Role of nitrogen distribution in asymmetric Stone–Wales defects on electronic transport of graphene nanoribbons

Phys. Status Solidi B 249, No. 1, 128–133 (2012) / DOI 10.1002/pssb.201147371 p s sb

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basic solid state physics

Role of nitrogen distribution in
asymmetric Stone–Wales defects onelectronic transport of graphene nanoribbons
Hui Zeng1, Jun Zhao*,1, Jianwei Wei2, and Dahai Xu1

1College of Physical Science and Technology, Yangtze University, Jingzhou, Hubei 434023, P.R. China2College of Optoelectronic Information, Chongqing University of Technology, Chongqing 400054, P.R. China

Received 26 July 2011, revised 13 September 2011, accepted 14 September 2011

Published online 6 October 2011

Keywords ab initio calculations, electronic transport in graphene, graphene, substitutional doping

*Corresponding author: e-mail [email protected], Phone: þ86-716-8062070, Fax: þ86-716-8060942Hui Zeng and Jun Zhao contributed equally to this work.

The authors performed first principles calculation to inves-

tigate the influences of nitrogen dopant distribution in the

asymmetric Stone–Wales (SW) defect on the electronic

transport of zigzag-edged graphene nanoribbon (ZGNR).

The stability of doped configurations are evaluated in terms of

total energies. It is found that the dopant placed near the edge

of the ribbon is the most energetically favorable site. Our

results reveal that the doped nanostructures can be substan-

tially modulated as a result of modifications on electronic

bands induced by substitutional dopant. Moreover, the

individual dopant gives rise to one or two complete electron

backscattering centers associated with impurity states in the

doped configurations, and the location is determined by the

dopant site.
Schematicsof the atomic structure after asymmetricStone–Wales
defects introduced and different nitrogen substitutional sites.

� 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction Graphene, the two-dimensionalcrystalline material made from sp2 hybridized carbon atoms,has attracted tremendous attention owing to its uniqueelectronic [1, 2] and transport properties [3, 4] since itsdiscovery [5]. However, graphene has to be modifiedbecause the absence of a bandgap in perfect graphene doesnot allow sufficient switching for practical applications.Using lithographically patterned technology or patternedadsorption of atomic engineering at nanoscale, a tunablebandgap opening has been experimentally realized in narrowgraphene nanoribbon (GNR) [6, 7], turning this nanostruc-ture into a promising material for circuit fabrication [8].Experimental [9] and theoretical [10] studies of GNRs havebeen carried out for the understanding of their electronic

[11], transport [12], and optical properties [13]. It ispredicted that GNRs have a major impact on electrictransport properties and, most importantly, GNR-baseddevices are expected to behave as molecular devices withelectronic properties [14] similar to those of carbonnanotubes (CNTs) [15].

As is well known, the electronic properties of nano-ribbons depend on the width and atomic geometry of theiredge, namely, zigzag or armchair [10, 11]. One of the mostintriguing issue is the research of edge states in the electronicstructure of zigzag GNR (ZGNR) because the nanosystemsare expected to have great possibilities for novel spintronicdevices [16]. The presence of either native or physicallyintroduced structural defects in GNRs has been explicitly


Phys. Status Solidi B 249, No. 1 (2012) 129

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Figure 1 (online color at: www.pss-b.com) Schematics of themolecular device considered in the calculation of ZGNR.Thewholedevice is composed of scattering region and two electrodes consist-ing of the pristine ZGNRs. (a) The pristine 6-ZGNR and (b) the 6-ZGNRwithasymmetricSWdefects.TheasymmetricSWdefectsarehighlighted by yellow atoms.

evidenced in several experimental studies. Furthermore,the electronic properties of ZGNR can be effectivelyfunctionalized via structural defects such as vacancies [17],adatoms [18, 19], topological defects [20], adsorption [21],substitution [22], edge reconstruction [23, 24]. Specifically,Stone–Wales (SW) defects, as one type of topologicaldefects, are formed by rotating a carbon–carbon bond by 908,as clearly visualized by using transmission electronmicroscopy (TEM) [25]. Recently, the investigation of theformation and annealing of SW defects in graphenemembranes reveals that the existence of SW defects isenergeticallymore favorable than inCNTs or fullerenes [26].And previous studies predicted that it is more likely to beobserved for the asymmetric SW defects in ZGNR [27].Meanwhile, the functionalization of GNRs can be achievedthrough substitutional doping, as implemented by high-power electrical annealing (e-annealing) or ion irradiationin experiments [28, 29]. Boron substitutional doping inGNRs could inducemetal to semiconductor (M–S) transition[22]. Hence, the predicted extraordinary properties ofnitrogen-doped nanomaterials have now been experimen-tally confirmed and they exhibit the potential applicationsin electronic nanodevices [30, 31]. It is well knownthat the ratio and substitutional position of the dopanthave a crucial influence on the electronic properties ofGNRs. The influence of substitutional impurity hascorrespondingly received particular attentions. In addition,taken the chemically synthesized and lithographicallypatterned approaches of GNRs fabrication into consider-ation, the occurrence of many types of defects, especially forthe N-doped composite, is widely regarded to be inevitable[28]. However, systematic investigation of the effects ofcomplex defects on the electronic properties of GNRs is sofar lacking [32, 33].

In this article, we carried out the spin-polarized densityfunctional theory (DFT) calculation to study the influence ofindividual N-doped GNRwith various substitutional sites onthe electronic transport properties of ZGNRs with asym-metric SW defects. The substitutional impurity is energeti-cally more favorable to distribute near the edge, and theimpurity state induced by the nitrogen is located below orabove the charge neutrality point (CNP), which is dependenton the doped sites.

2 Model Weemploy density functional theory utilizedin the SIESTA code [34, 35] to assess the stability of eachatomic-scale nanostructure from energetic and structuralconsiderations. The exchange correction term is calculatedwithin the generalized gradient approximation (GGA) in theform proposed by Perdew et al. [36]. The standard norm-conserving Troullier–Martins [37] pseudopotentials are usedto calculate the ion-electron interaction. The Brillouin zonewas sampled by 6� 2� 1 k-point mesh based on theMonkhorst–Pack Scheme [38]. The numerical double-zpolarization is chosen for atomic orbital basis set and theplane cutoff energy is chosen as 200Ry. All geometries wereconverged until the force acting on all atoms is less than

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0.01 eV/A, and the calculations are performed at electronictemperature T¼ 300K.

The quantum transport properties in the individualN-doped nanostructures are then evaluated on the basis ofthe non-equilibriumGreen’s function technique [39, 40].Weconsider the two-probe geometry system in such a waythat the central region consists of an optimized supercell(168 atoms) containing the composite defects, which issurrounded by two leads made of two perfect supercellson each side, as shown in Fig. 1. The transmission coefficientT as a function of the electron energy E is given by

T E;Vbð Þ ¼ 4Tr Im SLGrSRG

að Þ½ � (1)

whereSL (SR) represents the self-energies of the left (right)electrode,Gr (Ga) is retard (advanced) Green’s function. It iscalculated from the relation:

GrC ¼ ESC�HC�S

rL�S

rR

� �¼ Ga

C

� �y(2)

where SC and HC are single-electron Hamiltonian matrixand overlap matrix. The conductance G(E) is evaluated atthe Fermi level of the device such that GðEÞ ¼ G0TðEÞ,with G0 ¼ ð2e2Þ=h denoting the quantum conductance.More details about the NEGF formalism can be found in theRef. [41].

Following previous work [11], the length of ZGNRwidth is classified by the number (N) of the zigzag chains, werefer to a ZGNR with N zigzag dimers contained in its unitscell as N-ZGNR. In this work, we present a theoreticalinvestigation of electronic transport properties of 6-ZGNRcontaining 12 unit cells.

3 Results and discussions The optimized atomicnanostructure consisting of the asymmetrical SW is shown inFig. 2, as can be seen that some C–C bond lengths associated


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Figure 2 (online color at: www.pss-b.com) Schematics of theatomic structure after asymmetric SW defects introduced anddifferent substitutional sites in the structural model of defective6-ZGNR with asymmetric SW defects. (a) The asymmetric SWdefects are highlighted by yellow atoms, some C–C bond lengths(in A) and angles (in degree) are depicted by the red numeraland green numeral, respectively. (b) Different doping sites inthe SW defects, the substitutional impurity is denoted by A, B, C,and D.

Table 1 Substitutional sites dependent transformation energiesfor N-doped defective ZGNRs with asymmetric SW defects.

configurations transformation energy (eV)

SW-NA 4.89SW-NB 4.94SW-NC 4.90SW-ND 4.92

with the defect area change after relaxation. Assessing thestability of the asymmetric SW defects and symmetric SWdefects reveals that the asymmetric SW defects areenergetically more favorable than the symmetric SWdefects, as indicated in previous study [27]. At first glance,the asymmetric SW defects twist the whole structure byshifting the left side upward,while the right side is downwardshifted, thereby the mirror symmetry is broken. The bondangle of the edge near the pentagon of the asymmetric SWdefects could be increased from 1208 to 1298, andcorrespondingly the bond angle of the edge near theheptagon of the asymmetric SW defects is reduced to 1158.The conjunction C–C bond of the two adjacent heptagonsshrinks to 1.35 A, similar to the bond length in ethylene,suggesting more strain energy will be shared between thesetwo atoms. Compared to the case in the symmetric SWdefects, the asymmetric SWdefects further stretch from 5.38to 6.54 A, as denoted by the blue arrow in Fig. 2. The stretchof the C–C bonds that form the two heptagons caused by thepresence of the asymmetric SW defects is approximately0.02 A. Overall, the influence of asymmetric SW defects onthe geometry modification is not just limited to the defectivearea.

The substitutional dopant is known to incorporate intothe hexagonal network of ZGNRs. We consider only theindividual nitrogen substitution in the asymmetric SWdefects in the supercell containing 168 atoms. From theedge to inner, we investigate four dopant sites for the 6-ZGNR, labeled by A–D, as shown in Fig. 2b. In order toassess the stability of N-doped GNRs, we define thetransformation energy Et and calculate it by the following


equation:

Et ¼ Ed þ ECð Þ� Ep þ EN

� �(3)

where Ep is the total energy of the pristine GNR, Ed is thetotal energy of defective GNR, EC and EN is the energy ofsingle free nitrogen and carbon atom, respectively. Hence,the transformation energies of doped configurations Et arelisted in the Table 1. As can be seen clearly in the table, NA

doped site is the most energetically favorable site, whichmeans that the substitutional impurity is located preferablynear the GNR edges. Previous calculation for sole N-dopingleads to similar result [42]. Moreover, NC and ND are alsocomparatively preferable while NB doped site is the mostunfavorable site. It is found that the influence of impurity onthe atomic nanostructure change can be neglected throughthe comparisons of the atomic structures of the N-dopedZGNR with that of the undoped ZGNR. The impurityprefers to be at the edge for sole N-doping, thus in this casethe edge state is determined on the ribbon width [43]. Incontrast, as for the composite defects containing SW defectsand N-dopant, our calculations suggest that the stability ofthe composite defects strongly depends on the location andthe orientation of the SW defects.

The electronic structure results of the N-doped defectiveZGNRs in the occurrence of asymmetric SW defects aredisplayed in Fig. 3, and correspondingly, the pristine result isalso shown for comparison. As for the spin-polarized densityof states (DOS) of the pristine ZGNR, it is observed that thesharp peak at the charge neutrality point (CNP) splits intotwo striking peaks below (a-spin) and above (b-spin) theCNP, respectively. We attribute this phenomenon to thetwo spin states shifting in the opposite direction withrespect to the CNP arising from the edge state. This is ingood agreement with previous theoretical studies [11, 42].Moreover, the splitting between the a- and b-spin states inthe vicinity of CNP also demonstrates that ZGNRs areferromagnetic [11, 44]. In the case of ZGNR withasymmetric SW defects, the calculated DOS reveals thatthere are two substantial DOS peaks induced by the defects,where they are located near the CNP, and above the CNP inboth thea-spin state and theb-spin state. Indeed, not only thetwo defect states in both the a- and b-spin states, butalso the movement of the DOS peaks (located at�1.34 eV ina-spin states and�1.22 eV inb-spin states, respectively) aredirectly related to the introduction of the asymmetric SWdefects. Furthermore, the asymmetric SW defects also give

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Figure 3 (online color at: www.pss-b.com) The spin-polarizeddensity of states (DOS) for A, B, C, and D doped configurationsbased on defective ZGNR consisting of asymmetric SW defects aredisplayed in (c), (d), (e), and (f). The corresponding results of the (a)pristine and (b) defective ZGNR consisting of asymmetric SWdefects are also shown for comparison. The defect states inducedbytheSWdefectsaremarkedbythearrows,and thechargeneutralitypoint (CNP) is denoted by the dashed green line.

Figure 4 (onlinecolorat:www.pss-b.com)Conductances forA,B,C, and D doped sites based on defective ZGNR consisting ofasymmetric SWdefects are shown in (c), (d), (e), and (f). The resultsof the (a) pristine ZGNR and (b) defective ZGNR consisting ofasymmetric SW defects are also displayed for comparison. Thecharge neutrality point (CNP) is denoted by the dashed red line.

rise to remarkable decrease in DOS peaks. However, the twohighest peaks do not experience much change after theasymmetric SW defects introduced, thereby the influence ofthe asymmetric SW defects on the edge states contributed bythe unpaired p electrons is negligible. Figure 3c presentsDOS of defective ZGNR with NA doped nanostructure, ascan be seen clearly that the defects states moves to 0.19 eV ina-spin states and 1.03 eV in b-spin states. Specifically, thereexist a DOS gap at CNP in a-spin states, in contrast to theoccurrence of small DOS peak at 0.19 eV below the CNP inb-spin states. This doped site also induces two DOS valleysassociated to the impurity state above the CNP in a-spinstates, which are responsible for the resonance conductancedip located at 0.28 eV. Moreover, the DOS change arisingfrom the introduction of substitutional impurity has beenpronounced, indicating the electric transport of nanostruc-ture is significantly affected by the impurity. As for the NB

doped nanostructure, themost striking result is that the defectstate in the a-spin states moves to the location below theCNP while the defect state in the b-spin states is absent.Meanwhile, the impurity at this site also induces substantialincrease of DOS peak at 1.86 eV. NC doped site is the onenearest the inner of the nanoribbon. The defect state locatedat 0.13 eV ina-spin states resembles the nanostructure solelywith asymmetric SW defects, however, the other defect statein b-spin states moves to the location �0.12 eV below the

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CNP. The DOS valley located slightly below the CNP inb-spin states is also observed in this doped nanostructure,which evolves to the conductance dip (see Fig. 4). As for theND doped nanostructure, although the defect state in a-spinstates resembles theNC doped configuration, there has been adistinct change in the a-spin states, especially for twosmooth dips located at 0.05 and 1.01 eV. Moreover, thereemerges the other DOS dip at 2.11 eV below the CNP.The defect state in the b-spin states moves to 1.00 eV abovethe CNP, and such DOS peak is remarkably decreased.Similar changes have taken place along with the b-spinstates, that is, two smooth DOS dips distributed at 0.77 and1.20 eV, respectively. It should be noted that the emergenceof DOS dip at �2.07 eV accords with the dip located at�2.11 eV in thea-spin states, indicating remarkable electronbackscattering induced by the substitutional impurity.

Figure 4 presents the conductance for N-doped defectiveZGNRs consisting of asymmetric SW defects. Obviously,the states induced by H atoms at the edge produce aconductance peak in the vicinity of CNP in the pristineZGNR. The first conductance plateau corresponding to theoccupied and unoccupied states is G0. As for the transportproperties of asymmetric SW configuration, the absence ofconductance peak at the CNP derives from the breaking ofedge states. The localized states in the vicinity ofCNP lead toreduced conductance. Additionally, the main feature of thefirst conducting plateau below the CNP is maintained exceptfor the smooth dip below the CNP, which is originated fromthe similar wavefunctions coupling to that of the pristineGNR. The asymmetric SW defects are responsible for thetwo conductance valleys, namely, a smooth valley at�1.2 eV and a sharp valley at 1.48 eV, which are causedby the defect states. Moreover, the large reductionof conductance at these areas induced by the asymmetricSW defects thus corresponds to complete electron


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backscattering, which is different from the situation inCNTs, where SW defects induce suppression of only half ofthe conductance channels [45]. In the case of NA dopednanostructure, the conductance at CNP is substantiallydecreased, and the resonance dip at 0.28 eV corresponds tothe complete backscattering center, which is in accord withthe DOS dip near the location (see Fig. 3c). Unexpectedly,the smooth dip at�1.2 eV evolves into a sharp dip located at�1.36 eV. This effect may be related to the bands antic-rossing at this region and, eventually, the conductance islifted. Furthermore, the modifications of electronic bandsand their coupling induced by the impurity lead to thebreaking of the first conducting plateau above the CNP. As aresult, it produces the full suppression of electronic transportat about 1.36 eV and makes the sharp resonance dip locatedat 1.48 eV lift. The electronic transport of the NB dopednanostructure is very similar to that of the undoped case,especially for the results below the CNP, as opposed to thecase in the NA doped site. Although the conductance featurebelow the CNP is substantially preserved, the dopant movesthe complete electron backscattering center further awayfrom the CNP. Hence, a energy resonance dip arises slightlyabove theCNP and the resonance backscattering at�1.48 eVinduced by the asymmetric SW defects floats toward theCNP. As for the case of NC doped site, the conductance isprofoundly suppressed in the vicinity of CNP, and thepresence of two dips near the CNP derives from substantialelectron backscattering induced by the impurity. Weattribute this phenomenon to the occurrence of localizedstates evidenced by DOS peaks near the CNP that limitselectronic transport. In general, the introduction of impurityof this doped site gives rise to minor modifications onelectronic transport below the CNP, while prominentchanges taking place above the CNP are: (a) the vanishingof the small dip located at 0.64 eV in Fig. 4b; (b) the sharp dipis changed to a comparatively smooth dip and its locationmigrates toward the CNP (see Fig. 4b and e). Compared theND doped nanostructure with the undoped results, it is foundthat this dopant site induces remarkable modifications on theelectronic transport. The conductance in the vicinity of CNPis decreased, and the smooth dip below the CNP evolves intoa sharp dip. Similar to the case in the NA doped-site, thedopant yields a complete electron backscattering at about0.28 eV, and the suppression of the conduction channelobserved above the CNP also takes place here. In addition, inthe ND doped nanostructure, the electronic transport abovethe CNP resembles the NA doped configuration but the diparising from the breaking of the first plateau is shifted to1.32 eV toward the CNP. Our transport results indicate thatmodification of the electronic properties of ZGNR withasymmetric SWdefects bymeans of individual dopantmightnot be remarkable. The calculation results demonstrate thatthe presence of N-dopant in the asymmetric SW defects canintroduces resonance backscattering centers, which aredetermined by the position of doping with respect to itsedges.


4 Conclusion Weperform first principles calculationsto explore the influences of substitutional doping on theelectronic transport of defective ZGNRs with asymmetricSW defects, and four different N-doping sites are takeninto account in this communication. The transformationenergies of various doped nanostructures are assessed interms of total energies compared with the situation in thepristine results. The calculations suggest that the asymmetricStone–Wales (SW) defects ismore likely to be observed thanthe symmetric SW defects, and the nitrogen dopant in theasymmetric is energeticallymore favorable to locate near theedge. The substitutional impurity on the defective ZGNRswith the asymmetric SW defects gives rise to one or tworesonance backscattering, and the location of which dependson the dopant distribution.

Acknowledgements We are indebted to Prof. K.-L. Yaoand Dr. M. A. Kuroda for technical assistance on performing abinitio transport properties and the relax calculation in theMacOSXTuring cluster. This work is financially supported by NaturalScience Foundation of China under Grant Nos. 11047176 and10947161, and the Research Foundation of Education Bureau ofHubei Province of China under Grant Nos. Q20111305 andB20101303.

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Documents

Role of nitrogen distribution in asymmetric Stone–Wales defects on electronic transport of graphene nanoribbons