Journal of Materials Science & Technology xxx (2015) 1e8
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Journal of Materials Science & Technology
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Defects in Graphene: Generation, Healing, and Their Effectson the Properties of Graphene: A Review
Lili Liu 1, Miaoqing Qing 1, Yibo Wang 1, Shimou Chen 2, *
1 Department of Chemistry, School of Science, Beijing Technology and Business University, Beijing 100048, China2 Key Laboratory of Green Process and Engineering, Institute of Process Engineering (IPE), Chinese Academy of Sciences (CAS), Beijing 100190, China
a r t i c l e i n f o
Article history:Received 28 September 2014Received in revised form15 November 2014Accepted 19 November 2014Available online xxx
Key words:GrapheneVacancyDefect healingBand gap modulationProperties of defective graphene
Graphene has raised extensive interest in the worldwide for itsextraordinary thermal, mechanical, electrical and other proper-ties[1,2]. Among all properties, the unique electronic properties areassumed to be the most intriguing aspect of graphene, for example,outstanding ballistic transport properties and longest mean freepath at room temperature[3], distinctive integral and half-integralquantum hall effect[4,5], the highest mobility to increase thespeed of devices[6], and so on. The mobility of graphene is signifi-cantly higher than that of the widely-used Si, of approximately1400 cm2 V�1 s�1. Consequently, graphene has been considered as acandidate material for applications in post-silicon electronics.
Graphene has a honeycomb lattice structure and a unit cell thatcontains two carbon atoms. Just like in carbon nanotubes, there aretwo different kinds of graphene ribbon edges: armchair and zigzag,which can influence the electronic properties of graphene. How-ever, most electronic applications are handicapped by the absenceof a semiconducting gap in pristine graphene. For example, devicesmade from the zero-bandgap graphene are difficult to switch off,losing the advantage of the low static power consumption of the
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complementary metal oxide semiconductor (CMOS) technology.Quantitatively, the Ion/Ioff ratios for graphene-based field-effecttransistors (GFETs) are less than 100[7], while any successor to the SiMOSFET should have excellent switching capabilities in the range of104e107. Therefore, opening a sizeable and well-tuned band-gap ingraphene is a significant challenge for graphene-based electron-devices, introducing defects have shown great potential on thisimportant issue.
The electronic and mechanical properties of graphene sampleswith high perfection of the atomic lattice are outstanding, butstructural defects, which may appear during growth or processing,deteriorate the performance of graphene-based devices. However,deviations from perfection can be useful in some applications, asthey make it possible to tailor the local properties of graphene andto achieve new functionalities. Like in any other real material,structural defects do exist in graphene and can dramatically alter itsproperties. Defects can also be deliberately introduced into gra-phene, for example, by irradiation or chemical treatments.
Because sp2-hybridized carbon atoms can arrange themselvesinto a variety of different polygons to form different structures, thenonhexagonal rings may either introduce curvature in the sheet orleave it flat when the arrangement of polygons satisfies certainsymmetry rules. This property is not included in other bulk crystals,for example, semiconductors such as silicon. Reconstructions in theatomic network permit a coherent defective lattice without under-coordinated atoms. Although they have no dangling bonds, these
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reconstructed defects locally increase the reactivity of the structureand allow adsorption of other atoms on graphene[8].
In this review, we summarized the major progresses made indefect engineering of graphene, including the types of defects ingraphene, the generation and healing of the graphene defects aresummarized, as well as the effects of the defects on the chemical,electronic, magnetic, and mechanical properties of graphene. Tokeep the length manageable, our attention is mainly focused on themajor developments of graphene defects in recent five years.
2. Different Type of Defects in Graphene
There are two kinds of defects in graphene. One is point defects,typically vacancies or interstitial atoms are zero-dimensional. Theother is on one dimensional line of defects. It is well-known thatthe defects are not always stationary and that their migration canhave an important influence on the properties of a defective crystal.In graphene, each defect has certain mobility parallel to the gra-phene plane. The mobility might be immeasurably low, forexample, for extended vacancy complexes, or very high, forexample, for adatoms on an unperturbed graphene lattice. Themigration is usually governed by an activation barrier which de-pends on the defect type and therefore increases exponentiallywith temperature.
2.1. StoneeWales defect
Since the graphene lattice can be reconstructed by formingnonhexagonal rings, the simplest example is the StoneeWales (SW)defect[9], which does not involve any removed or added atoms. Asshown in Fig. 1, four hexagons are transformed into two pentagonsand two heptagons [SW(55-77) defect] by rotating one of the CeCbonds by 90�. The SW(55-77) defect has a formation energyEf ¼ 5 eV[10].
2.2. Single vacancies
The simplest defect in any material is the missing one latticeatom. Single vacancies (SV) in graphene have been experimentallyobserved by TEM[10]. As can be seen in Fig. 2, the SV undergoes aJahneTeller distortion which leads to the saturation of two of thethree dangling bonds toward the missing atom. One dangling bondalways remains owing to geometrical reasons. This leads to the
Fig. 1. StoneeWales defect SW(55-77), formed by rotating a carbonecarbon bond by 90�: (Density functional theory (DFT) calculations (Copyright 2008 American Chemical Society)[1
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formation of a five-membered and a nine-membered ring [V1(5-9)defect].
2.3. Multiple vacancies
Double vacancies (DV) can be created either by the coalescenceof two SVs or by removing two neighboring atoms. Because nodangling bond is present in a fully reconstructed DV, two pentagonsand one octagon [V2(5-8-5) defect] appear instead of four hexagonsin perfect graphene. The atomic network remains coherent withminor perturbations in the bond lengths around the defect. Simu-lations indicate that the formation energy Ef of a DV is of the sameorder as that of an SV (about 8 eV)[11,12]. As two atoms are nowmissing, the energy permissing atom (4 eV per atom) is much lowerthan that for an SV. Hence, DVs are thermodynamically favoredover SVs. Furthermore, the removal of more than two atomsmay beexpected to result in larger and more complex defect configura-tions. Generally, as an even number of missing atoms allows a fullreconstruction (complete saturation of dangling bonds), such va-cancies are energetically favored over structures with an oddnumber of missing atoms where an open bond remains[13].
2.4. One dimensional defects
This kind of defect has been observed in many experimentalstudies of graphene[14e17]. In general, these line defects are tiltboundaries separating two domains of different lattice orientationswith the tilt axis normal to the plane. Such defects can be thoughtof as a line of reconstructed point defects with or without danglingbonds[18e20], as shown in Fig. 3. One example is a domain boundarywhich has been observed to appear due to lattice mismatch ingraphene grown on a Ni surface[17]. This defect makes up of analternating line of pairs of pentagons separated by octagons (Fig. 3).Obviously, such a defect can be formed by aligning (5-8-5) diva-cancies along the zigzag lattice direction of graphene.
2.5. Defects at the edges of graphene
Each graphene layer is terminated by edges with the edge atombeing either free or passivated with hydrogen atoms. The simplestedge structures are the armchair and the zigzag orientation.Defective edges can appear because of local changes in the recon-struction type or because of sustained removal of carbon atomsfrom the edges. This can be achieved by sputtering edge atoms[21,22].
a) experimental TEM image of the defect; (b) its atomic structure as obtained from our0].
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Fig. 2. Single vacancy V1(5-9): (a) as seen in an experimental TEM image; (b) its atomic structure obtained from our DFT calculations (Copyright 2008 American ChemicalSociety)[10].
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Under these conditions, armchair edges can be turned to zigzagedges[21]. An intermediate structure can be regarded as a defectiveedge. A simple example of an edge defect is the removal of onecarbon atom from a zigzag edge. This leads to one pentagon in themiddle of a rowof hexagons at the edge. Other edge reconstructionsresult in different combinations of pentagons and heptagons at theedge as shown in Fig. 4[23]. Besides, hydrogen atoms and otherchemical groups that can saturate dangling bonds at the edge underambient conditions may be considered as disorder, dramaticallyincreasing the number of possible edge defects.
3. Generation of Defects in Graphene
The high formation energy of a single vacancy in graphene(7.5 eV) does not allow any detectable concentration of point
Fig. 3. (a) Grain boundary defect structure consisting of pentagon-pairs and octagons in grapthe calculated adsorption energies for two domains are similar, but both are lower in energ(Copyright 2010 Nature Publishing Group)[17].
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defects in thermal equilibrium at temperatures below the meltingtemperature. However, there are three mechanisms which can leadto nonequilibrium defects in graphene: (1) crystal growth; (2)irradiation with energetic particles, for example, electrons or ions;and (3) chemical treatment[8].
3.1. Crystal growth
Since the large-scale growth of a graphene layer does normallynot occur slowly atom-by-atom from one nucleus but rather as arelaxation of a metal carbon systemwith many nuclei, for example,in chemical vapor deposition (CVD), it is natural to expect defects inthe as-grown material. Generally, high temperature growth facili-tates the relaxation toward thermal equilibrium, and defects can beannealed rapidly. However, defects are a well-known problem in
hene grown on a Ni substrate; (b) the DFT relaxed geometry of the defect structure; (c)y than a third possible adsorption configuration with all carbon atoms on hollow sites
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low temperature growth. Because of the high formation energy ofvacancies and fast migration of adatoms in graphene, it is unlikelythat there are any isolated vacancies in graphene after growth. Thishas been confirmed by the high carrier mobility in CVD-growngraphene, which would not be expected at a considerable densityof vacancies. The temperature dependence of themobility indicatesthat impurity scattering dominates at the interface even for themerged domains with the same orientation[24].
3.2. Particle irradiation
Irradiation of graphene with ions or electrons can producepoint defects due to the ballistic ejection of carbon atoms[25e27].The atom can be kicked out from graphene or adsorb on the sheetand migrate on its surface as an adatom. The effect of irradiationhas been studied in detail by electron microscopy[28,29], whereirradiation and imaging can be done with the same electron beam,and the formation of defects is observable in situ at atomic reso-lution. Uniform irradiation of larger areas results in a generation ofrandomly distributed vacancies. However, due to increased strainand/or under-coordinated atoms, the defective areas, for example,where a vacancy already exists, show an increased rate of defectformation. Defects can also be generated in preselected positionswith a highly focused electron beam or by using masking tech-niques. Modern electron microscopes with aberration-correctedcondensers allow focusing an electron beam onto a spot ofapproximately 1 Å in diameter thereby creating vacancies withalmost atomic selectivity[30]. Another physical method which hasbeen used for defect production in graphene is ion irradi-ation[31e35]. It can be used to selectively produce certain defects orto pattern and cut graphene with a precision down to 10 nmutilizing a focused ion beam[36,37]. However, for the bilayer gra-phene, contrary to theoretical estimates based on the conven-tional binary collision model, experimental results indicate thatthe number of defects in the lower layer of the bilayer graphenesample is smaller than that in the upper layer (as shown inFig. 5)[35]. This observation is explained by in situ self-annealing ofthe defects.
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3.3. Chemical methods
The reactions of carbon atoms in a graphene layer with otherspecies can lead to the loss of atoms and hence to defects. However,the high inertness of graphene (apart from edge positions that arehighly reactive) only allows a very limited number of possible re-actions at room temperature. Oxidation is the most common one,for example, in an oxidizing acid (HNO3 or H2SO4). In such atreatment it is possible to attach oxygen and hydroxyl (OH) orcarboxyl (COOH) groups to graphene[38]. When graphene is coveredmore or less uniformly with hydroxyl or carboxyl groups, the ma-terial is called graphene oxide, which is essentially a highlydefective graphene sheet functionalized with oxygen groups[39].Plasma treatments and adsorption of atomic hydrogen on a gra-phene surface followed by its self-organization and hydrogen is-land formation can also be referred to in the context of graphenetreatment by chemical methods[40].
4. Healing of Defects in Graphene
It has been directed that defects play a crucial role in tailoringthematerial properties of carbon-based structures such as graphite,carbon nanotubes, and graphene sheets [26,41,42]. For example, itwas found that defects are responsible for the inherent ferromag-netic behavior of carbon-based materials, due to the presencearound the defects of localized electron states with energies closeto that of the Fermi level[43,44].
On the other hand, defects are well-known for their ability toscatter charge carriers and phonons, thus decreasing the ballistictransport path length and adversely affecting carrier mobility andthermal conductivity. The detrimental effects of defects areparticularly pronounced in graphene films. For example, defectswere held responsible for a remarkable reduction in charge carriermobility in graphene films obtained by micromechanical cleav-age[45]. The transport properties of graphene films produced bychemical methods, such as the exfoliation and chemical reductionof graphene oxide, have also been ascribed to defects[46]. In thisrespect, defects are undesirable, and the ability to “heal” them is
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Fig. 5. Schematic illustration of the experimental setups for creating defects on graphene. The samples were formed by subsequent transfer of 12C and 13C graphene sheets on Si/SiO2 substrate and irradiated by Arþ ions with various doses followed by Raman probing. The right panel is a snapshot from molecular dynamics simulations showing a typicalatomic configuration after an ion impact (Copyright 2013 WILEY-VCH Verlag GmbH & Co. KGaA)[35].
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important for generating carbon nanostructures with high elec-trical and thermal conductivities and, potentially, enhancedmechanical strength.
4.1. Thermal annealing
One promising approach for removing crystalline lattice defectsand restoring graphitic structures is high temperature processing inthe presence of a hydrocarbon gas. Utilizing appropriate conditions,the hydrocarbon gas might decompose to supply carbon atoms thatcan repair defective sites. Recently, L�opez et al. demonstrated thatchemical vapor deposition (CVD) processing of chemically derivedgraphene films using ethylene carbon source improved film con-ductivity by two orders of magnitude, to room temperature (RT)values of 10e350 S cm�1. The authors attributed the improvementto defect healing[47]. In addition, direct observation of the modifi-cation of defective sites on graphitic surfaces under gaseous hy-drocarbon atmospheres was reported by Liu et al. [48]. They studiedthe reactivity of defects on highly oriented pyrolytic graphite(HOPG) surfaces exposed to acetylene at elevated temperatures byscanning tunneling microscopy (STM).
4.2. Self-healing
By using first-principles calculations based on density-functional theory, Tsetseris et al. found that pairs of C adatoms
Fig. 6. A diagram of the vacancy migration between graphene layers leads to vacancies holeSociety of Chemistry)[50].
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and clusters of four or more self-interstitials stay idle unless thesystem is heated to very high temperatures, while clustering ofthree C adatoms leads to removal of hillock-like features and cre-ates mobile species, resulting in self-healing of defective struc-tures[49]. Liu et al. found that in the single layer vacancy defectsprefer to coalesce into larger vacancy holes, while in themulti-layergraphene the vacancies tend to be concentrated into a single hole inone layer through both intra- and inter-layer migrations (Fig. 6).The vacancy inter-layer migration is facilitated by the interaction ofdefects in neighboring layers[50].
4.3. Healing by absorption
Wang et al. proposed a strategy of controllable vacancy healingand N-doping of graphene[51], as shown in Fig. 7, vacancies can behealed by sequential exposure to CO and NO molecules in a two-step recipe. Firstly, the CO molecule can be easily absorbed at thesite of graphene defects. Then, NO can remove the extra O atom in achemical way by forming NO2 molecule that binds to grapheneweakly. Encouraged by this observation, they further study thecontrollable N-doping in graphene with a similar procedure, whichinvolved creating vacancy and subsequent exposure to NO mole-cules. That is to say, a combination of CO and NO molecules canpotentially provide simultaneous healing and doping at a desirableratio, which is very important for band-gap modulation ofgraphene.
s formation in one layer and the self-healing of other layers (Copyright 2014 the Royal
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Fig. 7. Schematic view of the vacancy healing and N-doping process of graphene withvacancies by CO and NO molecules (Copyright 2011 American Physical Society)[51].
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4.4. Metal-assisted healing
The healing of graphene grown from a metallic substrate isinvestigated by Karoui et al. using tight-binding Monte Carlo sim-ulations[52]. At temperatures (ranging from 1000 to 2500 K), anisolated graphene sheet can anneal a large number of defectssuggesting that their healings are thermally activated. Wherein, inthe presence of a nickel substrate, a perfect graphene layer can beobtained. The probable mechanism is that the nickel carbonchemical bonds keep breaking and reforming around defectedcarbon zones, providing a direct interaction, necessary for thehealing. As shown in Fig. 8, as in the case of the isolated graphenesheet, the sheet is far from being healed and a non-negligibleconcentration of defects remains at 1000 K (Fig. 8(b)). Once again,large rings are healed at 1000 and 1500 K, whereas pentagons andheptagons cancel out at higher temperatures. At 2500 K the gra-phene sheet is completely healed as seen in Fig. 8(c).
Fig. 8. Graphene sheet in the presence of the Ni lattice: (a) side and top views of the initialAmerican Chemical Society)[52].
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5. Properties of Defective Graphene
5.1. Chemical properties
It is well-known that defects associated with dangling bondsshould enhance the reactivity of graphene. Numerous simulationssuggested that hydroxyl, carboxyl, or other groups could easily beattached to vacancy-type defects[53,54]. Simulations also showedthat reconstructed defects without dangling bonds such as SWdefects or reconstructed vacancies locally changed the density ofp-electrons and may also increase the local reactivity[55,56]. Forexample, Pablo et al. found that when two phenyl groups areattached onto perfect graphene, the StoneeWales defect becomesmore reactive than the 585 double vacancy and 555e777 recon-structed double vacancy[56]. The largest increase of reactivity isobserved for the functional groups whose binding energy ontoperfect graphene is small. Thus, the controlled creation of defectswith a high spatial selectivity can be used for the local functional-ization of graphene, and for the creation of graphene ribbons withthe designed properties by various chemical methods.
5.2. Electronic properties
Defects strongly affect the electronic properties of graphene.From a theoretical point of view, the Dirac equation has to bemodified when defects are in the lattice. This will naturally have animpact on the electronic structure. The overlap of p-orbitals de-termines the electronic properties but is altered in the vicinity ofstructural defects. Firstly, bond lengths in the strain fields of defectsare different from those in the perfect lattice. Secondly, defects leadto a local rehybridization of sigma and piorbitals which againchange the electronic structure. A local curvature around defects
configurations; equilibrium configurations at (b) 1000 and (c) 2500 K (Copyright 2010
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Fig. 9. Schematic of strained graphene functionalization: (a) after being transferred to polydimethylsiloxane (PDMS), the polycrystalline graphene is strained by elongation; (b)after strain is applied, the aqueous solution of aryl diazonium salt is pipetted onto the graphene surface, the inset shows a photograph of several droplets on a graphene/PDMSsubstrate; (c) after functionalization, the solution is removed and the substrate rinsed and dried. Because of the increased reactivity of defect sites along boundaries, there is anincreased concentration of functional molecules at these locations. (Copyright 2013 American Chemical Society)[67].
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also has an influence on the rehybridization. Thirdly, all defects leadto scattering of the electron waves and change the electrontrajectories[57,58].
5.3. Magnetic properties
Magnetism in pure carbon systems has recently been the subjectof intense experimental and theoretical research, which is veryimportant to understand a fundamental problem: the origin ofmagnetism in a system which traditionally has been thought toshow diamagnetic behavior only. In addition to fullerenes, nano-tubes, graphite, and nanodiamonds, magnetism was recently re-ported for graphene produced from graphene oxide [8,59e62]. Basedon the calculations, the observed magnetic behavior in all thesesystems was explained in terms of defects in the graphitic network.Such defects have local magnetic moments and may give rise to flatbands and eventually to the development of magnetic ordering.Magnetism may also originate from impurity atoms which arenonmagnetic by themselves, but because the specific chemicalenvironment give rise to local magnetic moments.
5.4. Mechanical properties
The influence of defects on the mechanical properties of gra-phene has not yet been studied experimentally. However, based ona large body of experimental and theoretical data for carbonnanotubes[63e66], one can expect that point defects, in particularvacancies, will decrease the Young's modulus and tensile strengthof graphene samples. Existence of defects may remarkably reducethe tensile strength, and mechanical properties should bedecreased as the number of defects increase. Conversely, efficientreconstruction and healing of vacancy-type defects should mini-mize their detrimental effects. Line defects (dislocations) should beimportant for plastic deformation of graphene ribbons under ten-sile strain[8]. On the other hand, Bissett et al. found that mechanicalstrain can alter the structure of graphene, and dramatically increasethe reactivity of the graphene. As shown in Fig. 9, the reaction rateof aryl diazonium functionalization can be increased up to 10 timesby applying external strain to the graphene[67].
6. Concluding Remarks
Graphene have a big role in nanoscience today because of theirrich and promising electrical, mechanical and optical properties.However, achieving these properties requires understanding theunderlying structure and its behavior. In addition to ideal systems,
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defects are frequently unavoidable in experiments; hence theireffect on electronic properties of graphene, along with their healingto enrich the functionalities of graphene, should be investigated.Such studies can provide insight into the interplay of the defects ingraphene and related nanocarbon materials and facilitate therational design of novel carbon materials with new functionalities.Furthermore, the following key points are suggested for futurestudies of the graphene defects.
(1) Most of the study on the influence of defects on the elec-tronic properties of graphene is based on theoretical simu-lation, and graphene flakes with different sizes and bordersare employed. This should have some differencewith the realgraphene materials. Experimental data directly reveal thedefects effects on the electronic and other characteristics ofgraphene are urgently needed.
(2) It is also very important to find a way to heal vacancy defectsin graphene in a controlled way. It seems that a high tem-perature thermal annealing, adding foreign atoms or draw-ing support from somemetal substrates can serve as efficientapproaches to remove unwanted defects. However, it is stilldifficult to regulate the concentration of the defects in thereal experiments, especially for the large area of graphene orbatch processing. The nature of the healing mechanismshould be explored.
(3) There is a huge demand for developing the applications ofgraphene in electronics and optics, in which opening theband gap of graphene is the most important issue. Intro-ducing defects have shown promising prospect in the band-gap modulation of graphene, even though the influences ofthe defects on pristine graphene are widely studied. Moreattention should be paid on the understanding of defects ofgraphene in the vicinity of surface, interface, reactant, andenvironment, etc. In-situ studies of the graphene and theirprototype devices are also very important, which willprovide new insights into the structures and properties ofgraphene, and boost further exploration of grapheneapplications.
Acknowledgments
This work was supported by the National Natural ScienceFoundation of China (Nos. 21276257 and 2110600) and theResearch Foundation for Youth Scholars of Beijing Technology andBusiness University (No. QNJJ2014-14).
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