Graphene

Vijayaraghavan, Aravind

doi:10.1007/978-3-642-20595-8_2

Aravind Vijayaraghavan²

Part of the book series: Springer Handbooks ((SHB))

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Abstract

Graphene is the two-dimensional allotrope of carbon, consisting of a hexagonal arrangement of carbon atoms on a single plane. This chapter explores the history of graphene, as the theoretical building block for other carbon allotropes as well as its rise as a material in its own right in recent years. Graphene can be fabricated by different methods including mechanical exfoliation, chemical vapor deposition, and decomposition of SiC, although bulk-quantity production of pristine graphene remains a challenge. The atomic and electronic structure of graphene is described, highlighting the strong correlation in graphene between structure and properties, as is the case with other carbon allotropes. Graphene exhibits a number of unique and superlative electronic and optical properties. The intrinsic properties of graphene can be tailored by nanofabrication, chemistry, electromagnetic fields, etc. Various applications of graphene have been proposed in electronic, optoelectronic, and mechanical products. In addition, graphene has emerged as a candidate in chemical, biochemical, and biological applications. Derivatives of graphene such as graphene oxide or graphane are also of interest in terms of both fundamental properties and applications.

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Graphene: Synthesis and Functionalization

Graphene Oxide

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As a three-dimensional (3-D) material, carbon exists as three predominant allotropes: diamond, graphite, and amorphous carbon (historically knows as carbon black). These are distinguished by their crystalline structure and the hybridization of the carbon atoms therein. Carbon atoms in diamond are all sp³ hybridized and arranged in diamond cubic structure which comprises two interpenetrating face-centered cubic (fcc) lattices. Graphite has a layered structure, where the sp² hybridized carbon atoms are arranged in a hexagonal lattice in each plane, while the planes themselves are AB (Bernal) stacked and held together by van der Waals forces. Amorphous carbon, as the name indicates, does not have long-range crystalline order, although locally the atoms are bound together covalently and comprise a mix of sp² and sp³ carbons. While diamond can be reduced in size to the nanoscale to form nanodiamond, it is graphite that can be truly reduced to lower-dimensional allotropes. A single layer of graphite is defined as graphene, the topic of this chapter. Graphene has been used as the building block to conceptually visualize carbon allotropes such as graphite, carbon nanotubes, and fullerenes; it was believed that such a freestanding, two-dimensional (2-D) structure would not be stable. Carbon nanotubes (CNT) form its one-dimensional (1-D) counterpart, while fullerenes are the zero-dimensional (0-D) allotropes. These various forms of carbon are summarized in Fig. 2.1. It is important to note that CNTs or fullerenes are not unique structures, but rather describe a family of structures, which are described in detail in subsequent chapters. Nonetheless, their structure and properties are all derived from graphene.

Despite serving as the fundamental building block for these carbon allotropes, graphene remained a concept until 2004. It was substantially predated by its related allotropes, fullerenes being discovered and described in 1985 [2.1], while carbon nanotubes were synthesized and their atomic structure elucidated in 1991 [2.2]. The term “graphene” was coined in 1987 [2.3], to describe one of the two alternating layers in graphite intercalation compounds (GIC), the other layer being the intercalating agent. It was postulated that independent, freestanding graphene would not become a physical reality since it would voluntarily transform into a more stable allotrope in an attempt to minimize its surface energy. Supported monolayers of carbon, however, had been previously synthesized and described, including epitaxial graphene which has been known since the 1970s. Chemical derivatives of graphite such as graphite oxide can be traced back to the 1950s and can exist as single layers (graphene oxide), although these are not truly two-dimensional layers due to out-of-plane atoms which stabilize their structure.

Since graphene occurs naturally as a constituent of bulk graphite, it appeared to be the logical place to start the hunt for freestanding graphene. This effort culminated in the successful exfoliation of a single sheet of carbon atoms by Andre Geim and Kostya Novoselov at the University of Manchester in 2004 [2.4], using a technique referred to as micromechanical cleavage, or colloquially, the Scotch tape method. This discovery and the subsequent investigations into the properties of graphene were rewarded with the Nobel Prize in Physics in 2010 for Geim and Novoselov. The existence of graphene, however, does not contradict the physics that predicted that it could not exist. It was discovered that graphene is not truly flat; there exist atomic-scale ripples in the carbon sheet, which accommodate the excess surface energy, thereby stabilizing the 2-D structure of graphene. For this reason, it might be argued that graphene is a quasi-2-D material. However, it has been shown to exhibit a range of properties that are unique to 2-D physics, and therefore graphene will be identified as a 2-D material for the rest of this chapter, without qualification.

A surge of research into the structure and properties of graphene ensued, and graphene did not disappoint. Almost immediately, an anomalous quantum Hall effect was reported in graphene, which also serves as direct experimental evidence for the electrons in graphene behaving as massless Dirac fermions, confirming theoretical predictions. Graphene yielded record high values for various properties, such as tensile strength, carrier mobility, thermoelectric power, etc. Scientists have also succeeded in transferring epitaxial graphene from its native metal or silicon carbide substrate onto other substrates of interest or as freestanding structures. Since the early 1990s, carbon nanotubes have been described as rolled-up graphene sheets. This description has come full circle, with the recent unzipping of carbon nanotubes to yield graphene. While the number of publications on carbon nanotubes has leveled off in recent years at about 8000 papers per year, the publications on graphene are only just starting their exponential growth at a rate faster than that which was enjoyed by carbon nanotubes in their first few years (Fig. 2.2; over 3000 papers were published in the field of graphene in 2010 [2.5]). A similar trend is also observed in patent applications based on carbon nanotubes and graphene.

Any chapter on graphene would not be complete without discussion of its other, quasi-2-D derivatives based on the fundamental graphene structure. Perhaps the most interesting of these is the case where two graphene layers are AB stacked to form a bilayer. Unlike graphene, which has zero electronic bandgap and is therefore a quasimetal, this bilayer structure can have a bandgap. A bandgap is critical for electronic applications, and one of the most active areas of research in graphene is currently the generation of a stable, true, electronic bandgap in graphene. The oxidized derivative, graphene oxide (GO), has been alluded to before, and serves as a useful intermediate in a chemical route for graphite exfoliation. Hydrogenated graphene, christened graphane, and fluorinated graphene or fluorographene have been recently produced and characterized.

Methods of Production

Historically, graphene supported on substrates such as metals and SiC was synthesized first; however, such graphene was not liberated from the substrate support to form a truly two-dimensional structure. Freestanding graphene was not a reality until the ground-breaking publication of Novoselov and Geim in 2004. Consequently, this micromechanical cleavage method is presented first, followed by the epitaxial synthesis of graphene as well as chemical vapor deposition on metallic substrates. Graphene can also be exfoliated from graphite by sonochemical means in a solvent, followed by a purification step to extract the monolayers. Recently, islands of nanographene have also been synthesized by chemical routes, and this bottom-up approach is discussed. Finally, separate sections are devoted to production of graphene nanoribbons (GNR) and derivatives of graphene.

Micromechanical Cleavage of Graphite (Scotch Tape Technique)

Micromechanical cleavage (or exfoliation), as the name implies, refers to thinning down of graphite by mechanically reducing the number of layers in a repeated fashion. Graphite is known to cleave preferentially along the interlayer direction where layers are held together by weak van der Waals forces, rather than across the strong covalent bonds that bind the atoms within a layer. The most common procedure to accomplish this is using adhesive tape. Attaching a thick graphite flake to adhesive tape on both its exposed faces, and then peeling the two pieces of tape apart, results in two thinner flakes of graphite, stuck to each of the adhesive tape pieces. Repeating this process a sufficient number of times would in principle result in a single sheet of carbon atoms, i.e., graphene, adhered to the adhesive tape. This is still not freestanding graphene, since it is supported by the tape, and must be transferred to a suitable weakly coupling substrate or suspended across supports. The genericized Scotch trademark for transparent adhesive tape has subsequently lent its name to the micromechanical exfoliation of graphite. Different variations of this method exist.

One of the earliest such efforts was undertaken by Fernandez-Moran, who succeeded in thinning graphite down to ≈15 layers (5 nm) over a millimeter size, to serve as a support membrane for transmission electron microscopy [2.6]. This result remained relatively unknown outside the electron microscopy community, until the interest of condensed matter physicists turned to graphene and other lower-dimensional carbons. The first successful thinning down of graphite to its monolayer graphene form involved a wet/dry method [2.4]. The surface of highly oriented pyrolytic graphite (HOPG) was first patterned into square mesas, which were pressed into wet photoresist. After baking, the mesas attached to the now dry photoresist, and could be detached from the bulk of the HOPG. Scotch tape was used to repeatedly peel off layers of graphite from the mesas, thinning them down, until only very thin layers remained in the photoresist. The photoresist was then dissolved in acetone to release these thin flakes, which float on the solvent surface. The flakes were collected onto Si/SiO₂ wafer pieces dipped into the solvent. Thicker flakes adhering to the silicon could be cleaned off by sonication in 2-propanol, while thinner flakes were reported to adhere strongly to the substrate due to capillary forces.

In the resultant sample, the flakes of graphene, bilayer graphene, and few-layer graphene (FLG) must be distinguished from among a sea of flakes of various thicknesses. Fortunately, at certain thicknesses of the SiO₂ layer that covers the silicon wafer, for example, 300 nm, the interference contrast generated by graphene flakes on the surface makes them relatively easy to spot and identify by optical microscopy. A trained eye can, in fact, distinguish between graphene, bilayer graphene, and thicker flakes. This is described in detail in Sect. 2.2.4 on optical properties of graphene. Figure 2.3 shows the appearance of micromechanically cleaved graphene flakes of different thicknesses in an optical microscope [2.7], atomic force microscope (AFM) [2.8], and transmission electron microscope (TEM) [2.9]. These, along with Raman spectral mapping, are routinely used to characterize graphene flakes, and are described in Sect. 2.3 dedicated to graphene characterization.

The procedure has since evolved into a completely dry technique. It has been shown that rubbing the freshly cleaved surface of a layered material such as graphite on another solid surface results in a variety of flakes, among which monolayer flakes can be invariably found [2.8]. Alternatively, HOPG is mechanically cleaved repeatedly between two pieces of adhesive tape until the surface of the tape is covered by a layer of relatively thin graphite [2.10]. No specific criterion exists at the time of writing for the optimum degree of such exfoliation. Researchers rely on personal experience or historic parameters specific to their laboratory to carry out this procedure. Once a satisfactory degree of exfoliation has been accomplished with the adhesive tape, it is pressed against the surface of a desired substrate, such as Si/SiO₂ wafer. Again, various scientist-specific parameters exist for this process, such as duration, force, application and peeling-off procedure, etc. At the end of this procedure, the surface of the graphene as well as the substrate is often contaminated with adhesive residue from the tape, which has been shown to limit the carrier mobility in the graphene flake. Efforts to remove this residue have included annealing at 200 °C in a reducing atmosphere of Ar and H₂ [2.11], annealing in vacuum at 280 °C [2.12], and current-induced Joule heating after graphene device fabrication [2.13]. Variations such as applying an electric field perpendicular to the substrate during the transfer from the adhesive tape have also been explored [2.14]. Covalent linkers such as perfluorophenylazide between graphene and SiO₂ have been explored to aid in the exfoliation process to increase monolayer yield [2.15]. The residue issue can also be completely avoided by evaporating a thin film of gold on the HOPG surface prior to the transfer step, to avoid direct contact between the adhesive and the graphene [2.16]. The gold can be subsequently dissolved in a suitable etchant without affecting the graphene. The lack of standardization is indicative of the early stage of current graphene research, and is perhaps an indication that micromechanical exfoliation is not destined to evolve into a large-scale or industrial method for graphene production. Competing techniques, discussed subsequently, have reached much higher degrees of standardization and reproducibility, albeit with drawbacks of their own.

It should be noted that the best quality of graphene currently available is indisputably that produced by micromechanical cleavage, where the graphene quality is defined in terms of crystalline domain size, number of defects, carrier mobility, etc. The choice of initial graphite material having large grain size, using freshly cleaved graphite for further exfoliation, and the cleanliness and quality of the adhesive tape and SiO₂ substrate are all variables which significantly affect the quality of the final flakes obtained. Flakes of graphene hundreds of μm across are routinely produced in laboratories all over the world by this method, predominantly for fundamental research purposes. In some cases, millimeter-size flakes have also been reported. While this method has not matured for commercial applications, ventures such as Graphene Industries have been established to sell micromechanically cleaved graphene flakes.

Chemical Vapor Deposition (CVD)

The study of the deposition of thin graphitic layers on metal substrates by CVD dates back to the late 1960s [2.17,18]. One of the motivations for this was in fact to eliminate the formation of graphitic structures on metals such as platinum which results in degradation of catalytic activity. CVD is currently the preferred route for large-scale fabrication of carbon nanotubes, and therefore has generated substantial excitement as a potential method for large-scale production of graphene. In general, this involves thermal decomposition of gaseous hydrocarbon sources followed by dissolution and recrystallization of the cracked carbon on the surface of metallic substrates. The solubility of carbon in various metals, such as rhodium, ruthenium, iridium, and rhenium, has been measured [2.19], along with the observation that excess carbon dissolved in such metals at high temperatures can segregate as graphite on the surface upon cooling. Various metallic substrates and carbon feedstock have been explored in the effort to grow monolayer graphene, and some of the significant developments are mentioned next.

As early as 1991, monolayer graphene was grown on Pt(111) by hydrocarbon decomposition at 800 °C [2.20], resulting in islands of 20–30 nm size distributed uniformly over the surface. Upon annealing at higher temperatures, the graphene was found to accumulate into large, regularly shaped islands on terraces and step edges. Recently, a variation in which a beam of methane molecules with high kinetic energy (670 meV) impacting a Pt(111) surface at 890 K resulted in large domains of monolayer graphene covering the entire Pt surface [2.21]. Ni soon followed, requiring a minimum temperature of 600 °C, and monolayer graphite on Ni(111) was shown to have an arrangement whereby one carbon atom in a unit cell of the graphite overlayer is located at the on-top site of the topmost Ni atoms, while another carbon atom exists at the fcc hollow site [2.22]. Carbon has been shown to segregate on the surface of Ru(0001) as monolayer graphene [2.23], when annealed at 1400 K. STM reveals a (11 × 11) structure with good rotational alignment and structural perfection, a well-defined periodicity of ≈30 Å, and large domain sizes exceeding 100 μm. Graphene has also been grown by thermal decomposition of benzene on Ir(111) [2.24].

At present, the two predominant metallic substrates for CVD graphene growth are Ni and Cu. Large-size (cm²) films of monolayer and few-layer graphene have been grown on Ni [2.25], with monolayer regions as large as 20 μm in size. Cu does even better, and predominantly monolayer graphene covering many cm² is grown in various laboratories using methane CVD [2.26]. The solubility of C in Cu appears to make the process self-limiting, and at most 5% of the surface is covered by small islands of bilayer graphene. Most importantly, methods have been developed to detach these films from the metallic substrate and transfer them intact onto dielectric substrate (Fig. 2.4), where they can be lithographically patterned and processed for electronic or optical applications [2.25]. In another variation, graphene is grown on a thin copper film on arbitrary substrates, and the Cu dewets and evaporates during the growth process itself, leaving behind the graphene film intact on the substrate [2.27]. The first truly large-area production of graphene has recently been reported using a continuous CVD deposition and transfer process [2.28].

In general, for substrates with small lattice mismatch (<1%) such as Co(0001) and Ni(111), commensurate superstructures are formed, while substrates with larger mismatches such as Pt(111), Ir(111), and Ru(0001) yield incommensurate moiré superstructures. The first graphene monolayer on the metal surface has strong interaction with the substrate, and the spacing between the two is much shorter than between two layers of graphite (3.35 Å). For the case of Ru it is 1.45 Å, and for Ni it is 2.11 Å.

Decomposition of Carbides

The second substrate-supported route for graphene production involves thermal decomposition of surface layers of carbides such as SiC. About 250 different crystal structure of SiC are known, but α-SiC is the most commonly encountered polymorph and, until recently, the primary focus of epitaxial graphene growth. α-SiC has a hexagonal crystal structure, similar to wurtzite. The (0001) (Si) and ( $000 \bar{1}$ ) (C) faces of 6H-(α-SiC) [2.29,30,31] and 4C-(α-SiC) [2.32] have been shown suitable for the growth of epitaxial graphene.

6H-(α-SiC) is first cleaned for 20 min at 850 °C under a Si flux to prevent Si sublimation during the cleaning step. At higher annealing temperatures in ultrahigh vacuum (UHV), the surface of SiC undergoes various reconstructions, until the graphitization temperature when the surface graphene layers form. The Si surface of the hexagonal SiC undergoes the following reconstructions: 3 × 3 at 850 °C under Si flux, $\sqrt{3} \times \sqrt{3} R 3 0^{\circ}$ below 1000 °C, $6 \sqrt{3} \times 6 \sqrt{3} R 3 0^{\circ}$ (6R3) at 1150 °C, and graphitization at 1350 °C. On this face, the C atoms are in epitaxy with the SiC underneath after graphitization. The surface is passivated by the first C layer, the interface extends to two C layers, and subsequent C layers are decoupled from the substrate and exhibit the properties of graphene. Graphitization occurs at 1150 °C on the C face of the hexagonal SiC, and the C layer occurs on a SiC 2 × 2 native reconstruction. This reconstruction saturates the dangling bond states, so that the first C layer already exhibits graphene properties. However, this C layer is no longer epitaxial with the underlying SiC, so the long-range order of the SiC substrate no longer imposes itself upon the C layer. Therefore, it has not been possible to accomplish both long-range ordering as well as decoupling from the surface simultaneously using 6H-(α-SiC). Epitaxial graphene has also been grown on SiC(0001) in Ar atmosphere [2.33], at close to atmospheric pressure and a significantly higher annealing temperature of 1650 °C, resulting in morphologically and electronically superior graphene compared with vacuum annealing (Fig. 2.5).

Perhaps the greatest limitation of SiC as a substrate for graphene growth is cost. α-SiC wafers are relatively expensive, at about USD 300 for a 50 mm wafer. Cubic 3C-SiC (β-SIC), however, can be grown directly on the surface of Si wafers of 300 mm and larger, and is therefore a more commercially viable substrate. It was believed that, due to its cubic structure, β-SiC would be unsuitable for graphene growth. However, recently scientists have succeeded in growing graphene on the Si-rich (100) surface of β-SiC by a series of annealing cycles with temperature increasing from 1200 to 1550 K [2.34]. They found that the strong lattice mismatch between graphene and underlying SiC results in very weak coupling similar to the (000 $\bar{1}$ ) C face of α-SiC. However, it was found that graphene growth on β-SiC was guided along the [110] crystallographic direction despite the lattice mismatch, raising hopes that both substrate–graphene decoupling as well as substrate-guided large domain size might be simultaneously achievable after further process optimization and characterization of graphene on β-SiC.

Ribbons of graphene, a few nanometers wide, develop an electronic bandgap due to confinement effects, which is absent in larger dimensions of graphene, which is a zero-bandgap semimetal. The importance and methods of inducing a bandgap in graphene are discussed later. Here, we briefly discuss how SiC decomposition can be used to grow graphene nanoribbons [2.35]. It is known that the (0001) face of both 6H and 4C α-SiC with vicinal miscuts towards $〈 1 \bar{1} 00 〉$ displays bunching of parallel steps into ( $1 \bar{1} 0 n$ ) nanofacets up to 4–5 unit cells in height and oriented at an angle of ≈25° to the basal plane. The α-SiC ( $000 \bar{1}$ ) face generally does not show preferential orientation for nanofacets, but step-bunched ( $1 \bar{1} 0 n$ ) nanofacets can be induced by suitable pretreatment. It has also been observed that graphene grown on the (0001) and ( $000 \bar{1}$ ) faces of α-SiC are continuous over these steps. Controlled facets can be achieved by conventional photolithography and microfabrication. Few-layer graphene is shown to grow selectively on these facets. Facets of other crystallographic orientations are possible, and it is expected that the graphene quality, properties, and growth mechanism will depend significantly on the crystallographic surface. However, these preliminary results indicate that, with further research and optimization, the ideal facets and growth conditions might be determined for large-scale controlled growth of graphene nanoribbons.

Interestingly, there was significant research into the growth and characterization of graphene on other metal carbides [2.36,37,38], such as TiC, TaC, and HfC, as early as the 1980s. Then, it was referred to as monolayer graphite. Graphene has been grown on the (100) and (111) faces of these carbides by heating them to 1700 K in UHV. As with SiC, graphene nanoribbons as narrow as 1.3 nm with well-defined edge structure have been grown, for instance, on TiC (755) surface [2.39]. In all these cases, a significant degree of hybridization between the graphene π-electrons and the electronic bands of the substrate carbide was reported, similar to some of the crystallographic faces of SiC. Despite the revelation that the graphene is significantly decoupled from certain other SiC faces, similar exploration into other metallic carbides remains pending.

Exfoliation by a Solvent

Exfoliation of graphene from graphite involves overcoming the interlayer van der Waals bonds. This is the same interaction in play between individual CNTs in a bundle. Just as ultrasonication in a solvent has been used to overcome this weak force and separate and disperse individual CNTs from a bundle, it has also been used to individualize graphene layers from graphite. This process can be facilitated if the interlayer attraction can be compromised by intercalates. The resultant flakes of graphene in a solvent can be stabilized to prevent aggregation, and separated into fractions which are enriched in particular graphene thicknesses.

Graphite Intercalation Compounds

Due to the nature of hybridization of carbon atoms in graphite, it is capable of reactivity involving incorporation of atoms, ions, or molecules in its lattice while leaving its basic structure unchanged. Such graphite intercalation compounds (GIC) [2.40] may be broadly classified into those with homopolar bonding and polar bonding. Graphite oxide (GO) and graphite fluoride (GF) are examples of homopolar bonding, while potassium-, rhodium- and cesium-graphite are examples of polar bonding. GICs were well studied as early as the 1950s and are a staple of chemistry textbooks. Here, we restrict our discussion to exfoliation of GICs, in particular graphite oxide, and its reduction to graphene, which has been achieved with varying degrees of success. A family of GICs with interhalogen compounds offers control over the stage of intercalation and subsequently the layer distribution in the resultant graphene.

Graphite can be oxidized to GO in various ways. In the modified Staudenmaier method [2.41] a mixture of 97% sulfuric acid and fuming nitric acid is cooled down to 5 °C in an ice bath, graphite in flake or powder form is added, followed by repeated additions of potassium perchlorate every hour over a period of 3 days. The resulting solution, sometimes referred to as graphitic acid, is filtered and washed until the pH of the filtrate reaches 5 or more. The Brodie method [2.41] is identical, except that only nitric acid is used, and the potassium perchlorate is added every hour for 3 h. In the Hummers method [2.42,43], graphite is oxidized in a mixture of concentrated sulfuric acid, sodium nitrate, and potassium permanganate at 45 °C for 2 h. At this stage, the material is often referred to as expandable graphite, reasons for which are explained in the next section. In the electrochemical method [2.41], a graphite sheet electrode is anodically polarized in perchloric acid with a platinum wire as counterelectrode. When dried, the above methods result in a powder consisting of graphite oxide flakes. Graphite fluoride has also been used as a starting point for graphene dispersions. Graphite can be fluorinated under fluorine pressure of 200 mmHg, in a temperature range of 375–640 °C [2.44].

Interhalogen compounds such as IBr and ICl also form GICs, offering control over the stage of intercalation. Stage I GIC refers to intercalation of every layer of graphite, while stage II GICs only have every second layer of graphite intercalated, and stage III GICs have every third layer intercalated, etc. As discussed in subsequent sections, bilayer and trilayer graphene are electronically distinct from monolayer graphene and in certain instances, such as semiconductor electronics, might prove superior to monolayer graphene. Exfoliation of graphene from stage II and stage III GICs has been shown to yield solutions of predominantly bilayer and trilayer graphene [2.48], and is currently the only large-scale route available to synthesize these multilayer graphenes.

From GIC to Graphene

Usually, the next step involves expansion of intercalated graphite by decomposing and expelling the intercalate. Rapid annealing of expandable graphite to 1050 °C generates high-pressure gaseous decomposition products which force the individual layers apart. This results in a ≈ 100-fold expansion in the interlayer spacing in graphite, and the material is now referred to as expanded graphite (Fig. 2.6a) [2.45,47]. Similarly, interhalogen GICs can be expanded by expelling the entrapped intercalants.

Expanded graphite or graphite oxide is dispersed in a solvent by ultrasonication, resulting in graphene or GO solutions, respectively. In the case of GO, the predominant product in solution is monolayer GO, while stage II and III GICs of interhalogen compounds yield solutions of predominantly bilayer and trilayer graphenes. Alternatively, GO can be intercalated and exfoliated, for instance, by tributylammonium cations [2.49]. The phenol, carbonyl, and epoxy groups resulting from the oxidation of graphite ensured colloidal stability in polar solvents [2.50]. Polymers, surfactants, DNA, etc. can be used to provide additional stabilization of the GO flakes in colloidal suspension. Edge-selective diazonium functionalization [2.51] has also been demonstrated as a way to stabilize high-concentration graphene solutions without the stabilizing agents perturbing the bulk structure of the graphene sheets.

Exfoliated GO can be subsequently reduced to yield reduced GO. It cannot be referred to as graphene at this stage due to the incomplete nature of the reduction process. One route involves reduction in water with hydrazine hydrate [2.52,53] or dimethylhydrazine [2.54]. A reduced GO suspension can also be obtained by heating the exfoliated GO suspension under strongly alkaline conditions by addition of NaOH at 50–90 °C (Fig. 2.6b) [2.46]. Alternately, the flakes can be deposited in a substrate and reduced by hydrazine vapors or hydrogen plasma [2.55]. All these methods result in the formation of unsaturated and conjugated carbon atoms, which results in electrical conductivity and Raman signatures intermediate between those of GO and pristine graphene.

GF can be reacted with n-butyl and n-hexyl lithium reagents in hexane at 0 °C. The alkyl lithium reagent replaces the fluorine functionalization during this process. The product can then be dispersed in ethanol by sonication. The alkyl functionalization, followed by a subsequent annealing step, partially restores the pristine graphene structure similar to reduced GO [2.56]. A one-step electrochemical approach has been demonstrated to form ionic liquid functionalized graphite sheets, which are then exfoliated into functionalized graphene dispersed in polar aprotic solvents [2.57].

It is also possible to exfoliate noncovalent GICs to yield graphene flakes that do not suffer the disadvantage of high defect density; for instance, alkali-metal GICs have been shown to readily and spontaneously exfoliate in N-methyl-pyrrolidone (NMP), yielding a stable solution of negatively charged graphene sheets. Graphene can also be noncovalently functionalized and exfoliated with 1-pyrenecarboxylic acid by continuous sonication in water [2.58]. Interhalogen compounds do not covalently functionalize the graphite upon intercalation, and therefore the resultant solution is one of pure graphene, without any need for further reduction or reconversion.

Exfoliation Without Intercalation

In an effort to avoid disruption to the desirable structure and properties of graphene, efforts have been undertaken to directly exfoliate and disperse graphite in a solvent by ultrasonication, as has been successfully demonstrated for debundling CNTs. Systematic study has been undertaken in the case of CNTs to explore their solubility in various solvents without the assistance of stabilizing agents such as surfactants. It has emerged that certain solvents such as N-methyl-pyrrolidone and N,N-dimethylamide (DMA) are ideally suited to dissolve CNTs in significant concentration [2.60]. Dissolution of CNTs in aqueous media is only possible using stabilizing surfactants; however, these solutions have emerged as the premier option among researchers, since the adsorbed surfactants can be easily desorbed or disintegrated if and when required.

Sieved graphite powder was dispersed in NMP by bath sonication. The macroscopic particles and aggregates were sedimented by mild centrifugation (500–2000 rpm), resulting in a homogeneous dark dispersion which was found to contain a high fraction of monolayer and few-layer graphene flakes [2.61]. Other solvents such as DMA, γ-butyrolactone, and 1,3-dimethyl-2-imidazolidinone yield similar results. The procedure has been adopted successfully for using water as solvent, in the presence of sodium dodecylbenzene sulfonate or sodium cholate as stabilizing surfactant [2.62]. The predominant drawback of this process lies in the fact that the sonication breaks up the graphene into particularly small fragments, with the monolayer flakes having lateral dimensions of, on average, 100 nm. This is similar to the case of CNTs, where sonication appears to cut them down to ≈200 nm [2.63]. The aqueous graphene dispersion can now be processed by density-gradient ultracentrifugation (DGU) using iodixanol as density medium to yield fractions enriched in particular graphene thicknesses (Fig. 2.7) [2.59]. Highly enriched solutions of monolayer and bilayer graphene with the above size limitation are now available for research purposes from commercial sources such as Nanointegris, but not yet in industrial quantity.

Single- and few-layer graphene sheets with sizes up to 0.1 mm have been fabricated by quenching hot graphite in ammonium hydrogen carbonate aqueous solution [2.64]. Few-layer graphene has also been produced by immersing and intercalating graphite in supercritical CO₂ for 30 min followed by rapidly depressurizing the supercritical fluid to expand and exfoliate the graphite [2.65]. The expanding CO₂ gas containing the graphene flakes was collected directly in an aqueous solution containing stabilizing surfactant to avoid aggregation. Other supercritical fluids, such as ethanol, NMP, and DMF, can also be used to exfoliate graphite into graphene [2.66].

Synthetic Production Route

If the reduction of bulk graphite into graphene is viewed as a top-down approach, then the chemical synthesis of graphene from smaller aromatic hydrocarbons will constitute the bottom-up approach. If graphene is regarded as a polycyclic aromatic hydrocarbon (PAH), one of the largest of these synthesized involves 222 carbon atoms or 37 benzene units in a hexagonal structure, 3 nm in diameter [2.72], from an oligophenylene precursor which was planarized by oxidative cyclohydrogenation. These structures have also shown a high tendency to self-assemble on surfaces [2.73] and could potentially act as precursors for larger synthetic graphene.

Graphene Nanoribbon (GNR)

The techniques described here have been suitably modified and developed with particular focus on forming very narrow ribbons of graphene with widths of tens of nanometers and with well-defined edge structure and orientation (Fig. 2.8). This is of particular importance in electronic applications, since such nanoribbons of graphene are one of the means to engineer an electronic bandgap in otherwise gapless graphene, as discussed in detail in Sect. 2.3.6. Once graphene flakes have been deposited onto a substrate, nanoribbons can be fabricated on it using standard and nonconventional lithography and etching processes, such as electron-beam lithography [2.74] and nanowire lithography [2.75], respectively.

Nickel [2.76] and silver [2.77] nanoparticles have been shown to act as a knife for cutting patterns in surface graphite layers of HOPG. The cutting proceeds via catalytic hydrogenation of the graphene lattice, and preferentially along crystallographic directions. The particles can become deflected into proceeding along a different direction if they come within close proximity of each other, of defects in the graphene lattice, or of previously formed cuts. The result is a complex pattern of cuts which border various well-defined shapes of the surface graphene layers, including instances where two parallel cuts result in a narrow ribbon between them. These shapes can be transferred onto arbitrary substrates using the mechanical exfoliation methods described earlier [2.67]. The graphene can also be cut into ribbons after they have been transferred onto any arbitrary substrate [2.78].

Expanded graphite was dispersed in a 1,2-dichloroethane (DCE) solution containing a polymer poly(m-phenylenevinylene-co-2,5-dioctoxy-p-phenylenevinylene) (PmPV) by sonication for 30 min followed by centrifugation to remove larger aggregates. The supernatant after sonication was shown to contain an appreciable fraction of graphene nanoribbons and related morphologies such as ribbons with kinks, bends, and nonparallel sides [2.71]. The exact mechanism or variation to the liquid-phase exfoliation procedures described earlier that results in the significant yield of nanoribbons in this case is not clearly understood.

Graphene nanoribbons, 8–12 nm in length and 2–3 nm width, have also been synthesized by surface-assisted coupling of molecular precursors into linear polyphenylenes and their subsequent cyclohydrogenation [2.68].

CNTs have been described as rolled-up graphene sheets, and now graphene nanoribbons have been made from unraveling CNTs. Oxidized nanoribbons were obtained by suspending CNTs in concentrated sulfuric acid followed by treatment with 500 wt.% KMnO₄ for 1 h at 22 °C and 1 h at 55–70 °C. The process, described as CNT unzipping, could occur as a linear longitudinal cut or in a spiral manner depending on the chirality of the CNT [2.70]. CNTs have also been converted to GNR by controlled plasma etching of CNTs that are partially embedded in a polymer film [2.69].

Derivatives of Graphene

Graphane, a fully saturated hydrocarbon derived from graphene, with formula CH, was predicted to be stable based on first-principles total-energy calculations [2.79]. Experimentally, it was later shown that graphene can be hydrogenated and converted to graphane using a low-pressure (0.1 mbar) hydrogen-argon mixture (10% H₂) with direct-current (DC) plasma for 2 h [2.80]. The hydrogenation is stable but reversible, and the graphane can be reconverted to graphene by annealing at 450 °C in Ar atmosphere for 24 h. The reconverted graphene, however, contains remnant defects just as vacancies and oxygenated or hydrogenated carbon atoms. In the case of substrate-supported graphene, only one side is hydrogenated, while both sides can be hydrogenated in the case of suspended graphene.

Graphene can also be fluorinated with xenon difluoride. When one side is exposed, F coverage saturates at 25% (C₄F), whereas fluorination of both sides results in perfluorographene [2.81] and fluorographene [2.82], which are the nonstoichiometric and stoichiometric variations. Nonstoichiometric and multilayered fluorographene can also be exfoliated from graphite fluoride [2.56,83]. Hydrazine treatment has been shown to reverse the fluorination.

Properties

While its very existence as a freestanding two-dimensional material is a feather in grapheneʼs cap, it is the properties of graphene that make it the truly exceptional material that has stoked feverish research in this field. The individual properties of pristine graphene are discussed first, while the properties of graphene derivatives such as GO, graphane, and fluorographene are discussed in the final section.

Structure and Physical Properties

Graphene shares most of its structure and physical properties with graphite, its parent material. The carbon atoms are arranged in a two-dimensional hexagonal lattice (Fig. 2.9b), which can also be constructed as two interpenetrating triangular sublattices, which takes particular significance in bilayer and other multilayer graphenes. The carbon atoms are sp² hybridized, and the in-plane carbon–carbon bond length is a =1.42 Å. The remaining p-orbital is oriented perpendicular to the plane of carbon atoms and delocalizes to form the π (valence) and π^* (conduction) electronic bands which are discussed in detail in Sect. 2.2.3. The carbon layers are usually stacked in an ABAB (Bernal) stacking; however, in certain few-layer graphenes such as that grown by CVD, the layers are rotated with respect to this standard arrangement. The interplane spacing is 3.45 Å. A staggered ABCABC (rhombohedral) arrangement is also possible, but has not been realized by any of the graphene production routes.

Two-dimensional structures such as graphene have been postulated to be intrinsically unstable, and according to the Mermin–Wagner theorem [2.84], long-wavelength fluctuations destroy the long-range order of 2-D crystals. Even 2-D crystals embedded in 3-D space have a tendency to crumple. The puzzling stability of suspended 2-D graphene sheets has been attributed to intrinsic microscopic undulations in which the surface normal varies by several degrees and the out-of-plane deformation reaches 1 nm [2.9,85]. This observation by TEM is discussed further in Sect. 2.3.2 and also conforms to atomistic Monte Carlo simulations. Similar corrugation has also been reported on graphene supported on SiO₂ substrates, where it is a superposition of intrinsic rippling as well as extrinsic undulations imposed by the substrate surface morphology [2.86]. Periodic ripples have also been observed on weakly coupled graphene monolayers on substrates such as Ru(0001) [2.87]. Corrugations in substrate-supported graphene are primarily observed by STM and are discussed further in Sect. 2.3.3. In addition to ripples, substrate-supported graphene also exhibits ubiquitous wrinkles which could be several nanometers in width. Scrolling has been occasionally observed at the edges of graphene flakes, both suspended [2.88] and substrate supported [2.89], and this appears to rely on the fabrication method. Scrolling occurs when graphene is subjected to liquid-phase processing during microfabrication, while its solid-phase or gas-phase processing appears to avoid this [2.90], and it is possible to obtain large free-standing sheets of monolayer graphene (Fig. 2.9a). The ripples in graphene also result in perturbations in the electronic structure, and many electronic and chemical properties of graphene have been attributed to these ripples, rather than being intrinsic to graphene. However, it has been shown that graphene deposited on atomically flat terraces of cleaved mica surfaces is flat down to the atomic scale [2.91]. The height variation observed by AFM was less than 25 pm, and such ultraflat graphene is expected to permit exploration of various intrinsic physical and chemical properties of graphene.

Mechanical Properties

Carbon materials have made it a habit of setting records for their intrinsic mechanical properties. Diamond is the hardest known natural material, and is assigned a grade of 10 (highest) on the Mohs scale of mineral hardness [2.93]. Similarly, the record for tensile strength has been held by CNTs; a Youngʼs modulus of 1 TPa and tensile strength of 150 GPa coupled with elongation to failure as high as 20% have been experimentally reported [2.94].

The earliest experimental indication for the extraordinary stiffness of graphene was the observation that graphene beams supported on only one end do not scroll or fold, quite unlike the papery or cloth-like appearance of graphene. If the effective thickness of monolayer graphene is estimated to be 0.23 Å from elastic theory, a bending rigidity of 1.1 eV [2.85], and a Youngʼs modulus of 22 eV/Å² from the elastic modulus of bulk graphite [2.95], the lengths of unsupported graphene observed in TEM samples have been 10⁶ times larger than its effective thickness. Suspended graphene can gain additional thickness from large-scale corrugations by a factor of (H/a)², where H is the characteristic height of the corrugations. In addition to supporting its own weight, suspended graphene has been shown to support significant extra load such as copper nanoparticles [2.90], as well as surviving accidental shocks such as during handing.

Direct measurements of the elastic properties of graphene have been conducted by nanoindentation of suspended graphene layers in an AFM [2.96,97]. Details of the measurement technique are found in Sect. 2.3.3. Measurements conducted on few-layer graphene of less than 8 nm thickness yielded spring constants of 1–5 N/m. A Youngʼs modulus of 0.5 TPa was extracted by fitting the data to a model for doubly clamped beams under tension. For measurements on monolayer graphene, the force–displacement characteristics yield second- and third-order elastic stiffness of 340 and −690 N/m, respectively. The breaking strength was found to be 42 N/m, which represents the intrinsic strength of a defect-free sheet. This corresponds to Youngʼs modulus E =1.0 TPa, third-order elastic stiffness of 2.0 TPa, and intrinsic strength of 130 GPa. These figures mean that graphene is the strongest material ever measured.

Nonlinear finite elasticity theory for graphene resonators for both electrostatic and electrodynamic cases has been developed and agrees well with experiments on graphene resonators [2.98]. The dynamic response of clamped graphene resonators resembles that of coupled Duffing-type resonators. Similarly, a continuum plate model for the vibration of multilayered graphene sheets, including the van der Waals (vdW) interaction between the layers, suggests that the lowest natural frequencies are identical for various numbers of layered graphenes. Higher resonance frequencies, however, depend on the vdW interaction and are different for different layered graphenes [2.99]. In general, natural resonance frequencies in the THz regime are expected for graphene resonators, due to the combination of their extreme thinness and extraordinary stiffness. Experimentally, the mechanical vibrations in electrostatically actuated graphene resonators have been imaged by a special modification of atomic force microscopy [2.100]. Resonance frequencies in the tens of MHz have been recorded in graphene resonators (Fig. 2.10), with quality factors as high as 4000 at room temperature [2.101] and 10000 at 5 K [2.102].

Electronic Properties

Electronically, monolayer, bilayer, and trilayer graphene are electronically distinct materials. Beyond three layers, grapheneʼs electronic properties tend towards those of bulk graphite. In certain aspects, graphene of up 10 layers might exhibit deviation in electronic properties from bulk graphite and could be referred to as graphene, but beyond 10 layers all graphenes are indistinguishable from graphite.

Monolayer Graphene

The electronic structure of graphene was first described in 1946 [2.103], as a theoretical building block to describe graphite. The valence and conduction bands of graphene are conical valleys that touch at the high-symmetry K and K′ points of the Brillouin zone. Near these points, the energy varies linearly with the magnitude of momentum, i.e., follows a linear dispersion relation. In neutral graphene, this point of intersection coincides with the charge neutrality point, and is referred to as the Dirac point.

In every other material known to condensed matter physicists, the electrons behave as and can be described by the Schrödinger equation. In graphene, on the other hand, electrons have been shown to behave as relativistic particles, and should be described by the Dirac equation [2.104,105,106]. The interaction of electrons with the periodic potential of the graphene hexagonal lattice results in quasiparticles, which can be viewed as electrons devoid of their rest mass m ₀ and therefore called massless Dirac fermions. The linear energy dispersion means that the speed of electrons in graphene is a constant, independent of momentum, as in the case of the speed of photons. The velocity of electrons in graphene is ≈10⁶ m/s, about 300 times slower than the speed of light (photons).

The electronic states near the Dirac point are composed of states belonging to the two graphene sublattices, and as a result the quasiparticles possess pseudospin, similar to the electronʼs spin [2.107,108]. As a result, these Dirac fermions are said to be chiral. Another relativistic feature of these quasiparticles is the Klein paradox [2.107], wherein they tunnel through a potential barrier of any height and width with a transmission probability of 1 or without a reflected component. As a result, electrons in graphene can propagate over (relatively) vast distances of the order of microns through the graphene lattice, even in the presence of lattice defects or other external perturbing potentials [2.4].

Bilayer Graphene

If the hexagonal atomic structure of graphene is composed of nonidentical elements, such as in boron nitride, the lateral in-plane symmetry is broken and a large bandgap is formed between the π and π^* states. This is the case in bilayer graphene, where the AB (Bernal) stacking between the two graphene renders the two carbon atoms inequivalent and results in two graphene sublattices. As a result, the unit cell of bilayer graphene contains four atoms, and two additional bands result (π and π^* states). If the inversion symmetry between the two layers is broken, then an energy gap between the low-energy valence and conduction bands forms at the Dirac point (Fig. 2.11).

The first experimental demonstration of this effect was performed on bilayer graphene synthesized on SiC (6H, (0001) orientation) [2.109]. The as-grown graphene is n-doped due to the depletion of the substrateʼs dopant carriers. At low temperature, the SiC dopant electrons are frozen out and the substrate acts as a nearly perfect insulator while the excess electrons in graphene retain their high mobility. In this case, the symmetry of the bilayers is broken by the dipole field created between the depletion layer of the SiC and the accumulation of charge on the graphene layer next to the interface. Further n-type doping can be introduced by deposition of potassium atoms onto the vacuum side, which donate their lone valence electrons to the graphene layer, forming another dipole. The binding energy–momentum dispersion relation of π, π^*, and σ states along high-symmetry directions was measured by angle-resolved photoemission spectroscopy (ARPES) (Fig. 2.12). The relative potential of the top and bottom graphene layers is varied by changing the doping level by potassium adsorption. An apparent gap at the K point appears in the as-prepared graphene, disappearing and reappearing with increasing level of K doping.

The electronic gap in bilayer graphene can thus be controlled by applying an external transverse electric field, such as by a gate bias, making it the only known semiconductor material with a tunable energy gap. Using a tight-binding model, the value of the gap was extracted as a function of electron density, showing that it can be tuned to values larger than 0.2 eV, using fields of ≈1 V/m.

The two key semiconductor parameters, the electronic bandgap and carrier doping concentration, can also be independently tuned by using a dual-gate configuration. Reliable determination of the bilayer bandgap has been carried out in such a configuration using infrared microscopy [2.110]. Figure 2.13 shows the gate-modulated bilayer absorption spectra at the charge neutrality point. The two features present in the spectra, a peak below 300 meV and a dip around 400 meV, arise from different optical transitions between the bilayer electronic bands. Transition I shows pronounced gate tunability up to 250 meV at 3 V/nm, since it accounts for the bandgap-induced spectral response.

By examining the electronic band structure of graphene around the K point within a tight-binding approach, it has been shown that a single graphene layer is a zero-gap semiconductor with a linear Dirac-like spectrum around the Fermi energy, while graphite shows semimetallic behavior with band overlap of about 41 meV. Bilayer graphene has a parabolic band structure around the Fermi energy and is a semimetal like graphite; however, the band overlap is only 0.16 meV. This overlap increases with the number of graphene layers, and for 11 or more layers it is smaller than 10%.

Superconductivity

Andreev reflection at a metal–superconductor junction involving graphene is fundamentally different from normal metals [2.111]. In weakly doped graphene, electron–hole conversion involves electrons from the conduction band being converted into a hole from the valence band. This interband conversion is associated with specular reflection instead of the retroreflection found in normal metals where electron–hole conversion occurs within the conduction band (Fig. 2.14). The Josephson effect has also been experimentally studied in macroscopic junctions consisting of a graphene layer contacted by two closely spaced superconducting electrodes (SGS) [2.112,113]. A supercurrent is observed, which can be carried either by electrons in the conduction band or by holes in the valance band, as determined by the gate voltage. A finite supercurrent is also observed at zero charge density at the charge neutrality point, indicating phase-coherent electronic transport at the Dirac point. The diffusive junction model has been shown to yield quantitative agreement with experiments [2.114], while a ballistic SGS model is inconsistent with the data. This is attributed to potential fluctuations in graphene due to the influence of the substrate as well as metallic leads. Crossed Andreev reflection in graphene–superconductor–graphene junctions [2.115] and Andreev reflection in graphene nanoribbons [2.116] have been theoretically investigated, but experimental confirmation remains pending.

Optical Properties

Successful exfoliation of monolayer graphene depends on the recognition of the optical properties of graphene more than the exfoliation procedure [2.7]. The choice of 300 nm-thick SiO₂ on Si substrate allowed optical identification of the exfoliated monolayer graphene, which would otherwise have been invisible and not practically detectable; for instance, only flakes thicker than ten layers can be found in white light on top of 200 nm SiO₂, which also marks the commonly accepted transition from graphene to bulk graphite. The contrast of a graphene flake depends not only on the SiO₂ thickness but also on the wavelength λ of light used. Figure 2.15 summarizes the expected contrast as a function of SiO₂ thickness as well as wavelength of monochromatic illumination, derived using Fresnel theory. It was also inferred that the complex refractive index of graphene is the same as that of bulk graphite, n = 2.6 − 1.3i, which is independent of λ. This can be explained by the fact that the optical response of graphite with the electric field parallel to graphene planes is dominated by the in-plane electromagnetic response. Since changes in the light intensity due to graphene are relatively minor, the observed contrast can be used to determine the number of graphene layers.

The absorbance of light by monolayer and bilayer graphene has been measured to be 2.3 and 4.6%, respectively, in the visual regime (450–750 nm), and this extends linearity up to five layers. The optical transparency of noninteracting graphene is solely determined by the fine structure constant of quantum electrodynamics (α = e ²/ℏc = 1/137), which describes the coupling between light and relativistic electrons [2.117,118]. This is because, as discussed in the previous section, the electrons in graphene behave as relativistic Dirac particles and electron–electron Coulomb interactions can be neglected. The high-frequency (dynamic) conductivity G for Dirac fermions in graphene is a universal constant equal to e ²/4ℏ. The universal G implies that observable quantities such as grapheneʼs optical transmittance T and reflectance R are also universal and given by T ≡ (1 + 2πG/c)⁻² = (1 + 1/2πα)⁻² and R ≡ 1/4π ² α ² T for normal light incidence. This yields grapheneʼs opacity (1 − T) ≈ πα =2.3%.

Thermal and Thermoelectric Properties

CNTs are known to have very high thermal conductivity K with the experimentally determined value of K ≈3000 W/(m K) at room temperature for an individual multi-walled CNT [2.119] and K ≈3500 W/(m K) for an individual single-walled CNT [2.120]. These values exceed those of the best bulk crystalline thermal conductor, diamond, which has thermal conductivity in the range K =1000–2200 W/(m K) [2.121].

The first experimental determination of the thermal conductivity of suspended monolayer graphene pegged the value at 5300 W/(m K) and a phonon mean free path of 775 nm near room temperature [2.122], which was extracted from the dependence of the Raman G peak frequency on the excitation laser power and independently measured G peak temperature coefficient. Interestingly, this value is higher than the bulk graphite limit of K ≈2000 W/(m K) [2.123]. It has been experimentally shown that the room-temperature thermal conductivity decreases from ≈2800 to ≈1300 W/(m K) as the number of graphene layers in few-layer graphene (FLG) increases from two to four [2.124]. The observed evolution from two-dimensional graphene to bulk graphite is explained by the cross-plane coupling of the low-energy phonons and changes in the phonon Umklapp scattering, since more states are available for scattering owing to the increased number of phonon branches.

The thermoelectric power (TEP) is the voltage developed across a sample when a constant temperature gradient is applied. TEP of 80 μV/K was recently measured in graphene at room temperature (300 K) [2.125]. Similar to the quantum Hall effect in electronic transport, quantized TEP has also been observed in graphene at high magnetic fields [2.125]. The TEP can be tuned in graphene, even to negative values, under the application of a gate bias or chemical potential [2.126]. Very large TEP values have been predicted for graphene nanoribbons, for instance, 4 mV/K for a 1.6 nm-wide ribbon [2.127]. In comparison, the highest value experimentally reported so far is 850 μV/K for two-dimensional electron gases in SrTi₂O₃ heterostructures [2.128], while only a few μV/K has been reported for bulk graphite [2.123]. The TEP power of SWNTs has been theoretically and experimentally shown to be 60 μV/K [2.129], inferior to that of graphene. A giant thermoelectric coefficient of 30 mV/K was reported in a nanostructure consisting of metallic electrodes periodically patterned over graphene, deposited on a silicon dioxide substrate [2.130].

Chemical Properties

The chemistry of graphene is dominated entirely by its surface, since every carbon atom is a surface atom twice over, forming a part of two surfaces. For nanoribbons of graphene, the edges play an increasing role in determining their reactivity.

It has been shown that, for electron transfer chemistries, single graphene sheets are almost 10 times more reactive than bilayer or multilayer graphene (Fig. 2.16) according to the relative intensity of the disorder (D) peak in the Raman spectrum examined before and after chemical reaction [2.131,132]. Substrate-induced doping of the graphene resulting in electron-rich regions has been proposed to explain this trend. The effect of doping is greatest in monolayers because the screening length in the c-axis in graphite and graphene is only 5 Å, comparable to the interlayer spacing of 3.5 Å [2.133,134]. Similarly, the reactivity of edges is at least two times higher than the reactivity of the bulk graphene sheet [2.131]. Predictions based on Gerischer–Marcus electron transfer theory and tight-binding approximations predict that armchair and zigzag graphene nanoribbons (GNRs) have opposite trends in reactivity, with the former increasing with width and the latter decreasing. In zigzag ribbons the major reactivity contribution comes from edge states [2.135]. This reactivity trend for zigzag GNR is reversed for very narrow ribbons due to the presence of large semiconducting gaps with correspondingly low reactivities.

Graphene can be readily functionalized through diazonium or nitrene [2.136] reactions, which can introduce reactive species covalently linked to graphene. These groups then serve as templates for further chemistry and grafting of functional groups, for instance, through an azide linker. Chemical functionalization of graphene can be monitored through its effect on the conductivity of graphene, serving as a means to control the electrical transport properties of graphene [2.137,138]. Furthermore, p-doped and n-doped regions in graphene can be generated by suitably functionalizing them, for instance, with diazonium salts and polyethylene imine, respectively [2.139]. Such chemical modification can also be performed on different parts of a single sheet to form p–n junctions in graphene [2.140].

Properties of Graphene Derivatives

Graphane was theoretically predicted to take one of two configurations: a chair conformer with the hydrogen atoms alternating on both sides of the plane for the two graphene sublattices, and a boat conformer with the hydrogen atoms alternating in pairs [2.79]. These chair and boat conformers have a direct electronic bandgap of 3.5 and 3.7 eV, respectively. Graphane is a completely insulating material; its resistivity changes by two orders of magnitude with decreasing temperature from 300 to 4 K, and its carrier mobility decreases to ≈10 cm²/(V s) at liquid-helium temperatures for typical carrier concentrations of 10¹² cm⁻² [2.80].

Similarly, fluorographene [2.82] is a high-quality insulator with large optical bandgap of >3 eV and room-temperature resistivity of >10¹² Ω. The Youngʼs modulus of fluorographene was measured to be 0.3 TPa, which is about 30% the stiffness of graphene. Similarly, fluorination reduces grapheneʼs intrinsic breaking strength by 2.5 times. However, fluorographene is able to sustain the same ultimate strain of 15% as graphene. Fluorographene is also strongly hydrophobic, and can be considered the two-dimensional equivalent of Teflon.

Characterization

Each of the properties discussed in the previous section has to be measured and correlated using multiple characterization techniques, which are discussed in this section; for instance, electronic properties of graphene have to be independently verified by ARPES, optical spectroscopy, and electronic transport. This is essential, since just one measurement, for instance, electronic transport, might not be able to sufficiently distinguish between an electronic bandgap and a mobility gap. Similarly, mechanical properties have to be confirmed by a combination of tensile testing, electromechanical resonance, and Raman spectroscopy.

Optical Characterization

Based on the optical properties of graphene discussed in an earlier section, and the fact that green light is most comfortable for the eyes, optimal SiO₂ thicknesses of 90 and 280 nm can be recommended [2.7]. Similarly, it has been shown that graphene can be observed on 50 nm Si₃N₄ using blue light and on 90 nm poly-methyl methacrylate (PMMA) using white light [2.7]. Optical contrast can similarly be used to identify graphene oxide on Si/SiO₂ substrates, as well as to visualize its conversion to reduced GO upon annealing, since both the effective index of refraction and the effective extinction coefficient increase [2.141].

Rayleigh scattering can identify the number of graphene layers as well as probe their dielectric constant [2.142]. Rayleigh imaging relies on elastically scattered incident photons, while Raman spectroscopy, which is discussed later, collects inelastically scattered photons. For graphene on Si/SiO₂ substrate, under white-light illumination combined with interferometric detection, the contrast can be tailored by adjusting the SiO₂ thickness and the light modulations depend strongly on the graphene thickness. Up to six layers, the graphene behaves as a superposition of single sheets and the monochromatic contrast increases linearly.

Transmission Electron Microscopy

Transmission electron microscopy (TEM) is one of the most direct observation techniques to elucidate the structure of graphene. High-resolution TEM can resolve individual carbon atoms as well as adatoms, defects, and other anomalies in graphene (Fig. 2.17) [2.88]. The high-energy electrons in a TEM can also be used to engineer defects such as vacancies, cause edge reconstructions and graphene sublimation, as well as observe them in situ [2.10]. Various techniques have been developed to transfer micromechanically cleaved graphene flakes onto TEM grids. If folds occur in the transferred graphene flake, observation of the folded edge can yield information about the number of layers in the graphene flake [2.9]; a monolayer fold edge turns up as a single dark line, while a bilayer fold edge appears as two dark lines and so on, in analogy to single-walled and multi-walled carbon nanotubes. In addition, nanobeam electron diffraction (Fig. 2.17) can also be used to quantify the layering in graphene [2.9]. Monolayer graphene can be distinguished from higher-layered graphenes by the anomalous intensity ratio of the diffraction peaks; its $0 \bar{1} 10$ peaks being more intense than the $1 \bar{2} 10$ peaks. When measured as a function of incidence angle, it probes the whole 3-D reciprocal space. The total (integrated) intensity of the $0 \bar{1} 10$ and $1 \bar{2} 10$ peaks of monolayer graphene varies weakly with tilt angle and no minima in intensity are observed, since the intensities in reciprocal space for monolayer graphene are continuous rods. In contrast, the total intensity of bilayer graphene diffraction peaks varies strongly with tilt angle, including minima at certain angles where some peaks vanish [2.143]. However, while the total intensity in monolayer graphene only decreases slightly, significant peak broadening is observed with increasing tilt angle. This effect is most pronounced in monolayers, and decreases with increasing thickness of the graphene flake. This is attributed to nanoscale corrugations in 2-D graphene, with the surface normal deviating on average by ±5° in monolayers and ±2° in bilayers. Considering that the spatial extent of these corrugations cannot be drastically smaller than the coherence length of the diffracted electrons and that a large number of orientations should be included within the submicron electron beam in order to yield a smooth Gaussian shape of the diffraction peak, it is estimated that the corrugations occur on length scales of 10–25 nm. This nanoscale corrugation extending into the third dimension squares the existence of 2-D graphene with the theoretical prediction that perfect 2-D atomic crystals cannot exist.

Scanning Probe Techniques

Scanning probe techniques discussed here in the context of graphene characterization include atomic force microscopy (AFM), electrostatic force microscopy (EFM), and scanning tunneling microscopy (STM) and spectroscopy (STS).

AFM in tapping mode is commonly used to measure the thickness of graphene flakes on substrates; however, the correlation between measured thickness and actual thickness as well as number of layers is challenging [2.144]. Electrostatic interactions between the tip and the graphene, adsorbed moisture, and incorrect choice of AFM parameters such as free amplitude values can all influence the final measured thickness of a graphene flake. Therefore, while using AFM to characterize graphene flakes, an internal reference such as a fold in the flake, or a second characterization tool such as Raman spectroscopy, is often used to correlate the measured thickness and number of layers, and this process needs to be repeated at least for every different substrate and processing conditions involved in the graphene preparation.

In addition, AFM is used to measure the flatness of graphene on various substrates, and it is revealed that ultraflat graphene can be obtained on mica surface [2.91] with standard deviation of height and height correlation length of 24.1 pm and 2 nm, respectively, compared with 154 pm and 22 nm, respectively, for SiO₂ substrate. AFM can also be used in nanoindentation mode to probe the stiffness of suspended graphene (Fig. 2.18) [2.96]. This technique has the advantage that the sample geometry can be precisely defined and the sheet is clamped around the entire hole circumference; a Youngʼs modulus of 1 TPa and intrinsic breaking strength of 42 N/m have been measured. EFM has been used to confirm that the surface potential of few-layer graphene increases with film thickness, approaching bulk graphite values for five or more layers [2.145]. This is a measure of the extent of the electrostatic interaction between graphene and the substrate, and the screening of these perturbations by underlying graphene layers.

STM can image graphene with atomic resolution, and the correlation of the graphene hexagonal lattice to the direction of the edge of an exfoliated flake reveals the orientation of the edge as being either armchair or zigzag [2.146]. It has been shown that, in mechanically exfoliated graphene flakes, a majority of edges follow either of these orientations and intersect at angles that are multiples of 30°. STM imaging of graphene grown epitaxially on SiC [2.147] or metallic substrates [2.20,23,87,148] reveals the superlattice structure and the extent of coupling between the graphene and substrate. STM can also be used to locate and characterize point defects in the graphene lattice [2.149,150]. STS can be used to probe the atomically resolved local electronic structure of graphene [2.147,151,152]. A prominent gap in the tunneling spectrum unique to graphene has been observed and attributed to a phonon-mediated inelastic tunneling process.

Angle-Resolved Photoemission Spectroscopy (ARPES)

ARPES is a direct experimental technique that has measured the electronic density of states in graphene with both energy and momentum information. The shape of the π and π^* bands near E _F at the K-point from ARPES reveals the transition from 2-D to bulk character from one to four layers of graphene [2.153]. Fermi velocities and effective masses of the electrons can also be measured. ARPES on epitaxial AB-stacked bilayer graphene on SiC has revealed that the magnitude of the gap between the valance and conduction bands can be varied by controlling the carrier density, for instance, with a transverse electric field. On the other hand, APRES also reveals that individual graphene layers of multilayer graphene grown on SiC( $000 \bar{1}$ ) behave as decoupled monolayers with independent linearly dispersed bands at the K-point [2.154]. ARPES also allows studies of electron–electron, electron–phonon, and electron–plasmon interactions, and indicates that all three must be considered on an equal footing in understanding the quasiparticle dynamics in graphene [2.155]. Ab initio simulations of the ARPES intensity spectra of graphene has been able to reproduce key experimental observations including the indication of a mismatch between the upper and lower halves of the Dirac cone.

Raman Spectroscopy

The three significant Raman spectral features in graphene are the G peak at ≈1580 cm⁻¹, the D peak at ≈1350 cm⁻¹, and the 2D peak at ≈2700 cm⁻¹, as seen in Fig. 2.19 [2.156]. The G peak is due to the E _2g mode, i.e., in-plane vibrations of the carbon atoms. The D peak and 2D peak are strongly dispersive, with excitation energy due to the Kohn anomaly at the K-point, while the G peak is not.

The 2D peak is the second order of the zone-boundary phonons and therefore does not require defects. For monolayer and few-layer graphene, the 2D peak serves as a fingerprint for identification [2.156]. In general, the 2D peak of graphite has four components: 2-D_1B, 2-D_1A, 2-D_2A, and 2-D_2B. Monolayer graphene has a single sharp 2D peak, dominated by the 2-D_1A component. In bilayer graphene, the 2-D_1A and 2-D_2A peaks have higher relative intensity compared with the other two, and the 2D peak appears up-shifted and broader compared with monolayer graphene. In monolayer graphene, there is only one phonon satisfying the double-resonance conditions for the 2D Raman peak. In bilayer graphene, the interaction between graphene layers causes the π and π^* electronic bands to split into four bands. According to density functional theory dipole matrix elements, the incident light couples more strongly to two among four possible optical transitions (Fig. 2.19). The excited electrons can be scattered by phonons with momenta q _1B, q _1A, q _2A, and q _2B. The corresponding processes for holes are associated to identical phonon momenta, resulting in four components to the 2D peak of bilayer graphene. As the number of layers further increases, the 2D₁ peaks reduce in intensity, and beyond five layers, it resembles the 2D peak of bulk graphite. It is also important to note here that non-AB stacked graphene, such as multilayer CVD graphene, also shows a single 2D peak [2.157,158]. However, this can be distinguished from monolayer graphene by its full-width at half-maximum (FWHM) of 50 cm⁻¹, which is twice that of monolayer graphene.

A similar observation can also be made for the D peak [2.156]. The D peak of monolayer graphene is a single sharp peak, while in bulk graphite it can be resolved into two peaks, D₁ and D₂. The D peak is observed in defective graphene, and prominently at the edges of graphene flakes. In carbon nanotubes, confinement and curvature split the two degenerate modes of the G peak into G⁺ and G⁻ components, whereas only one G peak is observed in graphene. The D peak arises from a double-resonance process involving electron scattering by zone-boundary phonons as well as defects in graphene. Since these do not satisfy the Raman selection rule, they do not occur in the Raman spectra of defect-free graphene. A similar process involving intravalley scattering gives rise to a D′ peak at ≈1620 cm⁻¹ in defective graphene.

The Raman spectrum of graphene also responds to doping, i.e., changes in the Fermi surface of graphene [2.160,161]. Graphene can be doped intentionally or unintentionally, by electron transfer from adsorbed chemical species, and by modulation of the electronic band structure by a gate voltage or interaction with the substrate. The G peak upshifts for both hole and electron doping. The position of the 2D peak, however, decreases monotonically with increasing electron concentration or decreasing hole concentration, and the 2D peak can be used to distinguish between electron and hole doping. The changes in the G peak position are related to the nonadiabatic Kohn anomaly at the Γ point, while the shift in the 2D peak position is due to electron–electron scattering in addition to electron–phonon scattering. Taken together, a plot of 2D versus G peak positions can be used to distinguish between electron and hole doping in graphene (Fig. 2.20a) [2.159]. Doping trends can also be observed in the FWHM and intensities of Raman peaks. Raman peaks in graphene can also be shifted by biaxial strain induced, for example, by interaction with the substrate [2.162,163]. It has been proposed that the correlation between normalized shift of 2D and G peak positions, i.e., Δ2D/2D₀ and ΔG/G₀, where 2-D₀ and G₀ are the peak positions for undoped graphene, indicates whether the shift arises from doping or strain [2.164]. When Δ2D/2D₀ versus ΔG/G₀ is plotted from Raman spectra obtained at a number of points on a graphene samples, a linear fit with slope close to 1.58±0.18 indicates that strain plays a predominant role, while a smaller slope indicates increasing influence of doping. Highly doped samples yield a slope of < 1. In another approach, if the plot of FWHM versus position of the G peak is monotonically decreasing, it is related to doping, while if it is monotonically increasing, it is caused by strain or disorder (Fig. 2.20b) [2.161]. Under uniaxial strain, the G peak splits into two bands, G⁺ and G⁻, analogous to the effect of curvature on the G peak of carbon nanotubes [2.165].

Electrical Characterization

The first electrical characterization of graphene was carried out on micromechanically cleaved few-layer graphene flakes (Fig. 2.21) [2.4]. The sheet resistivity ρ of FLG flakes varies with applied gate voltage V _g, exhibiting a sharp peak of several kiloohms and decaying to ≈100 Ω at high V _g. The conductivity σ = 1/ρ increases linearly with V _g on either side of the resistivity peak (conductivity valley). The Hall coefficient R _H reverses sign at the same V _G as the resistivity peak. This resembles an ambipolar semiconducting field-effect transistor (FET), except that there is no zero-conductance region since there is no bandgap. This tunability of conductivity is achieved by transforming the graphene by electric-field doping from a completely electron to completely hole conductor, passing through a mixed state where both electrons and holes contribute equally. This behavior holds true for monolayer graphene as well as undoped bilayer graphene; however, doped bilayer graphene has an intrinsic bandgap and will be discussed subsequently. In both the electron and hole regions, R _H decreases with increasing carrier concentration as 1/ne as expected, and the resistivity follows the standard ρ = 1/neμ relation, where μ is the carrier mobility. Also significant is the minimum conductivity of graphene at the charge neutrality point (σ _min), which has been shown to be about 4e ²/h. This σ _min is not related to the physics of the Dirac point singularity, but instead related to charge-density inhomogeneities (electron–hole puddles) induced by the substrate or charged impurities [2.166,167]. Invariably, the position of the charge neutrality point (ρ peak) is shifted to large positive V _G, leaving the ungated graphene as a hole metal. This large shift is attributed to unintentional doping of the graphene by adsorbed species such as water. The peak position can also be shifted by intentional doping [2.166] or removal of dopants by thermal or current-induced annealing [2.13], but such charged impurities do not affect σ _min. The mobility and minimum conductivity also decrease as a result of defects, which can be induced in a controlled fashion to study this effect, for instance, by ion irradiation [2.168] or exposure to atomic hydrogen [2.169].

The earliest determination of carrier mobility by field-effect and magnetoresistance measurements in few-layer graphene yielded ≈10000 cm²/(V s), which was independent of the absolute temperature, indicating that it was limited by scattering defects. For multilayer graphene, the mobility reached 15000 cm²/(V s) at 300 K and 60000 cm²/(V s) at 4 K. Substrate-induced charge puddles are significantly reduced in suspended graphene, and low-temperature mobility approaching 200000 cm²/(V s) has been reported [2.170,171]. In such devices, the conductivity of suspended graphene at the Dirac point is strongly temperature dependent and approaches ballistic values at liquid-helium temperatures [2.171].

Graphene flakes also exhibit pronounced Shubnikov–de Haas (ShdH) oscillations in both longitudinal resistivity ρ _xx and Hall resistivity ρ _xy (Fig. 2.22). The oscillations depend only on the perpendicular component of the magnetic field B cos Θ, where Θ is the angle between the magnetic field and the graphene. The frequency of the SsdH oscillations B _F depends linearly on V _G, indicating that the Fermi energies ε _F of holes and electrons are proportional to their concentration n. This is different from the 3-D dependence ε _F proportional to n ^2/3, proving the 2-D nature of charge carriers in graphene.

QHE has been observed in graphene even at room temperature, since the electrons suffer little scattering due to their relativistic nature and have a large cyclotron gap which exceeds the thermal energy k _B T by a factor of 10.

Under the influence of strong magnetic field, electrons in a two-dimensional system such as graphene develop strong Coulomb interactions between them, leading to correlated states of matter such as a fractional quantum Hall liquid. This collective behavior in graphene was predicted to yield the fractional quantum Hall effect (FQHE); however, due to prevalent disorder effects, observation of this remained elusive in early measurements. The FQHE was eventually reported in suspended graphene devices when a plateau at filling factor ν = 1/3 was observed above a magnetic field as low as 2 T [2.173,174]. An insulating state was also observed at magnetic fields B >5 T and filling factors ν <0.15, which has been attributed to symmetry breaking of the zeroth Landau level by electron–electron interaction.

The first electron transport measurement of the tunable bandgap in bilayer graphene was conducted on micromechanically cleaved graphene on an oxidized silicon wafer (300 nm SiO₂) [2.172]. The silicon substrate was used as a back gate to modulate the carrier density n, while doping from adsorbed NH₃ on the exposed graphene surface was used to mimic a top gate and open a bandgap corresponding to a fixed electron density n ₀. Under applied magnetic field, a plateau at zero Hall conductivity σ _xy = 0 occurs in biased bilayer graphene, as a result of the gap opened between the valence and conduction bands. Plateaus at σ _xy = 4Ne ²/h occur as expected, including at N = 0 (Fig. 2.23a). This is the standard integer QHE that is expected for an ambipolar semiconductor with energy gap larger than the cyclotron energy. This plateau is absent in monolayer and unbiased bilayer graphene, which show an anomalous double step of 8e ²/h at n = 0, indicative of the metallic state at the charge neutrality point. A huge peak in the longitudinal resistivity ρ _xx at n = 0 was also observed, exceeding 150 kΩ at 4 K compared with 6 kΩ for the unbiased case. From Shubnikov–de Haas measurements, the cyclotron mass, m _c, in biased bilayer graphene is found to be an asymmetric function of the carrier density, which is a clear signature of a bandgap (Fig. 2.23b). Measurements with dual-gated bilayer graphene have also confirmed these results [2.175].

Due to the linear dispersion relation in graphene, intrinsic electron scattering by acoustic phonons is independent of carrier density and only contributed 30 Ω to the room-temperature resistivity of graphene. This would yield an intrinsic mobility of 2×10⁵ cm²/(V s) at carrier density of 1×10²/cm², which would be make it the highest known mobility, superior to those of InSb and semiconducting single-walled carbon nanotubes. However, a strong temperature dependence of mobility is observed in substrate-supported graphene devices, suggestive of extrinsic scattering, which limits the mobility to about 4×10⁴ cm²/(V s) [2.176].

Various approaches have been proposed to increase the performance of graphene devices, in particular to reduce impurity scattering and enhance mobility. Ultrahigh current density-induced removal of adsorbents, photoresist, or e-beam resist residue can be used to clean graphene in situ during transport measurements [2.13]. A parylene-coated SiO₂ substrate used as a dielectric stack for back-gating yields a stable charge neutrality point and low hysteresis [2.178], since the hydrophobic nature of the parylene surface suppresses moisture-related doping and charge-injection effects and yields mobilities of up to 10000 cm²/(V s). Similar results have been achieved by utilizing an organic polymer buffer between graphene and conventional top-gate dielectrics [2.179]. It was demonstrated that merely changing the dielectric to a high-k dielectric or media does not increase the carrier mobility beyond ≈10000 cm²/(V s), suggesting that Coulomb scattering is not the dominant limitation beyond this regime [2.180]. Phonon scattering or resonant scatterers with energy close to the Dirac point have been proposed as alternate mechanisms.

As discussed previously, another route to opening a bandgap in graphene is to exploit lateral confinement of charge carriers in a graphene nanoribbon, which creates an energy gap near the charge neutrality point [2.177]. Graphene nanoribbons of varying widths and different crystallographic orientations have been fabricated by lithographic patterning of monolayer exfoliated graphene (Fig. 2.24). An energy gap is observed for narrow ribbons, which scales inversely with ribbon width. Energy gaps in excess of 100 meV were observed for widths less than 20 nm, which could have potential technological relevance. It has also been shown that edge states do not contribute to the dominant electrical noise at low frequencies for nanoribbons as narrow as 20 nm [2.181]. However, the lack of a well-defined crystallographic structure of lithographically etched edges means that the effect of orientation is not observed in the bandgap produced in such nanoribbons.

It is also possible to fabricate quantum dot (QD) devices entirely out of graphene using a similar lithographic procedure [2.182,183,184]. Such a device consists of a graphene island connected to the source and drain via two narrow graphene constrictions and three fully tunable graphene lateral gates (Fig. 2.25). Larger QDs (>100 nm) show conventional single-electron transistor characteristics, with periodic Coulomb blockade peaks. For smaller QDs, the peaks become strongly nonperiodic, indicating a strong contribution from quantum confinement. The narrow constrictions remain conductive and show a confinement gap of ≈0.5 eV. This can be extended to a double QD system (Fig. 2.25) where the coupling of the dots to the leads and between the dots is tuned by graphene in-plane gates [2.185]. This structure has been proposed for the realization of spin qubits from graphene QDs [2.186]. It has been shown that, in an array of many qubits, it is possible to couple any two of them via Heisenberg exchange while the others are decoupled by detuning. This unique feature is a direct consequence of the quasirelativistic nature of carriers in graphene.

One of the important considerations in electronic device performance is the signal-to-noise ratio, where usually the low-frequency 1/f noise dominates. In monolayer graphene, the 1/f noise follows Hoogeʼs empirical relation with a noise level comparable to carbon nanotube and bulk semiconductor devices. However, in bilayer graphene, the 1/f noise is strongly suppressed and obeys a unique dependence on carrier density, due to effective screening of carrier scattering by external impurities [2.134]. In monolayer graphene, the noise amplitude is minimum at the Dirac point and increases with increasing carrier density. However, in bilayer graphene, the noise amplitude achieves a maximum at the Dirac point and decreases with increasing carrier density. In both cases, the noise is independent of carrier type.

In an effort to realize commercial viability of graphene electronics, reduced graphene oxide (RGO) has been explored as an alternative to pristine monolayer graphene. However, measurements in individual monolayer RGO flakes have yielded conductivities ranging between 0.05 and 2 S/cm and field-effect mobilities of 2–200 cm²/(V s) at room temperature. Conductivity decreases by up to three orders of magnitude when measured down to 4 K, following a T ^−1/3 dependence, suggesting variable-range hopping conduction between regions of highly reduced (nearly pristine) graphene islands separated by defective or poorly reduced regions.

Spintronics

When graphene devices are fabricated with ferromagnetic electrodes, such as the soft magnetic NiFe or Co, it is possible to inject spin-polarized current into the graphene. A thin Al₂O₃ or MgO tunnel barrier is used at the ferromagnet–graphene interface. High-quality graphene enjoys ballistic transport with spin relaxation lengths between 1.5 and 2 μm even at room temperature, which is only weakly dependent on charge density [2.187]. The switching fields of the electrodes can be controlled by in-plane shape anisotropy. Graphene spin valves have been constructed using either a local [2.188] or nonlocal [2.187,189] geometry, and clear bipolar spin signal has been observed which is indicative of the relative magnetization directions of the electrodes (Fig. 2.26), and magnetoresistance of up to 12% has been reported in local geometry. In addition, Henle-type spin precession has also been reported, and a sign reversal in the spin signal can be achieved by applying an orthogonal switching magnetic field. The nonlocal spin-valve signal changes magnitude and sign with back-gate voltage, and is observed up to T =300 K [2.189].

An alternative configuration, comprising a graphene monolayer sandwiched between two ferromagnetic layers, involves spin-polarized conduction perpendicular to the plane of the graphene in a conduction perpendicular to plane (CPP) geometry [2.191]. Graphene was sufficient to reduce the exchange coupling between the magnetic electrodes. in a NiFe/Au/graphene/NiFe stack, the graphene channels the spin current perpendicular to the plane and thus produces an enhanced magnetoresistance effect compared with a simple stack without the graphene.

Photocurrent Microscopy

The channel potential distribution in a graphene field-effect transistor can be imaged by scanning photocurrent imaging (Fig. 2.27) [2.190,192]. When graphene is contacted to a metal, it is doped by the metal due to the work-function mismatch. The potential step between the graphene that is p-doped by a Ti-Pd-Au contact and bulk graphene with no gate bias was estimated to be 45 meV. When light is shone on such potential steps which occur close to each contact, excited electron–hole pairs can be split by the potential gradient, leading to a photocurrent. At negative gate bias, before the flat-band condition, the graphene forms a p–p⁺–p channel. In the flat-band condition, the influence of the metal electrodes was measured to extend up to 450 nm into the graphene channel. For positive gate biases beyond the Dirac point, the graphene forms a p–n–p channel, and when light is focused on the p–n junction, an external responsivity of 0.001 A/W was measured. Scanning photocurrent microscopy has also revealed potential gradients occurring at monolayer–multilayer graphene interfaces [2.190].

Applications

While the field of experimental graphene research is still in its early years, grapheneʼs potential for applications is already evident. Graphene is currently under evaluation for a wide range of applications, which will benefit from its unique combination of excellent mechanical, electronic, optical, and chemical properties. Commercial viability of most applications is severely limited by the limited options available for large-scale production of graphene. As a case study, graphene was proposed as an excellent transparent conductor with potential for replacing indium tin oxide (ITO), but it was not possible to pursue this application commercially until a roll-to-roll fabrication process for graphene was recently developed. Other applications, particularly in electronic devices, are critically dependent on breakthroughs in wafer-scale, complementary metal–oxide–semiconductor (CMOS)-compatible integration of individual graphene electronic devices.

Structural and Electrical Composites

The remarkable mechanical properties of graphene coupled with its high electrical and thermal conductivity suggest that it would be ideal for use in composite materials for structural as well as electronic applications. This potential has been enhanced by recent advances in solution-phase dispersion of graphene oxide (GO) and graphene, even down to highly monolayer-enriched graphene solutions. Graphene oxide-polystyrene composites show a low percolation threshold of ≈0.1 vol.% for room-temperature electrical conductivity and ≈0.1 S/m at 1vol.%, which is sufficient for many electrical applications [2.54]. Such composites show ambipolar field-effect behavior with electron and hole mobilities of 0.2 and 0.7 cm²/(V s), respectively [2.193]. GO-silica composites have been fabricated by spin-coating GO-impregnated silica sols to yield transparent conducting composite films [2.194]. Layered GO-polymer composites have been fabricated by layer-by-layer (LBL) assembly, taking advantage of electrostatic interactions between anionic GO sheets and cationic polymer [2.43]. Graphene oxide composites with poly(3-hexylthiophene) (P3HT) and poly(3-octylthiophene) (P3OT) have been demonstrated as a superior active layer in organic photovoltaics [2.195], while TiO₂-graphene composite has been demonstrated as a high-performance photocatalyst [2.196]. Composites of functionalized graphene derived from GO with polymers such as PMMA, poly(acrylonitrile), and poly(acrylic acid) show the best performance in terms of Youngʼs modulus, glass-transition temperature, ultimate strength, and thermal degradation [2.197]. Composites of graphene with metal nanoparticles (Au, Pt, and Pd) have also been produced, and the graphene-Pt composite has been demonstrated as a catalyst in direct methanol fuel cells [2.198].

Transparent Conducting Films

Thin films of graphene have been deposited from solution-phase graphene with controllable thickness from a single monolayer to several layers over large areas (Fig. 2.28) [2.199]. The thickness of the film determines its conductivity, transparency, and mechanical integrity, making it suitable for various applications. Electronic properties can be tuned from graphene-like ambipolar field-effect behavior for the thinnest films to graphite-like semimetal conductivity for thicker films. Flow-based deposition, vacuum filtration, and layer-by-layer assembly are among the techniques used to deposit graphene thin films from solution. However, the predominant part of solution-phase research has involved reduced [2.200] or functionalized derivatives of graphene oxide, rather than pristine graphene.

Graphene conducting thin films are targeted at replacing indium tin oxide (ITO); however, it has so far been unable to match ITOʼs combination of 100 Ω per square sheet resistance at 90% transparency. Solution-processed reduced GO can be deposited as thin films of controllable thickness by Langmuir–Blodgett LBL deposition [2.201], and can achieve sheet resistance of 1 kΩ/ □ per square at 90% transparency. Such films have been demonstrated as transparent conductive anodes for inorganic, organic, and dye-sensitized photovoltaic cells, but the short-circuit current and fill factor are still lower than those of control devices using ITO [2.202,203]. However, they do have advantages such as tunable wettability, high chemical and thermal stability, and flexibility.

Pristine graphene films grown by chemical vapor deposition (CVD) on Ni or Cu substrates and transferred by a wet process can achieve ≈280 Ω per square at ≈80% transparency, but still fall short of ITOʼs benchmark. Still, the films show high electron mobility of 3700 cm²/(V s) and exhibit the half-integer quantum Hall effect typical of high-quality graphene, which cannot be accomplished with reduced or functionalized GO (Fig. 2.29). Most importantly, the graphene films can recover its original resistance after being stretched by up to 6% and the resistance shows little variation up to bending radius of 2.3 mm, corresponding to tensile strain of 6.5%. This gives graphene films a significant advantage over ITO for applications in flexible electronics [2.204,205]. A roll-to-roll dry transfer process has been developed for up to 30 inch monolayer (ML) graphene grown on Cu, yielding films with 97.4% transparency and 125 Ω per square sheet resistance (Fig. 2.30). The conductivity of graphene can be further improved by doping, for example, p-doping with HNO₃, and resistance as low as 30 Ω per square can be achieved at 90% transparency, making graphene a strong potential candidate for ITO replacement, particularly in flexible electronics [2.28].

Solution-processed graphene as well as CVD graphene have been demonstrated as electrodes for organic light-emitting diodes [2.206]. This, combined with graphene-based field-effect transistors and graphene transparent conducting electrodes, allows for fabrication of fully flexible and transparent touchscreen displays.

Graphene can be used as an electrode for polymer-dispersed liquid-crystal (PDLC) devices, for example, as a smart window. Light passing through the liquid crystal/polymer is strongly scattered, resulting in a milky film. If the liquid crystalʼs refractive index is close to that of the polymer, an electric field in the transverse direction causes the liquid crystals to align in the direction of light propagation, resulting in a transparent state [2.207].

Sensors

The ultimate detection limit of any chemical sensor is the ability to detect individual molecules of a desired species (Fig. 2.31). The exceptionally low-noise electronic characteristics of graphene allow for such single-molecule sensitivity [2.208]. Adsorbed gas molecules change the local carrier concentration one electron at a time, which can be detected as stepwise changes in device resistance.

Depending on the nature of the adsorbed species, the graphene can be either electron doped (NH₃) or hole doped (H₂O, NO₂). As there is no gap in the graphene density of states, even a small mismatch in chemical potential to the adsorbate is sufficient to provide an active donor or acceptor level, whereas in semiconductors, the chemical potential mismatch has to exceed half the gap energy to achieve doping [2.209]. Therefore, graphene sensors are expected to be more sensitive than conventional semiconductor sensors.

Reduced graphene oxide-based devices have shown parts-per-billion sensitivity to chemical warfare agents and explosives [2.210], and parts-per-million sensitivity to gasses such as NO₂ and NH₃ [2.211]. Reduced GO-based sensors have also been demonstrated in surface acoustic wave configuration, with parts-per-million sensitivity to H₂ and CO [2.212]. Electrolyte-gated graphene devices have been demonstrated as pH and biomolecule sensors with picomolar sensitivity [2.213].

Suspended graphene resonators can be electrically or optically actuated and detected, with fundamental mode frequencies in the MHz range [2.214]. Molecular structural mechanics modeling has shown that the principle frequency vibrations of monolayer graphene are sensitive to added mass of ≈10⁻⁶ fg [2.215]. Mass sensitivity of ≈2 zg has been experimentally demonstrated using graphene resonators with a high quality factor of 14000 at low temperature [2.102].

Electronic Applications

Charge carriers in graphene have very high mobility, which is not significantly affected by doping, leading to ballistic transport on a submicron scale even at room temperature. This is a much sought-after characteristic for the next generation of electronic materials, since it would allow for very fast switching times, perhaps less than 10⁻¹³ s. The low on–off ratio (< 100) in gapless graphene is not a fundamental limitation for high-frequency operation. Transistors fabricated on epitaxial graphene on SiC have achieved a cutoff frequency of 100 GHz (Fig. 2.32) [2.216], and those fabricated on conventional Si/SiO₂ substrates have reached a cutoff frequency of 26 GHz [2.217].

Large-scale integration of graphene devices can be achieved either by conventional top-down fabrication in the case of epitaxial graphene on SiC [2.218], or CVD graphene grown on metallic substrates and transferred to dielectric substrates. In the case of solution-phase graphene, bottom-up approaches such as dielectrophoretic trapping can achieve similar ultralarge-scale integration densities [2.219].

Photonics and Optoelectronics

Graphene enjoys broadband absorption of light, and therefore does not suffer from the long-wavelength limit of semiconductors, which become transparent at incident energies smaller than their bandgap. As a result, graphene-based photodetectors have been demonstrated to work over a much broader wavelength range. The photoresponse does not degrade for optical intensity modulations up to 40 GHz, with ultrafast response due to the high carrier mobility in graphene [2.220]. Graphene can also be used as the nonlinear saturable absorber in mode-locking for ultrafast laser systems, which turns a continuous wave into a train of ultrafast optical pulses [2.221,222]. Graphene dispersions have been used as wideband optical limiters covering the visible and infrared regions of the spectrum [2.223].

Conclusions and Outlook

The field of graphene research is still very much in its early stages, with a majority of researchers devoted to exploring the fundamental properties of graphene. Not only is graphene a new material; it is also quite literally a new dimension of possibilities. A lot of mystery still surrounds this exciting new material, and often one finds that theoretical predictions are well ahead of experimental data in an emerging field such as this. Exciting physics that only occurs in two dimensions and that was previously inaccessible in experiments is now being sought, and new results are published regularly. Now that graphene has laid to rest the question of whether two-dimensional materials can exist in a stable self-supported form, researchers have started the hunt for other such 2-D materials. Boron nitride is one of the candidates to attract significant attention, particularly for its potential in combination with graphene.

Only recently, applications of the extraordinary properties of graphene have been experimentally demonstrated, and a still greater number of potential applications are still on the drawing board. In fact, only recently has bulk production of graphene in sheet or solution form been achieved, but the economies of scale are still unfavorable for mass application. The commercial prospects of graphene remain unexplored, but it is hoped that, in the near future, the substantial research and investment into graphene will be vindicated. However, for a scientist motivated by the quest for new knowledge and understanding, graphene continues to reap rich rewards, as evidenced by the numerous results included here that were only published for the very first time during the duration of writing this chapter.

Lastly, it should be noted that graphene is a rapidly evolving field, and since the writing of this chapter, a large number of papers have been published covering every aspect discussed here. In many cases, these subsequent publications have added new knowledge about graphene, or provided better or even a different understanding of known phenomena. Consequently, the information compiled in this chapter should serve as a starting point for the reader to further investigate the properties, characterization and applications of graphene by referring to the latest publications.

Abbreviations

0-D:: zero-dimensional
1-D:: one-dimensional
2-D:: two-dimensional
3-D:: three-dimensional
AFM:: atomic force microscopy
ARPES:: angle-resolved photoemission spectroscopy
Ab:: antibody
CMOS:: complementary metal–oxide–semiconductor
CNT:: carbon nanotube
CPP:: conduction perpendicular to plane
CVD:: chemical vapor deposition
DC:: direct current
DCE:: 1,2-dichloroethane
DGU:: density-gradient ultracentrifugation
DMA:: dimethylamide
DMF:: dimethylformamide
DNA:: deoxyribonucleic acid
EFM:: electrostatic force microscopy
FET:: field-effect transistor
FLG:: few-layer graphene
GNR:: graphene nanoribbon
GO:: graphene oxide
HOPG:: highly oriented pyrolytic graphite
ITO:: indium tin oxide
LBL:: layer-by-layer
LEED:: low energy electron diffraction
ML:: monolayer
NMP:: N-methyl-pyrrolidone
P3HT:: poly(3-hexylthiophene)
P3OT:: poly(3-octylthiophene)
PAH:: polycyclic aromatic hydrocarbon
PDLC:: polymer-dispersed liquid-crystal
PDMS:: polydimethylsiloxane
PET:: polyethylene terephthalate
PMMA:: poly-methyl methacrylate
PmPV:: poly(m-phenylenevinylene-co-2,5-dioctoxy-p-phenylenevinylene)
QD:: quantum dot
QHE:: quantum Hall effect
RGO:: reduced graphene oxide
SDS:: sodium dodecyl sulfate
SEM:: scanning electron microscopy
SGS:: spaced superconducting electrode
STM:: scanning tunneling microscopy
STS:: scanning tunneling spectroscopy
SWNT:: single-walled nanotube
ShdH:: Shubnikov–de Haas
TEM:: transmission electron microscopy
TEP:: thermoelectric power
UHV:: ultrahigh vacuum
fcc:: face-centered cubic
vdW:: van der Waals

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Aravind Vijayaraghavan

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Vijayaraghavan, A. (2013). Graphene – Properties and Characterization. In: Vajtai, R. (eds) Springer Handbook of Nanomaterials. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20595-8_2

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