The role of defects and doping in 2D graphene sheets and ...

The role of defects and doping in 2D graphene sheets and 1D nanoribbons

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2012 Rep. Prog. Phys. 75 062501

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Rep. Prog. Phys. 75 (2012) 062501 (30pp) doi:10.1088/0034-4885/75/6/062501

The role of defects and doping in 2Dgraphene sheets and 1D nanoribbonsHumberto Terrones1,2, Ruitao Lv1, Mauricio Terrones1,3,4,7 andMildred S Dresselhaus5,6,7

1 Department of Physics, The Pennsylvania State University, University Park, PA 16802, USA2 Departamento de Fısica, Universidade Federal do Ceara, PO Box 6030, Fortaleza, CEP 60455-900,Brazil3 Department of Materials Science and Engineering and Materials Research Institute,The Pennsylvania State University, University Park, PA 16802, USA4 Research Center for Exotic Nanocarbons (JST), Shinshu University, Wakasato 4-17-1, Nagano-city380-8553, Japan5 Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology,Cambridge, MA 02139- 4307, USA6 Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA

E-mail: [email protected] and [email protected]

Received 24 November 2010, in final form 8 March 2012Published 23 May 2012Online at stacks.iop.org/RoPP/75/062501

AbstractDefects are usually seen as imperfections in materials that could significantly degrade theirperformance. However, at the nanoscale, defects could be extremely useful since they could beexploited to generate novel, innovative and useful materials and devices. Graphene andgraphene nanoribbons are no exception. This review therefore tries to categorize defects,emphasize their importance, introduce the common routes to study and identify them and topropose new ways to construct novel devices based on ‘defective’ graphene-like materials. Inparticular, we will discuss defects in graphene-like systems including (a) structural (sp2-like)defects, (b) topological (sp2-like) defects, (c) doping or functionalization (sp2- and sp3-like)defects and (d) vacancies/edge type defects (non-sp2-like). It will be demonstrated that defectsplay a key role in graphene physicochemical properties and could even be critical to generatebiocompatible materials. There are numerous challenges in this emerging field, and we intendto provide a stimulating account which could trigger new science and technologicaldevelopments based on defective graphene-like materials that could be introduced into otheratomic layered materials, such as BN, MoS2 and WS2, not discussed in this review.

(Some figures may appear in colour only in the online journal)

This article was invited by M-Y Chou.7 Authors to whom any correspondence should be addressed.

Contents

1. Introduction 22. Graphene and graphene nanoribbons 3

2.1. Graphene 32.2. Graphene nanoribbons: edge structure, width

and electronic properties 42.3. Synthesis and characterization of graphene

and graphene nanoribbons 52.4. Graphene as a substrate 8

3. Vacancies in graphene and graphene nanoribbons 9

3.1. Experimental generation of vacancies 103.2. Calculations of vacancies in graphene and

graphene nanoribbons 114. Topological defects 11

4.1. Heptagon–pentagon pairs and the Thrower–Stone–Wales transformation in graphene andnanoribbons 11

4.2. Grain boundaries and extended line of defectsin graphene and nanoribbons 15

0034-4885/12/062501+30$88.00 1 © 2012 IOP Publishing Ltd Printed in the UK & the USA

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Rep. Prog. Phys. 75 (2012) 062501 H Terrones et al

5. Doping and functionalization 165.1. Substitutional doping of graphene with N, B,

S, P, Si and reduced graphene oxide 165.2. Importance of the dopant site and property

changes 215.3. Functionalization 22

6. Applications 226.1. Graphene-based field-effect transistors 24

6.2. Transparent conductive electrodes 24

6.3. Graphene-based sensors 25

6.4. Energy storage and conversion 25

6.5. Other applications 267. Conclusions and perspectives 26Acknowledgments 27References 27

1. Introduction

John Desmond Bernal in his seminal paper on the structureof graphite in 1924 recognized the previous difficulties ofthe proposed structures by Hull [1], and Debye and Scherrerin 1917 [2] due to their lack of highly crystalline samples.Bernal solved the crystal structure of graphite using x-raydiffraction with the crystal rotation technique on a very goodquality natural crystal of ceylon graphite (see figure 1(a))[3]. Lipson and Stokes reported in 1942 that the graphiticlayers could also have a different order, not the ab, ab, . . .

stacking reported by Bernal, but abc, abc, . . . rhombohedralstacking [4]. Gibson in 1946 reported that the structure withabc, abc, . . . stacking was actually the structure reported byDebye and Scherrer in 1917 [5]. A few years later, RosalindFranklin in 1951 described non-graphitic turbostratic carbonswhere stacking symmetry was not preserved and exhibited aninterlayer spacing of 3.44 Å, slightly larger than the 3.35 Åspacing of graphite [6].

For these intervening 30 years, the main topic of graphite-related study involved the disorder or relative order of theconstituent graphene layers, and did not concentrate on thestudy of individual layers. In the 1960s researchers started tofocus on defects within individual layers, such as vacancies,interstitials and grain boundaries. Peter Thrower studiedthe role of vacancies and interstitials in the self-diffusion ingraphite, and also the formation of interstitials and vacancyloops in graphite under high irradiation [8–10]. Amelinckxand colleagues also studied dislocations in graphite by the mostadvanced transmission electron microscopy (TEM) techniquesthen available [11, 12]. In 1966 Roscoe and Thomas [7]proposed a small angle grain boundary exhibiting heptagon–pentagon pairs but, for some unknown reason, they did notdraw all the bonds in their published figures (see figure 1(b)).

Study of the intercalation of ions and molecules intographite started in the 1960s and became better known inthe 1970s. The intercalation process inserts guest speciesbetween graphite layer by a controlled method and is usedto generate large electron or hole carrier concentrations in thegraphene layers [13]. The staging phenomenon whereby asingle intercalant layer can be inserted periodically betweengraphene layers (up to perhaps seven layers) provides anexample of the use of controlled defects to change materialbehaviors by providing the host materials with unusual andwell-controlled properties [13].

Systematic studies of defects started to be carried outin 1981 when Elman used ion implantation to create point

defects in graphite [14]. In these studies the amount oflattice damage was controlled by the ion mass and its energy,with low mass ions such as 11B ions implanted at 20 keVand a fluence of 1012 ions cm−2, thereby providing low levelsof damage [14]. Typical control parameters that were usedinclude ion species of different masses ranging from boron tobismuth, ion energies from 20 to 200 keV and ion fluences from1012 to 1015 ions cm−2. The experimental characterizationtechniques used at that time were x-ray diffraction, TEM forstructural studies, Raman and infrared (IR) spectroscopy forstudying structural damage effects on the phonon response,and transport measurements to assess the damage to theelectronic properties. The findings of these defect studies aresummarized in some detail in a book written on the subjectof ion implantation in graphite [15]. Similar experimentalapproaches plus some new techniques, such as scanningtunneling probes, have recently been used more quantitativelyto study controlled defects in graphene using similar ionimplantation techniques with some further advances [16].

With the discovery of Buckminsterfullerene or carbon60 (C60) in 1985, a new area in carbon science started, notonly because C60 was a newly found carbon molecule but alsobecause C60 could be seen as a finite high symmetry graphiticnanostructure containing 20 hexagonal rings and 12 pentagonalrings of carbon that were required to close the molecularstructure [17]. The icosahedral C60 structure is highly stableagainst random defect formation, which can be documentedby the 200 or so different IR-active modes and ∼200 Raman-active modes that can be reproducibly observed. These modesare associated with the high icosahedral symmetry of the C60

molecule [18]. Soon after the bulk synthesis of C60 [19, 20],intense theoretical and experimental work followed [18] andthe quest for new sp2-like carbon cage molecules (knownas fullerenes) began. In this context, the idea of elongatingthese carbon cages along one direction was introduced. As aresult of this elongation, carbon nanotubes were predicted [21–23]. The synthesis and chirality identification of single-walledcarbon nanotubes (SWCNTs) by electron diffraction was soonreported [24]. It is important to mention that SWCNTs andmulti-walled carbon nanotubes (MWCNTs) were observed asearly as the 1970s by Endo using high-resolution transmissionelectron microscopy (HRTEM) [25]. The reader is encouragedto read some nanotube reviews or related books that have beenpublished elsewhere [18, 26]. From the above paragraphs,it is clear that intense research into the nanocarbon worldstarted in the late 1980s and had continued with the discoveryand isolation of other forms of carbon including graphene,graphene nanoribbons, platelets, doped CNTs, etc.

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Figure 1. (a) Original drawing by Bernal describing the structure of graphite. Reprinted with permission from [3]. Copyright 1924 by TheRoyal Society. (b) Roscoe and Thomas model for a grain boundary. Note that bonds are not drawn in the defective regions. Five–sevendefects can be drawn avoiding dangling bonds. Reprinted with permission from [7]. Copyright 1966 by Elsevier Ltd.

In 2004 a series of experiments showed that graphene,an individual sheet of graphite, could be isolated and theseexperiments showed unique and exciting physicochemicalproperties different from those observed in graphite, and anew field dedicated to atom-thick 2D carbon materials started[27–30]. The early entry of Boehm into the monolayergraphene field in 1961 was recognized, and it was Boehmwho gave graphene its name [31–33]. In 2010, Chuvilin andcolleagues showed the transformation of a graphene surfaceinto a fullerene using a transmission electron microscope [34],thus showing that fullerenes are indeed a metastable stateof graphene. In summary, one could transform grapheneinto fullerenes, graphene into nanotubes, fullerenes intonanotubes or nanotubes into graphene nanoribbons. Thesetransformations are all possible and have been demonstratedfrom both a theoretical and experimental standpoint [34–37].This makes carbon so diverse. It is fascinating to witness thata very old and common element, such as carbon, is capableof forming all of these novel morphologies with unusualproperties. We foresee that other novel and exotic carbonnanostructures will be synthesized and predicted in the years tocome, though it is difficult to predict the new forms of carbonthat will someday appear, but hybrid materials incorporatinggraphene, nanotubes, nanoribbons, fullerenes and diamondcould be a promising new research direction for future focus.

For graphene, defects occur within a single monolayer.For few-layer graphene, interlayer-type defects such asstacking faults also occur. Thus, the physicochemicalproperties of monolayer and few-layer graphene depend notonly on the presence of defects but also on the defect type,the defect environment and the arrangement of ensembles ofdefects. In this account, several defects that appear in grapheneare reviewed and studied, and several challenges associatedwith their atomic characterization and control are discussed.The study of defects in graphene is special because graphene isthe most fundamental form of sp2 hybridized carbon, and whatwe learn from the study of each defect can then be used as abasis for understanding related defects occurring in sp2-likecarbons more generally.

2. Graphene and graphene nanoribbons

In this section, we summarize the structure and properties ofgraphene and graphene nanoribbons in their pristine forms,prior to the introduction of defects.

2.1. Graphene

Graphene consists of a single and infinite layer of graphite inwhich each carbon atom possesses an sp2 hybridization. Byhybridization we mean that each carbon atom is connectedto three other carbon atoms via covalent bonds with lengthsof 1.42 Å and with 120◦ angles between each bonded pair(see figure 2). In addition, graphene could be considered asa network consisting of two triangular sublattices in whichthe electronic states form two energy bands intersectingat the K and K′ points in the Brillouin zone, and thesehigh symmetry points K and K′ are connected by inversionsymmetry. Close to these crossing points, the electronenergy E(k) depends linearly on the wave vector k obeyingthe relativistic Dirac equation; thus electrons and holes inmonolayer graphene are called Dirac fermions and points Kand K′ in reciprocal space are called Dirac points [28]. Diracfermions are responsible for many new phenomena in physics,which for the case of graphene cause the anomalous integerquantum Hall effect at room temperature [30, 38], insensitivityto external electrostatic potentials (Klein paradox), jitterymotion of the wave function (zitterbewegung) under confiningpotentials, and huge mean free paths (carrier mobilities ofmore than 100 000 cm2 V−1 s−1) [29, 39]. Experiments by theManchester group in 2004 with few-layer graphene opened upa new research era on 2D layered materials [27]. However, theamazing properties of graphene change by adding additionallayers, thus losing the real 2D character and also the Diracfermion behavior [40–42]. To date, intensive experimental andtheoretical studies of bilayer and tri-layer graphene have alsotaken place, including studies of different interlayer stackingorders.

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2.2. Graphene nanoribbons: edge structure, width andelectronic properties

Fujita and colleagues realized that, as in all realistic crystalstructures, graphene should have edges, in this case onedimensional (1D) edges, which in the context of unzippedCNTs can be regarded as graphene ribbons, with armchairedges and zigzag edges as the two special high symmetrycases (see figure 2) [43, 44]. Therefore, in this context,armchair graphene nanoribbons (AGNRs) exhibit differentwidths depending on the number ‘NA’ of dimer lines across theribbon width (NA-AGNRs), and likewise for zigzag graphenenanoribbons (ZGNRs) with a corresponding number ‘NZ’ forNZ-ZGNRs) (see figure 2).

Within a tight-binding approach, AGNRs could bemetallic or semiconducting depending on their ribbon width,

Figure 2. Molecular models of graphene nanoribbons with differentedge morphologies: (a) an eight-zigzag graphene nanoribbon(8-ZGNR). (b) A 14-armchair graphene nanoribbon (14-AGNR).The edges of both nanoribbons are here saturated with hydrogen(cyan) atoms so that all the in-plane carbon bonds are satisfied.

Figure 3. Molecular model of (a) a ‘chevron-like’ graphene nanoribbon and (b) a graphitic nanowiggle exhibiting a combination ofarmchair and zigzag edges.

but all ZGNRs are metallic, with a high density of electronicstates (DOS) at the edges. Therefore ZGNRs exhibitcharacteristic edge effects which are not present in AGNRs.These edge effects in ZGNRs are responsible for a flatband close to the Fermi level which implies a peak in theelectronic density of states, thus making the ZGNR edgesmore reactive [43, 44]. These fundamentally different edgeproperties for ZGNRs and AGNRs provide a handle towarddistinguishing armchair from zigzag edges at the nanoscaleusing local optical techniques which usually operate at themicrometer (10−6 m) size level. When using first-principlescalculations, all ZGNRs and AGNRs possess non-zero, directband gaps. For ZGNRs the gaps are mini-gaps caused byspin ordering effects at the edges, and for AGNRs the bandgaps arise from quantum confinement effects and can havelarger magnitudes than for ZGNRs [45]. If spin polarizationis considered in ZGNRs and quantum transport is studied,a band gap appears close to the Fermi level for the moststable antiferromagnetic configuration in which the total spinwithin the unit cell is zero: the spin is antiparallel acrossthe zigzag edges (up at one side and down at the other sideacross the ribbon). However, a metastable ferromagneticconducting configuration could also be calculated with anenergy difference, from the antiferromagnetic case, of a fewtens of meV [45, 46]. In the ferromagnetic case, the total spinwithin the unit cell is not zero and both zigzag edges acrossthe ribbon in the unit cell exhibit parallel spin orientations.

For GNRs, the band gap decreases as the ribbon widthincreases, so if a semiconductor with a desirable band gapis needed, then the nanoribbon width should be reducedaccordingly. This, of course, requires very precise controlover the edges and widths of an AGNR, if applications areenvisaged [45, 47, 48]. The bottom-up synthesis of graphenenanorribbons of different topologies and widths has beenreported by Cai and colleagues [49]. In this work, usingsurface-assisted coupling of molecular precursors into linearpolyphenylenes and a subsequent cyclodehydrogenation,‘chevron-like’ GNRs are fabricated (see figure 3(a)). With thisin mind, Costa-Girao et al have shown theoretically that themixture of armchair and zigzag nanoribbons, called ‘graphiticnanowiggles’ (see figure 3(b)), exhibit different band gaps andmagnetic behaviors, depending on the mixture of armchair andzigzag character within the same nanostructure [50].

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Armchair and zigzag edges in highly oriented pyrolyticgraphite (HOPG) have been characterized using scanningtunneling microscopy (STM) and scanning tunnelingspectroscopy (STS), finding electronic states close to the Fermilevel for zigzag edges, and defective armchair edges, butnot for homogeneous armchair edges [51–53]. Using a sub-nanometer-resolved STM-STS technique, Tao et al examinedthe dependence of electronic structure on the chirality ofatomically well-defined GNR edges [54]. The GNRs they usedwere synthesized by unzipping CNTs [55]. Zigzag edges wereobserved by STM, and the finite width of the GNR leads tono actual band gap, which can be attributed to the reducedon-site Coulomb repulsion. Interestingly, the existence ofspin-polarized magnetic edge states in chiral GNRs was alsoobserved [54]. Along this line, some theoretical calculationson chiral graphene edges have also been carried out [56–59].

As in 3D crystals, graphene sheets and GNRsexhibit defects which result in significant changes in theirphysicochemical properties, and these should be studied inorder to understand their properties with particular attentiongiven to special kinds of defective 2D layered materials thatcould lead to novel applications. In this paper, we focus onthe role of defects in these systems, how to control the defectbehaviors and how perhaps to utilize some of these behaviorsfor practical applications.

2.3. Synthesis and characterization of graphene andgraphene nanoribbons

The following subsections describe the various ways ofproducing graphene, few-layered graphene and graphiticnanoribbons. The methods range from the chemical vapordeposition (CVD) technique to the chemical longitudinalunzipping of CNTs. Novel routes are constantly beingfound and we expect that, with effort and proper know-how,it will be possible to achieve some control of the atomicedge morphology at the nanoscale. Until now, only a fewmethods have been able to report short segments of atomicallycontrolled and/or smooth edges for GNRs [42].

2.3.1. CVD of graphene and graphitic nanoribbons. In 1990,graphitic nanoribbons were first produced using a CVD processinvolving the disproportionation of carbon monoxide at 400–700 ◦C, which was catalyzed by Fe(CO)5 particles in flowingCO/H2 gas [60]. These graphitic nanoribbons consistedof filaments of 10 µm in length and 0.1–0.7 µm in width(10–200 nm thick), and a metal catalyst particle was alwayslocated at one of their ends. In these graphitic nanoribbons, thegraphitic layers exhibited a uniform orientation perpendicularto the filament axis. An alternative CVD production methodfor obtaining graphitic nanoribbons was reported by Campos-Delgado et al in 2009 (see figure 4) [61]. These authorsused micrometer-size droplets produced by an ultrasonicgenerator containing ferrocene, ethanol and thiophene, andthese droplets were carried by flowing Ar gas to a furnaceoperating at 950 ◦C. The resulting nanoribbons synthesizedby CVD consisted of flattened and piled up graphene sheetsand displayed GNRs several micrometers in length, 20–300 nm

Figure 4. Scanning electron microscopy (SEM) images ofCVD-grown graphitic nanoribbons and further heat-treated productsderived from these GNRs which were heat treated at differenttemperatures. Reprinted with permission from [61]. Copyright 2009by Elsevier Ltd.

wide and <15 nm thick. In contrast to the work of Murayamaand Maeda [60], catalytic particles were not found in theseribbons but the presence of ferrocene and thiophene wascrucial for their production. Jia et al found that electronbeam irradiation combined with Joule heating experimentsof these nanoribbons inside an HRTEM, resulted in thegeneration of atomically smooth zigzag and armchair edges(figure 5) [62]. These observations confirm that the most stableedges in graphene ribbons are indeed zigzag and armchairedges (see figure 5). An alternative CVD method involvingferrocene and tetrahydrofuran (THF) resulted in crystallinecarbon nanoribbons (figure 6) [63]. Unfortunately, the authorsof this work did not specify the dimensions of the producednanoribbons. In this case, the orientation of the (0 0 2) latticeplanes of the graphene sheets was perpendicular to the ribbongrowth axis.

Interestingly, GNRs could be fabricated using SiC tracksas a template [64, 65]. Sprinkle et al demonstrated theself-organized growth of GNRs with 40 nm widths on atemplate SiC substrate via scalable photolithography andmicroelectronics processing. Such as-grown GNRs can beused for the scalable fabrication of graphene devices, whichexhibit quantum confinement at 4 K, an on/off ratio of 10 and acarrier mobility of up to 2700 cm2 V−1 s−1 at room temperature[64]. Robinson et al also demonstrated the direct synthesisof epitaxial GNRs by utilizing a crystallographic confinementtechnique unique to SiC. These authors discovered that theepitaxial growth of graphene initiates at the SiC step edge andconsists of (1 1 0 n) lattice planes, and multilayer graphene canform along a SiC terrace edge prior to on the formation of theterrace itself [65].

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Figure 5. Edge motion of graphitic nanoribbons under Joule heating inside the transmission electron microscope. (a) A three-layerzigzag–armchair–zigzag–armchair edge array. The red arrow indicates the position of the zigzag–armchair edge junction at the beginning ofthe annealing process. After some time of Joule heating, the junction moves up ((b) and (c)), keeping the short zigzag-edge length almostunchanged. Eventually, the zigzag edge joins with the upper zigzag edge, forming a stable zigzag–zigzag–armchair edge array (d).Reprinted with permission from [62]. Copyright 2009 by the American Association for the Advancement of Science.

Figure 6. SEM images of CVD-grown carbon nanoribbons with different magnifications: (a) 1 µm scale, (b) 500 nm scale. Reprinted withpermission from [63]. Copyright 2008 by Elsevier Ltd.

2.3.2. CVD of graphene sheets. In addition to the‘Scotch Tape’ method used by Novoselov et al to obtainindividual graphene layers [27], other researchers havereported alternative routes to synthesize graphene. One routedeals with the growth of epitaxial graphite films by thethermal decomposition of SiC on the (0 0 0 1) surface [66].An alternative method for producing single- and few-layeredgraphene uses the CVD process under ambient conditionson a polycrystalline Ni substrate [67]. This technique wasmodified using different carbon sources (e.g. polymer filmsand small molecules deposited on a catalytic metal substrate)[68]. Large-area graphene sheets have also been reportedby Ruoff and co-workers using CVD with CH4 and H2

source gas mixtures at 1000 ◦C impinging on Cu foils [69].Although these techniques are somewhat efficient, a challengestill persists: producing large amounts of graphene sheets,unattached to a substrate. To produce such a material,additional experimental work is required. For example, theuse of other substrates, such as ZnS during the CVD ofCH4 at 750 ◦C has been reported, and further acid treatmentsto dissolve the ZnS ribbons produced few-layer graphene

nanoribbons (FLGNRs) [70]. It may be possible that otherceramic compounds could lead to a simpler formation ofgraphene sheets but further fundamental investigations arerequired.

2.3.3. Chemical synthesis of graphitic nanoribbons. Ithas been possible to synthesize graphene by electrophoreticdeposition of diamond nanoparticles on HOPG followed byheat treatment [71]. Using a similar method, Cancadoet al were successful in producing graphene edges, whichwere characterized by Raman spectroscopy [72]. Dai’sgroup appears to have been the first to produce GNRsby the sonochemical exfoliation of commercial graphite inthe presence of dichloroethane and a polymer, and theseribbons were used to construct field-effect transistor (FET)devices [48].

Pure organic chemical routes have been used to synthesizeGNRs by linking tetra- and hexa-phenylbenzenes via theSuzuki–Miyaura reaction [73]. These GNRs are highly solublein organic solvents due to the introduction of branched alkylside chains, which act as functional groups to solubilize the

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Figure 7. Bottom-up fabrication of GNRs. (a) Reaction scheme of chevron-type GNRs from tetraphenyl-triphenylene monomers. (b) STMimage of chevron-type GNRs fabricated on a Au(1 1 1) surface (T = 35 K, U = −2 V, I = 0.02 nA). The inset shows a high-resolutionSTM image (T = 77 K, U = −2 V, I = 0.5 nA). (c) STM image of straight GNRs from bianthryl monomers after cyclodehydrogenation at400 ◦C. The inset shows a higher resolution STM image. (d) High-resolution STM image with partly overlaid molecular model (blue) of theribbon. Reprinted with permission from [49]. Copyright 2010 by Nature Publishing Group.

GNRs. The lengths of these ribbons were found to be 8–12 nm, and they can form both aligned monolayers, as wellas crystallized monolayers from solution by π–π stacking.This appears to be the first bottom-up approach to producingGNRs with armchair edges. However, different variants ofthis reaction could lead to longer or branched nanoribbons. Inaddition, it seems that it is more likely to produce armchairedges rather than zigzag edges using this approach and furtherinvestigations are needed along this line (figure 7) [49].Hydrothermal synthesis involving Teflon-lined autoclaves hasbeen used to synthesize amorphous carbon nanoribbons. Inparticular, C6H6, Na and ferrocene were introduced in thehydrothermal reactor at 210 ◦C for 24 h [74]. Other alternativeapproaches to produce graphitic nanoribbons have consistedof collapsing CNTs [75–79].

2.3.4. Graphene nanoribbons by unzipping carbon nanotubes.A natural source of GNRs is CNTs. By unzipping them, onecould obtain single- and few-layered nanoribbons (figure 8).This unzipping technique was first developed in 2009 byseveral groups [37, 55, 80–82]. One of the methods, shownin figure 8(a), is based upon the intercalation of lithium inliquid ammonia into MWCNTs [37], followed by acid andthermal exfoliation treatments. Further improvements of thistechnique should be developed in order to obtain a completeunzipping of the tubes. The group led by James Tour [80]

reported a chemical route based on the partial oxidation ofMWCNTs using H2SO4 and KMnO4 (figure 8(b)). Thesenanoribbons exhibit oxidized edges, which make them highlysoluble in polar solvents. More recently, Dai and collaboratorsreported an additional chemical method for unzipping CNTsby treating MWCNTs in air at 500 ◦C followed by thesonication of the resulting material in a 1,2-dichloroethane(DCE) organic solution of poly(m-phenylenevinylene-co-2,5-dioctoxy-p-phenylenevinylene) (PmPV) [83]. The catalyticcutting of graphene planes has become an attractive method(figure 8(c)) when compared with other chemical methods.Unfortunately, the amount of nanoribbons produced by thistechnique is approximately 5% of the starting CNT sample. Inthe past, various researchers have demonstrated that catalyticmetal particles (e.g. Co, Ni, Fe) can cut graphene layersonly along armchair or zigzag atomic directions [84–86].Therefore, if metal nanoparticles are deposited on the surfaceof MWCNTs and these coated tubes are subsequently placedon Si wafers and treated at 850 ◦C, under a low flow ofH2–Ar, the resulting material should consist of unzippedCNTs. This unzipping process consists of the metal catalystdissociating carbon bonds, and these unbonded carbon atomsthen react with H2 to form CH4 [87]. This route wassuccessful in the unzipping of MWCNTs and N-dopedMWCNTs [81]. In addition, it was also demonstrated thatnanotubes could be easily unzipped by passing high electrical

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Figure 8. Unzipping CNTs into GNRs. (a) Intercalation-exfoliation of MWCNTs, involving treatments in liquid NH3 and Li, andsubsequent exfoliation using HCl and heat treatments, (b) a chemical route involving acid reactions that start to break carbon–carbon bonds(e.g. using H2SO4 and KMnO4 as oxidizing agents), (c) a catalytic approach, in which metal nanoparticles ‘cut’ the nanotube longitudinallylike a pair of scissors, (d) an electrical method by passing an electric current through a nanotube and (e) a physicochemical method byembedding the tubes in a polymer matrix followed by Ar plasma treatment. The resulting structures are either GNRs or graphene sheets (f ).Reprinted with permission from [42]. Copyright 2010 by Elsevier Ltd.

current inside a transmission electron microscope (figure 8(d))[82]. An alternative method was recently developed by Dai’sgroup. Their method consisted of embedding MWCNTs inpoly(methyl methacrylate), subsequently turning the MWCNTcomposite over and the tubes that were not covered by thepolymer were etched away by an Ar plasma (figure 8(e)) [55].Various challenges still remain in controlling the nanotubeopening processes, whether this opening occurs by exfoliation,etching, reduction or oxidation. In addition to challenges incontrolling the opening of MWCNTs, a scalable process wouldhave to provide conditions that prevent the agglomeration,wrinkling and entanglement of the produced nanoribbons, theentanglement being caused by attractive van der Waals forceswhich attract nanotube fragments. Finally, the unzipping oftubes preserving atomically smooth edges is still a challenge.Although a few groups have succeeded in observing atomicallysmooth edges in GNRs, more control on the edge morphologyis still needed.

2.4. Graphene as a substrate

A single layer of graphene has been shown to enhance theobserved Raman signal of another sp2 hybridized carbonmaterial placed on top of a graphene monolayer. In particular,the sp2 hybridized carbon sample could be another graphenelayer, a CNT or a graphene ribbon [88, 89]. Figure 9(a)shows a schematic illustration of molecules on graphene[88, 89]. The Raman signal can be enhanced for each feature

of an sp2 carbon sitting on a graphene layer when takinga Raman spectrum, and this effect has been called GERS,denoting graphene enhanced Raman spectroscopy, inspiredby the surface-enhanced Raman scattering (SERS) processbut produced by a different mechanism. A typical Raman-fluorescence spectrum of rhodamine 6G (R6G) in solutionusing 514 nm laser excitation is shown in figure 9(b) (theblue line). In contrast, for R6G adsorbed on graphene, thefluorescence emission could be effectively suppressed by amonolayer graphene substrate so that the Raman peaks of R6Gare clearly observed (red line in figure 9(b)). As a reminder,the SERS process produces enhancements of Raman signalsby many orders of magnitude when a sample sits on smallhighly faceted Ag nanoparticles, due to the interaction of thesample with the very strong electromagnetic field gradientsproduced by these tiny Ag nanoparticles. In the GERSprocess the signal enhancement is only about an order ofmagnitude, but it is expected that the GERS enhancementeffect is reproducible and can be used as a more quantitativecharacterization technique than SERS. Therefore it is expectedthat the GERS effect should be useful to study the Ramanspectra of defects sensitively. The use of gates to applynegative and positive voltages, and the use of different massesfor 12C and 13C, are also helpful for studying Fermi level-dependent effects and to distinguish one carbon layer fromanother [90]. Although the SERS technique has been studiedfor more than 30 years [91], the exact nature of SERS is still

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Figure 9. Graphene as a substrate for enhanced Raman spectroscopy. (a) Schematic illustration of the molecules on a graphene/SiO2/Sisubstrate. Reprinted with permission from [88]. Copyright 2010 by the American Chemical Society. (b) Raman-fluorescence spectra ofrhodamine 6G (R6G) in water (10µM) (blue line) and R6G on monolayer graphene (red line) at 514 nm excitation. Reprinted withpermission from [93]. Copyright 2009 by the American Chemical Society. (c) SEM images of a graphene surface-enhanced Ramanscattering (SERS) sample. (d) Representative Raman spectra measured across a line scan moving from the outside to the inside at the Audot patterned area using 633 nm laser excitation. SLG denotes single-layer graphene and dots refer to gold quantum dots. An enhancementof all Raman peaks can be seen. Reprinted with permission from [92]. Copyright 2010 by the American Chemical Society.

debated. Using graphene as a substrate and then depositingsome Au dots onto it, Novoselov’s group has demonstratedsignificant SERS enhancements at 633 nm laser excitation andhas studied the physics of SERS (figures 9(c) and (d)) [92]. Itis found that three issues are crucial for further improvementsof SERS: (1) a larger density of nanoparticle coverage, (2)a larger Mie enhancement and (3) a smaller nanoparticle–graphene separation. In particular, thin metallic nanodiscswill achieve the highest SERS enhancement for 2D systemslike graphene [92].

3. Vacancies in graphene and graphene nanoribbons

HRTEM has been a valuable tool to study and generatedefects, and to monitor structural reconstructions in carbonnanostructures [94–96]. Iijima and co-workers showedexperimental evidence of vacancies and heptagon–pentagonpairs in SWCNTs and nanohorns (see figures 10(a)and (b)) [97]. Banhart and Krasheninnikov have reviewed,theoretically and experimentally, how the electron beam ofa transmission electron microscope interacts with carbonnanostructures, thus changing their morphology via thegeneration, migration and reconstruction of defects (seefigure 10(b)) [98].

With the latest technological improvements of HRTEMinstrumentation, scientists are now operating transmissionelectron microscopes at lower accelerating voltages withatomic resolution, thus avoiding electron radiation damage incarbon samples. Using an aberration-corrected (AC-HRTEM)instrument operating at voltages of 80 keV, graphene could becharacterized and also graphene defects could be visualized,allowing the detailed study of mono- and di-vacancies [99],

heptagon–pentagon (7–5 pairs, Thrower–Stone–Wales defects(5–7–7–5), stacking faults and in situ reconstructions formingsingle carbon chains [100–104].

Molecular dynamics computer simulations and first-principles calculations of ion irradiation over graphene havedemonstrated that ion irradiation can produce vacancies,di-vacancies, tri-vacancies and Thrower–Stone–Wales defects[105]. When considering a perfect graphene lattice, everyatom is coordinated to three other carbon atoms and everyedge is shared by two faces. If an even number of carbonatoms is removed, dangling bonds could be healed in order topreserve the carbon connectivity. However, if the number ofvacancies is odd, there will be dangling bonds that make thestructure more unstable and more chemically active. Thesereactive sites could subsequently be doped with foreign atoms,thus improving the specificity of the dangling bonds forbinding other molecules. From a di-vacancy reconstruction,a 5–8–5 topological defect with no-dangling bonds (which isdiscussed in section 4.2) is the most energetically favored (seefigure 10(c)) [105]. Therefore, if vacancies or reconstructedregions are generated (with an electron beam from a TEMmicroscope, for example) in an ordered way, these sites couldbe used to functionalize graphene with different atoms ormolecules in a controlled manner for building specific sensordevices.

Although it is thought that magnetism is exclusivelyreserved for atoms with 3d or 4f electrons such as transitionmetals, it has been reported that vacancies induced by protonirradiation in graphitic systems could also be responsiblefor magnetism in carbon [106]. Density functional theory(DFT) calculations have shown that magnetism is possible inirradiated graphite [107]. Using magnetic force microscopy,

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Figure 10. (a) Graphene patch with two separated 5–7 defects(yellow) and a Thrower–Stone–Wales defect (green) which can beformed by a pair of 5–7 defects. Molecular models of vacancy-typedefects. (b) A vacancy and its reconstruction in graphene or in aGNR shown in blue could be reconstructed to save energy so as toform a pentagon and a defect with a dangling bond (atoms inyellow). Therefore, the reconstructed vacancy is more stable thanthe non-reconstructed case, which exhibits three dangling bonds.(c) Di-vacancy reconstruction in 2D graphene or in a GNR: adi-vacancy shown in blue could be reconstructed to form apentagon–octagon–pentagon (5–8–5) defect shown in yellow withno-dangling bonds, therefore, the (5–8–5) defect being more stable.

Cervenka and colleagues reported magnetic order in defectiveHOPG: the magnetism might be due to the arrangements ofvacancies [108]. Ugeda and colleagues have studied the roleof vacancies as the source of magnetism in carbon [109].Recently, it has also been demonstrated experimentally thatvacancies in graphene generate local magnetic moments whichinteract with the conduction electrons through the Kondoeffect, thus generating magnetism in graphene [110].

Edges could also produce magnetism in graphiticnanoribbons: in 2000 Enoki and colleagues found that themagnetic behavior of a sample of activated carbon was dueto the magnetic edge states of GNRs arranged in a disorderedway [111]. Magnetic edge states have also been foundin graphitic nanoribbons prepared by CVD [112]. The

ferrimagnetic properties of nanographene networks caused bythe electronic edge states have been studied by electron spinresonance (ESR) [113]. More recently, the role of danglingbonds and edge states in the magnetic properties of pristineand fluorinated graphene has been analyzed by near edgex-ray absorption fine structure (NEXAFS) [114]. Althoughsome progress has been achieved in studying magneticcarbon, the role of vacancies and their controlled formationneed to be better understood, and further experimental andcharacterization techniques also need to be developed.

3.1. Experimental generation of vacancies

In order to generate vacancies (di-vacancies, or larger vacancyclusters) in graphite or graphene in a controlled manner, theradiation damage by different energetic particles, such aselectrons, protons or ions, on the carbon nuclei, should befurther investigated. Thus, if the kinetic energy transferred tothe nuclei is greater than a threshold value for bond-breaking,the carbon nucleus would be displaced in a sub-picosecondtime scale generating a vacancy (knock-on displacement): forsp2 hybridized carbon atoms arranged in a graphitic lattice,the energy required to displace a carbon atom is between 15and 20 eV [115]. Knock-on displacements could be achievedwithin a transmission electron microscope, since the electronscan acquire energies up to 300 keV, which is a large enoughenergy to displace carbon atoms [98, 115]. Therefore, TEMcan be used to experimentally produce vacancies in a controlledfashion within carbon nanostructures. In fact, using TEMon SWCNTs, coalescence and covalent connections betweenthe tubes could be achieved, thus producing a novel type ofnanostructure different from the originally irradiated precursor.In these cases, the vacancies are responsible for merging thenanotubes due to the high reactivity of the dangling bonds thatare produced [95, 116]. Other TEM experiments for reducingan MWCNT diameter via controlled vacancy introduction havebeen performed [117]. In fact, TEM-induced vacancies havebeen used to connect the atomic planes of MWCNTs withmetallic nanoparticles [118]. Banhart’s group has used theelectron beam of a transmission electron microscope to createvacancies in double-layer graphene to trap metal atoms ormetallic clusters [119]. In this context, it could be envisaged touse the transmission electron microscope to connect graphenewith metals generating an almost perfect contact, similar tometal–nanotube covalent junctions [118].

In addition to the use of protons as mentioned above [106],another technique to produce vacancies in graphitic systemsinvolves the use of different types of ions. Ney and colleagueshave irradiated graphene flakes with 100 keV nitrogen ionsand they performed magnetic measurements at 5 K findingthat the paramagnetism originally measured (probably dueto edge states) increases up to doses of 1015 ions cm−2 andthen decreases for higher doses due to the amorphization ofthe graphene. These authors did not find ferromagnetism;however, the nature of the defects that were generated hasnot been addressed and the role of the nitrogen implantedatoms would need further studies in order to understand hownitrogen interacts with carbon [120]. Probably for this case, the

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vacancies generated by nitrogen involve the ejection of severalcarbon atoms, thereby producing large regions of danglingbonds in a disordered way. Certainly, one of the challengesfor the future is the generation of vacancies of different sizes(mono-vacancy, di-vacancy, etc) and the identification of theirprecise location on the hexagonal lattice in an automated way.

3.2. Calculations of vacancies in graphene and graphenenanoribbons

According to tight-binding molecular dynamics and MonteCarlo simulations, vacancies trigger the coalescence mecha-nism of SWCNTs observed under TEM [95]. Without thevacancies generated by the electron beam, the graphene sheetsthat form the SWCNTs could not interact and thus could notmerge the tubes. First-principles DFT calculations with thePerdew, Burke and Ernzerhof (PBE) approximation exchange-correlation density functional have been used to simulatedefect formation in graphite by assuming an initial transferof momentum to the carbon atoms. The results show that va-cancies, interstitials and Thrower–Stone–Wales-type defectsare indeed possible, and exhibit formation energies rangingbetween 5 and 15 eV [121].

Most of the calculations on vacancies in graphite andgraphene show a magnetic behavior. Using spin-polarizedDFT in graphite, Lahtinen and colleagues simulated thedifferences in magnetic behavior between a vacancy anda hydrogen-vacancy defect showing that the presence ofhydrogen in the vacancy makes the local magnetic momentincrease to double its magnitude when compared with thenaked vacancy case [107]. In this context, vacancy andhydrogen adsorption-induced magnetism has been studied byfirst-principles simulations showing that the ferromagnetismand antiferromagnetism depends on whether the defects belongto the same sublattice or not [122]. The mean field Hubbardmodel has been used to study theoretically the differentmagnetic properties that vacancies and voids (in which morethan one atom is removed from the graphene lattice) exhibitin graphene and GNRs, finding that there is a rich spectrumof possible behaviors, depending on the spatial arrangementof the defects and their sublattice imbalance [123]. Yazyevconcludes that only single-atom defects, such as vacanciesor chemical functionalizations, that are unevenly distributedin the two graphene sublattices, can produce a net magneticmoment [124]. Bao and colleagues have studied theoreticallythe magnetic properties of tetra-vacancies in graphene andalso such vacancies saturated with hydrogen. They found thatthe tetravacancy reconstructs by relaxation and the magneticmoment is lost; however, when the tetravacancy is saturatedwith hydrogen, there is a magnetic moment [125]. Cui et alhave studied with spin-polarized DFT different size-vacanciesor voids which the authors call nanoholes. They have found aremarkable stability for certain size nanoholes with the numberof atoms thus removed called magic numbers. A large numberof the nanoholes studied exhibit a magnetic state with a finiteenergy band gap [126].

Figure 11. (a) Original Thrower stick-ball model of a 5–7defect [127]. (b) Original Stone and Wales drawing of the bondrotation changing the symmetry of C60 from Ih to C2v . Reprintedwith permission from [128]. Copyright 2010 by Elsevier Ltd.(c) Thrower–Stone–Wales (TSW)-type defect obtained by rotatingone of the bonds in a ZGNR by 90◦. This defect consists of two 5–7defects joined together. (d) Triple five–triple seven (T5T7) defectdepicted in a GNR.

4. Topological defects

In the context of graphene and graphene-like nanostructures,including fullerenes, nanotubes and schwarzites, a topologicaldefect does not change the connectivity of the sp2 lattice, thatis, every carbon atom in the structure has exactly three nearestneighbors, even though, their physicochemical properties dochange. Generally speaking, these defects can change thecurvature of the system locally or globally. In this review,since planar graphitic nanostructures are studied (grapheneand nanoribbons), we will deal with those topologicaldefects that do not change the curvature globally; theseinclude heptagon–pentagon dislocations, Thrower–Stone–Wales transformations, double pentagon–octagon (5–8–5),double pentagon–heptagon (D5D7), triple pentagon–heptagon(T5T7) cluster defects, grain boundaries and extended line ofdefects.

4.1. Heptagon–pentagon pairs and the Thrower–Stone–Walestransformation in graphene and nanoribbons

In 1969, Peter Thrower, when he studied dislocations ingraphite, introduced the possibility of having a pentagon’–heptagon defects in a graphitic lattice (see figures 10(a)and 11(a)) [127] as a stable nano-cluster. However, notmuch progress in this area was made until the appearanceof fullerenes in 1985. Fullerenes, graphene, schwarzites

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and CNTs are locally similar in the sense that every carbonatom is connected to three other carbon atoms (sp2 character).With this line of reasoning in mind, some of the mechanismsthat apply to fullerenes could also be valid for CNTs andgraphene. This is the case of the bond rotation proposed byStone and Wales in 1986, and applied to BuckminsterfullereneC60 (Ih symmetry) to transform it into another isomer withdifferent symmetry (C2v) by rotating one bond by 90◦ (seefigure 11(b)) [128]. Therefore, based on the fact thatPeter Thrower proposed the existence of pentagon–heptagondefects and that Stone and Wales studied 90◦ bond rotationsin fullerenes, which produce heptagon–pentagon pairs ingraphene, we will refer to this bond rotation as the TSWtransformation (Thrower–Stone–Wales transformation) (seefigure 11(c)). Geometrically, the main effect of the TSWtransformation in fullerenes, CNTs and graphene is a change tothe local environment, but preserving the connectivity whileproducing no-dangling bonds. The TSW transformation isa matter of study in graphene, nanotubes, schwarzites andgraphitic onions: by applying the TSW transformation to giantfullerenes, the sphericity and stability of giant graphitic onionscould also be explained [129–131].

Crespi and co-workers applied the TSW transformation tographene in order to modify the hexagonal honeycomb latticeto form another lattice with only heptagons and pentagons(also known as pentaheptite), which had a metallic characterand exhibited a large density of states at the Fermi level[132]. Terrones et al took this idea further by havingthree 2D graphene-like systems with hexagons, heptagonsand pentagons, in an ordered way: these crystal structureswere called Haeckelites in honor of Ernst Haeckel, a famousGerman zoologist and biologist (1834–1919) who drew thefirst radialoria models with such topological similarities tographene and fullerenes. The Haeckelites also exhibit statesat the Fermi level and have high energetic stability [116]. Thetransport and vibrational properties of Haeckelites have alsobeen studied by first-principles calculations [133]. Differentfamilies of Haeckelites have been proposed theoretically,and their electronic and mechanical properties have beenstudied [134–136]. However, so far Haeckelites remain anexperimental challenge and have not been synthesized in thelaboratory. Graphene reconstruction producing heptagons andpentagons to preserve the structural connectivity has beenreported and TSW-type defects have also been identified inthese systems [137, 138]. Using aberration-corrected high-resolution transmission electron microscopy (AC-HRTEM)and STM techniques, 5–7 and TSW defects on isolatedgraphene surfaces could be directly observed. Some recentexperimental evidence, at the atomic scale, of several typesof defects in graphene obtained by different research groups[100, 101, 138–140] are depicted in figure 12.

4.1.1. Experimental evidence and characterization oftopological defects in graphene and graphene nanoribbons.As we have mentioned in section 3 devoted to vacancies,HRTEM is an ideal tool to visualize, generate and studydefects in situ in graphene-like lattices. TSW defectsand carbon rings with more than seven atoms, and their

dynamics under the electron beam have been characterizedwith HRTEM in SWCNTs that were previously heated [141].Regarding graphene, the formation and annealing of TSWdefects has been observed in situ using AC-HRTEM with amonochromator working at acceleration voltages of 80 keV;further, also in these observations defects exhibiting threeheptagons and three pentagons or the T5T7 defect (denotestriple five–triple seven) were identified [100] (see figure 11(d));T5T7 defects can be generated experimentally by a divancyreconstruction [142].

Raman spectra exhibit a blue shift during the oxidation andexfoliation of graphite which was thought to be caused by thepresence of TSW defects or 5–8–5 defects. However, Kudinand colleagues have demonstrated that although these defectsexhibit particular features worth studying, most probablythe observed Raman shift was caused by an alternation ofsingle–double carbon bonds within the sp2 hybridized carbonribbon, which could be due to the presence of sp3 hybridizedcarbon atoms on the edges of zigzag nanoribbons [143].The generation and study of T5T7 defects in graphene hasbeen carried out experimentally using HRTEM. In this in situobservation, tungsten atoms can be trapped by this defect [144].First-principles calculations show that among several possibledefects, such as single vacancies, di-vacancies (5–8–5) and theTSW, it was the T5T7 defect that was the one that could explainthe experimental observations [144].

Certainly, HRTEM offers advantages over other tech-niques to characterize and generate topological defects ingraphene-like structures. However, other tools which are gain-ing importance are STM, STS and Raman spectroscopy. Nev-ertheless, to gain a better understanding of the different typesof defects, new tools and combinations of tools to characterizedefects more quantitatively are needed in order to establish arobust defect engineering strategy for applications.

4.1.2. Theoretical studies of topological defects ingraphene and graphene nanoribbons. As has been shownexperimentally and theoretically by Cretu and colleagues in theprevious section [144], topological defects are more reactiveand could be used to trap atoms or molecules with differentstrengths depending on the defect geometry. In this context,Duplock and colleagues have studied theoretically the role ofTSW defects in attracting hydrogen and finding that certainlythis type of defect makes H2 chemisorption thermodynamicallyfavorable [145].

Study of the diffusion, coalescence and reconstruction ofdefects is crucial in order to shed light on the stability of specificdefects: Lee and co-workers have used tight-binding moleculardynamics and first-principles calculations to demonstrate thattwo single vacancies coalesce to form a 5–8–5 defect, and byheating, this is transformed into a T5T7 defect via a TSWtransformation [146]. In addition, these authors have foundthat four single vacancies coalesce to form a double T5T7defect which is the basic defect in the hexagonal Haeckelitestructure proposed by Terrones et al [116]. The stability ofT5T7 defects against a pair of 5–7 dislocation defects has beencompared using first-principles calculations, and it is foundthat two 5–7 pairs, separated by a distance determined by

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Figure 12. (a) TEM image of a TSW defect (55–77), formed by rotating a carbon–carbon bond by 90◦ and (b) a single vacancy as seen inan experimental TEM image. Reprinted with permission from [100]. Copyright 2008 by the American Chemical Society. (c) Top image:defect structure and superimposed defect model. Bottom image: line defect with image profile in the direction perpendicular to the wire(inset). The brighter area surrounding the defect originates from the states with wave functions localized at the defect. Reprinted withpermission from [139]. Copyright 2010 by Nature Publishing Group. (d) Top images: TEM image of a di-vacancy (V2(5–8–5)) and(e) image V2(5555–6–7777) di-vacancy. Bottom images: corresponding images of the defects shown in the top images of (d) and (e) inwhich the defects have been drawn in color for better identification. Reprinted with permission from [138]. Copyright 2011 by theAmerican Physical Society. (f ) Two grains (bottom left, top right images) intersect with a 27◦ relative rotation. An aperiodic line of defectsstitches the two grains together. The image from (g) with the pentagons (blue), heptagons (red) and distorted hexagons (green) of the grainboundary are outlined. Reprinted with permission from [140]. Copyright 2011 by Nature Publishing Group. (h) Molecular model showingthe transformation of four adjacent hexagons into a 5–7–7–5 defect or a TSW defect, and (i) AC-HRTEM images showing two 5–7–7–5defects located on the edges (red circles) of a hole in a graphene surface (images taken from movie supplementary material of [101].Copyright 2009 by the American Association for the Advancement of Science).

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the reconstruction of ten vacancies (around 7.32 Å), are morestable than a patch of five T5T7 defects tightly packed in agraphene lattice (five T5T7 defects can be generated by tenvacancies) [147].

Topological defects in graphene have also attracted theattention of scientists working in other fields, for example,the continuum theory of elasticity has been used to studyinteractions of TSW defects in graphene and also the propertiesof 5–8–5 defects and the results of continuum theory werefound to agree with the results using atomistic methods[148, 149]. In addition, using a cosmological analogy, Cortijoand co-workers have coupled the Dirac equation to a curvedspace to study topological defects in graphene [150].

STM and STS provide information on the different typesof defects, including the local density of states (LDOS), sincethe electronic behavior at the defects is different from electronsin the normal graphene lattice: Amara and colleagues havesimulated, using tight-binding calculations with the Tersoff–Hamann approach [151], the STM images from vacancies,5–8–5 defects, adatoms and TSW defects [152]. Thisinformation is valuable and useful to experimentalists forcomparisons with experimental TEM and STM images.

Topological defects can also be seen as centers forchemical activity, so their functionalization is relevant forgraphene nanoelectronics. Boukhvalov and Katsnelson haveused hydrogen to test theoretically the chemical properties ofgraphene with topological defects such as TSW and 5–8–5defects [153]. The chemical functionalization by carboxylgroups (COOH) of semiconducting GNRs possessing TSWdefects has been studied using first-principles calculations,finding that the electrical conductivity could be enhancedby mono- and double-adsorption of COOH at the TSWdefects. Therefore, the conductivity depends on the capabilityof adsorbing the COOH groups by the TSW defects;having a higher concentration of TSW defects augmentsthe adsorbing sites which can be functionalized by COOH,transforming the semiconducting nanoribbon into a p-typemetallic system [154].

Thermal transport in graphene zigzag nanoribbons withTSW defects has also been studied using the non-equilibriumGreen’s function method and the phonon-wave packetscattering method. The results demonstrate two uniquethermal transport phenomena: an edge localized thermalcurrent at low energies and a circulating thermal current alongthe heptagonal ring of the TSW defect [155].

Although stress and mechanical stability are usuallystudied by classical methods, at the nanoscale, quantum effectsalso occur. Huang and colleagues have studied the stress at theedges in AGNRs and ZGNRs using first-principles methods,finding quantum effects: for AGNRs the stress oscillates withthe ribbon width, and for ZGNRs the edge stress is smalland exhibits a very weak width dependence; moreover, theedge stress in ZGNRs is further reduced in antiferromagneticnanoribbons (ground state) compared with the paramagneticcase. These effects cause twisting and wrapping mechanicalinstabilities in the nanoribbon which cannot be explained bycontinuum or empirical approaches [156]. The authors alsoshow that hydrogen passivation at the edges of both AGNRs

and ZGNRS relieves the edge stress caused by dangling bonds.In this context, other atoms or molecules could be added atthe edges (instead of hydrogen) to relieve the edge stress.In addition, according to these authors [155], TSW edgereconstructions reduce the mechanical instability and improvethe chemical stability of the GNRs.

In addition to vacancies, topological defects can also alterthe two graphene triangular sublattices producing differentmagnetic effects, depending on the type of defect. In thiscontext, Lopez-Sancho and co-workers have used the Hubbardmodel to study the magnetic effects caused by the presenceof heptagons, pentagons, heptagon–pentagon dislocations andTSW defects [157]. With DFT and quantum Monte Carlocalculations, the long range effects of TSW defects in graphenehave been studied [158]. It turns out that TSW defects distortthe graphene lattice, causing adjacent atoms to move out of theplane, thus producing ripples in the graphene sheet. However,the rippling or buckling behavior of graphene with severalTSWs or other types of topological defects needs to be studiedin depth. For the case of Heackelites, depending on theirgeometry, there will be a certain local wrinkle in the sheets,that is, some atoms will protrude out of the sheet plane [116].

Quantum transport of ZGNRs has also been studied withfirst-principles calculations: the results indicate that ZGNRswhich are mirror symmetric with respect to the midplanebetween edges, exhibit small currents with the presence ofa conductance gap around the Fermi level, whereas non-symmetric ZGNRs possess a linear current–voltage ohmicbehavior [159]. However, when including spin polarizationin the transport calculations, both types of ZGNRs (symmetricand non-symmetric) are semiconductors, but for the symmetriccases, negative differential resistance is observed in the I–V

curves [160]. If a TSW defect is inserted into ZGNRs,the asymmetric ZGNRs exhibit lower currents in their I–V

curves but with a similar behavior as is seen in the perfectZGNRs. For symmetric ZGNRs with a TSW defect, strongdifferences in the currents with different spin polarizationsappear, and the negative differential resistance is reduced[160]. Although transport measurements have been carriedout in GNRs obtained from chemical methods (edges of theseGNRs are not atomically smooth), the GNRs are found to besemiconductors [48]. So far the effect of topological defectshas not been measured experimentally.

The reactivity of topological defects at the edges ofZGNRs has been studied with first-principles calculationsto explain the loop formation at the edges in Joule heatednanoribbons [62, 161]. It is has been shown that when aZGNR is previously irradiated with an electron beam, theedges reconstruct via topological defects such as pentagon–heptagon pairs called ‘reczag’ edges, which do not interact,or they interact very little with the layers above and below,thus avoiding loop formation. Without the presence of thesedefects, the loops can also be formed by Joule heating atthe edges of ZGNRs [161]. The observed dynamics of di-vacancies by Girit and co-workers under the HRTEM [101]has been studied theoretically with a first-principles approachin order to explain the migration, rotation and transformationof 5–8–5 and T5T7 defects [162].

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Figure 13. (a) Original drawing by Terrones and Mackay of a graphene grain boundary with heptagons and pentagons (5–7) defects joinedtogether. Reprinted with permission from [163]. Copyright 1992 by Elsevier Ltd. (b) Computer generated model of the boundary shown in(a), and the defect clusters are periodically separated by around 6.52 Å. (c) Graphene grain boundary in which the 5–7 defects areperiodically separated by 11.55 Å. (d) Joining armchair (blue) and zigzag (yellow) nanoribbons by a line of 5–7 defects (red).

4.2. Grain boundaries and an extended line of defects ingraphene and nanoribbons

As stated in the first section of this review, Roscoe and Thomasproposed a model for small angle grain boundaries in graphite,from which it is possible to identify the presence of pentagon–heptagon pairs, although for some reason they did not drawthe bonding in this regions [7, 10] (see figure 1(b)). Almostthree decades later, Terrones and Mackay, using the conceptof curvature in graphitic systems, introduced a twin boundaryin graphene using pentagons and heptagons (see figures 13(a)and (b)) [163].

Experimentally, in 1988 Albrecht and colleagues studiedtilt boundaries in graphite with STM [164]. From these STMstudies on HOPG and computer simulations, Simonis and co-workers proposed a grain boundary model which is similar tothe one proposed by Terrones and Mackay in 1992 [165]. Ponget al used STM to characterize small angle grain boundariesin graphite: these authors proposed a model based on 5–7dislocations separated periodically by a greater distance thanthe model proposed by Terrones and Mackay. By changingthe separation of the 5–7 defects, the angle between thegrains is also changed [166] (see figure 13(c)). Cervenkaand Flipse, used STS to characterize the electronic propertiesof grain boundaries in HOPG and found that the chargedensity at the boundaries was higher than that of graphiteand that the charge density exhibits two strongly localizedstates [167]. In addition, ferromagnetic behavior at roomtemperature has been identified in grain boundaries of HOPGby magnetic force microscopy (MFM) and superconductingquantum interference device (SQUID) measurements [108].

Andriotis and Menon studied theoretically the transportproperties of ‘T-shape’ GNRs exhibiting aligned 5–7 defectsto connect AGNRs with ZGNRs, finding that the conductivitydepended on the chirality, width and the 5–7 defects boundary[168]. Botello-Mendez et al, also using a 5–7 defect-boundaryto join AGNRs with ZGNRs, studied the electronic andtransport properties of hybrid GNRs and found that suchnanoribbon structures exhibited half-metallicity; this meansthat electrons with spin of just one type, spin up or down, butnot both, participate in the conduction. It is noteworthy thatthese hybrid nanoribbons possess a distortion of the graphenelattice which might affect their stability and their potential usefor spintronics applications (see figure 13(d)) [169].

Electronic properties, stability and STM simulations ofdifferent angle grain boundaries in graphene have been studiedwith first-principles calculations to show the differencesbetween small angle and large angle grain boundaries. Smallangle grain boundaries have a tendency to produce bucklingof the graphene sheet [170]. Quantum transport has also beenstudied theoretically, showing that depending on the boundary,two behaviors are present: high transparency of charge carriersand perfect reflection [171].

More recently, Lahiri et al [139] found that by growinggraphene on nickel [111] one could produce an extended line ofdefects (ELD) involving 5–8–5 defects arranged in a periodicway. Using STM, the authors found that the image contrastis brighter in the vicinity of the defect, thus correspondingto the electronic states with wavefunctions localized at thisspecific region. The same authors performed first-principlescalculations, demonstrating that the ELD 5–8–5 behaves asa nanowire embedded in a graphene lattice since this defect

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Figure 14. Molecular models of extended lines of defects: (a)5–8–5 defects in a ZGNR, (b) double pentagon–double heptagon(D5D7) defects in a ZGNR and (c) triple pentagon–triple heptagon(T5T7) defects embedded in a ZGNR.

produces electronic states at the Fermi level, and these statesextend along the defect. In fact, this ELD 5–8–5 couldbe observed in two graphene grains, with zigzag edges,joined together by a pair of atoms arranged periodically (seefigure 13(d)). Kou et al found, using the local spin densityapproximation, that there is a small magnetic moment ofaround 0.03µB per cell which can increase up to 0.7µB percell under strain [172]. As expected, the spin polarization islocalized ferromagnetically along the ELD 5–8–5 line.

Botello-Mendez et al used local density approximationand general gradient approximation (GGA) calculations tostudy different extended lines of defects in graphene and GNRsinvolving heptagons, octagons and pentagons (5–8–5 defect,D5D7 defect and T5T5 defect (see figure 14, [142]). Thecalculations reveal that all these ELDs compete in energyand that when nanoribbons possessing these ELDs areconsidered, stable ferromagnetic configurations might appear,in particular for the ELD T5T7 case [142]. These authors alsosimulated the STM images from first-principles calculationsusing the Tersoff–Hamann approach [151], and confirmedthat indeed, the Lahiri ELD 5–8–5 defect corresponds to astructure involving pentagons and octagons. The transportproperties were also calculated for these cases, finding

Figure 15. The low-energy band structure of graphene. Reprintedwith permission from [175]. Copyright 2011 by the AmericanPhysical Society.

that all ELDs should be observable in electron transportmeasurement. However, for the T5T7 case, there areextra conduction channels favoring electron conductance andmagnetic properties [142].

5. Doping and functionalization

Doping and functionalization with other atoms or moleculesare efficient ways to modify the electrical properties ofgraphene. The doping of graphene could be roughly classifiedinto two categories [173]. One is electrical doping bychanging the gate voltages of graphene devices; another ischemical doping using chemical routes, such as substitutionaldoping or the controlled reduction of graphene oxide. It isnoteworthy that the terminology ‘doping’ here is a little bitdifferent from the one widely used in semiconductor physics.The substitutional heteroatoms (B, N, etc) in the graphenelattice sometimes can reach relatively high doping levels (2%or higher [174]). In this section, some recent progress inthe chemical doping and functionalization of graphene andGNRs will be demonstrated and summarized. In addition,the importance of the dopant sites will be reviewed, and bychanging a dopant, one could tailor the properties of graphene.

5.1. Substitutional doping of graphene with N, B, S, P, Si andreduced graphene oxide

As a single layer of a hexagonal lattice, graphene is constructedby sp2 hybridized carbon atoms, and three strong σ bondsare established with the other three surrounding atoms. Thepz orbitals of these C atoms form a filled band of π orbitals(valence band) and an empty band of π∗ orbitals (conductionband) [173]. According to tight-binding calculations, thevalence and conduction bands touch at the Brillouin zone(figure 15) [175], thus making graphene behave like a zero-band-gap semiconductor [39, 66]. However, for grapheneapplications in digital electronics, such as in FETs, it is highlydesirable to open a band gap in graphene [176]. Many

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Figure 16. Molecular model showing the types of N doping in agraphene sheet, in which the gray and green atoms denote carbon(C) and nitrogen (N), respectively. The sites N1, N2 and N3

represent substitutional graphitic nitrogen, pyridine-like nitrogenand pyrrole-like nitrogen, respectively.

strategies, such as the substrate-induced method [177], theapplication of an electric field to bilayer graphene [178, 179]and the size confinement effect by forming GNRs [48], havebeen proposed to introduce an energy band gap. In additionto these possibilities, chemical modification of graphene, suchas by substitutional doping with other atoms (e.g. N, B, P,S, etc) [174, 180, 181] or the controlled reduction of grapheneoxide (GO) [182] could be effective routes to open a band gap ingraphene. Furthermore, the chemical and electronic propertiescould be modulated in a well-controlled manner by adjustingthe doping and reduction level in the two above-mentionedmethods. In this subsection, some typical advances in the areaof substitutional doping of graphene and reduced GO will bedescribed.

5.1.1. Substitutional doping of graphene with N, B, S, P, Si.Thrower and co-workers have investigated the doping effect ofheteroatoms (e.g. B, N, P) into carbon materials (e.g. graphite,carbon fibers), and these authors found that their propertiescould be remarkably tuned by substitutional doping [183–185].For graphene, substitutional doping implies that the carbonatoms in the hexagonal lattice are substituted with dopants (e.g.N, B, P, S), whose incorporation into the lattice would disruptthe sp2 hybridization of the carbon atoms, and would causesignificant changes to the electronic properties of graphene.Based on different substitutional sites, there are usually threekinds of ways of introducing N atoms within the hexagonallattice, and these are substitutional graphitic nitrogen (N1),pyridine-like nitrogen (N2) and pyrrolic nitrogen (N3), asshown in figure 16.

DFT calculations on ZGNRs have demonstrated that thedoping of N and B produces different effects, depending onthe position of the substitutional sites [186]. In particular,edge substitutions at low density do not significantly alterthe band gap, while bulk substitution promotes the onset ofa semiconducting-metal transition. In addition, pyridine-like

defects (at an N2 pyridinic site) induce a semiconducting-metal transition. The first experimental work on nitrogen-doped graphene (NG) was demonstrated using methane andammonia as precursors in a CVD system [174]. It was foundthat N atoms can be substitutionally doped into the graphenelattice. Electrical measurements show that the NG exhibitsan n-type electronic behavior, as demonstrated in figure 17.Furthermore, compared with pristine graphene (PG), NGshows a lower electrical conductivity and a larger on/off ratio.The room temperature mobilities of the PG and NG devicesare about 300–1200 cm2 V−1 s−1 and 200–450 cm2 V−1 s−1,respectively [174]. Thus, the mobility of NG is about 1–2orders of magnitude lower than that of mechanically exfoliatedgraphene (1.5 × 104 cm2 V−1 s−1) [27], and this loweredmobility might be attributed to carrier-defect scattering at thedoping and topological defect sites. More importantly, thesubstitutional doping of nitrogen within a graphene latticecould form covalent bonding with carbon atoms, which wouldmodify the electrical structure of graphene, and suppress thedevelopment of a high DOS of graphene near the Fermi energylevel. Therefore, a gap could be opened between the valenceand the conduction bands. Obtaining a controlled band gapis very meaningful for the possible future applications ofgraphene in semiconductor electronics.

Some of the recent achievements related to NG synthesisare summarized in table 1. Except for ammonia (NH3) gas,some other nitrogen-containing liquid precursors, such asacetonitrile (CH3CN) [187], pyridine (C5H5N) [188, 189] orsolid precursors, including cyanuric chloride (C3Cl3N3) [190],have also been used for the synthesis of NG with few-layers(usually no more than ten layers in thickness). Regardingthe synthesis, as shown in table 1, the CVD method is themost common due to its advantages in achieving a relativelyhigh crystallinity when compared with wet chemical methods.In addition, some post treatments on few-layer PG, suchas Joule heating [180] and plasma treatment [191, 192], innitrogen-containing gases (NH3, N2, etc) have been used forobtaining NG. These post-treatments have unique advantagesin transistor fabrication, especially for batch device production.

Theoretical calculations [43, 45] and experimental work[48, 197] have demonstrated that GNRs with narrow widths(<10 nm) and atomically smooth edges will exhibit bandgaps useful for FETs operated at room-temperature. TheGNR-derived FETs have demonstrated p-type behavior withexcellent on/off ratios (∼107 at room temperature) [48]. Byhigh-power electrical Joule heating of pristine GNR-FETs inammonia gas, n-type FETs could be produced [180]. Duringelectrical annealing, the more reactive carbon atoms at theedges of the GNRs could react with ammonia to form C–N bonds. The Dirac point shifts by about 20 V to negativegate voltages when compared with nanoribbons annealed bye-beam in vacuum, thus confirming the n-type doping effect ofnitrogen atoms. In addition, the n-doping level was found tobe approximately proportional to the density of substitutionalN atoms in the GNR edges [180].

Substitutional doping with boron is another interestingway to modulate the electronic properties of graphene.Theoretical work has been carried out along this direction

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Figure 17. Electrical properties of N-doped graphene. (a), (b) Ids/Vds characteristics at various gate voltages Vg for the PG and theN-doped graphene FET device, respectively. Here Ids, Vds and Vg denote source–drain current, source–drain voltage and gate voltage,respectively. The upper-left insets in each panel are the presumed band structures. The lower-right inset in (a) is the schematic deviceconfiguration. Reprinted with permission from [174]. Copyright 2009 by the American Chemical Society.

Table 1. Summary of some experimental work on nitrogen-doped graphene (NG) synthesis.

GrowthLayers Method Substrate Precursors parameters Reference

2–6 CVD Cu (25 nm) film Methane (CH4) and 800 ◦C, 10 min [174]on silicon wafer ammonia (NH3)

2–8 CVD Ni (300 nm) film Methane (CH4) and 1000 ◦C, 5 min [193]on silicon wafer ammonia (NH3)

�1 CVD Cu foil Acetonitrile (CH3CN) 950 ◦C, 500 mTorr, [187](25 µm thick) and ammonia (NH3) 3–15 min

1 CVD Cu foil (25 µm Pyridine vapor 1000 ◦C, 10 min [188]thick, 99.999%) at ∼7 Torr

1–2 CVD Cu foil (34 µm Ethylene (C2H4) 900 ◦C, 4.6 Torr, 30 min [194]thick, 99.95%) and ammonia (NH3)

�1 CVD Ni (300 nm) or Cu Methane (CH4) and 980 ◦C, 3 min (for Ni) [195](300 nm) film on silicon wafer Ammonia (NH3) or 20 min (for Cu)

1–3 Electrothermal Graphene nanoribbons Ammonia (NH3) e-annealed graphene [180]reactions on silicon wafer nanoribbons in NH3

>2 Arc No substrates Graphite rod, pyridine vapor Flowing H2 (200 Torr) [189]discharge or ammonia (NH3) and He (500 Torr)

through a pyridine bubbler1–2 Plasma post Pristine graphene Ammonia (NH3) NH3 plasma at a dose [192]

treatment of 3 × 1014 cm−2

>2 Plasma post No substrates Reduced graphene Treatment in nitrogen [191]treatment oxide and N2 plasma (500 W power,

14 Torr N2)>2 Vacuum Ni (100–300 nm)/B Boron-trapped 800–1100 ◦C, 60 min, [196]

annealing (5–15 nm) films nitrogen and nickel-trapped 10−3–10−4 Paon silicon wafers carbon atoms

1–6 Solvothermal No substrates Lithium nitride, 250–350 ◦C, 6–10 h [190]tetrachloromethaneand cyanuric chloride

[181, 198–203]. In this context, DFT has demonstratedthat substitutional boron atoms will act as scattering centersfor the electronic transport along the GNRs (substitutionalboron concentration is 1.4%) [181]. If the boron atomsare doped at the edges of ZGNRs, the B-doped ZGNRsmay show half-metallic behavior, which gives rise to azero band gap for electrons with one spin orientation anda semiconducting or insulating band gap for the other spin

orientation, thereby giving rise to a completely spin-polarizedcurrent. The half-metallicity of B-doped ZGNRs does notdepend on the ribbon width even in the absence of an electricfield, and this property is preserved for any field strength.This demonstrates the possibility of using B-doped graphenefor spintronics applications [203]. Figure 18(a) showsthe structure schematically of B-doped bilayer graphene.Theoretical work by Menezes et al has demonstrated that pure

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Figure 18. Boron-doped bilayer graphene and their band structures. (a) Representative 3 × 3 supercells, the red atom denotes asubstitutional boron atom. (b) Band structure for pure bilayer graphene (black full line) and for two short-range models for boron impuritiesin a 3 × 3 cell, using an on-site potential of 4.2 eV at the impurity site and nearest-neighbor hopping energies of −1.68 eV (red dotted line)and −3.12 eV (blue dashed line) between boron and carbon. (c) DFT (blue full line) and tight-binding (red dashed line) band structures ofsubstitutional boron-doped bilayer graphene in a 3 × 3 supercell. Reprinted with permission from [201]. Copyright 2010 by the AmericanPhysical Society.

Figure 19. Sulfur-doped graphene (SG) and its potential for detecting NO2 gas molecules. (a) The most stable configuration of SG withadsorbed NO2. (b) The DOS for NO2 on SG. The solid line is the DOS of the majority spin and the dashed red line is the minority spin. Thevertical dashed line represents the Fermi level of the system, which is set to zero here. The upper figure is the DOS versus energy of SGwithout NO2. Reprinted with permission from [207]. Copyright 2009 by the American Institute of Physics.

bilayer graphene does not show a band gap (figure 18(b)),whereas if a disordered arrangement is imposed on only one ofthe sublattices (blue dotted line), a band gap (∼0.2 eV) opensup. However, when disorder is imposed upon both sublattices(upper and lower graphene sheets; red dashed line), the gapshrinks again and shifts to higher energy (figure 18(c)). Thisdemonstrates that an energy-gap opening of bilayer graphenecould be caused by asymmetric doping [201]. In addition, andaccording to first-principles quantum transport calculations,the B-doped p-type GNR-FETs could exhibit high levels ofperformance, with high on/off ratios and low subthresholdswings. Furthermore, the performance parameters of GNR-FETs could be controlled by the p-type semiconductingchannel length [198]. Unfortunately, experimental researchon B-doped graphene is very scarce and only a few reportshave thus far been published [189, 204, 205]. Consideringtheir interesting properties predicted by the theoretical workmentioned above, further experimental work needs to becarried out along these directions, and other synthesistechniques different from CVD should be explored, sinceboron compounds or precursors are very unstable and airsensitive.

In addition to nitrogen and boron doping, substitutionaldoping of graphene with other heteroatoms, such as sulfur[206–208], phosphorus [208, 209] and silicon [210], hasalso been investigated theoretically. Using first-principlescalculations, it was found that sulfur doping could inducedifferent effects: the doped sheet can be a small-band-gap semiconductor, or it could exhibit enhanced metallicproperties when compared with a PG sheet [206]. Therefore,S-doped graphene (SG) may also be a smart choice forconstructing nanoelectronic devices, since it is possible tovary the electronic properties of the sheet by adjusting thedoping level of sulfur into the graphene lattice. Moreover,DFT investigations show that the DOS of SG at the Fermilevel actually increases upon NO2 adsorption, as is visible infigure 19, which demonstrates that S-doped graphene couldbe used as an efficient sensor for some toxic gases due to thehigh selectivity of this material [207]. Regarding phosphorus-doped graphene (PhG), our previous work has found out thatphosphorus will maintain an sp3 hybridization, and bonds tothe carbon atoms with tetrahedral orbitals, inducing structuralstrain in the carbon lattice (figure 20(a)) [211]. Using first-principles periodic calculations, Denis demonstrated that the

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Figure 20. Phosphorus-doped graphene (PhG) and the adsorption of different molecules. (a) Relaxed structure of PhG. Reprinted withpermission from [211]. Copyright 2009 by the American Chemical Society (b) Band structure of 4 × 4 phosphorus-doped monolayergraphene. Reprinted with permission from [212]. Copyright 2010 by Elsevier Ltd.

Figure 21. Silicon-doped graphene (SiG) and the interaction with a melamine molecule. (a) Optimized structure for bilayer graphenedoped with Si in vacancy sites. Reprinted with permission from [213]. Copyright 2011 by Elsevier Ltd. (b) GNRs with Si-dopant invacancy sites interacting with melamine. (c) Band structures of the Si-doped GNRs before (left panel) and after (right panel) adsorbing themelamine molecule. The Fermi level is indicated by the horizontal dotted line. The wave vector k is plotted from � to X in both cases.Reprinted with permission from [214]. Copyright 2010 by Elsevier Ltd.

doping of P atoms into the graphene lattice could openthe largest band gap (0.67 eV spin up, 0.66 eV spin down,figure 20(b)) compared with the cases of Si-, Al- or S-dopedmonolayer graphene [212]. If gases, such as NO2, NO, SO2,are adsorbed onto PhG, the electronic conductivity of thePhG will be changed [209]. By monitoring the conductivityvariation after the adsorption of molecules, the PhG can alsobe used as a sensitive detector of these toxic gases.

For Si-doped graphene, theoretical calculations havedemonstrated that it is more favorable to use bilayer graphenein order to reduce the formation energies. In this sense, a bondbetween the two Si atoms in each layer will be formed withoutsignificantly altering the stacking interaction (figure 21(a)).The formation of such bonds in bilayer graphene could

reduce the formation energy compared with that of monolayergraphene [213]. Based on these calculations, Si-dopedgraphene (SiG) will have potential applications in areas suchas toxic gas sensing [210] and organic compound detection[214]. For example, melamine (C3H6N6) is a deleteriouscompound for human health, which may appear in our foodnowadays and should be detected by suitable sensors. Usingfirst-principle calculations, Wang et al demonstrated that themelamine-SiG (figure 21(b)) has the most stable configurationwhen compared with P-, B- or N-doped graphene. The bandstructure of SiG will change remarkably before and after themelamine adsorption due to charge transfer (figure 21(c))[214]. However, more experimental efforts are also urgentlyneeded in research related to SiG.

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Figure 22. Chemically converted graphene by the reduction of GO. (a) The chemical route to the synthesis of solubilized graphene.Reprinted with permission from [216]. Copyright 2008 by Nature Publishing Group. (b) 3D molecular models of graphene oxide andchemically converted graphene demonstrate that the removal of the –OH and –COOH functionalities upon reduction restores a planarstructure. Reprinted with permission from [215]. Copyright 2009 by Nature Publishing Group.

5.1.2. Reduced graphene oxide. In order to tune theelectronic properties of graphene, the controlled reductionof GO appears to be an efficient route to modulate theband gap. GO shows a gap greater than 0.5 eV at roomtemperature, and GO could exhibit semiconducting behaviorwhen it is reduced into graphene [182], because some residualoxygen and structural defects remain within the structure ofreduced GO, as shown in figures 22(a) and (b) [215, 216]. Adetailed discussion, focused on the synthesis, properties andapplications of GO, can be found in various reviews availablein the literature [176, 217–219].

5.2. Importance of the dopant site and property changes

As mentioned above, the chemical doping of grapheneand GNRs could be considered as an efficient route ableto tune the electronic and quantum transport properties ofgraphene-like materials. In addition to the chemical natureof the dopant, the location of the doping atoms in thestructure and the dopant concentration are very importantfactors that control the physicochemical properties of dopedgraphenes. DFT calculations on GNRs have demonstratedthat edge functionalization of armchair ribbons does not showremarkable band gap changes against N or B edge substitutions.However, N, B and pyridine-like bulk substitutions could causesemiconductor–metal transitions, as shown in figure 23(a)[186]. Moreover, the concentration of vacancy or dopantdefects also affects the electrical properties of graphene.Figure 23(b) shows the variation of the electrical conductivityas a function of different vacancy or nitrogen dopingconcentrations in graphene. It demonstrates that a minimumresistivity could be found for around 0.5% vacancy or nitrogen

dopants. However, the resistivity in the metallic regime(concentration > 0.5%) is lower for nitrogen doping whencompared with a vacancy, which could partially be attributedto the N atoms, responsible for providing electron carriers tothe material, shifting the Fermi level much more than for thecase of vacancy defects [220].

The Terrones group has carried out structural relaxationand transport calculations on doped armchair nanoribbonsusing the DFT method [221]. The nanoribbons weresubstitutionally doped by replacing one carbon atom by B,N, O, Si, P or S atoms, and the edges were passivated withhydrogen. It can be observed from figure 24(a) that theoptimized structures when doping with N (or B) are slightlymodified but preserve the honeycomb lattice. Only the bondlengths surrounding the dopants are slightly altered. However,for S- and P-doped nanoribbons, the structures are significantlymodified; that is, the dopant in these cases prefers to ‘pop out’of the plane, and the carbon and hydrogen atoms located nearthe edges also remain out of the plane, as shown in figure 24(a).The quantum transport properties of chemically doped AGNRsare shown in figure 24(b). The quantum conductance plotsreveal similar features at and around the Fermi level, andthe doped nanoribbons exhibit semiconductor behaviors. Forlow doping levels (one doping site per ∼100 atoms), a linearI–V response could be observed for B-, N-, Si- and P-dopednanoribbons (figure 24(c)). However, for O- and P-dopedribbons, a higher applied voltage is needed to reach the samecurrent values as are observed for the above-mentioned dopingcases. Based on these calculations, it can be predicted thatGNRs doped with Si could be used in interconnector electricaldevices, whereas nanoribbons doped with P could be used forthe fabrication of sensors.

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Figure 23. The doping sites and the effect of doping and vacancy concentrations on the electrical properties of graphene. (a) Spin densityof states of functionalized AGNRs doped with nitrogen (N) and boron (B) atoms in various configurations as shown above each DOS plot.Reprinted with permission from [186]. Copyright 2008 by the American Physical Society. (b) Calculated resistivity of monolayer grapheneas a function of vacancy (left) or nitrogen (right) concentration. Reprinted with permission from [220]. Copyright 2010 by the AmericanPhysical Society.

5.3. Functionalization

In addition to the above-mentioned substitutional dopantsinto the graphene lattice, there are some other chemicalroutes to functionalize graphene, such as hydrogen passivation[153, 222], molecule grafting [223–225] or modificationwith different functional groups [154, 226]. Novoselov andco-workers have demonstrated that atomic hydrogen couldreact with graphene and transform this highly conductivezero-gap material into an insulator [222]. The as-obtainedgraphene derivative, so-called graphane, is crystalline andretains the hexagonal lattice, but its in-plane periodicitybecomes remarkably shorter than that of graphene, due to theatomic-scale buckling caused by the hybridization change fromsp2 to sp3 bonding. In addition, based on the configuration of agraphite intercalation compound (GIC), by inserting some ionsor molecules, such as diazonium cations (figure 25(a)) [224] orhydrophobin (figure 25(b)) [225], into the interlayer spacingsof graphite and then exfoliating the resulting intercalationcompound, a kind of surface-functionalized graphene couldbe obtained. This covalent functionalization could protect thesingle-layer graphene from re-aggregation. Furthermore, the

attachable functional groups might also provide graphene withsome tailor-made properties, such as customizable solubility,electron mobility and sensor activity. Using GGA for thedensity functional, Boukhvalov et al have considered thefunctionalization of bilayer graphene by different functionalgroups [226], namely, OH, CN, NH2, CH3, COOH as wellas by combination of the dopants and hydrogen, as shown infigure 25(c). It has been demonstrated by their calculationsthat the gap of graphene can be tuned smoothly between 2and 3 eV with an accuracy of about 0.2 eV [226]. Therefore,chemical functionalization will also be an efficient route fordeveloping high-performance applications of graphene- andgraphane-based materials in the area of molecular electronics,and further work along this research line is still needed.

6. Applications

In this section, some of the important applications of grapheneand GNRs will be demonstrated and summarized. We believethat the applications listed below, such as in high-performanceFETs, sensor devices, energy storage devices, transparent

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Figure 24. GNRs doped with different atoms. (a) Relaxed structures of substitutional doping in AGNRs. (b) Quantum conductance versusenergy for doped AGNRs compared with the pristine ones (see the dotted lines) for zero applied voltage. In all cases, the ribbons retain thesemiconductor feature in the conductance in the vicinity of the Fermi level; however, the detailed conductance curves depend sensitively onthe dopant atom. (c) Electronic current as a function of the applied voltage for doped and pristine AGNRs. Reprinted with permissionfrom [221].

Figure 25. The functionalization of graphene. (a) Representation of the 4-tert-butylphenyl functionalized graphene and transpolyacetylene(t-PA) chains formed by the introduced sp3 sites (hydrogen atoms are used in this example) in the sp2 carbon layer (highlighted in yellow).Reprinted with permission from [224]. Copyright 2011 by Nature Publishing Group. (b) Hydrophobin-functionalized graphene obtained byultrasonic waves. Reprinted with permission from [225]. Copyright 2010 by Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim. (c) Totaldensities of states versus energy for one-side (solid red lines) and two-side (dashed green lines) functionalizations of bilayer graphene forthe case of hydrogen (H), hydroxyl (OH) and other species. Insets show optimized atomic configurations for the case of two-sidefunctionalization. Reprinted with permission from [226]. Copyright 2008 by the American Physical Society.

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Figure 26. A wafer-scale graphene integrated circuit (IC). (a) Scanning electron image of a top-gated, dual-channel graphene transistorused in the mixer IC. The gate length is 550 nm and the total channel width (including both channels) is 30 µm. Scale bar: 2 µm. (b) Opticalimage of a completed graphene mixer including contact pads. Scale bar: 100 µm. (c) Schematic exploded (zoom) illustration of thisgraphene mixer circuit. (d) A snapshot of an output spectrum, between 0 and 10 GHz, of the mixer taken from the spectrum analyzer withtwo high-frequency input signals, an RF signal at a frequency of fRF = 3.8 GHz and a local oscillator (LO) signal at a frequency offLO = 4 GHz. Reprinted with permission from [233]. Copyright 2011 by the American Association for the Advancement of Science.

electrodes, only constitute the tip of the iceberg and moreand more fascinating applications will be developed in thenear future based on these interesting 2D and 1D carbonnanostructures with unique physical properties.

6.1. Graphene-based field-effect transistors

Due to their attractive properties, such as high electronmobility, electron-hole symmetry, quantum Hall effect[28, 227] and strong suppression of weak localization effects[228, 229], graphene has great potential in high-speed and

high-frequency electronics applications. A top-gated grapheneFET operating at high frequencies (gigahertz) was developed in2009 by IBM researchers [230], and soon after that, transistorsoperating at 100 GHz [231] and 300 GHz [232] were reportedin 2010. In June 2011, IBM researchers [233] reported theirwork on a wafer-scale integrated circuit (IC) using graphenefield-effect transistors (G-FETs) (figure 26). Graphene circuitswere fabricated on a semi-insulating SiC wafer. A two- orthree-layer graphene film was epitaxially grown on the Si faceof the SiC substrate at temperatures above 1400 ◦C. Fabricationof the graphene IC began with top-gated, two-finger G-FETs(figure 26(a)), followed by integration with on-chip inductors.In order to form the active channel of the transistor, theseauthors spin-coated the graphene-SiC wafer with a layer of140 nm thick PMMA (poly(methyl methacrylate)) followed bya layer of 20 nm thick HSQ (hydrogen silsesquioxane). The

FET channel was defined by e-beam lithography (EBL); thesurrounding graphene was removed by oxygen plasma with theexposed HSQ film as the protecting mask. The optical imageof a completed graphene mixer and its schematic illustrationare shown in figures 26(b) and (c), respectively. Figure 26(d)displays the output frequency spectrum of the graphene mixerwith input signals fRF = 3.8 GHz and fLO = 4 GHz and adrain bias of 2 V. This work [233] demonstrates that a grapheneIC can operate as a broadband RF mixer at frequencies upto 10 GHz with excellent thermal stability. The excellenttransistor performance achieved in such graphene-field-effecttransistor (G-FET) devices should open exciting opportunitiesin high-speed, high-frequency electronics.

6.2. Transparent conductive electrodes

Optoelectronic devices, such as touch screens, light-emittingdiodes and solar cells require materials with low sheetresistance and high optical transparency. As a 2D singleatomic layer of crystalline carbon, graphene exhibits highroom-temperature carrier mobility [234], a tunable band gap[197], ballistic transport [235] and a visible transparency of97.7% [236, 237]. Hence, ideal materials for applicationsin electronics and optoelectronics, include their use intransistors, photodetectors and saturable absorbers of light[238]. Graphene thin films exhibit a high optical transparencyin both the visible and near-infrared regions of the spectrum, a

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low electrical resistivity, high chemical and thermal stabilities,high carrier mobilities. These properties make graphenean excellent choice for transparent electrodes in variousoptoelectronic devices [239]. For instance, a liquid crystaldisplay (LCD) made using a sheet of peeled grapheneas the transparent conductor has been demonstrated [240].It was found that each layer of graphene absorbs about2.3% of the incident light, which is significantly lowerthan that of conventional indium tin oxide (ITO) (15–18%)[241]. Furthermore, graphene has shown great potential forcreating photovoltaic solar devices owing to its high opticaltransmittance and electrical conductivity. The graphene filmnot only serves as a transparent electrode for light transmissionbut also as an active layer for electron/hole separation andhole transport [242, 243]. Graphene microsheets have beendispersed into conjugated polymers to improve the polymerexciton dissociation and charge transport [244, 245]. Solution-processed thin films were used as conductive and transparentelectrodes for organic [246] and dye-sensitized [239] solarcells, although the cell efficiency is still lower than thosewith ITO and fluorine tin oxide (FTO) electrodes [239],and further work is needed to realize the full potential ofgraphene for these applications. The application of graphenein inorganic thin-film solar cells has also been explored. Liet al demonstrated an efficient solar cell by forming Schottkyjunctions between graphene sheets and Si [247]. This sheetconsisted of multiple layers of graphene that are overlappedand interconnected, which ensures a conducting pathway evenif there are cracks formed in one of the graphene layers. Themultilayer structure is expected to provide a higher carriermobility based on a recent study on graphene layers decoupledfrom bulk graphite [248]. Moreover, graphene thin films alsoexhibit great mechanical properties and can be used to makeflexible and stretchable electrodes [249, 250]. However, inorder to produce graphene-based transparent conductive film,there is still a long way to go. For example, graphene filmsshould exhibit optical transparency of 90% (λ = 550 nm) aswell as a sheet resistance below 80 �/sq, and they should besustainable after bending without degradation of performance.

6.3. Graphene-based sensors

The properties of graphene in biosensors and gas sensinghave been widely investigated. For example, using reducedgraphene oxide to construct a 3D structure of graphene-encapsulated SiO2 nanoparticles, the detection limit for targetcancer biomarkers has been remarkably improved [251].Wang et al have demonstrated that N-doped graphene canbe used for glucose biosensing with concentrations as low as0.01mM in the presence of interferences including ascorbicacid (AA) and uric acid (UA) for testing the selectivity[252]. Schedin et al showed that mechanically exfoliatedgraphene flakes can detect a single molecule of NO2 gas[253]. They fabricated micrometer-size sensors made fromgraphene, and such a device was capable of detecting anindividual gas molecule when it interacts with the graphenesurface. Each adsorbed molecule changes the local carrierconcentration in graphene by one electron, which leads to step-like changes in the resistance. The high sensitivity that is

achieved is due to the fact that graphene is an exceptionallylow-noise material electronically, which makes it a promisingcandidate not only for chemical detectors but also for otherapplications where local probes sensitive to external charge,magnetic field or mechanical strain are required. Graphene-based gas sensors allow the ultimate molecular sensitivitysince the adsorption of individual gas molecules can nowbe detected. Large arrays of such sensors would increasethe uptake area [254], allowing higher sensitivity for short-time exposures and the detection of active (toxic) gases inas low a concentration as would be practically desirable.Chemically modified graphene has been used in biosensorapplications. For example, immunoglobulin E aptamers withan approximate height of 3 nm were successfully immobilizedon a graphene surface. The aptamer-modified G-FET showedselective electrical detection of IgE protein, exhibiting goodaffinity and the potential for G-FETs to be used in biologicalsensors [255]. Hou et al found that graphene modified withethylenediamine triacetic acid (EDTA) can be used as anideal electrode material to fabricate biosensors [256]. Theyfabricated a dopamine electrochemical biosensor with a highselectivity and sensitivity, which might allow its potentialuse in the investigation and diagnosis of dopamine-relateddiseases.

6.4. Energy storage and conversion

Pristine and doped graphene has been demonstrated as anelectrode material for capacitors [257, 258] and lithium ionbatteries [259, 260], because of both its high specific surfacearea (2630 m2 g−1) and unique 2D structure. The dischargecapacity of graphene in a lithium ion battery was foundto be 540 mAh g−1, and this could be further improved to730 and 784 mAh g−1 by adding CNTs and fullerenes to thegraphene [261]. Graphene also showed a good ability tocoat silicone particles, and metal or metal oxide particlesin order to prevent the volume expansion of the electrodematerials during the charge and discharge cycles in batteries[261–263]. The supercapacitor is recognized as one ofthe important next-generation rechargeable power sourcesdue to its intrinsic ability to decrease the gap between thedielectric capacitor and the battery. In addition, the edgesite is known to have a differential capacitance ten timeshigher than that of the basal plane [264]. Thus, graphenecould be used as an electrode material for supercapacitors.Miller et al have demonstrated high-performance electricdouble-layer capacitors (DLCs) with electrodes made fromvertically oriented graphene nanosheets grown directly onmetal current collectors. This design minimized electronicand ionic resistances and produced capacitors with a resistor–capacitor (RC) time constant of less than 200 ms, which ismuch faster than that of typical DLCs (∼1 s). This fast timeconstant can be attributed to these aligned graphene nanosheetsshowing more exposed edge planes that greatly increase thecharge storage as compared with that of designs that rely onbasal plane surfaces only. Moreover, in order to improve theperformance of these graphene-based supercapacitors, severalapproaches have been developed, such as controlling the

25


surface area and edge sites [265], and by introducing metaloxide [266]. In addition to this, graphene can also be used in thefuel cell area by virtue of its excellent ability to support metalnanoparticles (Au, Pt and Pd) [267–270]. We believe that moreand more interesting electrochemical properties of graphenewill be explored for their applications in energy storage andconversion in the future.

6.5. Other applications

In addition to the above-mentioned applications, graphenecould also be used in areas such as SERS [271], hydrogenstorage [272], field-emission [273] or for catalyst supports[274]. Mulhaupt and co-workers demonstrated that palladiumnanoparticles dispersed on graphite oxide were able to catalyzeSuzuki–Miyaura coupling reactions [274]. (The Suzuki–Miyaura reaction is a valuable synthetic process for theconstruction of carbon–carbon bonds). Seger et al usedgraphene as a support material for the dispersion of Ptnanoparticles for the development of a fuel cell electrocatalyst[275]. In addition, graphene–TiO2 nanocomposites canbe employed as photo-anodes in a photo-electrochemicalcell. In this context, the role of graphene is mainlyto promote the collection and transport of photo-injectedelectrons [276]. Efforts are also being made to utilizegraphene-based composites for visible-light-induced photo-electrolysis of water [276].

7. Conclusions and perspectives

In this review, we focused on defects in graphene as a modelsystem for studying defects in 2D and 1D sp2 hybridized carbonsystems. We demonstrated that point defects and line defects ofvarious types produce different and significant changes in thephysical, magnetic and chemical properties of graphene-likenanomaterials. We showed that defects introducing disordercould in general be detrimental to the proper functioning ofvarious properties, but for other properties such as n-typeor p-type doping, the introduction of dopants which alsointroduce structural defects could be used to further controlthe carrier concentration, so there is a trade-off betweenthe materials benefit and the degradation that needs to bebalanced and optimized. Some defects, such as edges, areof great interest for the new physics they introduce. Foratomically smooth graphene edges, potential applications ofthe edges are contemplated, and the characterization of edgetypes has been important. HRTEM has been shown toprovide a powerful technique for carrying out such studies, butRaman spectroscopy coupled with theory has also provided asurprisingly useful and convenient probe of graphene edgesand graphene ribbons, even though the wavelength of lightis orders of magnitude larger than graphene ribbon widths,or CNT diameters for that matter. Defects are symmetrybreaking, and therefore allow vibrational modes that arenormally Raman or IR inactive to become activated. This toolhas not been sufficiently developed for the study of defects andshould be considered as an attractive topic for future study.It might be that one could identify and distinguish between

different defect types and quantify the density per unit areaor per unit volume for the different defect types by carryingout a perfectly designed spectroscopy experiment. From apractical standpoint, the functionalization of graphene couldbe used to improve certain chemical properties of graphene,such as solubility and dispersability. But at the same time,functionalization introduces foreign atoms into the latticeor edges, and the associated processing conditions also arelikely to introduce defects. Nevertheless, the benefits offunctionalization often outweigh the degradation effects of theforeign atoms as discussed above in general terms. Thus, itis crucial to synthesize perfect or atomically smooth edges inGNRs to establish baselines for comparison, and it is crucial tocontrol the location distribution and total amount of dopants ingraphene and GNRs. In addition, it is important to emphasizethat there are other defects we did not discuss in this review,such as screw dislocations and interlayer stacking faults, andthis is because such defects are not important for a monolayergraphene 2D crystal, but could become quite important in few-layered graphene. Therefore, these types of defects should nowbe studied and theoretical calculations should be performed.

In a 2D crystal such as graphene, 1D and pointdefects produce significant changes in their physicochemicalproperties which should be considered in the future to performdefect engineering at the nanoscale. Such defects include edgegeometry, vacancies, topological 5–7, D5D7, 5–8–5, T5T7,grain boundaries, extended lines of defects and doping, allof which might play a role in future applications. But alsothis knowledge can be extended to other layered materials,such as boron nitride and metal dichalcogenides (MoS2, WS2,MoSe2, etc) to broaden the spectrum of different behaviors andapplications (figure 27), with each system providing nuancesthat could enrich developments among the different layered

Figure 27. (a) BN-Haeckelite-8–4. (b) Extended line of defects ina WS2 sheet formed by octagonal-like defects and a square-likedefects, as shown in (c) and (d), respectively.

26


materials. Certainly, HRTEM, STM, STS, Raman and otherspectroscopies, and synthesis methods to study defects needto be further developed and improved not only to characterizedefects in graphitic nanostructures but also to produce specificdefects, in an ordered way in different layered systems in orderto create more reliable and useful functional materials.

Although there are numerous challenges remaining forfuture study, we can now see that when we gain some controlover the defect type, defect location and defect concentration,we will be able to produce novel materials with fascinatingproperties that could revolutionize energy-related applicationsand bio-nanotechnology.

Acknowledgments

We acknowledge the support from the Research Centerfor Exotic Nanocarbons, Japan regional Innovation StrategyProgram by the Excellence, JST (MT). MSD is grateful forsupport from MURI-Navy ONR, Contract: N00014-09-1-1063and HTM acknowledges funding from Programa ProfessorVisitante do Exterior-PVE as ‘Bolsista CAPES/BRASIL’. MTthanks the Penn State Center for Nanoscale Science for a seedgrant entitled ‘Defect Engineering of 2-D Sheets of LayeredMaterials’.

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