Graphene 48.Graphene - Springer · Graphene has attracted attention for this purpose for...

11
Graphene 1173 Part E | 48 48. Graphene Henry H. Radamson 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 elec- tronics. This task became more difficult when the problem with zero bandgap of graphene made an obstacle to close the current flow of transis- tor. 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 I on =I off for RF devices. Although many important achievements were made, but later graphene was considered as a better choice for photonic appli- cations. 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 trans- parent electronics. As example, electronics 48.1 Graphene Synthesis .......................... 1174 48.2 Band Structure and Electronic Applications ............... 1176 48.3 Characterization of Graphene Material ........................ 1178 48.3.1 AFM .................................................. 1178 48.3.2 Transmission Electron Microscopy ........ 1178 48.3.3 Raman Spectroscopy .......................... 1179 48.3.4 XRD Analysis ...................................... 1180 48.4 Photonic Applications ....................... 1180 References ................................................... 1182 giant producers have already integrated graphene for flexible screens. During recent years, many research efforts have been spent on other two-dimensional (2-D) crys- tals (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 prop- erties of carbon depend on how the atoms are packed in relation to their adjacent atoms. As an example, di- amond is a single crystalline form of carbon atoms with sp 3 hybridzation while graphene is a single-sheet arrangement of carbon atoms in a honeycomb shape with sp 2 hybridzation (Fig. 48.1a). These configura- tions place diamond in the group of wide bandgap materials while graphene is almost a zero bandgap ma- terial. 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 sp 2 bonds in comparison with sp 3 , which is the most common form and is quantum mechanically favorable for bonding of carbon atoms [48.1]. In graphene, sp 2 hybrids establish bonds with the neighboring atoms (Fig. 48.1b). 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 thick- ness [48.1]. The remaining 2p orbital is half filled and it creates an extended -bond where the electrons play the main role in electrical conduction and de- termine the photonic and electrical characteristics of graphene [48.2]. © Springer International Publishing AG 2017 S. Kasap, P. Capper (Eds.), Springer Handbook of Electronic and Photonic Materials, DOI 10.1007/978-3-319-48933-9_48

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Graphene1173

PartE|48

48. Graphene

Henry H. Radamson

More than a decade has passed since the graphenewas synthesized for the first time but still there aremany applications that have not been explored.The first intended application for graphene wasits high mobility property for high-speed elec-tronics. This task became more difficult when theproblem with zero bandgap of graphene madean obstacle to close the current flow of transis-tor. Different remedies, for example, downscalingthe dimensions to nano-ribbons and bilayerstructures were proposed to create a reasonablebandgap in graphene for electronic applications.The main idea was to improve the figure of meritIon=Ioff for RF devices. Although many importantachievements were made, but later graphene wasconsidered as a better choice for photonic appli-cations. For example, graphene was used as lightabsorber in the lateral direction for modulators,or sensitive to light in photodetectors when it isvertically illuminated. Nowadays the graphene hasinaugurated a new platform in flexible and trans-parent electronics. As example, electronics

48.1 Graphene Synthesis .......................... 1174

48.2 Band Structureand Electronic Applications ............... 1176

48.3 Characterizationof Graphene Material ........................ 1178

48.3.1 AFM .................................................. 117848.3.2 Transmission Electron Microscopy ........ 117848.3.3 Raman Spectroscopy . ......................... 117948.3.4 XRD Analysis...................................... 1180

48.4 Photonic Applications ....................... 1180

References ................................................... 1182

giant producers have already integrated graphenefor flexible screens.

During recent years, many research efforts havebeen spent on other two-dimensional (2-D) crys-tals (transition metal dichalcogenides, silicene,and germanene) as competitors to graphene butit is still a long way to integrate such materials forindustrial applications.

Carbon is the most fascinating material in the universewhich may be constructed into different forms andshapes. The electrical, optical, and mechanical prop-erties of carbon depend on how the atoms are packedin relation to their adjacent atoms. As an example, di-amond is a single crystalline form of carbon atomswith sp3 hybridzation while graphene is a single-sheetarrangement of carbon atoms in a honeycomb shapewith sp2 hybridzation (Fig. 48.1a). These configura-tions place diamond in the group of wide bandgapmaterials while graphene is almost a zero bandgap ma-terial.

In nature, stacks of graphene planes can be foundin graphite material and they can be ordered in thehexagonal or rhombohedral sequence. Graphene asa two-dimensional crystal material was experimentallydetached from graphite by Geim and Novoselov in

2004. The discovery led to Nobel prize in 2010 withmotivation of the synthesis of a 2-D carbon sheet withsp2 bonds in comparison with sp3, which is the mostcommon form and is quantum mechanically favorablefor bonding of carbon atoms [48.1].

In graphene, sp2 hybrids establish � bonds withthe neighboring atoms (Fig. 48.1b). These bonds havea length of 0:142 nm and are the main reason behindthe tremendous Young’s modulus close to 1 TPa, whichmakes the strong mechanical property of graphene.This amazing Young modulus value is roughly 100times larger than for steel with similar film thick-ness [48.1]. The remaining 2p orbital is half filledand it creates an extended �-bond where the electronsplay the main role in electrical conduction and de-termine the photonic and electrical characteristics ofgraphene [48.2].

© Springer International Publishing AG 2017S. Kasap, P. Capper (Eds.), Springer Handbook of Electronic and Photonic Materials, DOI 10.1007/978-3-319-48933-9_48

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PartE|48

.1

1174 Part E Novel Materials and Selected Applications

sp2sp2 sp2 sp2

�a) b)Fig. 48.1 (a) Schematic image ofgraphene with sp2 hybrids of carbonatoms and (b) the formed � and �

bonds. (After [48.3])

Graphene is mostly known for its high electronmobility, which is 2:5�105 cm�2V�1s�1 at room tem-perature. This high mobility value is a result of de-creased electron–phonon interaction resulting in signif-icantly lower carrier scattering. The electron mobilityin 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 forhigh-speed transistors.

Graphene has demonstrated excellent electron andthermal conduction. The electron saturation velocitiesup to 7�107 cm s�1 have been observed, which is re-markably higher than high field saturation velocities forIII–V and Si materials [48.6]. Similarly, current densityclose to 108A=cm2 have been measured, which is al-most five orders of magnitude larger than copper. Theoptical properties of graphene have also been widelystudied. Graphene has optical opacity of 2:3% withina broad spectrum, which is wavelength independent inthe interval of far-infrared and blue light [48.7].

Graphene absorbs more photons per unit thicknessand surface. This means that graphene has larger ef-

ficiency per volume and bigger chances to saturatewith high-intensity light pulses. Finally, graphene isa material with many outstanding properties, whichis not seen altogether in one material alone. How-ever, due to some undesired properties, there arestill obstacles for graphene to replace materials forelectronic technology in the present time. For exam-ple, graphene will not probably replace Si or III–Vmaterials in high-frequency electronics in very nearfuture. Meanwhile, graphene could be integrated intransparent electronics instead of today’s most usedmaterial, indium-tin oxide (ITO) which is expen-sive and difficult to synthesize for mass production.Graphene has attracted attention for this purpose forelectronics giant manufacturers such as Samsung andSony [48.8].

More work is also required to decrease thegraphene’s parasitic contact in order to integrate forhigh frequency and flexible electronic applications. Re-cently, graphene has inaugurated totally a new domainwithin 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 graphenesheet from graphite was published in 2004 byNovoselov and Geim [48.1]. Their method is theso-called exfoliation and uses a scotch-tape to at-tach flakes of graphene monolayers. The detachedgraphene can be transferred directly on Si (or BN)wafers or dissolved in acetone. The size of flakes isusually some micrometers and in the best case a fewmillimeters.

This method is simple, easy accessible, and flakeshave relative low defect density. The high-qualitygraphene is the key for the high electron mobility andexfoliated graphene layers have demonstrated typicalvalues of 2�104 and 2:5�105 cm2 V�1s�1 on SiO2 andhexagonal-BN (h-BN) substrates at room temperature,respectively [48.10]. Similar mobility values have beendemonstrated for suspended graphene [48.11] when thesubstrate interaction in this case is eliminated.

In many cases, the exfoliated graphene can besuspended in nonaqueous solvents or water-based sur-factants [48.12]. The benefit of this method is using thesurface tension of these solvents to make graphite tosplit in thinner platelets. Another approach is to oxidizegraphite to form graphene oxide, which is easily solublein water. Using ultrasound sonicationmay cause thiningof the graphene stack to a monolayer. However, a totalremoval of all oxide is hard to achieve [48.13]. Thereare many reports about patterning reduced grapheneoxide (RGO) and using laser scribing [48.14]. Thesematerials can be used for supercapacitors, printed, andflexible electronics. However the complexity of suchmanufacturing techniques makes them limited to lab re-search and not suitable for any industrial application.

Another method to synthesize graphene is thermaldecomposition of SiC. This method was demonstratedfor the first time by Berger et al. [48.15] and it is basedon the thermal annealing of SiC where sublimation of

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Graphene 48.1 Graphene Synthesis 1175Part

E|48

.1

Graphite

GrapheneTape

Substrate

Exfoliation

CVD

Liquid phase exfoliation

Quality

Manufacturing price

SiC substrate

Thermal decomposition

SiC substrate

SiC substrate

SiC

Fig. 48.2 A drawing of graphenequality versus manufacturing cost fordifferent synthesis methods

Si occurs and the C atoms are segregated on Si- andthe C-face of the wafer and form graphene layers. Theprocess temperatures are around 1600 ıC in 100mbarfor Si-face and 1450 ıC and 0:1�bar for C-face in Aratmosphere [48.16]. As a result of Si desorption, thesurface of SiC holds narrow terraces of graphene andthey are connected by steps.

This method has demonstrated electron mobilityvalues of around 3:0�104 cm2V�1s�1 [48.17] depend-ing on the alignment of SiC substrate terraces with thedirection of carrier transport through graphene stack.

This method provides high quality graphene layersbut has the drawbacks of the high cost of SiC substrateswafers and formation of small-sized graphene of a fewmicrometers which is too small for industrial applica-tions to process a complete transistor.

The formed graphene stack on SiC demonstratesa bandgap of � 260meV. This value may vary depend-ing on the stack thickness and it reaches almost zero for4 graphene monolayers [48.18] due to substrate interac-tion or induced strain by SiC [48.19].

During recent years, chemical vapor deposition(CVD) of graphene has become very popular methodto synthesize graphene. The method is based on thedecomposition of a carbon precursor, for example,methane (CH4) or ethanol (C2H6O) around 1000 ıC ona foil of a transition metal, for example, Cu, Ni, Feas catalyst material [48.20]. Later the formed grapheneis separated or peeled off from surface of catalystmetal by using a transfer polymer (typically poly-methylmethacrylate (PMMA) or polydimethylsiloxane(PDMS)) where the catalyst is etched away [48.21].However, there is a high risk to damage the graphenesheet by the mechanical stress during the removal ac-tion and the quality of the graphene also depends onthe surface roughness of catalyst metal. Different elec-tronic component producers have stepped in using CVDmethod [48.22]. Nowadays very large area graphene isproduced and developed for transparent electronics fordisplayer application. Using this method, carrier mobil-ity of 0:5 cm2V�1s�1 has been demonstrated on SiO2

surface.

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PartE|48.2

1176 Part E Novel Materials and Selected Applications

48.2 Band Structure and Electronic Applications

Six carbon atoms are bonded in graphene honey-comb configuration with hexagonal lattice. Therefore,graphene can be considered as a triangular lattice con-sisting of a basis of two atoms per unit cell present atthe two equivalent lattice sites A and B. A simple cal-culation gives the 2 lattice vectors, where a D 0:142 nmis the nearest-neighbor C-C spacing (Fig. 48.3a).

In principle, a honeycomb configuration has sixpoints at the corners of the first Brillouin zone (FBZ)where they are distinguished in two groups of threeequivalent points. These points are denoted by K and K0

(Fig. 48.3b). These corners are called Dirac points andthe electrons and holes in the vicinity of those points aremassless and follow linear relations (not the quadraticform) of energy momentum dispersion.

Graphene acts as a massless Dirac fermion and itselectronic properties are described by the Dirac equa-tion instead of the Schrodinger equation [48.23].

The graphene band structure has two notable prop-erties: at first, at the Dirac point positions the valenceand conduction band edges are very close (or intersect-ing), resulting in almost no energy gap (Fig. 48.3c).This places graphene in the category of zero band-gap semiconductors or as a semimetal. Secondly, asmentioned above the energy momentum dispersion haslinear behavior and this leads to a constant carrier groupvelocity over energy (where is the Fermi velocity andestimated to 8�105 ms�1/. As a result, the carriershave effective masses, which are directly related to mo-mentum and have zero value at zero energy. This isan exceptional characteristic of graphene which is dis-tinguished from common semiconductors, where thedispersion curves have parabolic shape and carrier ve-locity is dependent on the second derivative of thedispersion curves (Fig. 48.4).

M

M

KK K

�-band

a a1

a2

FBZ

K

K'

Г

a) b) c)

Fig. 48.3a–c A schematic view of graphene (a) honeycomb shape, (b) the first Brillouin zone, and (c) the band structureof graphene. (After [48.24])

Graphene has a linear density of states (DOS) aswell. Each point q appears with twofold spin degener-ate (gs D 2) and since there are two Dirac points K andK0 hence another twofold valley degenerate (gv D 2).Therefore DOS is written as [48.25]

�.E/ D gsgv2�.„�F/2 jEj ; (48.1)

where E stands for energy and �F for Fermi veloc-ity. This makes the DOS distribution of graphene verydifferent from metals and semiconductors (Fig. 48.5).The integral of DOS equation times the Fermi–Diracdistribution at a given temperature results in a no-ticeable electron-sheet density for graphene. Further-more, graphene sheet is not perfectly planar and hassome ripples and this makes charge inhomogeneities ingraphene.

Graphene possesses an ambipolar characteristicagainst an applied electric field. It means in contraryto metals, in the semimetal graphene, electrons mayconvert to holes in response to an applied electricfield [48.26]. This means that n-type or p-type grapheneis not predefined.

Graphene has extremely high carrier mobility.There are three macroscopic forces, which can affectthe carrier mobility in graphene. These forces are diffu-sion, drift, and drag force. Diffusion force is an outcomeof carriers’ random motion, drift force is generated byelectrostatic field and drag is the force due to the car-rier scattering within the lattice [48.22]. In graphene,four scattering mechanisms have influence on the mo-bility. These mechanisms are addressed to the chargedimpurities, acoustic or optical phonons, and surfaceroughness. Experimentally, it has been demonstratedthat the charged impurities in graphene have the crucial

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Graphene 48.2 Band Structure and Electronic Applications 1177Part

E|48.2

E

py

px

E

py

px

Semiconductors Graphene

Fermi velocity

vF = 8 × 105 m/s

Ec = E0c –

p2

2m*e

Ev = E0v –

p2

2m*h

E = ± vF p

Fig. 48.4 The energy band diagram in semiconductorsand graphene

effect on the carrier mobility. The charged impuritiescan be reduced in graphene by annealing or by usinga high-k dielectric [48.27].

Application of graphene in high speed electron-ics has been shadowed for years since the lack ofa bandgap makes it impossible to close the current flow.This blocks the application of graphene for logics sincea bandgap around 400�500meV is sought for this ap-plication. Integration of graphene as a channel materialin field effect transistors (FETs) offers a high transcon-ductance; however, the absence of a well-defined sat-uration region diminishes the benefit of a graphene

DOS

EEF Gap

Metal* Partially filled band* Finite density of states (DOS) at Fermi energy

Semiconductor* Filled band* Gap at Fermi energy

Graphene* Zero gap semiconductor* Zero DOS metal

DOS

E

DOS

E

Fig. 48.5 Electronic structure andDOS for metals, semiconductors andgraphene

Single sheet

Ribbon

Bilayer

Eg = 0

Eg > 0

Eg is tunable

Top gate

Silicon oxide

Back gate

S D

Fig. 48.6 Schematic of band diagramfor different graphene material andGNR transistor. (After [48.28])

power amplifier. A high Ion=Ioff ratio is the key criteriafor RF application.

One way to solve this problem is to decrease thelateral size of graphene to few a nanometers (so-called graphene nanoribbon (GNR)) where the elec-tronic wavefunction could be localized and a quasi 1-Dstructure could be established (Fig. 48.6). In this way,a ballistic quantum transport is built up in graphenewhich is compatible with High Electron Mobility Tran-sistor (HEMT) devices.

Another way to create a small bandgap in grapheneis to form a bilayer graphene (BLG) [48.29] (orso-called Bernal stacked graphene), where the twographene monolayers are placed on each other witha misalignment (Fig. 48.6).

Unfortunately Bernal BLG can mainly be synthe-sized by exfoliation method. Using BLG, a bandgap of130meV and the Ion=Ioff value of � 100 have been ob-tained [48.29].

Many research studies have proposed another alter-native: vertical graphene transistor. This type of tran-sistor functions by current tunneling from an electrodethrough a thin dielectric layer to graphene. In a morepractical way, another graphene layer can be depositedto act as a second electrode. This extra gate allowstriode modulation of the tunnel current [48.30]. This de-sign has demonstrated an Ion=Ioff ratio around 50 but noRF action has been shown so far.

An alternative to the above configuration is integra-tion of graphene in a graphene hot-electron transistor,

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PartE|48.3

1178 Part E Novel Materials and Selected Applications

a) b)

EFS

EFG EFM

eVBEEC

EV

Emitter(n++ Si)

Base(graphene)

Collector(metal)

Tunneling barrier(SiO2)

Filtering barrier(Al2O3)

OFF

EFS

EFG EFM

eVBE

EC

EV

Emitter(n++ Si)

Base(graphene)

Collector(metal)

Tunneling barrier(SiO2)

Filtering barrier(Al2O3)

ON

Fig. 48.7a,bVertical graphenetransistor (a) inoff and (b) onstate. (Af-ter [48.31])

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 appliedas low-resistivity base electrode and consists of anemitter base tunnel junction and a base collector filter-

ing dielectric (Fig. 48.7a,b). Although these transistorshave shown Ion=Ioff ratio around 105 they have a verylow current gain, which leads to collector currents 10orders of magnitude less than the other types of transis-tors [48.32].

48.3 Characterization of Graphene Material

Graphene material is usually in a few monolayerson a specific substrate and it is difficult to be dis-tinguished by optical microscopes. The characteriza-tion techniques, for example, atomic force microscopy(AFM), transmission electron microscopy (TEM), x-ray diffraction (XRD), and Raman spectroscopy aremainly applied to study graphene.

48.3.1 AFM

AFM is a common technique to estimate the thicknessof graphene material. In general, 2-D crystallites suchas graphene are a few nanometers thick elevated on thesurface. Tapping mode is mostly used for the thicknessmeasurements [48.33]. However, AFM technique haslow throughput and therefore the measured data are notwithout error.

As an example,Novoselov et al. [48.33] have showna monolayer graphene has 0:4 nm height, and Guptaet al. showed a height of 0:7 nm for single monolayer ofgraphene. One explanation for these different outcomes

in measurements could be that these groups used thedifferent amplitudes of the cantilever for their experi-ments.

This shows that extra care has to be taken toanalyze the AFM results in order to have a compara-ble and reliable method to measure the thickness ofgraphene [48.33, 34].

48.3.2 Transmission Electron Microscopy

Transmission electron microscopy (TEM) is one ofthe most accurate methods to study graphene and pro-vide atomic resolution (Fig. 48.8a–c). Graphene ap-pears both in single- and multilayers in a flat sheet orfolded form. The electron beam is parallel to the foldedgraphene sheets and they appear as one dark line forsingle sheets (Fig. 48.8a) and double dark lines for bi-layer sheets (Fig. 48.8b). In the case of multiple foldedsheets the number of dark lines could appear in anyshape [48.35]. This can make it difficult to determinethe number of graphene sheets.

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Graphene 48.3 Characterizationof Graphene Material 1179Part

E|48.3

a) b) c)

1 nm

Fig. 48.8a–c TEMimages: (a) cross-sectionof single-folded graphene,(b) cross-section ofdouble-folded grapheneand (c) top view ofgraphene material.(Reprinted from [48.36],with permission fromElsevier)

3000250020001500

Intensity (arb. units)

Raman shift (cm–1)

2D

G

n = 1

n = 2

n = 3

n = 6

Fig. 48.9 Raman curves of graphene with n layers. (Af-ter [48.37])

48.3.3 Raman Spectroscopy

Raman spectroscopy is a technique that is based on in-elastic interactions of phonons in a layer. For graphene,Raman can provide information about the number ofmonolayers and the quality of graphene material. Thereare three main bands in Raman analysis:

� The D band� The 2-D band� The G band.

1600

HOPG

n = 19

n = 8n = 5n = 4n = 3n = 2n = 1

Fig. 48.10 G-band ofgraphene for a seriesof graphene layers n.(After [48.38])

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

The 2-D BandThis band indicates the number of graphene sheets andalso 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 singlesheet. However, if the graphene consists of multilay-ers then the shape of the peak is broad with smallpeaks. Figure 48.9 shows different cases for graphene

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PartE|48.4

1180 Part E Novel Materials and Selected Applications

600

500

400

300

200

100

010 20 30 40 50

Intensity (arb. units)

2θ (degree)

(002)

(100)(101)

Fig. 48.11 X-ray curve for graphene. (After [48.40])

material. As an example, Raman results from a bi-layer graphene shows peaks at wavelengths of 514 and633 nm [48.41].

The G BandThe position of this band shows the number of graphenesheets. A peak is seen around 1587 cm�1 if thegraphene consists of a single sheet, otherwise the Gband moves downwards. Figure 48.10 shows the changeof G band for graphene layers with different numbers ofsheets [48.38].

48.3.4 XRD Analysis

X-ray diffraction is a technique that is usually used tostudy thin films. In the case of a very thin layer ofgraphene, a high-intensity x-ray beam is required. TheXRD technique provides information about the crys-talline quality and layer thickness of graphene. Thelatter parameter could be relatively determined by theintensity of the peaks. The XRD data of the graphenematerial gives three main peaks at reflections:

� (002) at 26:3ı

� (101) 44:6ı

� (100) 43:2ı (Fig. 48.11) [48.40, 42].

48.4 Photonic Applications

Graphene has very promising optical properties formodulators [48.43, 44], photodetectors [48.45, 46], andplasmonic structures. Despite its thin thickness, it ab-sorbs light in the vertical or lateral direction due todistinctive electronic structure [48.47]. The material ab-sorbs a large variety of wavelengths within interband,intraband, and collective plasmon excitations. The ex-traordinary benefit of graphene is tuning the absorptionby regulating the charge density.

The optical conductivity is written by a universalvalue of �uni D �e2=2 h. For photons with higher en-ergies, the optical conductivity is increased graduallytowards peaks, which lie in UV range with energy of4:62 eV (Fig. 48.12). This is related to nonlinear part ofdispersion relation, which is labeled by interband tran-sitions from the bonding to the antibonding � states inthe graphene Brillouin zone [48.48].

Graphene absorbs ideally 2:3% of the normal in-cident light through intra- and interband transitions.This absorption may deviate from the ideal univer-sal 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 presenceof phonons) [48.49].

Graphene can be placed on a waveguide to ab-sorb light along the lateral direction (Fig. 48.13b). Thelength of graphene sheet may determine the amount

of the absorption and for a long enough sheet a to-tal absorption can be obtained. The absorption of lightin the lateral direction occurs when a graphene sheetis placed on a waveguide. The length of graphene (orwaveguide) sheet determines the amount of absorptionand a complete absorption can be obtained if the lengthof graphene is long enough.

00 1 2 3 4 5

1

2

3

4

5

Photon energy (eV)

σ (In unit of �e2/2h)

4.62 eV

ExperimentUniversal optical conductivity

Fig. 48.12 Experimental optical conductivity (solid line)and the universal optical conductivity (dashed line) ofa single graphene layer. The discrepancy of the optical datafrom the universal values at low energies is due to sponta-neous doping. (After [48.48])

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Graphene 48.4 Photonic Applications 1181Part

E|48.4

97.7 %

~ 0 %

a) b)Fig. 48.13(a) Normalincident lightshines ona graphene layer.(b) Grapheneon a waveguideand the lightinteracts withgraphene alongthe waveguidesheet

Gate Absorber

Si waveguide

Vg

BOX

Fig. 48.14 A bilayer graphene mod-ulator integrated on a waveguide. Byapplying a voltage to the gate, charge-sheet density in the first graphenelayer is affected. (After [48.44])

G

G

A

Au

Au

Graphene

SiO2

Fig. 48.15 A photodetector with graphene active layer.(After [48.46])

An innovative method to deal with graphene lowDOS is to use two graphene sheets isolated by an ox-ide layer (Fig. 48.14). In this design, the first graphenesheet layer is for absorption, however, the second sheetoperates as a gate.

Si is a material with a bandgap of 1:12 eV, and istransparent for � > 1:1�m. Therefore, Si can be usedas a waveguide to conduct telecom wavelengths.

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

Graphene has also been used as active photonicmaterial in photodetectors. An electrical current wasgenerated when the contact electrode of graphene tran-sistor was illuminated [48.50, 51] (Fig. 48.15). In or-der to increase the absorption, the detector can beformed on a waveguide processed on an SOI sub-strate with a high-k material beneath the graphenesheet.

Although graphene can absorb a broad wave-length a graphene detector has a low responsivity of0:1mA=W, which is remarkably lower than III-V de-tectors.

During recent years, many research efforts havebeen spent on other 2-D crystals (transition metaldichalcogenides, silicene, and germanene) as competi-tors to graphene [48.52].

The transition metal dichalcogenides are a group ofmaterials which are known as MX2, where M is a tran-sition metal element from group IV (e.g., Ti, Zr or Hf),group V (e.g., V, Nb, or Ta), or group VI (e.g., Moor W), and X is a chalcogen material (e.g., S, Se, orTe).

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

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PartE|48

1182 Part E Novel Materials and Selected Applications

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