5�. Moreover, ZGNRs under the longitudinal strain show the same transmission conductance aroundthe Fermi level as that of the flat one. The edge states of ZGNRs still behave as excellent ballistic transportchannels under bending deformation, which makes them promising flexible and robust transparentconductors.

� 2012 Elsevier Masson SAS. All rights reserved.

1. Introduction

Rapid development of new electronic devices, such as touchscreens, flexible displays and printable electronics, leads to widerapplications for the flexible transparent conductors. The currentindustry standard for transparent conductor is indium tin oxide(ITO) due to its high optical transparency and favorable conduc-tance [1]. However, ITO is too brittle to satisfy the needs of thedevelopment of electronic devices with its large losses of conduc-tance from the bending deformation. Recently, many new mate-rials, such as thin metal foils [2], metal grids [3] and carbonnanotubes [4,5], have been proved to be promising candidates fortransparent conductors because their transparency and conduc-tance are outstanding and can be comparable with those of ITO.

Graphene, a single atomic plane of graphite, attracts greatinterest due to its unique electronic and transport properties [6]. Itshows many potential advantages as transparent conductors overITO, such as the high optical transparency, zero bang-gap, flexibilityand robustness [7e11]. Kim and co-workers demonstrated thatgraphene films show optical transparency of 80% and low resis-tance of less than 280 U per square [11]. Moreover, graphene showsanisotropy changes of conductance under longitudinal and trans-verse uniaxial strains. Its resistance recovers immediately when theexternal strains are released. Such transport characteristics make it

ong@xtu.edu.cn (J. Zhong).

son SAS. All rights reserved.

an excellent candidate for transparent electrodes in flexible,stretchable and foldable electronics. Additionally, more and moreflexible transparent conductors based on graphene oxide andhybrid graphene materials have been successfully prepared inexperiments [12e15], which further promotes its practical appli-cation in transparent electronics. For instance, Tung et al. reportedthat the resistance of the hybrid graphene-carbon nanotubetransparent conductor remains stable upon flexing [14].

Graphene nanoribbons (GNRs), quasi-one-dimensional mate-rials can be obtained by patterning from graphene by lithography[16], fabricating by chemical method [17] or unzipping from carbonnanotube [18,19], show great potential applications in the futurecarbon-based nanoelectronics due to their high carrier mobility[20]. In particular, zigzag GNRs (ZGNRs) with semi-metallic char-acteristics [21] can be potentially used as flexible transparentconductors due to their prominent electronic and mechanicalproperties. Mechanical deformations are inevitable for ZGNRs dueto the lattice mismatch between ZGNRs and substrate. Moleculardynamics simulations using reactive empirical bond-order poten-tials also show that the long GNRs tend to exhibit self-foldedconformations [22]. Therefore, it is crucial to systematically studythe evolution of the optical and transport properties of bent ZGNRsunder uniaxial strain.

To this end, in present work, we study the optical and transportproperties of ZGNRs with different bending deformation using thefirst-principles method coupled with the non-equilibrium Green’sfunction. We take ZGNRs with 7 zigzag chains as prototypic devicesto simulate the dependence of its transport and optical properties

Fig. 1. (a) Schematic diagram of the two-probe system of bent ZGNRs under the transverse strain. (b) Illustration of bent ZGNRs under the transverse strain laying on the substrate.(c) Schematic diagram of the two-probe system of bent ZGNRs under the longitudinal strain. (d) Side view of bent ZGNRs under longitudinal strain. The light yellow regionsrepresent the electrodes. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

H.P. Xiao et al. / Solid State Sciences 14 (2012) 711e714712

on the transverse strain. The transverse strain is achieved bygradually compressing the electrodes. To obtain the dependence ofthe transport and optical properties of ZGNRs on the longitudinalstrain, ZGNRs with 9 zigzag chains are taken as typical prototypicdevice. The studies can clearly show the evolution of the optical andtransport properties of bent ZGNRs under uniaxial strain, and itspromising applications in the flexible and transparent conductors.

2. Computational details

To investigate the geometric structures and optical properties ofZGNRs under uniaxial strain, we adopt the Vienna Ab initio Simu-lation Package (VASP) to perform the first-principles calculation[23,24]. The exchange and correlation are approximated by gener-alized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional [25]. A plane-wave basis set with thekinetic energy cutoff of 450 eV is employed. Atoms are relaxed withthe residual force less than 0.02 eV/Å, and the total energies areconverged to 10�5 eV. The optical properties of ZGNRs are deter-mined by the frequency-dependent dielectric function

a

Fig. 2. Absorption of ZGNRs under the (a)

εðuÞ ¼ ε1ðuÞ þ iε2ðuÞ. The imaginary part is calculated from theequation of states [26].

εð2Þab

ðuÞ ¼ 4p2e2

Ulimq/0

1q2

Xc;v;k

2wkdðεck�εvk�uÞ��uckþeaq

��uvk�

��uckþebq

��uvk��(1)

where, the parameters c and v refer to the conduction and valenceband states, respectively, and uck the cell periodic part of the wave-functions at the k-point k. Then, the absorption coefficient can beobtained from,

IðuÞ ¼ffiffiffi2

pu

� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiε1ðuÞ2þε2ðuÞ2

q� ε1ðuÞ

�1=2(2)

where, ε1(u) is the real part of the dielectric function which can bedetermined by ε2(u)via the Kramers-Kroning transformation.

The Atomistix ToolKit (ATK) implementation [27], basedon the first-principles method combined with non-equilibrium

b

transverse and (b) longitudinal strain.

Fig. 3. Transmission spectra of ZGNRs under the (a) transverse and (b) longitudinalstrain.

H.P. Xiao et al. / Solid State Sciences 14 (2012) 711e714 713

Green’s function, is used to calculate the transport properties.Double-plus z polarization numerical orbital basis set is chosenfor our systems. The exchange and correlation potential are alsoapproximated by GGA with PBE functional [25]. The energy cutoffis set to 150 Ry and the convergence of total energies is set to10�5 Ry. All the computational parameters used in our presentwork are optimized. According to previous studies, the energydifference between the spin-polarized and spin-unpolarizedstates for ZGNRs is too small to stabilize the spin-polarizedstate at finite temperature or in the presence of a ballisticcurrent through the device [28]. Thus, we only consider the spin-unpolarized state here.

In order to simulate the transverse strain, we choose theZGNRs containing 7 zigzag chains for the prototypic devices. Thescattering region consists of 20 unit cells, which is equivalent to4.9 nm long flat ZGNRs. Semi-infinite pristine ZGNRs are used forthe electrodes in order to avoid the influence of the hetero-electrodes. The ZGNRs are then gradually bent to construct thegeometric deformation by compressing the electrodes, as shownin Fig. 1(a) and (b). We fully relax the geometric structures of bentZGNRs with constraint electrodes. The bending deformation isthen illustrated by bending angles (q) and arch heights (H). Thearch heights of bent ZGNRs are about 0.97 nm, 1.29 nm, 1.51 nmand 1.72 nm corresponding to the bending angles of 35�, 52.5�,65� and 72.5�, respectively. We bend the ZGNRs with 9 zigzagchains to simulate the longitudinal strain and the bendingdeformation is also defined by bending angles (q). Semi-infiniteZGNRs with the same bending angles are used for the elec-trodes, as shown in Fig. 1(c) and (d).

3. Results and discussions

We first calculate the optical properties of ZGNRs under theuniaxial strain. Fig. 2(a) and (b) present the absorption coefficientof ZGNRs under the transverse and longitudinal strain comparedwith that of the pristine ZGNRs, respectively. The pristine ZGNRsshow two absorption peaks in the region of the visible light,namely, in the region of (1.61, 3.18) eV, which means that thevisible light is partially absorbed by ZGNRs. These two peaksslightly decrease under the transverse strain and remain evenwhen the bending angle increases to 72.5�. Moreover, a tiny peakoccurs at about 0.3 eV once ZGNRs are bent by the transversestrain, which implies that the infrared can be absorbed by thebent ZGNRs. The results are in good agreement with the experi-mental reports of Wang et al. [29] that the graphene films theyobtained exhibit a transparency of 70% over 1000e3000 nm.According to our present predication, the loss of the trans-parency over 1000e3000 nm in their samples is derived from theadsorption induced by the transverse strain. As for the ZGNRsunder the longitudinal strain, the high absorption coefficientremains in the region of the visible light, which means that theoptical properties in the visible light region are almost unchangedunder the longitudinal strain.

Fig. 3(a) and (b) present the transmission coefficient of ZGNRsunder transverse and longitudinal strain compared with that of thepristine ZGNRs. The transmission coefficient is about 1G0 aroundthe Fermi level for the pristine ZGNRs and it exhibits a peak of 3G0at the Fermi level due to the flat bands of ZGNRs. As for ZGNRsunder transverse strain, the transmission coefficient remains thesame within 2 eV around the Fermi level even when the bendingangle is up to 65�. When the bending angle increases to 72.5�, thereare several small dips in the transmission coefficient of ZGNRsaround the Fermi level, as shown in the inset of Fig. 3(a). However,these dips are so slight that the transport properties are nearlyunaffected by the bending deformation. As for ZGNRs under

longitudinal strain, the transmission coefficient of bent ZGNRs stillstays 3G0 at the Fermi level and 1G0 around the Fermi level. Thetransmission conductance remains the same in the region of (�2, 2)eV evenwhen the bending angel is up to 82.5�. This implies that thetransport properties of ZGNRs are insensitive to the uniaxial strain.Our results agree well with the study of bent graphene in experi-ment [11]. The ZGNRs are flexible and robust transparent conduc-tors due to its unchanged transport properties even under largebending deformation.

In order to clarify the reason of the robust conductance ofZGNRs under transverse and longitudinal strain, we focus on theirlocal Density of States (LDOS) at the Fermi level, as shown inFig. 4. The LDOS localize at the edges of the flat ZGNRs, whichoffers effective transport channels, as shown in Fig. 4(a). Inter-estingly, LDOS of the ZGNR under transverse and longitudinalstrain still localize at their edges though the structure is signifi-cantly changed by the bending deformation, as shown in Fig. 4(b)and (c). It means that the edge states of ZGNRs still offer excellentballistic transport channels under uniaxial strain. Such phenom-enon leads to the negligible loss of conductance for ZGNRs underuniaxial strain.

Fig. 4. LDOS in the real space for (a) flat ZGNRs, (b) bent ZGNRs under the transverse strain with bending angle of 72.5� and (c) bent ZGNRs under the longitudinal strain withbending angle of 75� .

H.P. Xiao et al. / Solid State Sciences 14 (2012) 711e714714

4. Conclusion

In summary, the optical properties remain almost the same inthe region of visible light under the uniaxial strain, while anabsorption peak occurs at 0.3 eV for bent ZGNRs under the trans-verse bending. This means that the infrared light can be absorbedby such bent ZGNRs. Moreover, the transport properties of ZGNRsare insensitive to bending deformations under uniaxial strain. Thetransport properties of ZGNRs around the Fermi level remainunchanged evenwith the bending angle of 65� and 82.5� under thetransverse and longitudinal strain, respectively. The underlyingmechanism is that the edge states are not affected by the bendingdeformations and still offer excellent ballistic transport channelseven under large bending deformation. Therefore, the ZGNRs arepromising flexible and robust transparent conductors. In view ofthe successful preparation of the ultra-narrow ZGNRs in experi-ments by unzipping nanotube and the obtainable of the bendingdeformations in experiments by modulating electrodes discussedin our present work, we look forward to the further evidences inexperiments in the future to confirm our theoretical prediction.

Acknowledgements

This work is supported by the National Natural Science Founda-tion of China (GrantNos.10874143, 5117291,11074211,11074213), theProgram for New Century Excellent Talents in University (Grant No.NCET-10-0169), and the Scientific Research Fund ofHunan ProvincialEducation Department (Grant Nos. 10K065, 10A118,09K033).

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