Biró, Laszlo P.

Lambin, Philippe

Márk, Geza I.

Nemes-Incze, Peter

Vancsó, Peter

English

Grain boundaries are constitutional elements of graphene grown on a solid metallic surface by CVD. The electronic properties of computer models of grain boundaries in graphene have been investigated by tight-binding calculations and compared with available ab-initio data and with recent experimental scanning tunneling spectroscopic measurements. It is shown that twofold coordinated atoms and non-hexagonal rings, both present in grain boundaries, give rise to specific features in the local density of states

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RESEARCH OUTPUTS / RÉSULTATS DE RECHERCHEAuthor(s) - Auteur(s) :Publication date - Date de publication :Permanent link - Permalien :Rights / License - Licence de droit d’auteur :Bibliothèque Universitaire Moretus PlantinInstitutional Repository - Research PortalDépôt Institutionnel - Portail de la Rechercheresearchportal.unamur.beElectronic structure of a disordered grain boundary in grapheneLambin, Philippe; Vancsó, Peter; Nemes-Incze, Peter; Márk, Geza I.; Biró, Laszlo P.Published in:Physics, chemistry and applications of nanostructuresPublication date:2013Document VersionEarly version, also known as pre-printLink to publicationCitation for pulished version (HARVARD):Lambin, P, Vancsó, P, Nemes-Incze, P, Márk, GI & Biró, LP 2013, Electronic structure of a disordered grainboundary i  graph ne. in VE Borisenko, SV Gaponenko, VS Gurin & CH Kam (eds), Physics, chemistry andapplications of nanostructures: Proceedings of the International Conference Nanommeting - 2013. WorldScientific, Singapore, pp. 203-206.General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal ?Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Download date: 23. Jun. 2020PHYSICS, CHEMISTRY AND APPLICATION OF NANOSTRUCTURESV.E. Borisenko, S.V. Gaponenko, V.S. Guri, C.H. Kam, editors(World Scientific, Singapore, 2013) p. 203-206.ELECTRONIC STRUCTURE OF A DISORDEREDGRAIN BOUNDARY IN GRAPHENEPh. LAMBINPhysics Department, University of Namur, 61 Rue de Bruxelles, B-5000 Namur, BelgiumP.  VANCSO, P. NEMES-INCZE, G. MARK, L.P. BIROInstitute for Technical Physics and Materials Science,H-1525 Budapest, P.O. Box 49, Hungary Grain  boundaries  are  constitutional  elements  of  graphene  grown  on  a  solid  metallic surface by CVD. The electronic properties of computer models of grain boundaries in graphene  have  been  investigated  by  tight-binding  calculations  and  compared  with available ab-initio data and with recent experimental scanning tunneling spectroscopic measurements.  It  is  shown  that  twofold  coordinated  atoms and non-hexagonal  rings,  both present in grain boundaries, give rise to specific features in the local density of  states.1.   IntroductionThe remarkable properties of graphene have triggered a race for the development of reliable  and large-scale  production  techniques.  Among them, the  chemical  vapor deposition  (CVD)  route  is  a  promising  technique.  It  consists  in  a  thermal decomposition of light hydrocarbon molecules at the surface of a metallic substrate. Copper is a widely-used substrate for that purpose, because it has little interaction with the adsorbed graphene layer. The d bands of this noble metal are indeed located too far below the Fermi level to hybridize with the   orbitals of carbon [1]. As a consequence, the graphene layer is floating in a shallow potential well above the Cu surface. In usual CVD conditions, graphene flakes are growing simultaneously at many places of the surface, the smallest grains being able to diffuse and to merge with largest ones [2]. The graphene sheet so obtained is necessarily a polycrystal with many grain boundaries [3].Like  in  all  solids,  the  grain  boundaries  affect  the  mechanical,  electronic, electromagnetic  ...  properties  of  the  graphene  layer  and  are,  therefore,  worth studying [4]. The present paper aims at making progress in the understanding of the electronic properties of grain boundaries in CVD graphene.2.   MethodologyThe grain boundary (GB) investigated in this paper were relaxed by minimizing their Author version © World Scientific (2013)Tersoff-Brenner energy with the constraint that the atomic structure, supposed to be adsorbed on a solid surface, remains flat. This procedure avoids the  and  orbitals of C to mix, even if sp2 hybdridization cannot be realized everywhere due to non-hexagonal rings and twofold coordinated atoms.The  electronic  structure  was  explored  with  the   tight-binding  Hamiltonian restricted  to  first-neighbor  hopping  interactions  Vij =  0(dCC/dij)2 where  dij is  the distance between the atoms i and j, 0 = -2.7 eV and dCC = 0.142 nm. The  orbitals were all supposed to lie at the same level, chosen as the zero of energy, irrespective of  the  atomic  environment.  Local  densities  of  states  (LDOS)  were  obtained  by application  of  the  recursion  algorithm.  For  each  LDOS,  155  pairs  of  recursion coefficients were computed on a cluster of about 63500 atoms.3.   Results and discussionThe grain boundary (GB) under consideration has been observed by STM on the surface of HOPG [5]: two graphene grains, mirror symmetric of each other, are tilted by an angle of +20.8° and -20.8°, respectively, from the GB line. The connection between the grains is periodic with length 0.65 nm. The tilt angle and the period correspond to the translation vector (2,1). An ideal structural model, shown in Fig.  1(a), consists in a periodic alternation along the GB line of a pentagon-heptagon (5-7) pair and a CC bond shared between two hexagons.LDOS were computed on 50 atoms contained in the box marked by dashed lines in Fig. 1(a). The GB DOS represented by the dashed line curve in Fig. 1(d) is the sum of these 50 LDOS. It was found to be in reasonable agreement with ab-initio VASP calculations performed for the same type of structure [6]. It has been checked that  neither  a  dislocation  in  graphene  (isolated  pentagon  or  heptagon)  nor  a dislocation core (isolated 5-7 pair) produces sharp low-energy peaks in the tight-binding density of states. The peaks at +0.5 and -0.8 eV in the DOS of the GB are  therefore attributed to the repetition of 5-7 pairs and their concomitant interactions.In the context of CVD, it is unlikely that two merging graphene grains can be connected exclusively with threefold coordinated atoms. For that  reason,  twofold coordinated atoms have been introduced in the GB of Fig. 1(c), whose structure  derives from that of Fig. 1(a) by removal of these atoms located on the pentagonal sites that lie on the symmetry axis. The GB is now formed by a succession of 7- and 11-membered rings. The DOS of this GB (dashed line curve in Fig. 1(e)) has a Dirac  delta peak located at  zero energy.  This peak results  from states localized on the twofold coordinated atoms, which do not couple together along the periodic axis. Interestingly, the peak at +0.5 eV survives to the introduction of vacancies on the GB line, whereas the peak at -0.8 eV does not.2 be  realized  by removing  atoms  on  a  fraction  0  <  c  <  1  of  the  aforementioned pentagonal sites.  Fig. 1(b) illustrates a configuration corresponding to c = 0.4. For a given value of  c,  atoms were removed randomly from the pentagonal  sites  with probability c and the GB DOS, computed in a box similar to that shown in Fig. 1(a),  were averaged over 72 configurations of the vacant sites. The results obtained are displayed in Figs. 1(d,e) for six values of c. The peak at -0.8 eV rapidly washes out with increasing c, whereas the peak at +0.5 eV remains and broadens somewhat. In the interval 0.5 < c < 0.8, additional well-resolved peaks show up between 0.1 and 0.3 eV (Fig. 1 (e)). The peak at zero energy, attributed to states localized around the vacant sites, emerges with an asymmetric shape in the DOS when c exceeds 0.2 (Fig. 1 (d)) and keeps growing with increasing c. These results  indicate  that  peaks observed  at  0.1 – 0.2  eV above the  Fermi energy  in  experimental  STS  spectra  recorded  on  and  near  disordered  grain boundaries  in  CVD graphene  [6,7]  can  be  attributed  to  the  presence  of  twofold coordinated atoms in the GB structure. In particular, the asymmetric peak observed at E=0 in Fig. 1(d) for, e.g., c = 0.3 might actually lie 0.1 eV above the Fermi level, in agreement with experiment, if the graphene sheet were slightly p doped.  AcknowledgmentsThis  research  was  supported  by  a  Marie  Curie  International  Research  Staff Exchange  Scheme  Fellowship  within  the  7th  European  Community  Framework Programme (MC-IRSES proposal  318617  FAEMCAR project).  It  also  benefited from MFA (Hungary) and F.R.S. (Belgium) co-operation grants. Calculations have been  performed on  the  inter-university Scientific  Computing  Facilities  (iSCF)  of Namur. The work in Hungary was supported by the Hungarian Scientific Research Fund under grant number OTKA K101599.References1.  A. Allard, PhD thesis, IEMN (Lille, 2011).2.  Ch. Hwang, K. Yoo, S.J. Kim, E.K. Seo, H. Yu, and L.P. Biró, J. Chem. Phys. C 115, 22369 (2011) .3.  B.I. Yakobson and F. Ding,  ACS Nano 5, 1569 (2011) .4.  Q. Yu , L.A. Jauregui, W. Wu, R. Colby, J. Tian, Z. Su, H. Cao, Z. Liu, D.  Pandey, D. Wei, T.F. Chung, P. Peng, N.P. Guisinger, E.A. Stach, J. Bao, S.S. Pei and Y.P. Chen, Nature Mater. 10, 443 (2011).5.  P.  Simonis, C. Goffaux, P.A. Thiry, L.P. Biró, Ph. Lambin, and V. Meunier, Surf. Sci. 511, 319 (2002).6.  P. Nemes-Incze et al, submitted to Phys. Rev B (December 2012).7.  L. Tapaszto, P. Nemes-Incze, G. Dobrik, K. Jae Yoo, C. Hwang, and L.P. Biró, Appl. Phys. Lett. 100, 053114 (2012).4

Electronic structure of a disordered grain boundary in graphene

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Electronic structure of a disordered grain boundary in graphene

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