Abstract

More than a decade has passed since the graphene was synthesized for the first time but still there are many applications that have not been explored. The first intended application for graphene was its high mobility property for high-speed electronics. This task became more difficult when the problem with zero bandgap of graphene made an obstacle to close the current flow of transistor. Different remedies, for example, downscaling the dimensions to nano-ribbons and bilayer structures were proposed to create a reasonable bandgap in graphene for electronic applications. The main idea was to improve the figure of merit Ion ∕ Ioff for RF devices. Although many important achievements were made, but later graphene was considered as a better choice for photonic applications. For example, graphene was used as light absorber in the lateral direction for modulators, or sensitive to light in photodetectors when it is vertically illuminated. Nowadays the graphene has inaugurated a new platform in flexible and transparent electronics. As example, electronics giant producers have already integrated graphene for flexible screens.

During recent years, many research efforts have been spent on other two-dimensional (2-D) crystals (transition metal dichalcogenides, silicene, and germanene) as competitors to graphene but it is still a long way to integrate such materials for industrial applications.

Carbon is the most fascinating material in the universe which may be constructed into different forms and shapes. The electrical, optical, and mechanical properties of carbon depend on how the atoms are packed in relation to their adjacent atoms. As an example, diamond is a single crystalline form of carbon atoms with sp3 hybridzation while graphene is a single-sheet arrangement of carbon atoms in a honeycomb shape with sp2 hybridzation (Fig. 48.1a). These configurations place diamond in the group of wide bandgap materials while graphene is almost a zero bandgap material.
Fig. 48.1

(a) Schematic image of graphene with sp2 hybrids of carbon atoms and (b) the formed π and σ bonds. (After [48.3])

In nature, stacks of graphene planes can be found in graphite material and they can be ordered in the hexagonal or rhombohedral sequence. Graphene as a two-dimensional crystal material was experimentally detached from graphite by Geim and Novoselov in 2004. The discovery led to Nobel prize in 2010 with motivation of the synthesis of a 2-D carbon sheet with sp2 bonds in comparison with sp3, which is the most common form and is quantum mechanically favorable for bonding of carbon atoms [48.1].

In graphene, sp2 hybrids establish σ bonds with the neighboring atoms (Fig. 48.1 b). These bonds have a length of 0.142 nm and are the main reason behind the tremendous Young’s modulus close to 1 TPa, which makes the strong mechanical property of graphene. This amazing Young modulus value is roughly 100 times larger than for steel with similar film thickness [48.1]. The remaining 2p orbital is half filled and it creates an extended π-bond where the electrons play the main role in electrical conduction and determine the photonic and electrical characteristics of graphene [48.2].

Graphene is mostly known for its high electron mobility , which is \({\mathrm{2.5\times 10^{5}}}\,{\mathrm{cm^{-2}V^{-1}s^{-1}}}\) at room temperature. This high mobility value is a result of decreased electron–phonon interaction resulting in significantly lower carrier scattering. The electron mobility in graphene is almost 200 times higher than Si [48.4] and 4 times larger than III–V semiconductors [48.5]. This would make graphene a very attractive material for high-speed transistors.

Graphene has demonstrated excellent electron and thermal conduction. The electron saturation velocities up to \({\mathrm{7\times 10^{7}}}\,{\mathrm{cm{\,}{}s^{-1}}}\) have been observed, which is remarkably higher than high field saturation velocities for III–V and Si materials [48.6]. Similarly, current density close to 108 A ∕ cm2 have been measured, which is almost five orders of magnitude larger than copper. The optical properties of graphene have also been widely studied. Graphene has optical opacity of 2.3% within a broad spectrum, which is wavelength independent in the interval of far-infrared and blue light [48.7].

Graphene absorbs more photons per unit thickness and surface. This means that graphene has larger efficiency per volume and bigger chances to saturate with high-intensity light pulses. Finally, graphene is a material with many outstanding properties, which is not seen altogether in one material alone. However, due to some undesired properties, there are still obstacles for graphene to replace materials for electronic technology in the present time. For example, graphene will not probably replace Si or III–V materials in high-frequency electronics in very near future. Meanwhile, graphene could be integrated in transparent electronics instead of today’s most used material, indium-tin oxide (ITO ) which is expensive and difficult to synthesize for mass production. Graphene has attracted attention for this purpose for electronics giant manufacturers such as Samsung and Sony [48.8].

More work is also required to decrease the graphene’s parasitic contact in order to integrate for high frequency and flexible electronic applications. Recently, graphene has inaugurated totally a new domain within THz electronics, millimeter waves, and room-temperature ballistic electronics [48.9].

48.1 Graphene Synthesis

There are many ways to synthesize graphene (Fig. 48.2). The first article about isolating graphene sheet from graphite was published in 2004 by Novoselov and Geim [48.1]. Their method is the so-called exfoliation and uses a scotch-tape to attach flakes of graphene monolayers. The detached graphene can be transferred directly on Si (or BN) wafers or dissolved in acetone. The size of flakes is usually some micrometers and in the best case a few millimeters.
Fig. 48.2

A drawing of graphene quality versus manufacturing cost for different synthesis methods

This method is simple, easy accessible, and flakes have relative low defect density. The high-quality graphene is the key for the high electron mobility and exfoliated graphene layers have demonstrated typical values of 2 × 104 and \({\mathrm{2.5\times 10^{5}}}\,{\mathrm{cm^{2}{\,}V^{-1}s^{-1}}}\) on SiO2 and hexagonal-BN (h-BN) substrates at room temperature, respectively [48.10]. Similar mobility values have been demonstrated for suspended graphene [48.11] when the substrate interaction in this case is eliminated.

In many cases, the exfoliated graphene can be suspended in nonaqueous solvents or water-based surfactants [48.12]. The benefit of this method is using the surface tension of these solvents to make graphite to split in thinner platelets. Another approach is to oxidize graphite to form graphene oxide, which is easily soluble in water. Using ultrasound sonication may cause thining of the graphene stack to a monolayer. However, a total removal of all oxide is hard to achieve [48.13]. There are many reports about patterning reduced graphene oxide (RGO ) and using laser scribing [48.14]. These materials can be used for supercapacitors, printed, and flexible electronics. However the complexity of such manufacturing techniques makes them limited to lab research and not suitable for any industrial application.

Another method to synthesize graphene is thermal decomposition of SiC. This method was demonstrated for the first time by Berger et al. [48.15] and it is based on the thermal annealing of SiC where sublimation of Si occurs and the C atoms are segregated on Si- and the C-face of the wafer and form graphene layers. The process temperatures are around 1600C in 100 mbar for Si-face and 1450C and 0.1 μbar for C-face in Ar atmosphere [48.16]. As a result of Si desorption, the surface of SiC holds narrow terraces of graphene and they are connected by steps.

This method has demonstrated electron mobility values of around \({\mathrm{3.0\times 10^{4}}}\,{\mathrm{cm^{2}V^{-1}s^{-1}}}\) [48.17] depending on the alignment of SiC substrate terraces with the direction of carrier transport through graphene stack.

This method provides high quality graphene layers but has the drawbacks of the high cost of SiC substrates wafers and formation of small-sized graphene of a few micrometers which is too small for industrial applications to process a complete transistor.

The formed graphene stack on SiC demonstrates a bandgap of ≈ 260 meV. This value may vary depending on the stack thickness and it reaches almost zero for 4 graphene monolayers [48.18] due to substrate interaction or induced strain by SiC [48.19].

During recent years, chemical vapor deposition (CVD ) of graphene has become very popular method to synthesize graphene. The method is based on the decomposition of a carbon precursor, for example, methane (CH4) or ethanol (C2H6O) around 1000C on a foil of a transition metal, for example, Cu, Ni, Fe as catalyst material [48.20]. Later the formed graphene is separated or peeled off from surface of catalyst metal by using a transfer polymer (typically polymethylmethacrylate (PMMA) or polydimethylsiloxane (PDMS)) where the catalyst is etched away [48.21]. However, there is a high risk to damage the graphene sheet by the mechanical stress during the removal action and the quality of the graphene also depends on the surface roughness of catalyst metal. Different electronic component producers have stepped in using CVD method [48.22]. Nowadays very large area graphene is produced and developed for transparent electronics for displayer application. Using this method, carrier mobility of \({\mathrm{0.5}}\,{\mathrm{cm^{2}V^{-1}s^{-1}}}\) has been demonstrated on SiO2 surface.

48.2 Band Structure and Electronic Applications

Six carbon atoms are bonded in graphene honeycomb configuration with hexagonal lattice. Therefore, graphene can be considered as a triangular lattice consisting of a basis of two atoms per unit cell present at the two equivalent lattice sites A and B. A simple calculation gives the 2 lattice vectors, where a = 0.142 nm is the nearest-neighbor C-C spacing (Fig. 48.3a).
Fig. 48.3a–c

A schematic view of graphene (a) honeycomb shape, (b) the first Brillouin zone, and (c) the band structure of graphene. (After [48.24])

In principle, a honeycomb configuration has six points at the corners of the first Brillouin zone (FBZ ) where they are distinguished in two groups of three equivalent points. These points are denoted by K and K (Fig. 48.3b). These corners are called Dirac points and the electrons and holes in the vicinity of those points are massless and follow linear relations (not the quadratic form) of energy momentum dispersion.

Graphene acts as a massless Dirac fermion and its electronic properties are described by the Dirac equation instead of the Schrodinger equation [48.23].

The graphene band structure has two notable properties: at first, at the Dirac point positions the valence and conduction band edges are very close (or intersecting), resulting in almost no energy gap (Fig. 48.3 c). This places graphene in the category of zero band-gap semiconductors or as a semimetal. Secondly, as mentioned above the energy momentum dispersion has linear behavior and this leads to a constant carrier group velocity over energy (where is the Fermi velocity and estimated to \({\mathrm{8\times 10^{5}}}\,{\mathrm{ms^{-1}}})\). As a result, the carriers have effective masses, which are directly related to momentum and have zero value at zero energy. This is an exceptional characteristic of graphene which is distinguished from common semiconductors, where the dispersion curves have parabolic shape and carrier velocity is dependent on the second derivative of the dispersion curves (Fig. 48.4).
Fig. 48.4

The energy band diagram in semiconductors and graphene

Graphene has a linear density of states (DOS ) as well. Each point q appears with twofold spin degenerate (gs = 2) and since there are two Dirac points K and K hence another twofold valley degenerate (gv = 2). Therefore DOS is written as [48.25]
$$\rho(E)=\frac{g_{\mathrm{s}}g_{\mathrm{v}}}{2\pi(\hbar\nu_{\mathrm{F}})^{2}}|E|\;,$$
(48.1)
where E stands for energy and νF for Fermi velocity. This makes the DOS distribution of graphene very different from metals and semiconductors (Fig. 48.5). The integral of DOS equation times the Fermi–Dirac distribution at a given temperature results in a noticeable electron-sheet density for graphene. Furthermore, graphene sheet is not perfectly planar and has some ripples and this makes charge inhomogeneities in graphene.
Fig. 48.5

Electronic structure and DOS for metals, semiconductors and graphene

Graphene possesses an ambipolar characteristic against an applied electric field. It means in contrary to metals, in the semimetal graphene, electrons may convert to holes in response to an applied electric field [48.26]. This means that n-type or p-type graphene is not predefined.

Graphene has extremely high carrier mobility. There are three macroscopic forces, which can affect the carrier mobility in graphene. These forces are diffusion, drift, and drag force. Diffusion force is an outcome of carriers’ random motion, drift force is generated by electrostatic field and drag is the force due to the carrier scattering within the lattice [48.22]. In graphene, four scattering mechanisms have influence on the mobility. These mechanisms are addressed to the charged impurities, acoustic or optical phonons, and surface roughness. Experimentally, it has been demonstrated that the charged impurities in graphene have the crucial effect on the carrier mobility. The charged impurities can be reduced in graphene by annealing or by using a high-k dielectric [48.27].

Application of graphene in high speed electronics has been shadowed for years since the lack of a bandgap makes it impossible to close the current flow. This blocks the application of graphene for logics since a bandgap around 400–500 meV is sought for this application. Integration of graphene as a channel material in field effect transistors (FET s) offers a high transconductance; however, the absence of a well-defined saturation region diminishes the benefit of a graphene power amplifier. A high Ion ∕ Ioff ratio is the key criteria for RF application.

One way to solve this problem is to decrease the lateral size of graphene to few a nanometers (so-called graphene nanoribbon (GNR )) where the electronic wavefunction could be localized and a quasi 1-D structure could be established (Fig. 48.6). In this way, a ballistic quantum transport is built up in graphene which is compatible with High Electron Mobility Transistor (HEMT ) devices.
Fig. 48.6

Schematic of band diagram for different graphene material and GNR transistor. (After [48.28])

Another way to create a small bandgap in graphene is to form a bilayer graphene (BLG ) [48.29] (or so-called Bernal stacked graphene), where the two graphene monolayers are placed on each other with a misalignment (Fig. 48.6).

Unfortunately Bernal BLG can mainly be synthesized by exfoliation method. Using BLG, a bandgap of 130 meV and the Ion ∕ Ioff value of ≈ 100 have been obtained [48.29].

Many research studies have proposed another alternative: vertical graphene transistor. This type of transistor functions by current tunneling from an electrode through a thin dielectric layer to graphene. In a more practical way, another graphene layer can be deposited to act as a second electrode. This extra gate allows triode modulation of the tunnel current [48.30]. This design has demonstrated an Ion ∕ Ioff ratio around 50 but no RF action has been shown so far.

An alternative to the above configuration is integration of graphene in a graphene hot-electron transistor, which is the application of hot electrons in a metal-insulator-metal-insulator-metal (MI-M-I-M ) transistor, an approach similar to Bipolar Junction Transistor (BJT ). In this type of transistor, graphene is applied as low-resistivity base electrode and consists of an emitter base tunnel junction and a base collector filtering dielectric (Fig. 48.7a,b). Although these transistors have shown Ion ∕ Ioff ratio around 105 they have a very low current gain, which leads to collector currents 10 orders of magnitude less than the other types of transistors [48.32].
Fig. 48.7a,b

Vertical graphene transistor (a) in off and (b) on state. (After [48.31])

48.3 Characterization of Graphene Material

Graphene material is usually in a few monolayers on a specific substrate and it is difficult to be distinguished by optical microscopes. The characterization techniques, for example, atomic force microscopy (AFM ), transmission electron microscopy (TEM ), x-ray diffraction (XRD ), and Raman spectroscopy are mainly applied to study graphene.

48.3.1 AFM

AFM is a common technique to estimate the thickness of graphene material. In general, 2-D crystallites such as graphene are a few nanometers thick elevated on the surface. Tapping mode is mostly used for the thickness measurements [48.33]. However, AFM technique has low throughput and therefore the measured data are not without error.

As an example, Novoselov et al. [48.33] have shown a monolayer graphene has 0.4 nm height, and Gupta et al. showed a height of 0.7 nm for single monolayer of graphene. One explanation for these different outcomes in measurements could be that these groups used the different amplitudes of the cantilever for their experiments.

This shows that extra care has to be taken to analyze the AFM results in order to have a comparable and reliable method to measure the thickness of graphene [48.33, 48.34].

48.3.2 Transmission Electron Microscopy

Transmission electron microscopy (TEM) is one of the most accurate methods to study graphene and provide atomic resolution (Fig. 48.8a–c). Graphene appears both in single- and multilayers in a flat sheet or folded form. The electron beam is parallel to the folded graphene sheets and they appear as one dark line for single sheets (Fig. 48.8a) and double dark lines for bilayer sheets (Fig. 48.8b). In the case of multiple folded sheets the number of dark lines could appear in any shape [48.35]. This can make it difficult to determine the number of graphene sheets.
Fig. 48.8a–c

TEM images: (a) cross-section of single-folded graphene, (b) cross-section of double-folded graphene and (c) top view of graphene material. (Reprinted from [48.36], with permission from Elsevier)

48.3.3 Raman Spectroscopy

Raman spectroscopy is a technique that is based on inelastic interactions of phonons in a layer. For graphene, Raman can provide information about the number of monolayers and the quality of graphene material. There are three main bands in Raman analysis:
  • The D band

  • The 2-D band

  • The G band.

The D Band

This band is an indicator of the defects in the graphene material and the presence of sp3 bonds of carbon. The intensity of the D band is low for graphene (or graphite) with high quality. This peak normally appears at the edges of graphene flakes [48.39].

The 2-D Band

This band indicates the number of graphene sheets and also reveals if the graphene lies on a specific substrate. If the 2-D band is a single peak with narrow full-width-half-maximum (FWHM ) then the graphene is a single sheet. However, if the graphene consists of multilayers then the shape of the peak is broad with small peaks. Figure 48.9 shows different cases for graphene material. As an example, Raman results from a bilayer graphene shows peaks at wavelengths of 514 and 633 nm [48.41].
Fig. 48.9

Raman curves of graphene with n layers. (After [48.37])

The G Band

The position of this band shows the number of graphene sheets. A peak is seen around 1587 cm−1 if the graphene consists of a single sheet, otherwise the G band moves downwards. Figure 48.10 shows the change of G band for graphene layers with different numbers of sheets [48.38].
Fig. 48.10

G-band of graphene for a series of graphene layers n. (After [48.38])

48.3.4 XRD Analysis

X-ray diffraction is a technique that is usually used to study thin films. In the case of a very thin layer of graphene, a high-intensity x-ray beam is required. The XRD technique provides information about the crystalline quality and layer thickness of graphene. The latter parameter could be relatively determined by the intensity of the peaks. The XRD data of the graphene material gives three main peaks at reflections:

48.4 Photonic Applications

Graphene has very promising optical properties for modulators [48.43, 48.44], photodetectors [48.45, 48.46], and plasmonic structures. Despite its thin thickness, it absorbs light in the vertical or lateral direction due to distinctive electronic structure [48.47]. The material absorbs a large variety of wavelengths within interband, intraband, and collective plasmon excitations. The extraordinary benefit of graphene is tuning the absorption by regulating the charge density.

The optical conductivity is written by a universal value of \(\sigma_{\text{uni}}=\pi\mathrm{e}^{2}/2\,h\). For photons with higher energies, the optical conductivity is increased gradually towards peaks, which lie in UV range with energy of 4.62 eV (Fig. 48.12). This is related to nonlinear part of dispersion relation, which is labeled by interband transitions from the bonding to the antibonding π states in the graphene Brillouin zone [48.48].
Fig. 48.12

Experimental optical conductivity (solid line) and the universal optical conductivity (dashed line) of a single graphene layer. The discrepancy of the optical data from the universal values at low energies is due to spontaneous doping. (After [48.48])

Graphene absorbs ideally 2.3% of the normal incident light through intra- and interband transitions. This absorption may deviate from the ideal universal value of 2.3% depending on the underneath layer (Fig. 48.13a). This deviation is related to phonons (where interband absorption is allowed in the presence of phonons) [48.49].
Fig. 48.13

(a) Normal incident light shines on a graphene layer. (b) Graphene on a waveguide and the light interacts with graphene along the waveguide sheet

Graphene can be placed on a waveguide to absorb light along the lateral direction (Fig. 48.13b). The length of graphene sheet may determine the amount of the absorption and for a long enough sheet a total absorption can be obtained. The absorption of light in the lateral direction occurs when a graphene sheet is placed on a waveguide. The length of graphene (or waveguide) sheet determines the amount of absorption and a complete absorption can be obtained if the length of graphene is long enough.

An innovative method to deal with graphene low DOS is to use two graphene sheets isolated by an oxide layer (Fig. 48.14). In this design, the first graphene sheet layer is for absorption, however, the second sheet operates as a gate.
Fig. 48.14

A bilayer graphene modulator integrated on a waveguide. By applying a voltage to the gate, charge-sheet density in the first graphene layer is affected. (After [48.44])

Si is a material with a bandgap of 1.12 eV, and is transparent for λ > 1.1 μm. Therefore, Si can be used as a waveguide to conduct telecom wavelengths.

The modulator in Fig. 48.14 may function when the first graphene sheet is grounded and the second one is biased with a gate voltage, Vg [48.44].

Graphene has also been used as active photonic material in photodetectors. An electrical current was generated when the contact electrode of graphene transistor was illuminated [48.50, 48.51] (Fig. 48.15). In order to increase the absorption, the detector can be formed on a waveguide processed on an SOI substrate with a high-k material beneath the graphene sheet.
Fig. 48.15

A photodetector with graphene active layer. (After [48.46])

Although graphene can absorb a broad wavelength a graphene detector has a low responsivity of 0.1 mA ∕ W, which is remarkably lower than III-V detectors.

During recent years, many research efforts have been spent on other 2-D crystals (transition metal dichalcogenides, silicene, and germanene) as competitors to graphene [48.52].

The transition metal dichalcogenides are a group of materials which are known as MX2, where M is a transition metal element from group IV (e. g., Ti, Zr or Hf), group V (e. g., V, Nb, or Ta), or group VI (e. g., Mo or W), and X is a chalcogen material (e. g., S, Se, or Te).

Even though, there are many reports about the synthesis and properties of these materials there is a long way to go before they can be mass-produced for industrial applications in near future [48.52].

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Inst. of MicroelectronicsChinese Academy of ScienceBeijingChina
  2. 2.School of Information and Communication TechnologyKTH Royal Institute of TechnologyStockholmSweden

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