Graphene's potential in materials science and engineering

Abstract

Materials serve as the basis of societal development and the material of choice of a given era is often a defining point. Everything we see and use in our daily life is made from materials such as metals, polymers, ceramics, semiconductors and composites. Materials science involves the study of the structure, properties and behavior of all materials, aiming to establish the basis and fundamentals for every modern technology. Things that were considered impossible have been made possible through the integrated approach of “needs driven” and “discovery driven” research. One such approach resulted in a breakthrough with the discovery of graphene, which was considered practically impossible. Graphene is the simplest and the strongest material ever found, and it has demonstrated its potential in multifarious fields; moreover, graphene has consolidated itself as an invaluable material that can enhance or overhaul the existing paradigm in so many applications. This work is a consolidated review about exotic properties, various fabrication approaches, characterization techniques and promising applications of graphene.

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1. Introduction

The term “graphene”, which takes its roots from “graphite” and “alkene”, was first coined to describe the single 2D sheets of graphite, as one of the constituents of graphite intercalation compounds.¹ According to the definition of IUPAC, graphene can be defined as a single carbon layer of the graphite structure, the nature of which can be described analogous to a polycyclic aromatic hydrocarbon of quasi infinite size, and the term should be used only when the reactions, structural relations or other properties of individual layers are discussed.² Simply put in a layman's words, it is a thin, two-dimensional sheet of sp²-bonded carbon, just an atom thick, densely packed into a hexagonal benzene ring-like structure, which makes it a building block for carbon-based structures of all other dimensionalities.

The monolayer graphene is composed exclusively of six membered rings; however, with the structural defects, it has five- or seven-membered rings or a combination of both, which makes it appear skewed or bent from its flat surface. The difference between the two defects is that the pentagonal defect occupies lesser space and causes the structure to roll into a cone, whereas the heptagonal conformation needs more space and yields a saddle-like distortion Note that a combination of these results in the formation of fullerene.³ Graphene can be righteously called as the mother of all other graphitic forms since it can be stacked one over the other to make 3D graphite, or rolled into sheets of 2D carbon nanotubes, or wrapped up to form 0D fullerenes (Buckyballs or cage molecules) and this has been shown in Fig. 1.

Fig. 1 Graphene – the source of graphitic nanomaterials of 0D, 1D and 3D dimensions. Reprinted with permission from ref. 12. Copyright 2007, Nature Publishing Group.

2. Exotic properties

Graphene is the first truly available two-dimensional material stable at room temperature, a feat long thought to be impossible^4–7 because of the thermal fluctuations in low-dimensional crystal lattices that result in displacement of atoms such that they become comparable to the interatomic distances at any finite temperature. The stability of the monolayer graphene can be attributed to the ripples⁸ or corrugations observed at the microscopic level. These imperfections prevent the surface from getting rolled into tubes owing to the thermodynamic stability⁹ and also to suppress thermal vibrations,⁸ which offers stability for the planar dimensioned material. Graphene is also transparent, chemically inert and crystalline under ambient conditions. It is stronger and stiffer than diamond, but still as flexible as rubber, stretched by a quarter of its length. It has the largest known surface area to weight ratio. The strongest bond in nature, the C–C bond covalently locks these atoms in place, giving them remarkable mechanical properties.^8,10,11

2.1 Dirac fermions

Normally, the electronic properties of materials are described by the Schrödinger equation; however, the charge carriers in graphene strongly resemble the relativistic particles. Moreover, the interaction between the electrons and the 2D honeycomb lattice of graphene makes the electrons moving in it to behave as if they are massless. Because of this interaction and the symmetric nature of the honeycomb lattice, the electrons are governed by a more easier model that uses the nearest neighbour, tight binding approach, i.e., Dirac's equation,¹² for describing relativistic fermions (with spin, s = 1/2). However the speed of light that is used in this equation is replaced by the Fermi velocity, which is nearly 10⁻⁶ m s⁻¹. Hence the solution of Dirac's equation gives a linear dispersion relation for the fermions. As a result, we can deduce that the fermions could be considered massless particles (zero effective mass) inside graphene.

2.2 Berry's phase

The linear low energy dispersion equation can be given by a spinor wave function, where σ is the pseudo-spin indicating the sub lattices A and B, which is parallel to the momentum of electrons and anti-parallel for holes. The projection of the pseudo-spin onto the direction of motion gives rise to a new internal degree of freedom, known as chirality. The origin of chirality can also be explained based on the Berry phase concept. When a quasiparticle (electron or hole) encircles a closed contour in the momentum space, the wave function of a quasiparticle gains a phase shift known as “Berry's Phase”. This phase shift occurs due to the rotation of the pseudo-spin, when a quasiparticle repetitively moves between various carbon sub lattices (A and B for single layer graphene; A1 and B2 for bi-layer graphene and so on).

2.3 Zero effective mass

The model as presented in Fig. 2 gives a Dirac cone-like spectrum of quasiparticles.¹³ This peculiar electronic structure is what accounts for the unique properties of graphene. The Fermi surface of graphene is characterized by six double cones. In undoped graphene, the Fermi level is located at the points connecting the valence and conduction bands. At the Fermi level, the density of states is zero. In other words, no states can be occupied at that corresponding level, which indicates that the electrical conductivity is pretty low. However, the conductivity can be improved by changing the Fermi level using an electric field in such a way that graphene becomes n-doped (with electrons) or p-doped (with holes) depending on the nature of polarity of the applied field. The electron dispersion relation becomes linear and the electrons behave as if they have zero effective mass. Hence, the electrical conductivity is unparalleled at even room temperatures (greater than silver, which is the least resistive metallic material). Moreover, bi-layer graphene has a tuneable band gap and hence by using an electric field, it can be changed from a conductor to a semi-conductor.

Fig. 2 Dirac cone arrangement (electronic band structure) in real space and in k-space. Reprinted with permission from ref. 13. Copyright 2012, IOP Publishing.

2.4 Quantum Hall effect

The Hall effect arises when a magnetic field is applied perpendicular to an electric field, leading to the charges experiencing magnetic Lorentz force and accumulation at one end of the conductor. An asymmetric distribution of charge carriers over the surface occurs because of the equally opposite charged material deflection to the opposite side. This separation between the charges establishes yet another electric field that prevents further build-up of charge. As long as charges flow, there exists a steady electric potential, and the Hall voltage and the magnetic field strength determine the resistivity of the conductor. The quantum Hall effect is a quantum phenomenon of the Hall effect occurring at a macroscopic scale. It is exclusive to two-dimensional materials with quantized values of conductivity and has elucidated various key aspects of quantum physics. The limitation is that it can be observed only in large magnetic fields and at very low temperatures (nearly 1 K). Fortunately, graphene exhibits this phenomenon even at room temperature. Bi-layer graphene agrees with the standard Hall effect and exhibits the integer Hall effect, whereas the single layer graphene has a shift of 1/2 and falls under the fractional Hall effect.

The valence and conductance band of graphene meets at the Dirac point (Fig. 3(b)), whereas that of conventional materials has a considerable band gap (Fig. 3(a)). Moreover, the recent ARPES studies of undoped graphene have demonstrated that there is an inward curvature (Fig. 3(c)), indicating electronic interactions occurring at increasingly longer range and leading to greater electron velocities. This electronic structure of graphene not only bridges the gap between the valence band and the conduction band, but also the gap between condensed matter physics and quantum electrodynamics.

Fig. 3 The energy bands of two-dimensional graphene (a) are smooth-sided cones, which meet at the Dirac point. The band structure of a conventional three-dimensional material (b) is parabolic with a band gap between the lower-energy valence band and the higher-energy conduction band. The ARPES spectrum of undoped graphene (c) exhibiting a distinct inward curvature.

2.5 Zitterbewegung

The electrons move effectively close at nearly 300 times lesser than the speed of light under vacuum allowing their relativistic effects to be observed without the use of particle accelerators. For instance, in quantum electrodynamics (QED), the Zitterbewegung (the oscillatory motions—helical or circular—of the relativistic particles) arises due to the interference between particle and anti-particle states (positive and negative energy states). This interference produces an effect of fluctuation of the position of electrons at the speed of light. Generally, this oscillatory motion is too fast to be spotted; however, in graphene, the Compton wavelength of the Dirac fermions, which is of the order of one nanometer, enables us to see this effect under a high resolution microscope.

According to classical physics, the rapid motion of the relativistic particles can also be attributed to the behaviour of an electron in the presence of a potential created due to the presence of disorders in a crystal. The oscillating nature is the reason for the conductivity at zero temperature and zero chemical potential, in other words, the Zitterbewegung is similar to the intrinsic defects, which cause non-zero minimal conductivity in crystals without defects. This motion is also responsible for the particle spin and magnetic moment.

2.6 Klein paradox

Another peculiar property of graphene is that it exhibits the “Klein paradox” effect, whereby the relativistic electrons are able to pass through a very large potential barrier. Moreover, the transmission of the quantum particles through the barrier is sensitive to the barrier height. If the barrier heights are different for various spin orientations (magnetic gates), one can produce spin-polarized effects, which allows one to manipulate the electron spin (Fig. 4). This tunnelling effect has opened up a possibility to study about the exotic but normally inaccessible relativistic, QED effects. For instance, this unimpeded penetration of relativistic particles through high, wide barriers predicts the pair production phenomenon, which would normally require super-heavy nuclei or black holes.

Fig. 4 Klein paradox effect.

2.7 Atomic structure

Graphene consists of sp²-bonded hybridised carbon atoms consisting of one “s” orbital and two “p” orbitals with a bond length of 1.42 Ǻ. This type of hybridisation makes it possess a trigonal planar structure. The s, p_x, and p_y orbitals form σ-bonds with the nearest neighbouring carbon atoms. In general, the σ-bonds are the ones that determine the strength of a lattice structure, which is robust. Since the σ bands in graphene are completely filled, they form a deep valence band; however, the p_z state is perpendicular to the planar structure and it laterally overlaps with the orbitals of the neighbouring carbon atoms, resulting in a π-bond. Since each p-orbital has an excess electron, the band hence formed is half-filled.

2.8 Other peculiar behaviours

The basic properties of graphene are summarized in Table 1. In terms of high mobility semiconductors, graphene ranks the highest with a mobility of about 200 000 cm² V⁻¹ s⁻¹, compared to silicon with 1400 cm² V⁻¹ s⁻¹ and indium antimonide with 77 000 cm² V⁻¹ s⁻¹, the highest mobility conventional semiconductor ever known. The very high mobility facilitates graphene to be employed in transistors, and chemical and bio-chemical sensing applications.¹⁴ It can carry large current densities up to 10⁸ A cm⁻². Being a stable semi-metal with a tiny overlap between valence and conductance bands under ambient conditions, they exhibit a strong ambipolar electric field effect,¹⁵ allowing the control of both positive and negative charge carriers with concentrations equivalent to 10¹³ cm⁻². It is quite interesting that the composites when reinforced with graphene, perform better in terms of strength, stiffness and failure resistance when compared to other nano-materials like carbon nanotubes, which might be a key to the next era of nano-composite materials.^16–18

Table 1 Properties of graphene: at a glance

Properties	Graphene	Carbon nanotubes
Young's modulus	∼1 TPa (ref. 125)	∼1 TPa (SWNT)^247
		∼1.28 TPa (MWNT)^248
Fracture strength	130 GPa (ref. 125)	∼30 GPa (ref. 247)
Thermal conductivity	∼5000 W m^−1 K^−1 (ref. 137)	∼2000–7000 W m^−1 K^−1 (SWNT)^249−251
		>3000 W m^−1 K^−1 (MWNT)^252
Thermal resistance (interface)	∼4 × 10^−8 K m^2 W^−1 (rGr–SiO2)^253	1.72 × 10^−8 K m^2 W^−1 (rCNT–SiO2)^259
Specific surface area	2630 m^2 g^−1 (ref. 215)	15–2240 m^2 g^−1 (ref. 260 and 261)
Optical transmittance	∼97.7% (ref. 103)	∼90–97% (ref. 262)
Sheet resistance	1.3 × 10^4–5.1 × 10^4 Ω sq^−1 (ref. 103)	200–500 Ω sq^−1 (ref. 262)
Phase coherence length	3–5 μm (ref. 254)	150 Å (ref. 263)
Spin R	1.5–2 μm (ref. 190)	Over tens of μm (ref. 264)
Elaxation length	15 000 cm^2 V^−1 s^−1 (ref. 15)	10 000 cm^2 V^−1 s^−1 (ref. 265)
Mobility (typical)	200 000 cm^2 V^−1 s^−1 (ref. 255)	100 000 cm^2 V^−1 s^−1 (ref. 266)
Mobility (intrinsic)	10^8 A cm^−2 (ref. 256 and 257)	∼4 × 10^9 A cm^−2 (ref. 267)
Current density	c/300 = 1 000 000 ms^−1 (ref. 258)	8.1 × 10^5 ms^−1 (ref. 268)
Fermi velocity	300–500 nm (ref. 258)	0.01–2.2 μm (as produced CNTs), 0.2–13 μm (purified CNTs)
Mean free path (ballistic electron behaviour)

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3. Fabrication methods and approaches

3.1 Conventional approaches

To understand the trajectory of the research undertaken with respect to graphene, it is a pre-requisite to know about the graphite oxide (GO), graphene intercalation compounds (GIC) and reduced graphene oxide (RGO) since graphene has been synthesised by manipulating either of these materials. GICs are formed by the insertion of atomic or molecular layers of a different chemical species called the intercalant between layers in a graphite host material. Graphite oxide is obtained by the strong oxidation of graphite with compounds like carbon, oxygen and hydrogen in variable ratios or by exfoliation of graphite powders. Graphene oxide is a monolayer of the graphite oxide, usually obtained by exfoliating graphite oxide (GO).

Since time immemorial, preparation of the mono layer graphite has been a holy grail of material science. The quest for the wonder material dates back to the early 19^th century when a network of interwoven graphite layers with the intercalants was reported to be present in the GICs and a scope for widening the interlaminar spacing was discovered.¹⁹ On the verge of finding the structure of graphite, the research was taken to the next phase with the crystalline lamellar structure of graphite being brought to the limelight and confirmed using X-ray spectra. A distinct line of demarcation was drawn between the graphite and amorphous carbon by concluding that the former varies from the latter by its greater degree of sub-divisions, the lamellae, and the experiments were brought in the context of the chemical oxidation results.²⁰

By making chemical modifications in the previous research studies, the successive research studies were able to produce not only the intercalation compounds (GICs)^21–23 but also, graphite oxide²⁴ by chemical oxidation; however, these were only the stepping stones for the delamination of the graphite to its integral layers.

Then, another group was able to make freely suspended platelets of reduced graphene oxide. The extremely fine lamellar carbon thus produced was obtained by either the deflagration of graphite oxide upon heating or reduction of graphite oxide in alkaline suspension.²⁵ The presence of monolayer graphite, otherwise called graphene, was confirmed by the LEED ring patterns developed while heating platinum under ultra-high vacuum.^26,27

Further advancements were carried out on the analysis of the graphene growth over the metals through the investigations of the surface coverage of carbon over temperature. These observations rendered a common conclusion that while heating to higher temperatures, the carbon dissolved in the metal alloys tends to undergo a phase separation as single and multiple layers of carbon over the metal surfaces, which confirmed the previous renditions by LEED and Auger electron spectroscopy.^28–30

Then, experimentations were carried out on epitaxial growth of silicon by sublimation of an insulating substrate SiC and a monolayer of carbon, i.e., graphene, was obtained by the electrical isolation. The sample was then subjected to LEED and Auger spectroscopy and successful synthesis of graphene on SiC was achieved. The process was explained by the graphitisation mechanism of Badami.^31,32 Similarly, numerous studies have been carried out in the field of isolation of atomically thin graphene films over materials like lanthanum hexaboride (LaB₆),³³ nickel,³⁴ iridium,³⁵ rhenium,³⁶ platinum,³⁷ tantalum carbide,³⁸ and titanium carbide.³⁹

In addition to these chemical approaches, a unique yet simpler micromechanical approach was put forth to tailor the highly oriented pyrolytic graphite (HOPG) into uniformly spaced, small graphite islands, which was again an effort towards creating thin layers of graphite.⁴⁰ Moreover, there was an exclusive review encompassing the prediction and conception of graphene; however, multiple lamellae were not completely exfoliated into the corresponding monolayers of graphene previously. Therefore, this approach was further honed and the task of obtaining pristine graphene layers was successfully accomplished by previous studies.^15,41–43 Despite all these approaches for graphene film synthesis in the research lab, preparing large area, defect-free graphene for commercial applications in real industry, remains the biggest challenge for the scientists due to the difficulty in the scale up and reproducibility.

Although the invention of pencil shed light on the presence of stacked layers of graphene building graphite, which are weakly coupled by van der Waals forces, it took nearly 440 years to isolate and spot it. This delay in time was due to the past thought that a material cannot be stable in its two dimensional form. Also, it was difficult to pinpoint how many layers the graphene sample was comprised of and no experimental tools were available to determine exactly the layers of a tiniest flake of just an atom thick. With the aid of an optical instrument, the optical effect created over the SiO₂ substrate by graphite can clearly be viewed through an optical microscope, resulting in the successful spotting of graphite. It took a long journey to prove and visualize the existence of 2D graphene. In this review, we shall discuss the fabrication methods first and then move on to the characterization methods used to analyze the fabricated graphene samples.

3.2 Novel approaches

3.2.1 Top-down approach. The fabrication of graphene involves two basic approaches: a top-down approach (large scale exfoliation) and a bottom-up approach (large scale synthesis). The top-down approach is the one in which the individual layers are peeled off or separated from the host molecule. This approach has been studied extensively by the researchers previously: preparation of graphene from the graphene intercalation compounds, graphene oxide or graphite oxide (discussed earlier), which includes chemical exfoliation. This follows a sequential process of oxidation of graphite; exfoliation of graphite oxide and reduction of the graphene oxide thus obtained;^18,44–48 liquid phase exfoliation, i.e., exfoliation of graphitic materials in chemical solvents,^49,50 preparation of precise graphene nanoribbons by unzipping the carbon nanotubes (Fig. 5),^51–55 which are considered the rolled sheet of graphene longitudinally; and the popular micro-mechanical exfoliation of graphite compounds like highly ordered pyrolytic graphene using a scotch tape, which results in graphene formation.¹⁵

Fig. 5 Illustration of unzipping of CNTs to form graphene nanoribbons. Reprinted with permission from ref. 55. Copyright 2010, Elsevier.

Mechanical exfoliation when compared with liquid phase exfoliation provides a single layer or few layers of graphene with much higher quality, although the quantity will be considerably lower. The concept of mechanical exfoliation was further refined and highly ordered patterns of graphene were developed by stamping and nanoimprinting, which offers better control and scalability than the conventional exfoliation process. In this method, a stamp is pressed onto the graphite substrates to cleave the graphene islands, and then the stamp with the cleavages of graphene is imprinted onto the device-ready substrates. The stamps used to imprint on the graphite substances are Si/SiO₂ pillars prepared by patterned plasma etching,⁵⁶ or gold film stamp,⁵⁷ or PDMS,⁵⁸ or graphite.⁵⁸ A typical mechanical exfoliation, stamping and nanoimprinting process is illustrated in Fig. 6.

Fig. 6 Exfoliation of graphite and attachment of thin graphene flakes on the Si/SiO₂ substrate. Reprinted with permission from ref. 15. Copyright 2004, American Association for the Advancement of Science.

Moreover, some more variations have been proposed for these exfoliation methods like the extraction of single-layered graphene crystallites by rubbing a layered crystal against another surface (like drawing on a blackboard using chalk),⁴² electric field assisted exfoliation,^59,60 exfoliation of oxidised graphite with the use of strong acids by rapid thermal expansion⁶¹ or by ultrasonic dispersion.⁶² Although this top-down approach is very simple, it has a major disadvantage that it does not offer any control over the process. Hence, it is not possible to get the graphene of the desired quality or with a particular number of layers.

3.2.2 Bottom-up approach. The bottom-up approach, on the contrary, is based on the deposition of the material from the scratch and it is conducted in a controlled environment with controlled parameters like temperature, pressure, and flow rate. Hence, it is possible to obtain a defect-free graphene with the desired number of layers that can be employed in utilizable applications. The techniques that use this approach are epitaxial growth,⁴¹ high temperature annealing of single crystal SiC,^63–65 molecular beam deposition⁶⁶ under ultra-high vacuum (i.e., evaporation of atomic carbon and subsequent annealing, solvothermal synthesis⁶⁷), high temperature thermo-chemical decomposition of a solvothermal or hydrothermal product, and Chemical Vapour Deposition (CVD).^29,68–72

The epitaxial growth and CVD are more or less the same, except for the type of growth of materials over the substrate; i.e., for the epitaxy, the material is deposited such that the material takes up the same crystalline form as that of the substrate onto which it is deposited. In other words, the layer formed from the epitaxy is only another extension of the crystalline substrate. However, for the CVD, the material can be deposited even on single layer crystals and can be independent of the substrate. Hence, chemical vapour deposition has its edge over the other synthesis methods. Note that the synthesis of high quality graphene has remained a subject of extensive research for over 30 years. Moreover, many refined CVD methods^73–76 have recently been proposed after numerous research studies having been carried out on the fabrication of thin layer graphite films. However, the graphene formed from chemical vapor deposition requires post processing, i.e., transferring of the films to other substrates^73,74,77 to make it device-compatible.

CVD is the decomposition of chemical precursors (in vapour state) over a heated substrate to yield a non-volatile solid thin film. Based on the reaction conditions and the chemical precursors used, the films may be epitaxial, polycrystalline or amorphous films. CVD enables us to have deliverables with high throughput, better purity, high directionality and also three-dimensional structures with large aspect ratios, which make it attractive for large scale synthesis of thin films. However, the quality of the films depends on the deposition variables like temperature, pressure, flow rate, precursor gases concentration, duration of heating, and cooling rate.

The graphene formation by CVD basically involves two major steps: pyrolysis of precursor chemicals to form carbon and settling of the dissociated carbon atoms to form a graphenic structure. However, to prevent the slightest possibility of clustering of carbon atoms (soot-like formation) onto the fabricated graphene, pyrolysis should be performed only on the substrate surface (heterogeneous decomposition). For heterogeneous decomposition to take place, transition metals are used as catalysts. The addition of catalysts also lowers the temperature range (from 2500 °C to around 1000 °C) and the energy consumption for achieving good quality graphene by reducing the energy barrier of the reaction. Based on the catalyst used, the graphenization mechanism differs as surface deposition (for Cu^78–81) and surface segregation (for Ni^73,74,77,82) as shown in Fig. 7.

Fig. 7 Graphenization mechanism for (a) Ni and (b) Cu. Reprinted with permission from ref. 81. Copyright 2009, American Chemical Society.

The kinetics of the CVD can further be detailed as:

-Pressurised gas lines supply the input reactant gases to the reaction chamber.

-Mass transport of reactant gases from the flow area to the substrate through the boundary layer (1).

-Adsorption of the precursor atoms on the surface of substrate due to heating (2).

-Chemical reaction on the surface (3).

-Diffusion of atoms on the substrate to the nucleation sites (grain boundaries).

-Removal of the left-over gases and sludge resulting from the reactions (4).

-Mass transport of the exhaust gases to the flow area (5).

A typical illustration of kinetics of the CVD process is presented in Fig. 8.

Fig. 8 Kinetics of the CVD process.

Types of CVD processes used. The three commonly used CVD processes for fabricating graphene are: ambient pressure CVD (APCVD),^{73,74,82–85} low pressure CVD (LPCVD),^78,86 and plasma-enhanced CVD (PECVD).^87–91 The working principle is the same for all the processes, but each process differs by a small streak of line by their working conditions. The comparisons of these three CVD process are presented in Table 2. APCVD systems, as their name suggest, are operated under normal atmospheric pressure conditions. They allow for high throughput and even continuous operation, while LPCVD operates at low pressures and it yields superior conformal step coverage and better film homogeneity. Furthermore, PECVD lowers the temperature to about 250 °C and hence it is used when lower temperatures are required. The deposition time is shorter (<5 min) but the film quality is often poor.

Table 2 Comparison of CVD processes

Methods	APCVD	LPCVD	PECVD
Temperature (°C)	800–1200	500–900	600–700
Throughput	High	High	Low
Step coverage	Poor	Conformal	Poor
Film properties	Good	Excellent	Poor

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Variables affecting deposition. The three factors that affect the growth rate of the film are the feed rate of the inlet gases, the degree of diffusion and the surface kinetics. Note that the deposition rate of the film and the quality depends on the deposition variables (i.e., temperature, pressure, flow rate, cooling rate, and concentration of the gases involved). In general, the deposition rate varies directly with temperature and follows the Arrhenius equation, R = A exp(−E_a/kT), where R is the deposition rate, E_a is the activation energy, T is the temperature (K), A is the frequency factor, and k is Boltzmann's constant (1.381 × 10⁻²³ J K⁻¹).

Table 3 exhibited the comparisons of various graphene fabrication methods. At the high temperatures the rate of deposition is limited by the mass transport, which indicates that the rate of surface reaction is faster than the rate at which inlet gases are moved to the surface. In certain cases, the ratio of partial pressure of each of the reactants also plays a crucial role. The concentration level of the carbon supplying precursor such as methane and the cooling rate also affect the deposition rate. For instance, too low a concentration or too high a cooling rate will hinder the graphene growth. Now with the deposition of graphene over the substrate, we need to confirm whether what we have, is graphene or not, for which we have a lot of characterization techniques.

Table 3 Comparison of fabrication methods of graphene

Methods	Mechanism	No. of layers	Precursors used	Nature of graphene obtained	Electronic quality of layers	Size of layers	Through-put
Mechanical exfoliation	Peeling layers off using scotch tape	SLG, FLG	Graphite	Pristine	High	10 μm	Low
Chemical exfoliation	Decomposition of graphite based compounds, reduction and subsequent exfoliation	SLG, FLG	Graphite oxide (or) graphene oxide obtained by processing GICs	Chemically modified graphene (CMG)	Low	Few 100 nm	High
Liquid phase exfoliation	Exposing graphite or GO to solvents and applying sonification	SLG, FLG	Graphite (or) graphite oxide	Pristine	High	Tens of μm to few nm	High
Epitaxial growth	Thermal decomposition of hydrocarbons on top of crystals like SiC or Ru	SLG, FLG	SiC or Ru	Pristine	High	>50 μm	Low
Chemical vapor deposition	Carbon segregation or precipitation over transition metals	SLG, FLG	Polycrystalline Ni films, copper foils, and other transition metals	Pristine	High	>100 μm (can be in wafer sizes)	Low
Solvo-thermal synthesis	Pyrolysis and filtering of a solvothermal product	SLG, FLG	Solvothermal product (e.g. Na + C2H5OH)	CMG	High	Tens of μm to few nm	High
Unzipping carbon nanotubes	Longitudinal unzipping of carbon nanotubes	SLG, FLG	Multi-walled carbon nanotubes	CMG	Low	Sub-10 nm	High

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4. Characterization techniques

Graphene is one of the thinnest materials in the world with its dimension ranging from the size of nanometers to tens of micrometers, and the prevalent mode of characterization is the microscope imaging techniques. The aim is to find the number of layers, single layers in particular, and to position and locate the layers over the given substrate to find their respective sizes.

The characterization techniques can be categorised into two groups based on the application they are used for, i.e., structural and elemental analysis (imaging or analysis). The structural analysis is used to image the structure, “spot” it, and deduce important information pertaining to the functionality such as number of layers, defects, chemical impurities, crystallite size, and so on. The elemental analysis of graphene gives us a storehouse of both qualitative (the elemental structure) and quantitative (how much of each element) information. The techniques engaged in the structural and elemental analysis are optical microscopy, scanning probe microscopy, Raman spectroscopy, low energy electron diffraction^{26,27,37,92–100} (LEED), low energy electron microscopy^65,101 (LEEM), and reflective high energy electron diffraction¹⁰² (RHEED). The summary of graphene characterization technologies, including mechanism, speed, substrate requirements and the types of analysis, are presented in Table 6.

4.1 Optical microscopy

A simple, sensitive, non-destructive and a fast technique among the many existing techniques for imaging material is probably optical microscopy. Identifying a single layer of graphene in the sample is equivalent to finding a needle in a haystack, which makes the optical microscope observation tedious. The refractory index or the optical density of the mechanically exfoliated graphene is found to be 2.3% per single layer in the visible range.^103,104 Under the bright field transmitted illumination, the optical images of graphene layers can generally be seen.

Moreover, it has been found that the incorporation of a dielectric substrate between the material and a reflective surface enhances the visibility of monolayers through the optical microscope using fluorescence interference-contrast (colour change).¹⁰⁵ This visibility phenomenon is basically because of the contrast that occurs from the interference of the reflected optical radiations at the interfaces of air–graphene, graphene–dielectric (e.g. graphene–SiO₂), dielectric–substrate (e.g. SiO₂–Si).¹⁰⁶ SiO₂ and Si₃N₄ are the widely used dielectric substrates over silicon wafers for enhancing the contrast of graphene layers.¹⁰⁷ Moreover, it has been reported that a triple-layered system gave better contrast compared to a double-layered system. In other words, the insertion of a thin dielectric substrate between the graphene and the substrate yielded better results over a single bulk dielectric substrate.¹⁰⁸ However, due to the deposition of graphene over substrates, there is a possibility of the absorption of optical radiation by the free atoms in gaseous state over a considerable wavelength range, named as broadband absorption by free molecular species. This makes it difficult to identify the graphene layers over the substrate. To enhance the clarity of the optical imaging, the major factors affecting the contrast have been analysed, and they are found to be the type of the light source, intensity of the light source, wavelength of the light source, thickness of the specimen (graphene), dielectric material, thickness of the dielectric film, substrate used with the dielectric film, angle of incidence at the air–graphene interface, angle of incidence at the graphene–dielectric interface and optical absorbance of the specimen and the substrate.^107–109 It was also proven that the visibility of graphene depends on the thickness of the dielectric substrate used and the wavelength of light. For a particular thickness, even a monolayer offers a feeble yet sufficient contrast to locate the graphene crystallites from the graphitic sheets. Notably, even a 5% deviation in thickness of the SiO₂ can make the graphene invisible.¹²

Various optical methods employing reflective lighting techniques based on interferometry,^{15,42,106,109–112} ellipsometry,^113,114 Rayleigh scattering,¹¹⁵ fluorescence quenching microscopy,^116,117 broadband spectrophotometry¹¹⁸ were proposed for better contrast optical imaging of graphene.

Interference techniques have been in use for over a century for the characterization of materials. By applying few modifications in the parameters, involving interferometry techniques, the contrast level and the resolution of the microscopy have been improved. This technique facilitates the visibility of graphene crystallites by utilising the phase contrast that occurs due to the small phase shifts in the light passing through the transparent graphene flakes that yield some colour changes in the optical image with respect to an empty wafer and the substrate of appropriate thickness.¹⁵

Ellipsometry, on the other hand, is yet another effective and non-destructive testing for the determination of optical constants and thicknesses of the thin films. In particular, imaging ellipsometry has proven its usefulness for the determination of such parameters.^114,119 Unlike interferometry, this method measures the change in the polarization state of the reflected light from the surface of the sample and it is very accurate, highly sensitive and reproducible even at low light levels. An elucidation showing the characterization using spectroscopic ellipsometry (a & b) and imaging ellipsometry (c & d) has been made in Fig. 9.

Fig. 9 (a) An optical image exposed to visible light, showing a multi-layer graphene (dark blue). (b) Spectroscopic ellipsometric scan of the map, in which white dots indicate the spectra that can be attributed to originate from graphene only. The shape enclosing the white dots also resembles the shape of the real flake. (Optical constants of graphene were measured by spectroscopic ellipsometry.) Reprinted with permission from ref. 113. Copyright 2010, AIP Publishing LLC. (c) Optical image and (d) imaging ellipsometric intensity image of a sample on SiO₂/Si showing regions with a graphene monolayer covering up to thin graphite. Numbers in (c) correspond to the layer numbers – Wurstba – Imaging ellipsometry of graphene. Reprinted with permission from ref. 114. Copyright 2010, AIP Publishing LLC.

Rayleigh imaging involves the basic elastic Rayleigh scattering of photons. The elastically scattered photons provide another very efficient and quick way (since they form the majority of the reflected photons) to identify single and multilayer specimens, and a direct way to measure their dielectric constants¹¹⁵ and the probing of size, shape, concentration and optical properties of nanoparticles.^120,121 Fluorescent quenching microscopy¹¹⁶ is a relatively new technique for the imaging of graphene and graphene-based sheets. Unlike other optical methods, which illuminate graphene and make them bright, this one utilizes the strong quenching effect of the fluorescent dyes, which when coated on graphene, upon excitation, could reveal the underlying graphene as dark sheets in a bright background as illustrated in Fig. 10. The advantages and disadvantages of optical microscopy are discussed in Table 4.

Fig. 10 Mechanically exfoliated graphene on a SiO₂/Si substrate taken by (a) AFM, (b) optical microscopy, (c) FQM using PVP/fluorescein. Reprinted with permission from ref. 116. Copyright 2009, American Chemical Society.

Table 4 Advantages and disadvantages of optical microscopy

Advantages	Disadvantages
Relatively simple to use	Limited resolution due to the fixed wavelength of light (400–700 nm for visible light)
Rapid identification and characterization of the optical response of thin sheets	Diffraction limits the spatial resolution by nearly half the wavelength of light
Magnifications ranging between 4× to 1000×	Depth of focus decreases with increasing magnification
Non-destructive technique	Requires dielectric coated substrates and optimized parameters for a high contrast image

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4.2 Scanning probe microscopy

Scanning probe microscopy (SPM) has facilitated the researchers for imaging material surfaces at nano-scale resolutions with relative ease. The accurate height measurements in nano-scale have in turn provided a direct probe of the number layers in graphene. The advantages and disadvantages of optical microscopy are summarized in Table 5.

Table 5 Advantages and disadvantages of scanning probe microscopy

Advantages	Disadvantages
Resolution not limited by diffraction, but by the size of probe-sample interaction volume; generally high resolution	Low throughput and costly and time consuming for examining large area samples
Accurate height measurements at the nano scale and resolution at the atomic scale, i.e., for counting the number of layers	Operating platform should be of low vibration and sample deposition should be done on low roughness surfaces
True 3-D surface maps possible	Small field of view, i.e., it requires large quantity of data to make it representative
Can operate in a variety of environments such as liquid, vacuum, variable temperature/RH	Images are produced in grayscale, which might exaggerate a specimen's actual shape or size

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Table 6 Characterization techniques: at a glance

Methods		Mechanism	Relative speed	Substrate requirements	Other requirements	Type of analysis
Optical microscopy	Interference	Interference contrast	Fast	Dielectric-coated Si	Optimized dielectric thickness and wavelength	Structural
	Ellipsometry	Change in polarization	Fast	Dielectric-coated Si	Optimized dielectric thickness and wavelength	Structural
	Broadband spectrophotometry	Frequency measurement of absorbed light	Fast	Complex substrates (bulk Si & SiO2, Ni, Co, Fe, etc.)	Optimized wavelength range or light incident angle	Structural
	Rayleigh imaging	Elastic light scattering	Fast	Anti-reflection-coated dielectric over Si	Monochromatic light/laser, optimised spacer thickness	Structural
	Fluorescence quenching microscopy	Quenching of fluorescent dyes	Fast	Dielectric-coated Si	Fluorescein/PVP-coated graphene	Structural
Scanning probe microscopy	Scanning tunnelling microscopy	Electron tunnelling, piezoelectric effect	Low scan speed	Conductive, smooth surface	Vacuum	Structural
	Atomic force microscopy	Force between sample & tip	Low scan speed	Smooth surface	Vibration-free environment	Structural
Electron microscopy	Scanning electron microscopy	Backscattered/secondary electrons	Medium scan speed	Conductive surface	Vacuum	Structural
	Transmission electron microscopy	Transmitted electrons	Slow	Surface transparent to electrons	Vacuum	Structural
	Low energy electron microscopy	Elastically scattered low energy electrons	Fast as no rastering needed	Conductive surface	Ultra high vacuum	Structural, elemental
	Low energy electron diffraction	Bombardment with collimated beam of low energy electrons	Slow if accurate results needed	Single crystal substrates	Vacuum	Structural, elemental
	Reflective high energy electron diffraction	Diffraction of high energy electrons	Fast	Single crystal, clean surface	Vacuum	Structural
	Auger electron microscopy	Auger electrons	Fast	Conductive/grounded	High vacuum	Elemental
Energy dispersive X-ray analysis (EDX) in SEM		Ejection of e^−, de-excitation	Slow	Conductive/compact	Moderate vacuum	Elemental
X-ray diffraction		Elastic scattering of X-rays	Fast	Fine powder, randomly distributed	X-rays	Structural
Spectroscopy techniques	Raman spectroscopy	Inelastic photon scattering	Fast	Low fluorescence	Laser	Structural
	Angle resolved photoemission spectroscopy	Photoelectric effect	Fast	Clean, atomically flat surfaces	Ultra-high vacuum	Structural- electronic
	X-ray photo electron spectroscopy	Irradiating with a beam of X-rays	Fast	Flat surface	X-rays, ultra high vacuum	Elemental
	UV photo electron spectroscopy	Ionizing using UV photons	Rapid	Clean, ordered surface	UV radiation source, ultra high vacuum	Elemental
	Ion scattering spectroscopy	Backscattered ions	Rapid	Conducting surface	Vacuum	Elemental
	Electron energy loss spectroscopy	Scattered inelastic electrons	Fast	Surface transparent to electrons	Thin samples	Elemental
	High-res electron energy loss spectroscopy	Scattered inelastic electrons	Slow	Flat, conducting surfaces	Ultra-high vacuum	Elemental
	Nuclear magnetic resonance spectroscopy	RF waves at different magnetic field strength	Fast	NMR-active materials	RF waves, magnetic field	Elemental

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4.2.1 Scanning tunnelling microscopy (STM). Scanning tunnelling microscopy is used when atomic scale resolution is needed.¹²² Images of graphitic materials with atomic resolution that are taken using STM¹²³ are shown in Fig. 11. The STM is based on the following principles: (1) tunnelling of electrons: generally, an object impinging an impenetrable barrier will not pass through. In contrast, objects with relatively negligible mass, such as the electrons, having wave-like characteristics permit such an event, referred to as tunnelling. The tunnelling current depends exponentially on the tip-surface distance, making it a sensitive measuring device. This effect helps us to “see” the surface. (2) Piezoelectric effect: this effect assists in a precise control of scanning of the material surface with the tip at sub-nanoscale levels. (3) Feedback control: this loop allows us to monitor the tunnelling current and to manipulate the positioning of the probe tip accordingly.

Fig. 11 Atomic resolution STM image of (a) single layer graphene (b) tri-layer graphene and (c) bi-layer graphene. The honeycomb structure of graphene is indicated by hexagons, showing equivalent atoms for a monolayer case and inequivalent atoms for the tri-layer case and part of the bi-layer case. Reprinted with permission from ref. 123. Copyright 2008, American Physical Society. Atomic and electronic structure of a few-layer graphene on SiC(0001) studied using scanning tunneling microscopy and spectroscopy. (d) High resolution STM image of a mesoscopic graphene sheet. (e) Atomic resolution STM Image of a graphite structure (zoomed portion shows the honeycomb lattice structure). Reprinted with permission from ref. 122. Copyright 2007, National Academy of Sciences, U.S.A.

4.2.2 Atomic force microscopy (AFM). Atomic force microscopy is used to measure the interaction force between the tip and the sample surface, which is eventually detected by a deflection of the cantilever holding the probe tip or by a change in the resonant frequency of the cantilever. This technique overcomes the major drawback of STM, i.e., its capability of imaging only the conducting and semi-conducting surfaces.

The common materials used for micro-fabrication of probe tips and cantilevers are Si or Si₃N₄. The force can be found using Hooke's law: F = −kx. It has been found that the attractive mode of AFM has a significant influence on the determination of the thickness of the graphene layers.¹²⁴ In addition to imaging and thickness detection, AFM is very useful for characterizing the physical properties of graphene, such as mechanical,¹²⁵ frictional, elastic,¹²⁶ electric and magnetic properties, as it can resolve the small forces involved in the deformation process.

Some variants of the AFM process that have also been employed in the characterization of graphene are as follows: force modulation microscopy for elastic properties; Kelvin probe microscopy for surface potential; electrostatic force microscopy for charge distribution; lateral force microscopy for frictional properties; scanning thermal microscopy for heat conductivity within the graphene film and heat transfer to the substrates lying beneath it; and ultrasonic force microscopy in which the cantilever beam is made infinitely rigid utilising the very high frequency ultrasonic vibrations, which in turn are used to find the elastic moduli of materials ranging from soft to hard. The vibrations are detected due to the non-linearity of the nanoscale contact of the tip and the sample; moreover, this mode has a unique feature called ultrasonic superlubricity (zero friction between the tip and the sample) that prevents the damage to the tip and the sample.

4.3 Raman spectroscopy

Raman spectroscopy is a form of vibrational spectroscopy similar to infrared (IR) spectroscopy. The difference lies in the fact that the Raman bands arise from the change in the polarizability, whereas the IR bands originate from a change in the dipole moment of the molecule. It is a powerful tool widely used for the imaging of graphene and graphene-based materials. It provides better insight into the behaviour of phonons and electrons inside the sample, which in turn provides versatile information about various parameters like crystallite size,¹²⁷ clustering of the sp² phase (which helps to deduce optical and electronic properties¹²⁸), doping,^129,130 crystal defects,¹³¹ disorders,^129,132,133 chemical impurities,¹³⁴ edge chirality and crystal orientation,¹³⁵ strain,¹³⁶ thermal conductivity¹³⁷ and most importantly, the number of graphene layers, stacking order and quality of the number of layers.^138–140

The Raman fingerprint region proves to be a very resourceful tool to analyse the graphene structure. While discussing about the bands in the spectrum, three bands are extensively used, namely, the G-band (at ∼1583 cm⁻¹), D-band (at ∼1350 cm⁻¹) and 2D-band (at ∼2680 cm⁻¹). There are other very small bands like the D′-band (at ∼1620 cm⁻¹) and D + G band (at ∼2947 cm⁻¹); however, they offer less significant details when compared to the previous ones. Let us have a closer look at each of the bands. Raman spectra for different number of layers for graphene is shown in the Fig. 12,¹⁴¹ in which the Raman spectra for various materials like graphite, single layer graphene (SLG), metallic and semiconducting carbon nanotubes, low and high sp³ amorphous carbons, and diamond have been demonstrated.

Fig. 12 Raman spectra of different layers of graphene. Reprinted with permission from ref. 141. Copyright 2011, IOP Publishing.

4.3.1 The G-band. The G-band is the primary mode in the graphene and graphite, which is due to the E_2g state phonon in the Γ-point in the Brillouin zone. This highly intense band arises from the stretching of the C–C bond, and it represents the planar configuration sp²-bonded carbon that forms the foundation of graphitic systems. The position of the band is quite independent of the excitation laser frequency unlike the other Raman modes of graphene.

A great deal of information can be extracted out of this band if we know the band position and its shape. The band position is highly sensitive to strains and doping, which can be used to probe the surface features of graphene, i.e., whether it is flat or not. Another common application is finding the graphene layer thickness with respect to the band position. The band position shifts to the lower energies as the layer thickness increases, which is a representation of the softening of bonds as layer thickness increases.

4.3.2 The D-band. The D-band is commonly known as the disorder band since it is caused by the disordered structure of graphene. This band occurs due to the interactions of the localised vibration modes to the extended phonon modes of graphene. This band generally does not occur explicitly in graphene or graphite. For this band to be activated, it needs to be a defect or a graphene edge. If its presence is significant, then that is a direct implication of the presence of defects in the specimen. In contrast, if the structure is perfect, there will be no D-peak. For this reason, this band is also referred to as the defect band.

The intensity of the D-band directly varies with the level of defects in the material. This band exhibits a dispersive behaviour, i.e., it possesses weak sub bands within itself. Various underlying modes can be enhanced by using excitation lasers. Here both the band position and the shape depend on the laser excitation frequency. Hence, it is to be ensured that the same excitation frequency is used for all the measurements while characterizing the D-band.

4.3.3 The 2D-band. Commonly referred to as the overtone of the D-band or the G′-band, this band is the second order incarnation of the D-band. All sp² hybridised carbon materials exhibit a very high intensity or a strong peak in the interval of this spectrum (2500 cm⁻¹–2800 cm⁻¹). It is a two phonon vibrational process and this mode does not need defects at its proximity to be activated, making it gain an edge over the D-band. This is used to determine the layer thickness like the G-band; however, this is not as simple as a band shift in the G-band. With the increase in layer thickness, not only is there a shifting, but also there is a considerable change in the shape of the band, which is attributed to the active components involved in the vibration.

For a single-layer graphene, there is only a single component in the spectrum, whereas for a bilayer graphene, four components are present in the 2D-band.¹⁴² It has a strong frequency dependence on the excitation laser energy; thus, the band position and the shape can vary significantly with various excitation lasers used. It is important that the same excitation frequency is used throughout the process; moreover, it should be noted that the 2D-band is sensitive to graphene folding, and this band along with the G-band forms the Raman signature of sp² materials. The Raman spectrum of the 2D band of graphene on Si/SiO₂ substrates as a number of layers changes from one to five, as illustrated in Fig. 13.

Fig. 13 Raman spectrum of the 2D band of graphene on Si/SiO₂ substrates as the number of layers changes from one to five. Reprinted with permission from ref. 142. Copyright 2007, AIP Publishing LLC.

4.4 Other techniques

The following passage explains some of the techniques used for the structural and elemental analysis of graphene and what information is extracted using those techniques.

(1) X-Ray photoelectron spectroscopy (XPS)⁶⁵ – measure elemental composition, empirical formula, chemical and electronic states of the particles in a material.

(2) Auger electron microscopy (AES)^28–30,143 – quantitative determination of elements and its atomic concentration on material surface, qualitative fingerprinting spectral analysis, depth profiling and interface analysis.

(3) Ultraviolet photoelectron spectroscopy (UPS)⁶⁹ – determination of molecular energy levels in the valence band using the kinetic energy spectra of emitted photoelectrons.

(4) Ion-scattering spectroscopy (ISS)¹⁴⁴ – determination of the structure and composition of a substance, addressing catalytic surfaces, thin film coatings, adhesion, as well as arrangement of surface atoms.

(5) Electron energy loss spectroscopy (EELS)⁷⁶ – measurement of atomic composition, chemical bonding, valence and conduction band electronic properties, surface properties, and element-specific pair distance distribution functions.

(6) High-resolution electron energy loss spectroscopy (HREELS)^145–153 – investigation of surface structure, catalysis, dispersion of surface phonons and the monitoring of epitaxial growth.

(7) Electron microscopy – for probing the surface features of materials using a surface imaging technique.

(8) Energy dispersive X-ray analysis (EDX) in SEM¹⁵⁴ – determining particle size, examination of surface morphology and characterization, i.e. structural analysis, defect and failure analysis.

(9) Nuclear magnetic resonance (NMR) spectroscopy⁴⁹ – determination of structures.

(10) Angle-resolved photo emission spectroscopy – tTo analyse the electronic structure of graphene, and using this method we can confirm the existence of massless Dirac fermions.^101,155,156

(11) Low energy electron microscopy^65,101 (LEEM) – investigation of surface crystallography.

(12) Low energy electron diffraction^{26,27,37,92–100} (LEED) – for investigating the crystallography of surfaces and overlayers or films adsorbed on surfaces.

(13) Reflective high energy electron diffraction¹⁰² (RHEED) – for probing the surface structures of solids.

5. Application possibilities

5.1 Electronic devices

Graphene is considered capable of outdating the Si-based electronics and form the post Si era of electronics due its superior transport properties. Various graphene nano-electronic devices have been fabricated,^10,157–159 and there has been a constant probing towards the application oriented fabrication ever since.

5.1.1 Transistors. Transistors made out of graphene have been reported to have a hole and electron mobility of about 3735 cm² V⁻¹ s⁻¹ and 795 cm² V⁻¹ s⁻¹ with the highest ever reported maximum drive current at room temperature⁵⁶ (1.7 mA μm⁻¹ at V_ds = 1 V) and an intrinsic cutoff frequency of up to 300 GHz.¹⁶⁰ Its potential incorporation into the radio frequency-based applications has called for a great interest in the fabrication of transistors using graphene.^161–165

5.1.2 Plasmonic device – terahertz plasmon oscillators^166,167. The simulation of an energy band of graphene with absorption and emission of plasmons is illustrated in Fig. 14. By inversely populating the graphene layers and by coupling the plasmons (a quantum of plasma oscillations – self-sustained collective oscillations of conduction electrons) with the interband electron–hole transitions in those layers, it is possible to facilitate the plasmons to experience very large gains through a stimulated emission process. The plasmon amplification with even a small excitation is considered to occur when the frequency of the exciting light field is in resonance with the Eigen frequency of the collective oscillation of electrons.

Fig. 14 Energy bands of graphene showing stimulated absorption of plasmons (left). Population inverted graphene bands showing stimulated emission of plasmons (right).

The concept of obtaining negative conductivity in graphene at terahertz frequencies, which necessitates population inversion through optical and electrical pumping, has been discussed extensively. The same concept has been extended to design plasmon oscillators, in which the graphene strips act as the plasmon cavity and the pumping assist in the electron–hole recombination. A schematic of a graphene terahertz oscillator under load is given in Fig. 15(a). Moreover, under negative impedance conditions with population inversion, the graphene strip can be used for terahertz amplifiers shown in Fig. 15(b).

Fig. 15 Plasmonic Devices. (a) Illustration of a graphene oscillator under load (left). (b) Illustration of a graphene terahertz amplifier. Reprinted with permission from ref. 167. Copyright 2009, IEEE.

5.1.3 Ultrafast lasers. Due to its non-linear and electro optical properties, graphene is used in the field of nano-photonics, particularly for ultra-fast lasers (nano to sub-picosecond pulses). In a laser optical cavity (an arrangement of mirrors), the mirror-like arrangement takes care of the light emission at well-defined wavelengths, which are known as modes. Each mode oscillates with a different phase in due course of time, and when these modes superimpose with each other, they form constructive and continuous laser waves.

Non-linear optical elements, which are called saturable absorbers, are selective laser absorbers that absorb only the laser with higher intensities, and damp the lower intensity laser waves. When all these modes with strong intensity oscillate in phase after undergoing many repeated circulations inside the cavity, the continuous wave output is converted into a train of short and intense (pulsed) waves. A wideband tuneability can be obtained when graphene is used as a saturable absorber due to its zero band gap and significant optical absorbance,¹⁶⁸ whereas the conventional, semiconductor saturable absorbing mirrors require band gap engineering for utilising them in ultra-fast lasers.

An example of the mode-locking laser using graphene has been illustrated in Fig. 16. Here, the graphene/PVA (polyvinyl alcohol is the host polymer)-based saturable absorber is slid and sandwiched between two fibre connectors. The gain medium used for this laser is Erbium-doped fibre (EDF), and the pumping is made possible through a diode laser (pump laser) by means of a wavelength division multiplier (WDM). To maintain a unidirectional operation, an isolator (ISO) is used, whereas to have an optimized mode-locking, a polarization controller (PC) is used. Graphene ultra-fast photonic devices¹⁶⁹ composed of graphene,^170–174 such as graphene–polymer nanocomposites^{169,171,174–177} or solution-processed graphene,^178–180 have been demonstrated.

Fig. 16 Graphene mode-locked fiber laser and mode-locker assembly. ISO, isolator; WDM, wavelength division multiplexer; PC, polarization controller; EDF, erbium-doped fiber. Reprinted with permission from ref. 174. Copyright 2010, American Chemical Society.

5.1.4 Spintronic device^181,182 – digital memory devices¹⁸³. The electronic devices that utilize the quantum spin of the electrons, instead of the conventional way of using electric charges to process information, are termed as spintronic devices. The recent experimental observations report magnetism in graphitic materials, which was considered unlikely in the carbon-based systems due to their lack of d or f electrons. This has led to a surge in the research of graphene-based novel spintronic devices, in which the graphene helps in integrating the nanoscale quantum properties with device environments, due to their particular combination of high 2D aspect ratios with unique conductivity properties, such as bipolar tunability of charge and high mobility along with the expected long spin coherence lifetimes and lengths.¹⁸¹

Moreover, the vacancies in graphene have been found to be acting as tiny magnets themselves since they have magnetic moment.¹⁸⁴ Various approaches have been tried, expecting to bring out spin current in graphene to make the material magnetically active. One idea is through spin splitting in monolayer graphene using the magnetic properties of graphene (the ferromagnetic proximity effect) and adiabatic quantum pumping.¹⁸² Another thought is shaping the graphene (e.g., a single-walled carbon nanotube of few nanometers in diameter) since the spin is strongly affected by their motion and the spin will be forced to move around the tube.¹⁸⁵ Other ideas include using graphene–magnet multilayers (graphene brought in contact with magnetic and non-magnetic layers)¹⁸⁶ and by properly arranging the magnetization of the magnetic layers by localizing spin polarization at one-dimensional zigzag edges of graphene.^187–190

A hybrid spintronic nano-device has been developed by functionalizing magnetic particles over a planar sheet of graphene¹⁸¹ to trap the molecules chemically, capture the magnetic flux, and generate a corresponding electric signal, thereby measuring even the smallest magnetic signal down to molecular levels (Fig. 17).

Fig. 17 (a) Schematic representation of the TbPc₂ single molecule magnet (SMM). (b and c) Schematic view of the device, showing (b) the molecule attached to graphene and (c) the nanoconstriction contacted by source (S) and drain (D) electrodes. The magnetic moments of the TbPc₂ SMMs (hexyl and pyrenyl groups here omitted for clarity) on top of the constriction add another degree of freedom to tune the conductivity of the device. (d) False-color SEM image of the device presented in the text. The SiO₂ substrate and etched graphene are colored in purple. Graphene conductive regions are colored in green. Reprinted with permission from ref. 181. Copyright 2011, American Chemical Society.

5.1.5 Quantum computing¹⁹¹. When the term quantum computing is used, a spin quantum bit can be replaced by the term qubit. The relative spin of electrons localized in semiconductor quantum dots with proper position and orientation control can be utilized as carriers of quantum information in the quantum computers. These qubits require materials with weaker spin–orbit coupling and hyperfine interactions of the electron spins with the neighbor nuclear spins. Carbon-based materials have weaker spin–orbit coupling and hyperfine interactions because of their lower atomic weights and atomic constituents. Moreover, the spin polarization in the graphitic materials decays more slowly, resulting in long term information storage.

However, because of the absence of a band gap in the electronic spectrum and Klein tunnelling, it is very difficult to confine particles and form tunable quantum bits using grapheme; moreover, due to the valley degeneracy, it is difficult to form two qubit gates using Heisenberg exchange coupling. To overcome the abovementioned limitations, a method has been proposed to form the spin qubits in graphene quantum dots with armchair boundaries. The system is developed based on graphene nanoribbons with semiconducting armchair edges,¹⁹² as shown in Fig. 18.

Fig. 18 Schematic Illustration of a graphene double quantum dot. Reprinted with permission from ref. 192. Copyright 2007, Nature Publishing Group.

The confinement is achieved by tuning the applied voltage to the barrier gates (indicated in blue). To shift the energy levels of the dots, additional gates (indicated in red) have been introduced. Universal two-qubit gates have been generated by the tunable exchange coupling formed between the left and the right quantum dots due to the virtual hopping of electrons through the barrier 2. Thus, the system formed can be used for fault tolerant computations, offering low error rates and high error thresholds.

5.2 Optoelectronic device

Graphene-based transparent conductive films have been employed in optoelectronic devices.^111,193 Although graphene has superior optical properties, the major hurdles faced by the implementation of graphene in optoelectronics are the higher sheet resistance offered by graphene prepared by CVD techniques (approximately 280 Ω sq⁻¹) compared to ITO (100 Ω sq⁻¹), the robust substrate requirements to withstand higher temperatures and the transfer of the graphene films onto the foreign substrates.

5.2.1 Touch screen. Two major types of touch screens have been employed in industries: resistive and capacitive touchscreens.^169,194 The resistive touch screens are majorly classified as the matrix and analogue type. The former has a matrix-like structure, in which the patterned electrodes over substrates like glass or plastic face each other, whereas in the latter, the transparent electrodes only face each other without the need of patterning. However, the analogue type touch screen continuously changes in resistance and the resistance needs to be high as well (500–2000 Ω sq⁻¹). The schematics for both these types have been given in the Fig. 19.

Fig. 19 Schematic sketch of the resistive touch panel: (a) matrix-type, (b) analogue-type.

The capacitive touch screens, on the other hand, utilizes the electrostatic field distortion induced by the touching of screen and converts it into a measurable change of capacitance. Graphene-based transparent conductive films offer higher sheet resistance and better transparency along with a long range uniformity when compared to the conventional films based on ITO. A schematic of capacitive touch screen is given in Fig. 20.

Fig. 20 Schematic sketch of the capacitive touch panel. Reprinted with permission from ref. 169. Copyright 2010, Nature Publishing Group.

The previously discussed limitations were overcome by a roll-to-roll production of high quality graphene,¹⁹⁴ which involves three major steps: attaching polymer to the graphene together onto the copper foil, etching of the copper layers and releasing graphene layers and transferring onto a target substrate, as shown in Fig. 21. In the attachment of a polymer support and graphene onto the copper foils, the graphene film deposited on a copper foil is attached to a thin polymer film coated with an adhesive layer by passing between two rollers.

Fig. 21 (a) Schematic of the roll-based production of graphene films grown on a copper foil. (b) An assembled graphene/PET touch panel showing outstanding flexibility. (c) A graphene-based touch-screen panel connected to a computer with control software. Reprinted with permission from ref. 194. Copyright 2010, Nature Publishing Group.

5.2.2 FE Displays. Field emission (FE), as its name suggests, is an electron-field emission process, in which electrons are emitted from a material induced by a high electrostatic field. The simplest way to attain such a field is by making the electron emitter a sharp pointed tip of a sharp object (called a field emitter) and through its field enhancement. Graphene can be used as a field emitting structure, as long as the FLG density is controlled, since it might cause a field screening effect. Graphene electrodes prepared out of spin coating of graphene oxide dissolved in polystyrene,¹⁹⁵ electrophoretic deposition,¹⁹⁶ thermal CVD¹⁹⁷ and microwave plasma enhanced CVD (MW-PECVD)¹⁹⁸ have been reported to be of good quality suitable for FE-based applications.

5.2.3 Light-emitting diodes⁸⁴. Graphene could be made luminescent by inducing a band gap through either physical or chemical treatments or through the alteration of graphene into nanoribbons or quantum dots. When made electro-luminescent (combining the luminescence and the conductive layers together), graphene can be clubbed together to form light-emitting diodes. An organic light-emitting diode (shown in Fig. 22) has an organic light emitting layer sandwiched between two electrodes that inject holes and electrons into the orbitals of the anode (the highest occupied molecular orbital) and cathode (the lowest unoccupied molecular orbital), respectively.

Fig. 22 A Schematic of the working mechanism of an organic light-emitting diode.

The traditionally used material for OLEDs is the ITO with a work function of about 4.4–4.5 eV; however, it provides only limited flexibility, and the diffusivity of indium into the OLED layers affects the performance of the devices. Since graphene also has the same range of work function of about 4.5 eV and it has better flexibility, it can be considered an excellent alternative for the ITO-based OLEDs.

5.2.4 Light-bending switchable graphene metamaterials. Metamaterials are a new generation of materials with dimensions much smaller than the relevant wavelength, and they display distinct optical properties, mostly associated with negative refraction. This property can be utilized in sensing devices, high resolution microscopy, and invisibility cloaks. Metamaterials are from the artificially arranged structural elements. By using the properties like renormalisation of plasmonic modes and frequency shift of the trapped-mode transmission resonance in the presence of the highly polarizable graphene, a photonic device has been developed based on graphene over metamaterials.¹⁹⁹

The device is built using a two-dimensional array of asymmetrically split ring slits on a gold film. Metamaterials have characteristic Fano anti-symmetric resonant lines with enhanced local fields which are responsible for the high contrast detection of graphene as well as the sensing applications based on metamaterials. In this setup, graphene acts as a continuous adsorption layer, and the addition of graphene to metamaterials results in a dramatic change of the transmission spectrum; moreover, a 250% increase in the transmission is observed.

5.2.5 Transparent conductive device. Transparent conductive devices made using large-scale graphene^200,201 can be used for flexible (stretchable) electronics. An optical absorbance of only 2.3% of the total light makes graphene one of the most transparent conductors reported to date. Indium tin oxide (ITO), the conventional material for the transparent conductors, has now a superior alternative offering high performance,²⁰² i.e., graphene, which can be used for the applications in transparent conductive devices.

5.3 Energy generation device

The long standing energy crisis has led to constant research into the alternate renewable energy sources or into alternates that enhance the existing power generation capabilities. Graphene is a promising material for power generation and has been employed in the fuel cells,^203–208 photovoltaic cells,^209–213 and possibly solar thermal fuel cells^209–213 as their tunable band gap and large optical absorbance are desirable for efficient light harvesting; moreover, their large carrier concentrations help in the charge collection in the solar cells.

Photovoltaic cells are those devices that convert light into electrical energy. The widely known photovoltaic devices are based on mostly the organic photovoltaic cells and dye-sensitized photovoltaic cells. The organic photovoltaic cells offer flexibility, good light absorption and charge transport but are limited by the polymer used compared to the inorganic cells (Fig. 23(a)). An organic solar cell consists of a transparent conductor, a photoactive layer and an electrode (Fig. 23(b)). The recent advancements in photovoltaic devices report a sub-category of the organic polymer-based photovoltaic cells, i.e., quantum dot-sensitized solar cells, which are used as electron acceptor materials in photovoltaics.

Fig. 23 Schematics of inorganic (a), organic (b) and dye-sensitized (c) solar cells. Reprinted with permission from ref. 169. Copyright 2010, Nature Publishing Group.

Quantum dots have beneficial properties such as their size-tuned optical response, efficient multiple carrier generation, and low cost, which makes them attractive for photovoltaic devices. However, quantum dots that have been made to date have toxic materials like cadmium and lead that would pose threat to the environment if we go for large-scale device applications. However, the devices made out of graphene quantum dots (GQD) are not toxic and offer similar electronic properties that are suitable for the photovoltaic device applications. Moreover, its high charge carrier mobility results in a quick transport of charges to the electrodes, which in turn indicates reduction in current losses and improvement of solar cell efficiency. Furthermore, it has been found that, when combined with a conjugated polymer, the graphene quantum dots exhibit superior functionality when compared with graphene sheets that are blended with the same polymer.

The other major category is the dye-sensitized solar cells (Fig. 23(c)), which use a liquid electrolyte as a charge transport medium. These cells consist of a highly porous nano-size crystalline photo-anode, comprising TiO₂ and dye molecules, which are both deposited on a transparent conductor. When light is incident on these cells, the dye molecules capture the incident photons and generate electron–hole pairs. Then, the electrons are injected into the conduction band of the TiO₂, and subsequently they move to the other electrode. Regeneration of dye molecules occurs by capturing electrons from the liquid electrolyte. ITO is a commonly used material, which can be applied as both an anode and a cathode; however, for its use as a cathode it requires platinum coating. In photovoltaic devices, graphene is multifunctional and can be used as a transparent conductor window, photoactive material, channel for charge transport, and catalyst.

5.4 Energy storage devices

With the ever increasing demand for electronic and energy generation devices, there exists an equal constant demand for energy storage. Ultracapacitors or electrochemical capacitors based on electrochemical double layer capacitance (EDLC) are good electrical energy storage devices that store and release energy by nanoscopic charge separation at the electrochemical interface between an electrode and an electrolyte.²¹⁴ These ultracapacitors offer high energy density, high power capability, long life and low weight compared to the conventional dielectric capacitors. They consistently give a good performance and reliability over a wide range of voltage scan rates for short load cycles with graphene as the electrode materials.^215–217

The nearly negligible effect of thermal vibrations on the electron conduction in graphene and hence the very low resistivity of about 1 μΩ at room temperature (nearly 35% lesser than the resistivity of copper) makes this an interesting specimen for superconducting applications, although some extrinsic sources in graphene with quite some impurities available at present results in added resistivity to graphene.¹⁴ Thus, graphene can be used in applications in energy storage, especially supercapacitors, due to its high specific area and its supreme electron transport properties, when its individual monolayers are stacked onto one another and the layers of the chemically modified graphene (CMG) are wet.²¹⁸ Since graphene is atom-level thick and it has very low surface energy, it can be used to reduce the adhesion and friction while coating over various surfaces. It is the thinnest solid lubricant found to date, and it shows exceptional adhesion and frictional characteristics when fabricated by the chemical vapour deposition over Ni and Cu catalysts.²¹⁹ Nano-electromechanical systems fabricated from single layer and multilayer graphene sheets by mechanically exfoliating thin sheets from graphite over trenches in silicon oxide form the thinnest resonator consisting of a single suspended layer of atoms and represents the ultimate limit of two-dimensional nano-electromechanical systems.¹⁰

Architectural graphene structures have been proposed to enhance the existing energy storage capacities. Nano-architecture pillared graphene when doped with lithium cations can store up to 41 g H₂ per L under ambient conditions for mobile applications.²²⁰ Graphene has also found its application in batteries^{203,221–224} (as the electrode materials) and flexible energy storage devices.²²⁵ The proposed structure with a hybrid of graphene and CNTs has been shown in the Fig. 24(a), and the simulated illustration of non-doped graphene storing hydrogen (green) and that of graphene doped with the lithium (purple) storing hydrogen (green) is shown in Fig. 24(b) and (c). A 3D foam-like graphene macrostructure can be directly grown on Ni foam. After chemical etching the Ni foam, a 3D graphene foam can be obtained with a unique network structure and the outstanding electrical and mechanical properties (Fig. 25).²²⁶

Fig. 24 (a) Schematic of pillared graphene. (b) Snapshot from the GCMC simulations of a pure pillared structure at 77 K and 3 Bar. Hydrogen molecules are represented in green. (c) Snapshot from the GCMC simulations of a lithium doped pillared structure at 77 K and 3 Bar. Hydrogen molecules are represented again in green while lithium atoms are in purple. Reprinted with permission from ref. 220. Copyright 2008, American Chemical Society.

Fig. 25 (a) Synthesis of a graphene foam and integration with PDMS. (b) Photograph of a 170 × 220 mm² free-standing graphene foam. (c) SEM image of a graphene foam. Reprinted with permission from ref. 226. Copyright 2011, Nature Publishing Group.

5.5 Bio-imaging and bio-sensing applications

The chemical inertia and the non-toxicity under physiological conditions call for the entry of graphene into the fields ranging from medical diagnosis to catalysis. In particular, graphene is employed as an effective fluorescent probe for bio-imaging.^227–229

The high sensitivity of graphene—up to the molecular level—a resolution that has been beyond the reach of any detection technique to date, has enabled its application in the field of electro-chemical sensors^230–235 and bio-sensors.^236,237 This high sensitivity and its ability to detect elements ranging from gases to biomolecules can be attributed to the variation of the electrical conductivity of graphene as the function of its surface adsorption,¹²⁵ and its large specific surface area.¹² In general, the change in the conductance of graphene is due to the change in charge carrier densities (carrier concentrations) induced by the immediate environment; i.e., acceptor or donor-like behaviour of the adsorbed gases depends on the interaction with the graphene lattice in our case.

5.6 Environmental applications

Water dispersible graphene oxide nano-composite removes almost 99.9% of the toxic and carcinogenic arsenic from the water within 1 ppb; hence, it can be employed in water purification.²³⁸ Ni-doped graphene/carbon crygels exhibit 93% of the motor oil absorption capacity and a maximum absorption capacity of 151 mg g⁻¹ for organic pollutants (methyl blue).²³⁹ Reduced graphene oxide-coated polyurethane sponge delivered oil absorption capabilities higher than 80 g g⁻¹ and 160 g g⁻¹ for chloroform.²⁴⁰

5.7 Biomedical applications

Paper-like materials formed using graphene have remarkable thermal, mechanical and electrical properties. Their biocompatibility and ease of handling make them an ideal material for cell culture experiments, biomedical applications like inclusion in heart valves,²⁴¹ and batteries.^242,243

5.8 Other applications

An atom-level thick membrane of graphene is impermeable to almost all standard gases including helium due to the electron density of its aromatic rings. This property allows us to measure the elastic constants and the mass of the graphene membranes. The single atomic layer membranes, which when combined with the micro-fabricated structures, can create a new class of atomic scale membrane-based devices.¹¹ It has been demonstrated that robust atomic-level graphene membranes are capable of storing mesoscopic volumes of gases.²⁴⁴ With this, it is possible to make pressure sensors, stretchable strain gauges,⁸⁰ atomic-scale mechanical devices capable of gas storage and separation, proton exchange membranes for fuel cells, and carbon sequestration from flue gases.²⁴⁵ Polymer-based nano-composites offer enhanced gas barrier and mechanical properties,²⁴⁶ which when infused with graphene as a filler material, can revolutionize the food packaging and processing applications.

6. Conclusion

In summary, we have reviewed the principle and fundamental of exotic properties of graphene, i.e., the Dirac Fermions and the Dirac cone arrangement of its electronic structure, quantum Hall effect, Klein paradox, Zitterbewegung effect, non-zero minimal conductivity, the fabrication approaches of graphene, characterization techniques for structural and elemental analysis, and finally the applications in which the wonder material is employed in numerous applications (Fig. 26). As illustrated in Fig. 27, with the source of Web of Science & World Intellectual Property Office (WIPO), there is an exponential increase in the number of publications in this field and the interest is constantly growing. There has been a proportionate increase in the number of patents, which proves that the industrial value of graphene is being exploited simultaneously. The quest for the perfection and more applications is still under further investigation, which is why it is apt to state that graphene can be termed as the Philosopher's stone of the modern age.

Fig. 26 The percentage of various applications of graphene.

Fig. 27 Timeline of journal papers and patents based on graphene.

Acknowledgements

Dr X. Zhang thanks the financial support provided by Public Sector Research Funding (Grant number 1121202012), Agency for Science, Technology, and Research (A*STAR). Dr H. Liu thanks the postdoc fellowship from Yong Loo Lin School of Medicine, NUS and Cardiovascular Research Institute, NUHS.

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