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

Graphene consists of a single and infinite layer of graphite in which each carbon atom possesses an sp² hybridization. By hybridization we mean that each carbon atom is connected to three other carbon atoms via covalent bonds with lengths of 1.42 Å and with 120° angles between each bonded pair (see figure 2). In addition, graphene could be considered as a network consisting of two triangular sublattices in which the electronic states form two energy bands intersecting at the K and K' points in the Brillouin zone, and these high symmetry points K and K' are connected by inversion symmetry. Close to these crossing points, the electron energy E(k) depends linearly on the wave vector k obeying the relativistic Dirac equation; thus electrons and holes in monolayer graphene are called Dirac fermions and points K and K' in reciprocal space are called Dirac points [28]. Dirac fermions are responsible for many new phenomena in physics, which for the case of graphene cause the anomalous integer quantum Hall effect at room temperature [30, 38], insensitivity to external electrostatic potentials (Klein paradox), jittery motion of the wave function (zitterbewegung) under confining potentials, and huge mean free paths (carrier mobilities of more than 100 000 cm² V⁻¹ s⁻¹) [29, 39]. Experiments by the Manchester group in 2004 with few-layer graphene opened up a new research era on 2D layered materials [27]. However, the amazing properties of graphene change by adding additional layers, thus losing the real 2D character and also the Dirac fermion behavior [40–42]. To date, intensive experimental and theoretical studies of bilayer and tri-layer graphene have also taken place, including studies of different interlayer stacking orders.

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Fujita and colleagues realized that, as in all realistic crystal structures, graphene should have edges, in this case one dimensional (1D) edges, which in the context of unzipped CNTs can be regarded as graphene ribbons, with armchair edges and zigzag edges as the two special high symmetry cases (see figure 2) [43, 44]. Therefore, in this context, armchair graphene nanoribbons (AGNRs) exhibit different widths depending on the number 'N_A' of dimer lines across the ribbon width (N_A-AGNRs), and likewise for zigzag graphene nanoribbons (ZGNRs) with a corresponding number 'N_Z' for N_Z-ZGNRs) (see figure 2).

Within a tight-binding approach, AGNRs could be metallic or semiconducting depending on their ribbon width, but all ZGNRs are metallic, with a high density of electronic states (DOS) at the edges. Therefore ZGNRs exhibit characteristic edge effects which are not present in AGNRs. These edge effects in ZGNRs are responsible for a flat band close to the Fermi level which implies a peak in the electronic density of states, thus making the ZGNR edges more reactive [43, 44]. These fundamentally different edge properties for ZGNRs and AGNRs provide a handle toward distinguishing armchair from zigzag edges at the nanoscale using local optical techniques which usually operate at the micrometer (10⁻⁶m) size level. When using first-principles calculations, all ZGNRs and AGNRs possess non-zero, direct band gaps. For ZGNRs the gaps are mini-gaps caused by spin ordering effects at the edges, and for AGNRs the band gaps arise from quantum confinement effects and can have larger magnitudes than for ZGNRs [45]. If spin polarization is considered in ZGNRs and quantum transport is studied, a band gap appears close to the Fermi level for the most stable antiferromagnetic configuration in which the total spin within the unit cell is zero: the spin is antiparallel across the zigzag edges (up at one side and down at the other side across the ribbon). However, a metastable ferromagnetic conducting configuration could also be calculated with an energy difference, from the antiferromagnetic case, of a few tens of meV [45, 46]. In the ferromagnetic case, the total spin within the unit cell is not zero and both zigzag edges across the ribbon in the unit cell exhibit parallel spin orientations.

For GNRs, the band gap decreases as the ribbon width increases, so if a semiconductor with a desirable band gap is needed, then the nanoribbon width should be reduced accordingly. This, of course, requires very precise control over the edges and widths of an AGNR, if applications are envisaged [45, 47, 48]. The bottom-up synthesis of graphene nanorribbons of different topologies and widths has been reported by Cai and colleagues [49]. In this work, using surface-assisted coupling of molecular precursors into linear polyphenylenes and a subsequent cyclodehydrogenation, 'chevron-like' GNRs are fabricated (see figure 3(a)). With this in mind, Costa-Girao et al have shown theoretically that the mixture of armchair and zigzag nanoribbons, called 'graphitic nanowiggles' (see figure 3(b)), exhibit different band gaps and magnetic behaviors, depending on the mixture of armchair and zigzag character within the same nanostructure [50].

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Armchair and zigzag edges in highly oriented pyrolytic graphite (HOPG) have been characterized using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS), finding electronic states close to the Fermi level for zigzag edges, and defective armchair edges, but not for homogeneous armchair edges [51–53]. Using a sub-nanometer-resolved STM-STS technique, Tao et al examined the dependence of electronic structure on the chirality of atomically well-defined GNR edges [54]. The GNRs they used were synthesized by unzipping CNTs [55]. Zigzag edges were observed by STM, and the finite width of the GNR leads to no actual band gap, which can be attributed to the reduced on-site Coulomb repulsion. Interestingly, the existence of spin-polarized magnetic edge states in chiral GNRs was also observed [54]. Along this line, some theoretical calculations on chiral graphene edges have also been carried out [56–59].

As in 3D crystals, graphene sheets and GNRs exhibit defects which result in significant changes in their physicochemical properties, and these should be studied in order to understand their properties with particular attention given to special kinds of defective 2D layered materials that could lead to novel applications. In this paper, we focus on the role of defects in these systems, how to control the defect behaviors and how perhaps to utilize some of these behaviors for practical applications.

The following subsections describe the various ways of producing graphene, few-layered graphene and graphitic nanoribbons. The methods range from the chemical vapor deposition (CVD) technique to the chemical longitudinal unzipping of CNTs. Novel routes are constantly being found and we expect that, with effort and proper know-how, it will be possible to achieve some control of the atomic edge morphology at the nanoscale. Until now, only a few methods have been able to report short segments of atomically controlled 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 process involving the disproportionation of carbon monoxide at 400–700 °C, which was catalyzed by Fe(CO)₅ particles in flowing CO/H₂ gas [60]. These graphitic nanoribbons consisted of filaments of 10 µm in length and 0.1–0.7 µm in width (10–200 nm thick), and a metal catalyst particle was always located at one of their ends. In these graphitic nanoribbons, the graphitic layers exhibited a uniform orientation perpendicular to the filament axis. An alternative CVD production method for obtaining graphitic nanoribbons was reported by Campos-Delgado et al in 2009 (see figure 4) [61]. These authors used micrometer-size droplets produced by an ultrasonic generator containing ferrocene, ethanol and thiophene, and these droplets were carried by flowing Ar gas to a furnace operating at 950 °C. The resulting nanoribbons synthesized by CVD consisted of flattened and piled up graphene sheets and displayed GNRs several micrometers in length, 20–300 nm wide and <15 nm thick. In contrast to the work of Murayama and Maeda [60], catalytic particles were not found in these ribbons but the presence of ferrocene and thiophene was crucial for their production. Jia et al found that electron beam irradiation combined with Joule heating experiments of these nanoribbons inside an HRTEM, resulted in the generation of atomically smooth zigzag and armchair edges (figure 5) [62]. These observations confirm that the most stable edges in graphene ribbons are indeed zigzag and armchair edges (see figure 5). An alternative CVD method involving ferrocene and tetrahydrofuran (THF) resulted in crystalline carbon nanoribbons (figure 6) [63]. Unfortunately, the authors of this work did not specify the dimensions of the produced nanoribbons. In this case, the orientation of the (0 0 2) lattice planes of the graphene sheets was perpendicular to the ribbon growth axis.

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Interestingly, GNRs could be fabricated using SiC tracks as a template [64, 65]. Sprinkle et al demonstrated the self-organized growth of GNRs with 40 nm widths on a template SiC substrate via scalable photolithography and microelectronics processing. Such as-grown GNRs can be used for the scalable fabrication of graphene devices, which exhibit quantum confinement at 4 K, an on/off ratio of 10 and a carrier mobility of up to 2700 cm² V⁻¹ s⁻¹ at room temperature [64]. Robinson et al also demonstrated the direct synthesis of epitaxial GNRs by utilizing a crystallographic confinement technique unique to SiC. These authors discovered that the epitaxial growth of graphene initiates at the SiC step edge and consists of $(1\,\bar {1}\,0\,n)$ lattice planes, and multilayer graphene can form along a SiC terrace edge prior to on the formation of the terrace itself [65].

2.3.2. CVD of graphene sheets

2.3.3. Chemical synthesis of graphitic nanoribbons

It has been possible to synthesize graphene by electrophoretic deposition of diamond nanoparticles on HOPG followed by heat treatment [71]. Using a similar method, Cançado et al were successful in producing graphene edges, which were characterized by Raman spectroscopy [72]. Dai's group appears to have been the first to produce GNRs by the sonochemical exfoliation of commercial graphite in the presence of dichloroethane and a polymer, and these ribbons were used to construct field-effect transistor (FET) devices [48].

Pure organic chemical routes have been used to synthesize GNRs by linking tetra- and hexa-phenylbenzenes via the Suzuki–Miyaura reaction [73]. These GNRs are highly soluble in organic solvents due to the introduction of branched alkyl side chains, which act as functional groups to solubilize the GNRs. The lengths of these ribbons were found to be 8–12 nm, and they can form both aligned monolayers, as well as crystallized monolayers from solution by π–π stacking. This appears to be the first bottom-up approach to producing GNRs with armchair edges. However, different variants of this reaction could lead to longer or branched nanoribbons. In addition, it seems that it is more likely to produce armchair edges rather than zigzag edges using this approach and further investigations are needed along this line (figure 7) [49]. Hydrothermal synthesis involving Teflon-lined autoclaves has been used to synthesize amorphous carbon nanoribbons. In particular, C₆H₆, Na and ferrocene were introduced in the hydrothermal reactor at 210 °C for 24 h [74]. Other alternative approaches to produce graphitic nanoribbons have consisted of collapsing CNTs [75–79].

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2.3.4. Graphene nanoribbons by unzipping carbon nanotubes

A natural source of GNRs is CNTs. By unzipping them, one could obtain single- and few-layered nanoribbons (figure 8). This unzipping technique was first developed in 2009 by several groups [37, 55, 80–82]. One of the methods, shown in figure 8(a), is based upon the intercalation of lithium in liquid ammonia into MWCNTs [37], followed by acid and thermal exfoliation treatments. Further improvements of this technique should be developed in order to obtain a complete unzipping of the tubes. The group led by James Tour [80] reported a chemical route based on the partial oxidation of MWCNTs using H₂SO₄ and KMnO₄ (figure 8(b)). These nanoribbons exhibit oxidized edges, which make them highly soluble in polar solvents. More recently, Dai and collaborators reported an additional chemical method for unzipping CNTs by treating MWCNTs in air at 500 °C followed by the sonication 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 catalytic cutting of graphene planes has become an attractive method (figure 8(c)) when compared with other chemical methods. Unfortunately, the amount of nanoribbons produced by this technique is approximately 5% of the starting CNT sample. In the past, various researchers have demonstrated that catalytic metal particles (e.g. Co, Ni, Fe) can cut graphene layers only along armchair or zigzag atomic directions [84–86]. Therefore, if metal nanoparticles are deposited on the surface of MWCNTs and these coated tubes are subsequently placed on Si wafers and treated at 850 °C, under a low flow of H₂–Ar, the resulting material should consist of unzipped CNTs. This unzipping process consists of the metal catalyst dissociating carbon bonds, and these unbonded carbon atoms then react with H₂ to form CH₄ [87]. This route was successful in the unzipping of MWCNTs and N-doped MWCNTs [81]. In addition, it was also demonstrated that nanotubes could be easily unzipped by passing high electrical current inside a transmission electron microscope (figure 8(d)) [82]. An alternative method was recently developed by Dai's group. Their method consisted of embedding MWCNTs in poly(methyl methacrylate), subsequently turning the MWCNT composite over and the tubes that were not covered by the polymer were etched away by an Ar plasma (figure 8(e)) [55]. Various challenges still remain in controlling the nanotube opening processes, whether this opening occurs by exfoliation, etching, reduction or oxidation. In addition to challenges in controlling the opening of MWCNTs, a scalable process would have to provide conditions that prevent the agglomeration, wrinkling and entanglement of the produced nanoribbons, the entanglement being caused by attractive van der Waals forces which attract nanotube fragments. Finally, the unzipping of tubes preserving atomically smooth edges is still a challenge. Although a few groups have succeeded in observing atomically smooth edges in GNRs, more control on the edge morphology is still needed.

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A single layer of graphene has been shown to enhance the observed Raman signal of another sp² hybridized carbon material placed on top of a graphene monolayer. In particular, the sp² hybridized carbon sample could be another graphene layer, 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 taking a Raman spectrum, and this effect has been called GERS, denoting graphene enhanced Raman spectroscopy, inspired by the surface-enhanced Raman scattering (SERS) process but produced by a different mechanism. A typical Raman-fluorescence spectrum of rhodamine 6G (R6G) in solution using 514 nm laser excitation is shown in figure 9(b) (the blue line). In contrast, for R6G adsorbed on graphene, the fluorescence emission could be effectively suppressed by a monolayer graphene substrate so that the Raman peaks of R6G are clearly observed (red line in figure 9(b)). As a reminder, the SERS process produces enhancements of Raman signals by many orders of magnitude when a sample sits on small highly faceted Ag nanoparticles, due to the interaction of the sample with the very strong electromagnetic field gradients produced by these tiny Ag nanoparticles. In the GERS process the signal enhancement is only about an order of magnitude, but it is expected that the GERS enhancement effect is reproducible and can be used as a more quantitative characterization technique than SERS. Therefore it is expected that the GERS effect should be useful to study the Raman spectra of defects sensitively. The use of gates to apply negative and positive voltages, and the use of different masses for ¹²C and ¹³C, are also helpful for studying Fermi level-dependent effects and to distinguish one carbon layer from another [90]. Although the SERS technique has been studied for more than 30 years [91], the exact nature of SERS is still debated. Using graphene as a substrate and then depositing some Au dots onto it, Novoselov's group has demonstrated significant SERS enhancements at 633 nm laser excitation and has studied the physics of SERS (figures 9(c) and (d)) [92]. It is found that three issues are crucial for further improvements of SERS: (1) a larger density of nanoparticle coverage, (2) a larger Mie enhancement and (3) a smaller nanoparticle–graphene separation. In particular, thin metallic nanodiscs will achieve the highest SERS enhancement for 2D systems like graphene [92].

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In order to generate vacancies (di-vacancies, or larger vacancy clusters) in graphite or graphene in a controlled manner, the radiation damage by different energetic particles, such as electrons, protons or ions, on the carbon nuclei, should be further investigated. Thus, if the kinetic energy transferred to the nuclei is greater than a threshold value for bond-breaking, the carbon nucleus would be displaced in a sub-picosecond time scale generating a vacancy (knock-on displacement): for sp² hybridized carbon atoms arranged in a graphitic lattice, the energy required to displace a carbon atom is between 15 and 20 eV [115]. Knock-on displacements could be achieved within a transmission electron microscope, since the electrons can acquire energies up to 300 keV, which is a large enough energy to displace carbon atoms [98, 115]. Therefore, TEM can be used to experimentally produce vacancies in a controlled fashion within carbon nanostructures. In fact, using TEM on SWCNTs, coalescence and covalent connections between the tubes could be achieved, thus producing a novel type of nanostructure different from the originally irradiated precursor. In these cases, the vacancies are responsible for merging the nanotubes due to the high reactivity of the dangling bonds that are produced [95, 116]. Other TEM experiments for reducing an MWCNT diameter via controlled vacancy introduction have been performed [117]. In fact, TEM-induced vacancies have been used to connect the atomic planes of MWCNTs with metallic nanoparticles [118]. Banhart's group has used the electron beam of a transmission electron microscope to create vacancies in double-layer graphene to trap metal atoms or metallic clusters [119]. In this context, it could be envisaged to use the transmission electron microscope to connect graphene with metals generating an almost perfect contact, similar to metal–nanotube covalent junctions [118].

In addition to the use of protons as mentioned above [106], another technique to produce vacancies in graphitic systems involves the use of different types of ions. Ney and colleagues have irradiated graphene flakes with 100 keV nitrogen ions and they performed magnetic measurements at 5 K finding that the paramagnetism originally measured (probably due to edge states) increases up to doses of 10¹⁵ ions cm⁻² and then decreases for higher doses due to the amorphization of the graphene. These authors did not find ferromagnetism; however, the nature of the defects that were generated has not been addressed and the role of the nitrogen implanted atoms would need further studies in order to understand how nitrogen interacts with carbon [120]. Probably for this case, the vacancies generated by nitrogen involve the ejection of several carbon atoms, thereby producing large regions of dangling bonds in a disordered way. Certainly, one of the challenges for the future is the generation of vacancies of different sizes (mono-vacancy, di-vacancy, etc) and the identification of their precise location on the hexagonal lattice in an automated way.

According to tight-binding molecular dynamics and Monte Carlo simulations, vacancies trigger the coalescence mechanism of SWCNTs observed under TEM [95]. Without the vacancies generated by the electron beam, the graphene sheets that form the SWCNTs could not interact and thus could not merge the tubes. First-principles DFT calculations with the Perdew, Burke and Ernzerhof (PBE) approximation exchange-correlation density functional have been used to simulate defect formation in graphite by assuming an initial transfer of momentum to the carbon atoms. The results show that vacancies, interstitials and Thrower–Stone–Wales-type defects are indeed possible, and exhibit formation energies ranging between 5 and 15 eV [121].

Most of the calculations on vacancies in graphite and graphene show a magnetic behavior. Using spin-polarized DFT in graphite, Lahtinen and colleagues simulated the differences in magnetic behavior between a vacancy and a hydrogen-vacancy defect showing that the presence of hydrogen in the vacancy makes the local magnetic moment increase to double its magnitude when compared with the naked vacancy case [107]. In this context, vacancy and hydrogen adsorption-induced magnetism has been studied by first-principles simulations showing that the ferromagnetism and antiferromagnetism depends on whether the defects belong to the same sublattice or not [122]. The mean field Hubbard model has been used to study theoretically the different magnetic properties that vacancies and voids (in which more than one atom is removed from the graphene lattice) exhibit in graphene and GNRs, finding that there is a rich spectrum of possible behaviors, depending on the spatial arrangement of the defects and their sublattice imbalance [123]. Yazyev concludes that only single-atom defects, such as vacancies or chemical functionalizations, that are unevenly distributed in the two graphene sublattices, can produce a net magnetic moment [124]. Bao and colleagues have studied theoretically the magnetic properties of tetra-vacancies in graphene and also such vacancies saturated with hydrogen. They found that the tetravacancy reconstructs by relaxation and the magnetic moment is lost; however, when the tetravacancy is saturated with hydrogen, there is a magnetic moment [125]. Cui et al have studied with spin-polarized DFT different size-vacancies or voids which the authors call nanoholes. They have found a remarkable stability for certain size nanoholes with the number of atoms thus removed called magic numbers. A large number of the nanoholes studied exhibit a magnetic state with a finite energy band gap [126].

In 1969, Peter Thrower, when he studied dislocations in graphite, 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, not much progress in this area was made until the appearance of fullerenes in 1985. Fullerenes, graphene, schwarzites and CNTs are locally similar in the sense that every carbon atom is connected to three other carbon atoms (sp² character). With this line of reasoning in mind, some of the mechanisms that apply to fullerenes could also be valid for CNTs and graphene. This is the case of the bond rotation proposed by Stone and Wales in 1986, and applied to Buckminsterfullerene C₆₀(I_h symmetry) to transform it into another isomer with different symmetry (C_2v) by rotating one bond by 90° (see figure 11(b)) [128]. Therefore, based on the fact that Peter Thrower proposed the existence of pentagon–heptagon defects and that Stone and Wales studied 90° bond rotations in fullerenes, which produce heptagon–pentagon pairs in graphene, we will refer to this bond rotation as the TSW transformation (Thrower–Stone–Wales transformation) (see figure 11(c)). Geometrically, the main effect of the TSW transformation in fullerenes, CNTs and graphene is a change to the local environment, but preserving the connectivity while producing no-dangling bonds. The TSW transformation is a matter of study in graphene, nanotubes, schwarzites and graphitic onions: by applying the TSW transformation to giant fullerenes, the sphericity and stability of giant graphitic onions could also be explained [129–131].

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

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4.1.1. Experimental evidence and characterization of topological defects in graphene and graphene nanoribbons

4.1.2. Theoretical studies of topological defects in graphene and graphene nanoribbons

As stated in the first section of this review, Roscoe and Thomas proposed 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 draw the bonding in this regions [7, 10] (see figure 1(b)). Almost three decades later, Terrones and Mackay, using the concept of curvature in graphitic systems, introduced a twin boundary in graphene using pentagons and heptagons (see figures 13(a) and (b)) [163].

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Experimentally, in 1988 Albrecht and colleagues studied tilt boundaries in graphite with STM [164]. From these STM studies on HOPG and computer simulations, Simonis and co-workers proposed a grain boundary model which is similar to the one proposed by Terrones and Mackay in 1992 [165]. Pong et al used STM to characterize small angle grain boundaries in graphite: these authors proposed a model based on 5–7 dislocations separated periodically by a greater distance than the model proposed by Terrones and Mackay. By changing the separation of the 5–7 defects, the angle between the grains is also changed [166] (see figure 13(c)). Červenka and Flipse, used STS to characterize the electronic properties of grain boundaries in HOPG and found that the charge density at the boundaries was higher than that of graphite and that the charge density exhibits two strongly localized states [167]. In addition, ferromagnetic behavior at room temperature has been identified in grain boundaries of HOPG by magnetic force microscopy (MFM) and superconducting quantum interference device (SQUID) measurements [108].

Andriotis and Menon studied theoretically the transport properties of 'T-shape' GNRs exhibiting aligned 5–7 defects to connect AGNRs with ZGNRs, finding that the conductivity depended on the chirality, width and the 5–7 defects boundary [168]. Botello-Méndez et al, also using a 5–7 defect-boundary to join AGNRs with ZGNRs, studied the electronic and transport properties of hybrid GNRs and found that such nanoribbon structures exhibited half-metallicity; this means that electrons with spin of just one type, spin up or down, but not both, participate in the conduction. It is noteworthy that these hybrid nanoribbons possess a distortion of the graphene lattice which might affect their stability and their potential use for spintronics applications (see figure 13(d)) [169].

Electronic properties, stability and STM simulations of different angle grain boundaries in graphene have been studied with first-principles calculations to show the differences between small angle and large angle grain boundaries. Small angle grain boundaries have a tendency to produce buckling of the graphene sheet [170]. Quantum transport has also been studied theoretically, showing that depending on the boundary, two behaviors are present: high transparency of charge carriers and perfect reflection [171].

More recently, Lahiri et al [139] found that by growing graphene on nickel [111] one could produce an extended line of defects (ELD) involving 5–8–5 defects arranged in a periodic way. Using STM, the authors found that the image contrast is brighter in the vicinity of the defect, thus corresponding to the electronic states with wavefunctions localized at this specific region. The same authors performed first-principles calculations, demonstrating that the ELD 5–8–5 behaves as a nanowire embedded in a graphene lattice since this defect produces electronic states at the Fermi level, and these states extend along the defect. In fact, this ELD 5–8–5 could be observed in two graphene grains, with zigzag edges, joined together by a pair of atoms arranged periodically (see figure 13(d)). Kou et al found, using the local spin density approximation, that there is a small magnetic moment of around 0.03μ_B per cell which can increase up to 0.7μ_B per cell under strain [172]. As expected, the spin polarization is localized ferromagnetically along the ELD 5–8–5 line.

Botello-Mendez et al used local density approximation and general gradient approximation (GGA) calculations to study different extended lines of defects in graphene and GNRs involving heptagons, octagons and pentagons (5–8–5 defect, D5D7 defect and T5T5 defect (see figure 14, [142]). The calculations reveal that all these ELDs compete in energy and that when nanoribbons possessing these ELDs are considered, stable ferromagnetic configurations might appear, in particular for the ELD T5T7 case [142]. These authors also simulated the STM images from first-principles calculations using the Tersoff–Hamann approach [151], and confirmed that indeed, the Lahiri ELD 5–8–5 defect corresponds to a structure involving pentagons and octagons. The transport properties were also calculated for these cases, finding that all ELDs should be observable in electron transport measurement. However, for the T5T7 case, there are extra conduction channels favoring electron conductance and magnetic properties [142].

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As a single layer of a hexagonal lattice, graphene is constructed by sp² hybridized carbon atoms, and three strong σ bonds are established with the other three surrounding atoms. The p_z orbitals of these C atoms form a filled band of π orbitals (valence band) and an empty band of π ^* orbitals (conduction band) [173]. According to tight-binding calculations, the valence 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 graphene applications in digital electronics, such as in FETs, it is highly desirable to open a band gap in graphene [176]. Many strategies, such as the substrate-induced method [177], the application of an electric field to bilayer graphene [178, 179] and the size confinement effect by forming GNRs [48], have been proposed to introduce an energy band gap. In addition to these possibilities, chemical modification of graphene, such as by substitutional doping with other atoms (e.g. N, B, P, S, etc) [174, 180, 181] or the controlled reduction of graphene oxide (GO) [182] could be effective routes to open a band gap in graphene. Furthermore, the chemical and electronic properties could be modulated in a well-controlled manner by adjusting the doping and reduction level in the two above-mentioned methods. In this subsection, some typical advances in the area of substitutional doping of graphene and reduced GO will be described.

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5.1.1. Substitutional doping of graphene with N, B, S, P, Si

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

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DFT calculations on ZGNRs have demonstrated that the doping of N and B produces different effects, depending on the position of the substitutional sites [186]. In particular, edge substitutions at low density do not significantly alter the band gap, while bulk substitution promotes the onset of a 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 and ammonia as precursors in a CVD system [174]. It was found that N atoms can be substitutionally doped into the graphene lattice. Electrical measurements show that the NG exhibits an n-type electronic behavior, as demonstrated in figure 17. Furthermore, compared with pristine graphene (PG), NG shows a lower electrical conductivity and a larger on/off ratio. The room temperature mobilities of the PG and NG devices are 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 1–2 orders of magnitude lower than that of mechanically exfoliated graphene (1.5 × 10⁴ cm² V⁻¹ s⁻¹) [27], and this lowered mobility might be attributed to carrier-defect scattering at the doping and topological defect sites. More importantly, the substitutional doping of nitrogen within a graphene lattice could form covalent bonding with carbon atoms, which would modify the electrical structure of graphene, and suppress the development of a high DOS of graphene near the Fermi energy level. Therefore, a gap could be opened between the valence and the conduction bands. Obtaining a controlled band gap is very meaningful for the possible future applications of graphene in semiconductor electronics.

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Some of the recent achievements related to NG synthesis are summarized in table 1. Except for ammonia (NH₃) gas, some other nitrogen-containing liquid precursors, such as acetonitrile (CH₃CN) [187], pyridine (C₅H₅N) [188, 189] or solid 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). Regarding the synthesis, as shown in table 1, the CVD method is the most common due to its advantages in achieving a relatively high crystallinity when compared with wet chemical methods. In addition, some post treatments on few-layer PG, such as Joule heating [180] and plasma treatment [191, 192], in nitrogen-containing gases (NH₃, N₂, etc) have been used for obtaining NG. These post-treatments have unique advantages in transistor fabrication, especially for batch device production.

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

Layers	Method	Substrate	Precursors	Growth parameters	Reference
2–6	CVD	Cu (25 nm) film on silicon wafer	Methane (CH4) and ammonia (NH3)	800 °C, 10 min	[174]
2–8	CVD	Ni (300 nm) film on silicon wafer	Methane (CH4) and ammonia (NH3)	1000 °C, 5 min	[193]
⩾1	CVD	Cu foil (25 µm thick)	Acetonitrile (CH3CN) and ammonia (NH3)	950 °C, 500 mTorr, 3–15 min	[187]
1	CVD	Cu foil (25 µm thick, 99.999%)	Pyridine vapor	1000 °C, 10 min at ∼7 Torr	[188]
1–2	CVD	Cu foil (34 µm thick, 99.95%)	Ethylene (C2H4) and ammonia (NH3)	900 °C, 4.6 Torr, 30 min	[194]
⩾1	CVD	Ni (300 nm) or Cu (300 nm) film on silicon wafer	Methane (CH4) and Ammonia (NH3)	980 °C, 3 min (for Ni) or 20 min (for Cu)	[195]
1–3	Electrothermal reactions	Graphene nanoribbons on silicon wafer	Ammonia (NH3)	e-annealed graphene nanoribbons in NH3	[180]
>2	Arc discharge	No substrates	Graphite rod, pyridine vapor or ammonia (NH3)	Flowing H2 (200 Torr) and He (500 Torr) through a pyridine bubbler	[189]
1–2	Plasma post treatment	Pristine graphene	Ammonia (NH3)	NH3 plasma at a dose of 3 × 1014 cm−2	[192]
>2	Plasma post treatment	No substrates	Reduced graphene oxide and N2	Treatment in nitrogen plasma (500 W power, 14 Torr N2)	[191]
>2	Vacuum annealing	Ni (100–300 nm)/B (5–15 nm) films on silicon wafers	Boron-trapped nitrogen and nickel-trapped carbon atoms	800–1100 °C, 60 min, 10−3–10−4 Pa	[196]
1–6	Solvothermal	No substrates	Lithium nitride, tetrachloromethane and cyanuric chloride	250–350 °C, 6–10 h	[190]

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

Substitutional doping with boron is another interesting way to modulate the electronic properties of graphene. Theoretical work has been carried out along this direction [181, 198–203]. In this context, DFT has demonstrated that substitutional boron atoms will act as scattering centers for the electronic transport along the GNRs (substitutional boron concentration is 1.4%) [181]. If the boron atoms are doped at the edges of ZGNRs, the B-doped ZGNRs may show half-metallic behavior, which gives rise to a zero band gap for electrons with one spin orientation and a semiconducting or insulating band gap for the other spin orientation, thereby giving rise to a completely spin-polarized current. The half-metallicity of B-doped ZGNRs does not depend on the ribbon width even in the absence of an electric field, and this property is preserved for any field strength. This demonstrates the possibility of using B-doped graphene for spintronics applications [203]. Figure 18(a) shows the structure schematically of B-doped bilayer graphene. Theoretical work by Menezes et al has demonstrated that pure bilayer graphene does not show a band gap (figure 18(b)), whereas if a disordered arrangement is imposed on only one of the sublattices (blue dotted line), a band gap (∼0.2 eV) opens up. However, when disorder is imposed upon both sublattices (upper and lower graphene sheets; red dashed line), the gap shrinks again and shifts to higher energy (figure 18(c)). This demonstrates that an energy-gap opening of bilayer graphene could be caused by asymmetric doping [201]. In addition, and according to first-principles quantum transport calculations, the B-doped p-type GNR-FETs could exhibit high levels of performance, with high on/off ratios and low subthreshold swings. Furthermore, the performance parameters of GNR-FETs could be controlled by the p-type semiconducting channel length [198]. Unfortunately, experimental research on B-doped graphene is very scarce and only a few reports have thus far been published [189, 204, 205]. Considering their interesting properties predicted by the theoretical work mentioned above, further experimental work needs to be carried out along these directions, and other synthesis techniques different from CVD should be explored, since boron compounds or precursors are very unstable and air sensitive.

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In addition to nitrogen and boron doping, substitutional doping of graphene with other heteroatoms, such as sulfur [206–208], phosphorus [208, 209] and silicon [210], has also been investigated theoretically. Using first-principles calculations, it was found that sulfur doping could induce different effects: the doped sheet can be a small-band-gap semiconductor, or it could exhibit enhanced metallic properties when compared with a PG sheet [206]. Therefore, S-doped graphene (SG) may also be a smart choice for constructing nanoelectronic devices, since it is possible to vary the electronic properties of the sheet by adjusting the doping level of sulfur into the graphene lattice. Moreover, DFT investigations show that the DOS of SG at the Fermi level actually increases upon NO₂ adsorption, as is visible in figure 19, which demonstrates that S-doped graphene could be used as an efficient sensor for some toxic gases due to the high selectivity of this material [207]. Regarding phosphorus-doped graphene (PhG), our previous work has found out that phosphorus will maintain an sp³ hybridization, and bonds to the carbon atoms with tetrahedral orbitals, inducing structural strain in the carbon lattice (figure 20(a)) [211]. Using first-principles periodic calculations, Denis demonstrated that the doping of P atoms into the graphene lattice could open the 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-doped monolayer graphene [212]. If gases, such as NO₂, NO, SO₂, are adsorbed onto PhG, the electronic conductivity of the PhG will be changed [209]. By monitoring the conductivity variation after the adsorption of molecules, the PhG can also be used as a sensitive detector of these toxic gases.

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For Si-doped graphene, theoretical calculations have demonstrated that it is more favorable to use bilayer graphene in order to reduce the formation energies. In this sense, a bond between the two Si atoms in each layer will be formed without significantly altering the stacking interaction (figure 21(a)). The formation of such bonds in bilayer graphene could reduce the formation energy compared with that of monolayer graphene [213]. Based on these calculations, Si-doped graphene (SiG) will have potential applications in areas such as toxic gas sensing [210] and organic compound detection [214]. For example, melamine (C₃H₆N₆) is a deleterious compound for human health, which may appear in our food nowadays and should be detected by suitable sensors. Using first-principle calculations, Wang et al demonstrated that the melamine-SiG (figure 21(b)) has the most stable configuration when compared with P-, B- or N-doped graphene. The band structure of SiG will change remarkably before and after the melamine adsorption due to charge transfer (figure 21(c)) [214]. However, more experimental efforts are also urgently needed in research related to SiG.

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5.1.2. Reduced graphene oxide

In order to tune the electronic properties of graphene, the controlled reduction of GO appears to be an efficient route to modulate the band gap. GO shows a gap greater than 0.5 eV at room temperature, and GO could exhibit semiconducting behavior when it is reduced into graphene [182], because some residual oxygen and structural defects remain within the structure of reduced GO, as shown in figures 22(a) and (b) [215, 216]. A detailed discussion, focused on the synthesis, properties and applications of GO, can be found in various reviews available in the literature [176, 217–219].

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As mentioned above, the chemical doping of graphene and GNRs could be considered as an efficient route able to tune the electronic and quantum transport properties of graphene-like materials. In addition to the chemical nature of the dopant, the location of the doping atoms in the structure and the dopant concentration are very important factors that control the physicochemical properties of doped graphenes. DFT calculations on GNRs have demonstrated that edge functionalization of armchair ribbons does not show remarkable band gap changes against N or B edge substitutions. However, N, B and pyridine-like bulk substitutions could cause semiconductor–metal transitions, as shown in figure 23(a) [186]. Moreover, the concentration of vacancy or dopant defects also affects the electrical properties of graphene. Figure 23(b) shows the variation of the electrical conductivity as a function of different vacancy or nitrogen doping concentrations in graphene. It demonstrates that a minimum resistivity 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 when compared with a vacancy, which could partially be attributed to the N atoms, responsible for providing electron carriers to the material, shifting the Fermi level much more than for the case of vacancy defects [220].

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The Terrones group has carried out structural relaxation and transport calculations on doped armchair nanoribbons using the DFT method [221]. The nanoribbons were substitutionally doped by replacing one carbon atom by B, N, O, Si, P or S atoms, and the edges were passivated with hydrogen. It can be observed from figure 24(a) that the optimized structures when doping with N (or B) are slightly modified but preserve the honeycomb lattice. Only the bond lengths surrounding the dopants are slightly altered. However, for S- and P-doped nanoribbons, the structures are significantly modified; that is, the dopant in these cases prefers to 'pop out' of the plane, and the carbon and hydrogen atoms located near the edges also remain out of the plane, as shown in figure 24(a). The quantum transport properties of chemically doped AGNRs are shown in figure 24(b). The quantum conductance plots reveal similar features at and around the Fermi level, and the doped nanoribbons exhibit semiconductor behaviors. For low doping levels (one doping site per ∼100 atoms), a linear I–V response could be observed for B-, N-, Si- and P-doped nanoribbons (figure 24(c)). However, for O- and P-doped ribbons, a higher applied voltage is needed to reach the same current values as are observed for the above-mentioned doping cases. Based on these calculations, it can be predicted that GNRs doped with Si could be used in interconnector electrical devices, whereas nanoribbons doped with P could be used for the fabrication of sensors.

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In addition to the above-mentioned substitutional dopants into the graphene lattice, there are some other chemical routes to functionalize graphene, such as hydrogen passivation [153, 222], molecule grafting [223–225] or modification with different functional groups [154, 226]. Novoselov and co-workers have demonstrated that atomic hydrogen could react with graphene and transform this highly conductive zero-gap material into an insulator [222]. The as-obtained graphene derivative, so-called graphane, is crystalline and retains the hexagonal lattice, but its in-plane periodicity becomes remarkably shorter than that of graphene, due to the atomic-scale buckling caused by the hybridization change from sp² to sp³ bonding. In addition, based on the configuration of a graphite intercalation compound (GIC), by inserting some ions or molecules, such as diazonium cations (figure 25(a)) [224] or hydrophobin (figure 25(b)) [225], into the interlayer spacings of graphite and then exfoliating the resulting intercalation compound, a kind of surface-functionalized graphene could be obtained. This covalent functionalization could protect the single-layer graphene from re-aggregation. Furthermore, the attachable functional groups might also provide graphene with some tailor-made properties, such as customizable solubility, electron mobility and sensor activity. Using GGA for the density functional, Boukhvalov et al have considered the functionalization of bilayer graphene by different functional groups [226], namely, OH, CN, NH₂, CH₃, COOH as well as by combination of the dopants and hydrogen, as shown in figure 25(c). It has been demonstrated by their calculations that the gap of graphene can be tuned smoothly between 2 and 3 eV with an accuracy of about 0.2 eV [226]. Therefore, chemical functionalization will also be an efficient route for developing high-performance applications of graphene- and graphane-based materials in the area of molecular electronics, and further work along this research line is still needed.

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Due to their attractive properties, such as high electron mobility, 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 graphene FET operating at high frequencies (gigahertz) was developed in 2009 by IBM researchers [230], and soon after that, transistors operating at 100 GHz [231] and 300 GHz [232] were reported in 2010. In June 2011, IBM researchers [233] reported their work on a wafer-scale integrated circuit (IC) using graphene field-effect transistors (G-FETs) (figure 26). Graphene circuits were fabricated on a semi-insulating SiC wafer. A two- or three-layer graphene film was epitaxially grown on the Si face of the SiC substrate at temperatures above 1400 °C. Fabrication of 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, these authors spin-coated the graphene-SiC wafer with a layer of 140 nm thick PMMA (poly(methyl methacrylate)) followed by a layer of 20 nm thick HSQ (hydrogen silsesquioxane). The FET channel was defined by e-beam lithography (EBL); the surrounding graphene was removed by oxygen plasma with the exposed HSQ film as the protecting mask. The optical image of a completed graphene mixer and its schematic illustration are shown in figures 26(b) and (c), respectively. Figure 26(d) displays the output frequency spectrum of the graphene mixer with input signals f_RF = 3.8 GHz and f_LO = 4 GHz and a drain bias of 2 V. This work [233] demonstrates that a graphene IC can operate as a broadband RF mixer at frequencies up to 10 GHz with excellent thermal stability. The excellent transistor performance achieved in such graphene-field-effect transistor (G-FET) devices should open exciting opportunities in high-speed, high-frequency electronics.

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Optoelectronic devices, such as touch screens, light-emitting diodes and solar cells require materials with low sheet resistance and high optical transparency. As a 2D single atomic layer of crystalline carbon, graphene exhibits high room-temperature carrier mobility [234], a tunable band gap [197], ballistic transport [235] and a visible transparency of 97.7% [236, 237]. Hence, ideal materials for applications in electronics and optoelectronics, include their use in transistors, photodetectors and saturable absorbers of light [238]. Graphene thin films exhibit a high optical transparency in both the visible and near-infrared regions of the spectrum, a low electrical resistivity, high chemical and thermal stabilities, high carrier mobilities. These properties make graphene an excellent choice for transparent electrodes in various optoelectronic devices [239]. For instance, a liquid crystal display (LCD) made using a sheet of peeled graphene as the transparent conductor has been demonstrated [240]. It was found that each layer of graphene absorbs about 2.3% of the incident light, which is significantly lower than that of conventional indium tin oxide (ITO) (15–18%) [241]. Furthermore, graphene has shown great potential for creating photovoltaic solar devices owing to its high optical transmittance and electrical conductivity. The graphene film not only serves as a transparent electrode for light transmission but also as an active layer for electron/hole separation and hole transport [242, 243]. Graphene microsheets have been dispersed into conjugated polymers to improve the polymer exciton dissociation and charge transport [244, 245]. Solution-processed thin films were used as conductive and transparent electrodes for organic [246] and dye-sensitized [239] solar cells, although the cell efficiency is still lower than those with ITO and fluorine tin oxide (FTO) electrodes [239], and further work is needed to realize the full potential of graphene for these applications. The application of graphene in inorganic thin-film solar cells has also been explored. Li et al demonstrated an efficient solar cell by forming Schottky junctions between graphene sheets and Si [247]. This sheet consisted of multiple layers of graphene that are overlapped and interconnected, which ensures a conducting pathway even if there are cracks formed in one of the graphene layers. The multilayer structure is expected to provide a higher carrier mobility based on a recent study on graphene layers decoupled from bulk graphite [248]. Moreover, graphene thin films also exhibit great mechanical properties and can be used to make flexible and stretchable electrodes [249, 250]. However, in order to produce graphene-based transparent conductive film, there is still a long way to go. For example, graphene films should exhibit optical transparency of 90% (λ = 550 nm) as well as a sheet resistance below 80 Ω/sq, and they should be sustainable after bending without degradation of performance.

The properties of graphene in biosensors and gas sensing have been widely investigated. For example, using reduced graphene oxide to construct a 3D structure of graphene-encapsulated SiO₂ nanoparticles, the detection limit for target cancer biomarkers has been remarkably improved [251]. Wang et al have demonstrated that N-doped graphene can be used for glucose biosensing with concentrations as low as 0.01mM in the presence of interferences including ascorbic acid (AA) and uric acid (UA) for testing the selectivity [252]. Schedin et al showed that mechanically exfoliated graphene flakes can detect a single molecule of NO₂ gas [253]. They fabricated micrometer-size sensors made from graphene, and such a device was capable of detecting an individual gas molecule when it interacts with the graphene surface. Each adsorbed molecule changes the local carrier concentration 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 exceptionally low-noise material electronically, which makes it a promising candidate not only for chemical detectors but also for other applications where local probes sensitive to external charge, magnetic field or mechanical strain are required. Graphene-based gas sensors allow the ultimate molecular sensitivity since the adsorption of individual gas molecules can now be detected. Large arrays of such sensors would increase the uptake area [254], allowing higher sensitivity for short-time exposures and the detection of active (toxic) gases in as low a concentration as would be practically desirable. Chemically modified graphene has been used in biosensor applications. For example, immunoglobulin E aptamers with an approximate height of 3 nm were successfully immobilized on a graphene surface. The aptamer-modified G-FET showed selective electrical detection of IgE protein, exhibiting good affinity and the potential for G-FETs to be used in biological sensors [255]. Hou et al found that graphene modified with ethylenediamine triacetic acid (EDTA) can be used as an ideal electrode material to fabricate biosensors [256]. They fabricated a dopamine electrochemical biosensor with a high selectivity and sensitivity, which might allow its potential use in the investigation and diagnosis of dopamine-related diseases.

Pristine and doped graphene has been demonstrated as an electrode material for capacitors [257, 258] and lithium ion batteries [259, 260], because of both its high specific surface area (2630 m² g⁻¹) and unique 2D structure. The discharge capacity of graphene in a lithium ion battery was found to be 540 mAh g⁻¹, and this could be further improved to 730 and 784 mAh g⁻¹ by adding CNTs and fullerenes to the graphene [261]. Graphene also showed a good ability to coat silicone particles, and metal or metal oxide particles in order to prevent the volume expansion of the electrode materials during the charge and discharge cycles in batteries [261–263]. The supercapacitor is recognized as one of the important next-generation rechargeable power sources due to its intrinsic ability to decrease the gap between the dielectric capacitor and the battery. In addition, the edge site is known to have a differential capacitance ten times higher than that of the basal plane [264]. Thus, graphene could be used as an electrode material for supercapacitors. Miller et al have demonstrated high-performance electric double-layer capacitors (DLCs) with electrodes made from vertically oriented graphene nanosheets grown directly on metal current collectors. This design minimized electronic and ionic resistances and produced capacitors with a resistor–capacitor (RC) time constant of less than 200 ms, which is much faster than that of typical DLCs (∼1 s). This fast time constant can be attributed to these aligned graphene nanosheets showing more exposed edge planes that greatly increase the charge storage as compared with that of designs that rely on basal plane surfaces only. Moreover, in order to improve the performance of these graphene-based supercapacitors, several approaches have been developed, such as controlling the surface area and edge sites [265], and by introducing metal oxide [266]. In addition to this, graphene can also be used in the fuel cell area by virtue of its excellent ability to support metal nanoparticles (Au, Pt and Pd) [267–270]. We believe that more and more interesting electrochemical properties of graphene will be explored for their applications in energy storage and conversion in the future.

In addition to the above-mentioned applications, graphene could also be used in areas such as SERS [271], hydrogen storage [272], field-emission [273] or for catalyst supports [274]. Mülhaupt and co-workers demonstrated that palladium nanoparticles dispersed on graphite oxide were able to catalyze Suzuki–Miyaura coupling reactions [274]. (The Suzuki–Miyaura reaction is a valuable synthetic process for the construction of carbon–carbon bonds). Seger et al used graphene as a support material for the dispersion of Pt nanoparticles for the development of a fuel cell electrocatalyst [275]. In addition, graphene–TiO₂ nanocomposites can be employed as photo-anodes in a photo-electrochemical cell. In this context, the role of graphene is mainly to promote the collection and transport of photo-injected electrons [276]. Efforts are also being made to utilize graphene-based composites for visible-light-induced photo-electrolysis of water [276].