Raman characterization of defects and dopants in graphene · Raman characterization of defects and dopants in graphene Ryan Beams1, Luiz Gustavo Canc¸ado2 and Lukas Novotny3

Journal of Physics: Condensed Matter

J. Phys.: Condens. Matter 27 (2015) 083002 (26pp) doi:10.1088/0953-8984/27/8/083002

Topical Review

Raman characterization of defects anddopants in graphene

Ryan Beams1, Luiz Gustavo Cancado2 and Lukas Novotny3

1 Institute of Optics, University of Rochester, Rochester, NY 14627, USA2 Departamento de Fısica, Universidade Federal de Minas Gerais, Belo Horizonte, MG 31270-901, Brazil3 ETH Zurich, Photonics Laboratory, 8093 Zurich, Switzerland

Received 18 October 2014Accepted for publication 26 November 2014Published 30 January 2015

AbstractIn this article we review Raman studies of defects and dopants in graphene as well as theimportance of both for device applications. First a brief overview of Raman spectroscopy ofgraphene is presented. In the following section we discuss the Raman characterization of threedefect types: point defects, edges, and grain boundaries. The next section reviews thedependence of the Raman spectrum on dopants and highlights several common dopingtechniques. In the final section, several device applications are discussed which exploit dopingand defects in graphene. Generally defects degrade the figures of merit for devices, such ascarrier mobility and conductivity, whereas doping provides a means to tune the carrierconcentration in graphene thereby enabling the engineering of novel material systems.Accurately measuring both the defect density and doping is critical and Raman spectroscopyprovides a powerful tool to accomplish this task.

Keywords: Raman scattering, graphene, defects, dopants

(Some figures may appear in colour only in the online journal)

1. Introduction

Modern semiconductor technologies rely on controllingdopants and minimizing defect generation during fabricationprocesses. Perhaps the most notable example being thep-n junction. In order to fabricate devices that exploitdoping induced material modifications, methods capable ofquantifying the doping level and defect density are required.Raman spectroscopy has been used extensively to characterizethe strain, defect density, and doping levels in semiconductors,such as silicon, germanium, and gallium arsenide [1–3].While silicon and other bulk semiconductors have drivenresearch and technology for more than 50 years, carbon-based materials have begun to receive considerable attentionin part due to carbon’s natural abundance and a smallerelectron wavefunction, which allows for smaller devicefootprints before quantum effects dominate [4, 5]. The lowdimensionality of graphene and carbon nanotubes also allowsfor direct fabrication of one- and two-dimensional devices.As with semiconductor materials, Raman spectroscopy is

a powerful tool for characterizing doping and defects ofgraphene, both of which play critical roles in determiningits properties. In many cases graphene devices require theFermi level to be controllably changed through doping withoutintroducing defects that impede the performance.

In this paper, we review the Raman process in graphene(section 2) and the impact of defects and dopants, aswell as a few device applications. Section 3 investigatesstructural defects such as edges, vacancy sites, and finite-sized crystallites. Generally defects degrade the attractiveaspects of graphene. Therefore, characterization techniquessuch as Raman spectroscopy are crucial for implementing anytype of graphene-based technology. Edges also significantlyalter the properties of graphene, but the effects can beengineered to be favorable, such as opening a bandgap.Doping provides a means to control many of the electronicproperties of graphene, such as the carrier concentration andconductivity. Similar to semiconductors, this has openedthe possibility to study fundamental physical phenomena like

0953-8984/15/083002+26$33.00 1 © 2015 IOP Publishing Ltd Printed in the UK

http://dx.doi.org/10.1088/0953-8984/27/8/083002

http://crossmark.crossref.org/dialog/?doi=10.1088/0953-8984/27/8/083002&domain=pdf&date_stamp=2015-01-30

J. Phys.: Condens. Matter 27 (2015) 083002 Topical Review

D,2DG

Γ K M Γ0

200

400

600

800

1000

1200

1400

1600

Freq

uenc

y (c

m )-1

iLO

iTO

iLA

iTA

oTA

oTO

Figure 1. Phonon dispersion of graphene. The phonons associatedwith important Raman bands are highlighted. The �, K, and Msymmetry points are shown. Adapted with permission from [25].Copyright 2009 Elsevier.

the quantum Hall effect [6–9] as well as creating devices,including photodetectors [10–12] and field-effect transistors(FETs) [13, 14]. The dependence of the Raman signal ondoping as well as several methods for doping graphene arediscussed in section 4. Finally, several graphene devices thatdepend on doping and defects are discussed is section 5.

2. Overview of Raman scattering in graphene

Raman spectroscopy has proven to be an incredibly powerfultool for characterizing graphene flakes. It is commonlyused to determine the number of graphene layers, the defectdensity, the edge chirality, strain, thermal properties, and theamount of doping [15–21]. More recently it has been used todetermine the stacking order and the sheet mis-orientation inbilayer graphene [22, 23]. In this section the Raman processin graphene is reviewed. For a more detailed study of theRaman process in graphene, references [24–27] are excellentresources.

2.1. Phonon dispersion and the Kohn anomaly

To understand the Raman modes in graphene it is important tostart with the phonon dispersion, which is shown in figure 1.Since the graphene unit cell has two atoms, there are six phononbranches, three acoustic (A) and three optical (O) phonons.Four of the phonon branches are in-plane (i): two acousticand two optical. The other two branches are out-of-plane (o).Depending if the direction of the zone-center mode is along thecarbon–carbon (C–C) bonds or perpendicular, the modes areknown as transverse (T) or longitudinal (L). The six phononbranches are labeled in figure 1.

The iLO and iTO phonons are responsible for the mainRaman bands observed in graphene. It is important to note thatthe iTO and iLO phonon energies are highly dispersive at the� and K points. The phonon energy softening at these pointsis known as the Kohn anomaly [28, 29] and is often observedin metals. The Kohn anomaly is caused by the phonon energyrenormalization due to electron–phonon coupling. In this

process the phonon creates a virtual electron–hole pair thatthen re-combines and creates another phonon. As a resultthe phonon lifetime and energy are lowered. The degree towhich the phonon energy is renormalized is determined bythe strength of the electron–phonon coupling [24]. Ordinarilyin crystals the electrons move adiabatically with the ionsas the lattice vibrates. However, as the electron–phononcoupling increases the electrons no longer fully relax to theirground states during the lattice vibrations and therefore theyno longer move adiabatically with the ions, which reduces thephonon energy [30, 31]. In graphene the Kohn anomaly canbe suppressed by changing the Fermi level, which decreasesthe electron–phonon coupling [30, 32]. This will be discussedin more detail in section 4.

Figure 2(a) shows a spectrum of a pristine graphene flakeand the primary bands, G and 2D, or 2D′, are labeled. Adamaged flake is shown in figure 2(b), which has several otherRaman bands appearing, such as D, D′, and their combinationD+D′. All these bands are discussed below.

2.2. First order and intervalley Raman modes

The main first order Raman band in graphene, known asthe G band (∼1580 cm−1), is a doubly-degenerate in-planesp2 C–C stretching mode that belongs to the E2g irreduciblerepresentation [33]. This band exists for all sp2 carbonsystems, including amorphous carbon, carbon nanotubes, andgraphite, except the lineshape varies based on the samplequality [26]. The G band originates from phonons at the �

point in the center of the first Brillouin zone. Figure 3(a)shows an illustration of the two G band stretching modes ingraphene. The mechanism giving rise to the G band starts withan incident photon that resonantly excites a virtual electron–hole pair in the graphene (figure 4(a)). The electron or thehole is scattered by either a iTO or a iLO zone-center phonon.The electron–hole pair then radiatively re-combines and emitsa photon that is red shifted by the amount of energy given to thephonon, as shown figure 4(a). As can be seen from the phonondispersions (figure 1), the phonons involved in this processhave very little momentum (i.e. the process is at the � point).For graphene and graphite these two modes are degenerate, butthe degeneracy can be lifted by rolling the graphene sheet intoa carbon nanotube, which splits the G band into the G+ and G−

bands [34]. In this way, the width of the G band can also beused to measure the deformation and strain on a sample [18].

The strongest peak in graphene is the 2D, or G′ band,(∼2700 cm−1), which is a second order Raman processoriginating from the in-plane breathing-like mode of thecarbon rings (figure 3(b)). It belongs to the totally symmetricirreducible representation A′

1 at the K (or K′) point in the firstBrillouin zone. Figure 4(b) shows a diagram of the Raman 2Dprocess. The top panel shows the double resonance process inwhich an electron–hole pair is created by an incident photonnear the K point. The electron is inelastically scattered by aiTO phonon to the K′ point.

Since the Raman process must conserve energy andmomentum, the electron must scatter back to K beforerecombining with the hole. In the case of the 2D band the

2


2700 3200

(b)

1200 17000

2

4

6

8

10

12

Relative Wavenumber (cm−1)

Inte

nsity

(a.

u.)

D

G

2D

5

10

15

20

1500 2000 2500 3000

Relative Wavenumber (cm−1)

Inte

nsity

(a.

u.)

(a)

G

Figure 2. Example spectra of a graphene flake. (a) A pristine flake showing only the G, 2D, and 2D′ bands. (b) A damaged flake, whichshows the D and D′ bands, as well as their combination D+D′.

iLO at ΓG Band

iTO at ΓD and 2D Band(a) (b)

iTO at K

Figure 3. Sketch of the phonon vibrations contributing to the main Raman bands in graphene. (a) G band vibration modes for the iTO andiLO phonons at the �-point. (b) D vibration mode for the iTO phonon at the K-point [26].

2D BandG Band

EF

Γ

qq

-qK K

q

q

K K

q

-dK

D Band

(a) (b)

(c)Triple Resonance

Double Resonance

K

Figure 4. Sketch of the main Raman processes in graphene. (a) G band (b) 2D or G′ band generated through a second-order process that iseither double resonant (top) or triple resonant (bottom). (c) D band double resonant process involving a scattering from a defect (horizontaldotted line).

3


(a) SLG

(b) BLG

(c) Graphite

2600 2650 27002550 2750 2800 2850

Raman shift (cm )-1

Figure 5. Spectra of the Raman 2D band. (a) SLG (b) BLG (c)graphite. Adapted with permission from [25]. Copyright 2009Elsevier.

electron is back-scattered by a second iTO phonon. Of course,the same process can also occur for the hole instead of theelectron. This process is known as double resonant (DR),because the incident or scattered photon and the first or secondphonon scattering are resonant with electronic levels in thegraphene. Alternatively, the 2D band process can also be tripleresonant, which is shown in the lower panel of figure 4(b). Inthis case, both carriers are scattered by iTO phonons fromnear the K point to the K′ point and recombine by emitting aphoton. Experimentally the 2D band can be used to determinethe number of graphene layers in a flake [16]. For single layergraphene (SLG), the 2D band is a single Lorentzian. Howeverthe 2D bands splits into four peaks in bilayer graphene (BLG)[16, 35]. Example spectra of the 2D band for SLG, BLG, andgraphite are shown in figure 5 [25].

Another important band is the disorder-induced D band,which occurs near 1350 cm−1 for laser excitation energies of2.41 eV [33]. This band involves an iTO phonon around theK-point like the 2D band. However, unlike the G or 2D bands,the D band requires a defect for the momentum conservation.In this case, the electron is inelastically scattered by an iTOphonon to the K′ point and then is elastically back-scatteredto the K point by a defect [36–38]. Since only one phonon isinvolved in the process, the energy shift for the D band is halfthat of the 2D band. For the momentum conservation, a defectis any breaking of the symmetry of the graphene lattice, suchas sp3-defects [39], a vacancy sites [19, 40], grain boundaries[41], or even an edge [15, 42, 43]. The defect density canbe controllably increased using ion bombardment [19, 40],electron beam irradiation [44, 45], or plasma fuctionalization[39, 46]. The Raman spectroscopy of defects is discussed indetail in section 3.

2.3. Intravalley Raman modes

The D and 2D bands discussed above are intervalley processes,since the process involves electronic states near both the K and

2D Bandq

-q

K

q

-d

K

D Band(a) (b)

Figure 6. Sketch of two intravalley double resonance Raman bandsin graphene. (a) 2D′ band (b) D′ band.

K KB

A

BA

G Band 2D Band(a) (b)

Figure 7. Sketches of the Raman process for the (a) G and (b) 2Dbands for two different excitation energies.

K′ points. However, similar mechanisms exist for intravalleyRaman processes [37]. Figure 6 shows a diagram of the 2D′

(or G′′) and D′ modes. The D′ band (∼1620 cm−1) requires adefect, like the D band. 2D′ (∼3240 cm−1) is a two phononprocess and the overtone of the D′ band. These bands aresignificantly weaker than the 2D and D band.

2.4. Dispersion

Raman processes associated with phonons in the interior ofthe first Brillouin zone in graphene can be dispersive, whichis not the case for zone-center processes. In the case of the Gband, the energy of the incident photon does not change thefrequency of the phonon involved in the Raman process (seefigure 7(a)). However for DR bands, like the 2D band, theincident photon energy changes the frequency of the phononthat is involved. As the photon energy increases, phononsfarther from K point are required for momentum conservation,as can be seen by comparing paths A and B in figure 7(b).Therefore, measuring the 2D band as a function of excitationenergy maps out the phonon dispersion relationship, whichwas demonstrated in [47]. The 2D band dispersion has beenshown to continue into the ultraviolet spectral range [48].

3. Raman characterization of defects in graphene

In the Raman spectra of graphene and other sp2 carbonsamples containing defects, several additional symmetry-breaking features are found. The feature with the highestintensity is usually the D band. The D band is associatedwith near-K point phonons [33]. Another common symmetry-breaking feature in the first-order spectrum is the D′ band near1620 cm−1, associated with near-� (q �= 0) point phonons,where q refers to the magnitude of the phonon wave vector

4


(a) (b)

Figure 8. (a) Raman spectra of single layer graphene samples exposed to Ar+ ion-bombardment with distinct ion doses. The data wereobtained using a 514 nm (2.41 eV) laser line. The ion doses (in units of Ar+ cm−2) are indicated next to each respective spectrum. (b) Theplot ID/IG as a function of the average distance between point defects LD for samples exposed to distinct Ar+ doses. Adapted withpermission from [19]. Copyright 2010 Elsevier.

[49], as discussed in section 2. The D and D′ bands canalso give rise to overtones and combination modes, therebyresulting in additional symmetry-breaking modes in the Ramanspectra [50, 51]. The most common reasons for symmetrybreaking are the presence of vacancies, interstitial atoms, andsubstitutional atoms, which can be intentionally introduced byion implantation [19, 52] or by introducing interfaces at theborders of crystalline areas [33, 53]. In this section, we reviewthe Raman spectra of defective graphene-like structures,showing how these disorder-induced Raman features can beused to quantify the amount of disorder in these systems. Thesection is divided into three subsections, each one dedicatedto one particular type of defect, starting with point-likedefects (section 3.1), continuing with edges (section 3.2), andfinalizing with crystallite borders (section 3.3).

3.1. Point defects

A point defect is the simplest and most symmetric type ofdefect that can be generated in a graphene lattice. Because itis highly localized in real space, its spatial frequency spectrumis extremely broad. In other words, it is highly delocalizedin the reciprocal space, thereby always providing the extramomentum necessary to satisfy the q ≈ 0 selection rulein one phonon Raman processes. In order to study theRaman spectrum of this important type of defect, Luccheseand collaborators generated a protocol for sample productionusing ion-bombardment, followed by scanning tunnelingmicroscopy (STM) characterization [19]. This work deservesspecial attention, and in this section we summarize its mainresults. At the end of the section we review an extension ofthis work to Raman spectra of ion-bombarded samples usingdifferent laser energies [40].

Figure 8(a) shows Raman spectra of single layer graphenesamples intentionally damaged by Ar+ ion-bombardment withdistinct ion doses [19]. The ion-bombardment process waspreviously performed in HOPG samples and monitored by

STM images, from which the defect density (nD) was extractedas a function of the ion dose. From figure 8(a) it is clear that theRaman spectra of graphene, mildly disordered graphene, andvery highly disordered graphene (close to amorphization) aredistinctly different. The D band process is activated from thepristine sample (bottom spectrum) to the lowest bombardmentdose (1011 Ar+ cm−2, or one defective site per 4 × 104 Catoms), showing a small intensity if compared to the G peak,that is, a small ID/IG ratio. Within the bombardment doserange 1012–1013 Ar+ cm−2, the D band intensity increases.The second disorder-induced peak, the D′ band, also becomesevident within this bombardment dose range. However, above1013 Ar+ cm−2, the graphene Raman spectra start to broadensignificantly and reflects the phonon density of states for thehighest ion dose of 1014 Ar+ cm−2. Figure 8(b) shows theplot ID/IG as a function of the average distance betweendefects LD, which quantifies the degree of disorder. Asshown in the plot, the ID/IG ratio increases with increasingLD up to 3–5 nm, where ID/IG reaches a maximum value, anddecreases for LD � 3–5 nm. The trend suggests the existenceof two disorder regimes contributing to the Raman D bandintensity. These two different ranges were first introducedfor nanostructured graphite samples by Ferrari and Robertsonin [54], who named the low- and high-disorder regimes asstages I and II, respectively. The mechanism that gives rise tothese two stages in point-like defective samples was introducedin [19], and is described in the following paragraphs.

To explain the ID/IG dependence on LD, Luccheseand collaborators proposed an activation model for D bandscattering, as illustrated in figure 9 [19]. The model assumesthat a single impact of an ion on the graphene sheet generatesmodifications on two length scales, denoted by rA and rS (withrA > rS), which define, respectively, the radii of two circularareas centered at the ion impact point (see figure 9(a)). Theinner area defined by the radius rS, defines the structurallydisordered S-region caused by the impact of the ion. Fordistances larger than rS, but shorter than rA, the Raman D

5


(d) (e)

(c)(b)

(a)

Figure 9. (a) Illustration of a point defect obtained from the impactof an ion on the graphene sheet. The model considers two distinctareas: the activated A-region (green), and the structurally disorderedS-region (red). The respective radii rA and rS are measured from theion impact point. (b)–(e) Snapshots of the simulation for thestructural changes in the graphene layer for different defectconcentrations: (b) 1011 Ar+ cm−2; (c) 1012 Ar+ cm−2; (d)1013 Ar+ cm−2; (e) 1014 Ar+ cm−2, like the four top spectra infigure 8(a). Reprinted with permission from [19]. Copyright 2010Elsevier.

band is activated and the lattice structure is preserved. For thisreason, this region was called as ‘activated’ or A-region in [19].In qualitative terms, a photoexcited electron–hole pair willbe able to sense the structural defect if the excitation processtakes place in a region sufficiently close to the defect site. Inother words, a photoexcited electron–hole pair must reach thedefective site during the time interval in which the Ramanprocess occurs. Therefore, the difference rA − rS shouldbe related to the correlation length of photoexcited electronsparticipating in the double-resonance mechanism giving riseto the D band. The physical picture for this correlation lengthhas also been explored in other works [42, 43, 55–57], and willbe discussed in greater detail in section 3.2.

To understand the activation model, Lucchese et alperformed stochastic simulations. Snapshots of distinctdisorder levels are illustrated in figures 9(b)–(e) for the sameAr+ ion concentrations as in figure 8(a). This simulation

process gave rise to a phenomenological equation on the form

ID

IG= CA

(r2A − r2

S)

(r2A − 2r2

S)

[e−πr2

S/L2D − e−π(r2

A−r2S )/L2

D

]

+CS

[1 − e−πr2

S/L2D

]. (1)

The parameters CA = 4.2, CS = 0.87, rA = 3 nm, andrS = 1 nm were extracted from the fit of the experimental dataaccording to equation (1) (solid line in figure 8(b)) [19]. TheCA parameter gives the maximum possible value of the ID/IG

ratio in graphene, which would occur in a hypothetical situationin which the double-resonance process giving rise to the Dband would be allowed everywhere in a perfect graphene layer.Looking at figures 9(b)–(e), we can picture that CA would bethe value of ID/IG in a sample completely covered by green(activated A areas), with no red spots (structurally damaged Sareas). CA is therefore related to the electron–phonon matrixelements, and the value CA = 4.2 is in rough agreement withthe ratio between the electron–phonon oscillation strengths forthe TO phonons evaluated between the K (related to the Dband) and � (related to the G band) points in the Brillouinzone [58]. The CS parameter corresponds to the oppositelimit, that is, when a sample is completely covered by red(structurally damaged S areas), where a high-disorder limit isachieved. For larger values of LD (LD > 6 nm), a much simplerformula can be used:

ID

IG= A

L2D

, (2)

where the proportionality constant A assumes the value of A ≈100 nm2 for an incident laser wavelength of 514 nm. However,for the crystallite case discussed in section 3.3, the ID/IG

ratio strongly depends on the excitation laser wavelength, andtherefore the fitting parameters obtained in [19] have to beadjusted for other laser lines.

The dependence of the ID/IG on the excitation laser energy(or wavelength) was further explored in [40]. Figure 10(a)shows the ID/IG data (bullets) for monolayer graphene samplesexposed to distinct Ar+ ion doses (giving rise to differentvalues of LD). The three distinct experimental plots wereobtained using three different laser energies (1.58, 1.96, and2.32 eV). The lines are the fitting curves from equation (1),considering different values of CA (plotted in the inset(squares) as a function of the excitation laser energy (EL)).Notice that CA decreases as the laser energy increases, andthis trend is associated with the dependence of the D bandintensity on the phonon wave vector involved in the double-resonance scattering process. The solid line in the inset offigure 10(a) is the fitting of the experimental data consideringa dependence on the inverse fourth power of EL, giving CA =160 E−4

L . The same trend is observed in the Raman spectra ofnanocrystallites, as discussed in section 3.3 [53, 59]. The E−4

Ldependence is not yet understood, and may be restricted to theoptical range. Although CS could present some dependence onexcitation laser energy, the experimental data set did not allowfor a clear determination of any type of dependence of CS onthe excitation laser energy, and for this reason the authors haveset CS for all values of EL used in this experiment. The fitting

6


(a)

(b)

Figure 10. (a) ID/IG for single layer graphene samples exposed todistinct Ar+ ion doses (giving rise to different values of LD),obtained using three different laser energies (1.58, 1.96, and2.32 eV). Solid lines are fits according to equation (1) withrA = 3.1 nm, rA = 1, and CS = 0. The inset plots CA as a functionof EL. The solid curve is given by CA = 160 E−4

L . (b) Takenfrom [40]. Plot of the product E4

L(ID/IG) versus LD for theexperimental data shown in panel (a). The dashed blue line is theplot obtained from the substitution of the relation CA = 160 E−4

L inequation (1). The solid line is the plot of the product E4

L(ID/IG)according to equation (4). The gray area accounts for experimentalerror. Adapted with permission from [40]. Copyright 2011American Chemical Society.

procedure also gives rA = 3.1 nm, and rA = 1 nm, in excellentagreement with the values obtained in [19]. Figure 10(b)shows the plot of the product E4

L(ID/IG) versus LD for theexperimental data shown in panel (a). From this plot, onecan clearly see that all the data with LD > 10 nm obtainedwith different laser energies fall on the same curve. Thedashed blue line is obtained from the substitution of the relationCA = 160 E−4

L in equation (1).We now turn our attention to the samples with LD >

10 nm (low defect density regime) for which LD > 2rA.In this regime, the total area contributing to the D bandscattering is proportional to the number of point defects, andtherefore we have (ID/IG) ∝ L2

D, as previously indicated in

equation (2). By considering LD � (rA, rS), equation (1) canbe approximated as

ID

IG� CA

π(r2A − r2

S)

L2D

. (3)

By taking rA = 3.1 nm, rS = 1 nm, and also the relationCA = 160E−4

L , equation (3) can be rewritten as

L2D (nm2) = 4.3 × 103

E4L

(ID

IG

)−1

. (4)

In terms of excitation laser wavelength λL (in nanometers), wehave

L2D (nm2) = (1.8) × 10−9λ4

L

(ID

IG

)−1

. (5)

Equations (4) and (5) are valid for Raman data obtained fromgraphene samples with point defects separated by LD �10 nm using excitation lines in the visible range [40]. Thesolid line in figure 10 is the plot of the product E4

L(ID/IG)

according to equation (4).

3.2. Edges

The crystallite borders in nanographitic samples form one-dimensional defects. However, because the crystallites havedifferent sizes and their boundaries are randomly oriented inreal space, the wave vectors associated with the defectiveborders exhibit all possible directions and values in reciprocalspace. Therefore, it is always possible to have a defect withmomentum exactly opposite to the phonon momentum, givingrise to double-resonance processes connecting any pair ofpoints (electron wave vectors) around the K and K′ pointsin the first Brillouin zone of graphite or graphene [36, 37].Because the crystallite borders are isotropically distributed,the D band intensity is also isotropic and does not depend onthe polarization direction of the incident or scattered fields.However, in the case of straight edges, the D band intensityis anisotropic because the double-resonance process cannotoccur for any arbitrary pair of electron k vectors [15, 42, 56].Since the defect in this case is completely delocalized alongthe direction parallel to the edge in real space, the associatedwave vectors are completely delocalized along the directionperpendicular to the edge in reciprocal space, assuming allpossible values in this direction. Therefore, a straight edgedefect has a one-dimensional character and is only able totransfer momentum in the direction perpendicular to the edge.

In this section, a review of the D band scattering neargraphene and graphite edges is presented. It will be shownhow this momentum-related selection rule can be explored inorder to define the atomic structure of the edges in the armchairor zigzag arrangements, as well as to quantify their local degreeof order in polarized Raman experiments. At the end of thesection we show that the D band scattering is strongly localizedat the edges. The origin of the localization is discussed in termsof the correlation length of photo-excited electrons involved inthe double-resonance scattering process.

7


(a)

(b) (c)

Figure 11. (a) Raman spectra recorded at three different regionsnearby the edges of a terrace in a highly oriented pyrolytic graphite(HOPG) sample. The inset shows a micrograph of the sample.Regions 1 and 2 are at step edges, while region 3 is situated at aninterior point of the HOPG sample. (b) Idealized structure of theedges shown at the inset to part (a). The bold green lines highlightthe edge structures (armchair for edge 1 and zigzag for edge 2). Thewave vectors of the defects associated with these edges arerepresented by �da and �dz for armchair and zigzag, respectively.(c) The first Brillouin zone of graphene oriented according to thereal space representation illustrated in (b). Note that the armchair �da

vector is the only one able to connect points belonging toequienergy contours surrounding two inequivalent K and K′ points.Adapted with permission from [15]. Copyright 2004 by theAmerican Physical Society.

3.2.1. Influence of the atomic structure of the edges on the Dband intensity.

Figure 11(a) shows three Raman spectra recorded at threedifferent regions nearby the edges of a terrace in a highlyoriented pyrolytic graphite (HOPG) sample. The inset tofigure 11(a) shows a micrograph of the sample, indicatingthe positions of these three distinct regions. Whereas regions1 and 2 are at step edges, region 3 is situated at an interiorpoint of the HOPG sample. The polarization of the incidentlight is kept parallel to the edge direction in spectra 1 and 2.The G band (≈1580 cm−1) is measured in all three regionswith approximately the same intensity. On the other hand,the disorder-induced D (≈1340 cm−1) and D′ (≈1620 cm−1)bands are observed in spectra 1 and 2, but not in spectrum 3,since spectrum 3 was taken at a pristine region with crystallineorder (see inset to figure 11(a)). As shown in figure 11(a),

while the D band is remarkably different in spectra 1 and2 (about four times less intense in spectrum 2), the D′ bandintensity is roughly the same for both spectra.

Atomically-resolved STM images of the edges (shown in[15]) revealed that edge 1, shown in the inset to figure 11(a), hasan armchair structure, whereas edge 2 has a zigzag structure.Figure 11(b) illustrates the idealized structure of the edges ina two-dimensional approach. The bold green lines highlightthe edge structures (armchair for edge 1 and zigzag for edge2). The wave vectors of the defects associated with theseedges are represented by �dz and �da for zigzag and armchairedges, respectively. Figure 11(c) shows the first Brillouin zoneoriented according to the real space representation illustratedin figure 11(b). Note that the armchair �da vector is the onlyone able to connect points belonging to equienergy contourssurrounding two inequivalent K and K′ points. On the otherhand, �dz cannot connect K↔K′ points in intervalley scattering,which explains why a much less intense D band is observedin zigzag edges. However, the �dz vector is still able toconnect K↔K or K′↔K′ in intravalley scattering. Since D′

band is activated by intravalley processes in which the defectwave vector connects points belonging to the same equienergycontour around the K (or K′) point [37], the D′ band intensitymust be independent of the edge structure. The experimentalresult shown in figure 11(a) confirms this assumption [15],since the D′ band has a similar intensity in both spectra obtainedfrom armchair and zigzag edges (spectra 1 and 2, respectively).The observation of a weak D band in spectrum 2, where itshould be absent, can be justified by taking into considerationa realistic atomic structure of the edges, which cannot beexpected to be perfectly zigzag or armchair along the wholeextension. These residual variations on the atomic structureallow for the occurrence of defects with wave vectors notperpendicular to the edge [15, 42, 56, 57].

The anisotropy in the D band intensity was extensivelystudied in [60], where the authors performed statistical analysison Raman images obtained from monolayer graphene sampleswith straight edges forming different relative angles to eachother (figure 12) [60]. The upper and bottom imagesin figures 12(a)–(d) render the D and G band intensities,respectively. The images shown in panels (a)–(d) wereobtained from distinct regions, each one containing a pairof edges with relative angles of 30◦, 60◦, 90◦, and 60◦,respectively. In all cases the green arrows indicate thepolarization direction of the incident laser, and the G bandintensity is uniform over the whole graphene area. In panel(a), the D band intensity is remarkably stronger in the upperedge when compared to the bottom edge. Since the relativeangle between these two edges is 30◦, the authors concludedthat the atomic structure of the upper and bottom edges shouldbe predominantly armchair and zigzag, respectively. A similarsituation is observed in panel (c), but in this case the edgesform a relative angle of 90◦. In panel (b), the graphene piecepresents two edges forming a relative angle of 60◦. In this case,the D band present similar intensities at both edges, followingthe six-fold symmetry of the graphene lattice (both edges musthave the same preferential crystallographic orientation). Asimilar situation is observed in panel (d). However, the D

8


Figure 12. Raman images of monolayer graphene samples with straight edges forming different relative angles to each other. The upper andbottom images in panels (a)–(d) render the D and G band intensities, respectively. The images shown in panels (a)–(d) were obtained fromedges with relative angles of 30◦, 60◦, 90◦, and 60◦, respectively. In all cases the green arrows indicate the polarization direction of theincident laser. The superimposed hexagonal frameworks are guides to the eye indicating the edge ‘chirality’. Adapted with permissionfrom [60]. Copyright 2009, AIP Publishing LLC.

band intensity is clearly weaker at the edges shown in panel (b)when compared with the D band intensity obtained at the edgesshown in panel (d). Based on these two different contrasts, theauthors concluded that the edges shown in panels (b) and (d)have zigzag and armchair orientations, respectively.

Similar measurements performed on closely relatedarmchair and zigzag graphene edges showing different Dband intensity ratios have been shown in the literature [61,62]. In [61], the authors obtained direct determination ofcrystallographic orientation of a monolayer graphene sampleby performing atomically-resolved STM imaging. Ramanspectra obtained from the same sample (figure 13(a)) revealedthat the D band measured at edges with preferential zigzagorientation is considerably less intense than at edges withpreferential armchair orientation. In [62], the authorsperformed Raman analysis of monolayer graphene samples

with holes produced by the etching of pits using carbothermaldecomposition of SiO2. They produced two types of samples:one type with hexagonal holes, and another one with circularholes. While the hexagonal pits were proven (from priorSTM measurements) to be composed of zigzag edges, thecircular holes are formed by edges consisting of a mixture ofarmchair and zigzag segments (see illustration in the bottompart of figure 13(b)). Accordingly, statistical Raman analysisperformed in these two types of samples showed that the ID/IG

ratio obtained from the boundaries of the hexagonal holes(zigzag edges) is up to a factor of 30 smaller than for the edgesof round holes (see figure 13(b)).

3.2.2. Polarization effects in D band scattering. We nowturn our attention to the dependence of the D band scattering

9


Figure 13. (a) Raman spectra obtained from the edges of a monolayer graphene sample whose crystallographic orientation was previouslydetermined by atomically-resolved STM imaging. The D band measured at the edge with preferential zigzag orientation (dashed linespectrum) is considerably less intense than the D band obtained at the edge with preferential armchair orientation (solid line spectrum).Taken from [61]. (b) Representative spectra of monolayer graphene samples with rounded (left panel) and hexagonal (right panel) etchedholes. The ID/IG obtained from the samples with hexagonal holes (proved to have zigzag edges from prior STM measurements) is up to afactor of 30 smaller than from the samples with round holes (consisting of a mixture of armchair and zigzag segments). The illustration onthe bottom shows the two types of holes. Reprinted with permission from [62]. Copyright 2010 American Chemical Society.

intensity on the polarization of the incident and scatteredlight relative to the edge direction. Figure 14(a) shows thetopographic image of a single graphene layer on a glasssubstrate [55]. Figures 14(b)–(d) present the correspondingRaman images showing the G, 2D and D band intensities,respectively. Notice that the G band intensity is roughlyuniform along the graphene surface. A similar situationoccurs for the 2D band, which is the overtone of the D bandbut does not require a disorder-induced process to becomeRaman active, since momentum conservation is guaranteed intwo-phonon Raman processes [16, 35]. On the other hand,the D band can be detected only near the graphene edges.Figure 14(e) shows Raman spectra acquired at two differentlocations (indicated in figure14(a)). The upper spectrum was

acquired near the edge of the graphene layer, whereas the lowerspectrum was recorded ≈1 µm from the edge. The D bandappears only in the spectrum acquired near the edge, indicatingthat the graphene sheet is essentially free of structural defects.The Raman scattering spectra also reveal that the 2D band iscomposed of a single peak, which confirms that the sample isa single graphene sheet [16, 35]. All confocal Raman imagesshown in figures 14(b)–(d) were recorded with the polarizationvector �P of the excitation laser beam oriented parallel to thegraphene edge (vertical direction in figures 14(b)–(d)). Noticethat, although the three edges shown in these images shouldhave the same preferential crystallographic orientation (theyform relative angles of 60 and 120◦), the D band intensityat the top edge in figure 14(d) is weaker than that obtained

10


(g)(f)

(e)

3 mµ

(a) (b)

(c) (d)

2D

Figure 14. (a) Topographic image of a single graphene layer on a glass substrate. (b)–(d) Corresponding Raman images showing the G, 2Dand D band intensities, respectively. (e) Raman scattering spectra acquired at two different locations of the graphene layer shown in part (a).The upper spectrum was acquired near the edge of the graphene layer (position indicated by the white square in panel (a)) whereas the lowerspectrum was recorded ≈1 µm from the edge (position indicated by the white circle in panel (a)). (f ) Idealized structure of the edges of thegraphene layer shown in panel (a). The wave vectors of the defects associated with these edges are represented by �ds for the left side edge and�dt for the top edge. Notice that due to the six-fold symmetry of the graphene lattice, both edges have the same crystallographic orientationwhich, based on the strong D band scattering intensity from the side edges, are identified as armchair edges. (g) The first Brillouin zone ofgraphene oriented according to the real space representation shown in part (f ). �P is the polarization vector of the incident light used in theexperiment that generated the images shown in parts (b)–(d). The thickness of the gray region around the K and K′ points in (g) illustratesthe anisotropy on the optical absorption (emission) introduced in equation (6). The absorption/emission of light has a maximum efficiencyfor electrons with wave vectors perpendicular to �P , and is null for electrons with wave vectors parallel to �P . Adapted from [55].

from the side edges. In fact, this effect is not caused by thestructural selective effect explained in the last section, but isassociated with the relative direction between the polarizationof the incident light and the edges, as explained below.

In 2003, Gruneis et al predicted an anisotropy in the opticalabsorption and emission coefficients of graphene given by

Wabs/ems ∝ | �P × �k|2 , (6)

where �k is the wave vector of the electron (measured fromthe K or K′ point), and �P is the polarization vector ofthe incident (scattered) field for the absorption (emission)process [63]. The thickness of the gray region around theK and K′ points in figure 14(g) illustrates the anisotropy onthe optical absorption (emission) introduced in equation (6).As shown in the graphics, the absorption/emission of lightin graphene has a maximum efficiency for electrons withwave vectors perpendicular to �P , and is null for electronswith wave vectors parallel to �P . As discussed in the lastsection, the one-dimensional double-resonance intervalley

process giving rise to the D band restricts the wave vectorof the scattered electron to the direction perpendicular to thearmchair edge (�k0 and �k ′

0 in figure 14(g)). However, accordingto equation (6), these electrons will only absorb/emit lightefficiently if the polarization vector of the incident/scatteredlight is perpendicular to their wave vectors. By putting togetherthese two selection rules, we reach the conclusion that a strongdouble-resonance process will only occur if the polarizationvector of the incident light is parallel to the edge. As shown infigure 14(g), this is the case for D band scattering that originatesfrom the side edges of the graphene piece shown in figure 14(a),which generate defects whose wave vector �ds (see figure 14(f ))connects electron wave vectors �k0 and �k ′

0 that are located atmaxima in the light absorption/emission efficiency around theK and K′ points, respectively. On the other hand, the top edgein figure 14(a) generates defects whose wave vectors �dt (seefigure 14(f )) connect electron wave vectors �k0 and �k ′

0 whichare located near nodes in the light absorption efficiency aroundthe K and K′ points, respectively (see figure 14(g)). This is the

11


−300 −200 −100 0 100 200 300

0.2

0.4

0.6

0.8

1

θ (degrees)

SLG BLG cos4(θ)

Nor

mal

ized

I /

I

(ar

b. u

nits

)D

G

Figure 15. Dependence of the D band intensity on the polarizationdirection of the excitation field. θ is defined as the angle betweenthe edge and the polarization vector �P of the incident and scatteredlights. The solid line is the plot of cos4θ . Similar plots can be foundin [15, 42, 57].

reason why the intensity of the D band signal obtained from thetop edge in figure 14(d) (forming a relative angle of 60◦ with�P ) is weaker than that obtained from the side edges, which

are parallel to �P . Notice that if the incident light polarizationvector is perpendicular to the edge, D band Raman scatteringcannot be observed even for armchair edges [15, 42, 57, 64].The same arguments hold for the polarization vector of thescattered light.

Figure 15 shows the dependence of the D band intensityon the polarization direction of the excitation field (similarplots can be found in [15, 42, 57]). θ is defined as the anglebetween the edge and the polarization vector �P of the incidentand scattered lights. The circles and triangles are experimentaldata of the ID/IG ratio obtained at the armchair edges of amonolayer and a bilayer graphene, respectively. The datawere obtained in the VV configuration, in which the �P vectorhas the same direction for the incident and scattered lights.According to equation (6), the coefficients of absorption (Wabs)and emission (Wems) are both proportional to cos2θ , since thewave vector �k of the scattered electron (measured from theK point) is perpendicular to the edge direction. Because theRaman scattering process involves absorption and emissionof light, the D band intensity is expected to be proportional tocos4θ . The data is normalized to the maximum intensity, whichhappen to occur whenever the polarization vector �P is parallelto the edges (θ = 2nπ , with n integer). The minimum intensityoccurs for �P perpendicular to the edges [θ = (2n + 1)π/2].The solid line is the plot of cos4θ , in good agreement with theexperiment. It should be noticed, however, that the minimumintensity is not exactly zero, being ≈10% of the maximumvalue in this case. This residual intensity is attributed toinhomogeneities of the edges, which are not perfectly armchair[15, 42, 56, 57]. Although this residual intensity is relativelylow for edges found in exfoliated graphene samples, it can beconsiderably larger for edges generated by other methods suchas ion-beam lithography [65].

3.2.3. D band localization near graphene edges. Aspreviously discussed in section 2, the double-resonanceprocess giving rise to the D band involves the inelasticscattering of a photoexcited π electron by a TO phonon [54]whose wave vector �q lies near the vertices of the first Brillouinzone of graphene (K and K′ points) [36, 37]. Momentumconservation is only satisfied in the scattering process if theelectron is elastically back-scattered by a defect providing awave vector �d ∼ −�q. In this picture, it is physically sound toconsider that the closer a photoexcited electron is located tothe graphene edge, the higher the probability for that electronto be involved in the double-resonance process giving rise tothe D band scattering. The phase-breaking length Lφ of aconduction electron is defined as the average distance traveledbefore undergoing inelastic scattering [66]. Since the D bandscattering involves the inelastic scattering of an electron orhole with a lattice phonon, the average distance �D traveled byelectrons or holes during the time interval in which the D bandscattering process takes place should be proportional to Lφ .In this section we review several efforts to probe the D bandlocalization near graphene edges, as well as its relation to Lφ .

Figure 16(a) shows an AFM (topographic) image of agraphene flake sitting on a glass substrate [43]. Figure 16(b)shows the G band intensity image over the same area. In orderto probe the D and G band intensities along the graphene stripshown in figure 16(a), a hyperspectral line scan was performedin steps of 100 nm along the 5 µm long dashed line shown infigure 16(b). Two representative spectra are shown in panels(c) and (d). These two spectra were recorded at the locationsindicated by the square and circle in figure 16(c), respectively.The D band is only observed at the edges (spectrum shown inpanel (d)) showing that the interior region of the graphene stripis pristine. The G and D band intensity profiles obtained fromthe hyperspectral scan performed along the dashed line shownin panel (b) are presented in figures 16(e) and (f ), respectively.The vertical dashed lines indicate the position of the edges. Asthe graphene piece is scanned through the laser focus, the Gband intensity gradually increases to reach a maximum valueat the interior region of the graphene piece. On the other hand,the D band intensity achieves maximum values when the laserfocus is laterally positioned at the edges, indicating that theD band is highly localized near them. Because the intensityprofile of the incident laser beam is described by a finite point-spread function (PSF), the Raman intensity profiles shown infigures 16(e) and (f ) are composed by the spatial convolutionof the Raman material response (susceptibility derivative) withthe spatial distribution of the incident light. Initial attempts todetermine �D experimentally used prior information about thePSF of the incident laser to deconvolve the D band responsefrom the Raman intensity profile recorded at the edges ofgraphene samples [55, 57]. However, this method providedan upper limit of about 20 nm and is not accurate enough todetermine �D.

In [43], a defocusing technique was introduced to extract�D from the IG/ID ratio. The model is illustrated infigure 17(a). The method is based on the following geometricalinterpretation: while the G band intensity is proportional to thelaser focus area, the D band intensity is proportional to the area

12


2500

Inte

nsity

(ar

b. u

nits

)

Raman shift (cm−1)1300 1500 1700 2700

4.0 µm

2500

Raman shift (cm−1)1300 1500 1700 2700

2D

GD

0 1 2 3 4Position (µm)

I G (

a.u.

)

0 1 2 3 4

Position (µm)

I D (

a.u.

)

(a) (b)

(c) (d)

(e)

(f)

Figure 16. (a) Atomic force microscopy (AFM) image of a graphene strip sitting on a glass substrate. (b) G band intensity image over thesame area as shown in panel (a). (c) and (d) Representative spectra recorded at the locations indicated by the square and circle in panel (c),respectively. (e) and (f ) G and D band intensity profiles, respectively, obtained from a hyperspectral scan along the dashed line shown inpanel (b). The vertical dashed lines indicate the position of the edges. Adapted with permission from [43]. Copyright 2011 AmericanChemical Society.

defined by the product of �D with the length of the grapheneedge exposed to the incident light (red area in figure 17(a)).Therefore, IG/ID ratio should be proportional to the full widthat half-maximum (FWHM) of the point-spread function (�)of the incident laser beam. Figure 17(b) shows the plot ofID/IG as a function of � for the experimental data obtainedin the defocusing process. The solid line is a linear fit thatgives ID/IG = 42µm−1�. By combining this result withprior information about the ratio between the G and D bandresponses in graphene [19], the authors were able to obtain�D ≈ 3 nm. This is in excellent agreement with the radius ofthe D band activation area in ion-bombarded samples reportedin [19], as discussed in section 3.1.

In [42] the authors explain that, since the phonon energyhωph determines the energy uncertainty in a first order Ramanprocess, the minimum value for the electron–hole pair lifetimeis ω−1

ph (uncertainty principle). By using the relation �D =υ/ωph, where υ is the group velocity of the photoexcitedelectrons (also known as the Fermi velocity in graphene),the authors have found �D ≈ 4 nm, in excellent agreementwith the experimental results found in [19, 43]. However,this result corresponds to a lower limit determined by theenergy-time uncertainty relation, since the phase-breakinglength is expected to increase as the temperature decreases[67]. Accordingly, low temperature transport experimentshave shown Lφ ∝ 1/T 1/2 in graphene [68]. To probe thevalidity of this trend in the optical range, the defocusing

technique was carried out at low temperatures in [43], andthe results are shown in figure 17(c). The figure renders �D asa function of T −1/2, where T is the temperature of the samplelocated inside of a liquid helium cryostat. The dashed lineis a linear fit giving �D = 3 + 9/T 1/2, in agreement withtransport measurements [68]. This result shows that the limit�D ≈ 3 nm is accurate for high temperature regimes. Recently,tip enhanced Raman spectroscopy (TERS) was applied formeasuring D band localization near graphene edges, and avalue of �D = 4.2 ± 0.5 nm was derived [69].

3.3. Borders of crystallites

Now we turn to the final defect class: one-dimensional defectsrepresented by the borders of crystallites in nanographitesamples. This story started in 1969 with the famous worksof Tuinstra and Koenig [33]. The authors showed that theID/IG ratio is inversely proportional to the crystallite sizeLa in polycrystalline graphitic samples, that is, ID/IG =C/La, where C is a constant that depends on laser excitationenergy EL. This so-called Tuinstra and Koenig relation canbe understood in terms of a simple geometrical model, byconsidering square-shaped crystallites with sides measuringLa. The G band intensity in the Raman spectrum of such acrystallite varies as IG ∝ L2

a . On the other hand, the intensityof the D band depends on the width �D that contributes toD band scattering, and is given by ID ∝ L2

a − (La − 2�D)2.

13


0.2 0.3 0.4 0.5 0.60

10

20

∆ (µm)

I G/I D

(a) (b)

b

√

(nm

)

0 0.50.25 0.750

4

8

12

1/ T (K)

D

1

(c)

D

Figure 17. (a) Illustration of the defocusing technique introduced in [43] to extract �D from the ratio of G and D band intensities. The Gband intensity is proportional to the area of the graphene lattice that is exposed to the laser focus (green area), whereas the D band intensityis proportional to the area defined by �D and the length of the graphene edge exposed to the incident laser beam (red area). (b) Plot of ID/IG

as a function of the FWHM of the point spread function (�). The linear fit (solid line) gives ID/IG = 42µm−1�. (c) Plot of �D as a functionof T −1/2, were T is the temperature of the sample located inside of a liquid helium cryostat. The dashed line is a linear fit giving�D = 3 + 9/T 1/2. Adapted with permission from [43]. Copyright 2011 American Chemical Society.

(a) (b)

Figure 18. (a) First-order Raman spectra of a nanographite sample with La = 35 nm, for five different laser excitation energies (1.92 eV,2.18 eV, 2.41 eV, 2.54 eV and 2.71 eV). (b) First-order Raman spectra of nanographite samples with different crystallite sizes La using1.92 eV laser excitation energy. Adapted with permission from [53]. Copyright 2006, AIP Publishing LLC.

Therefore, the overall ratio is given by

ID

IG= α

[4

(�D

La− �2

D

L2a

)], (7)

where α depends on appropriate matrix elements. In the limitLa � �D, simplification of equation (7) yields the Tuinstra–

Koenig relation [33]

ID

IG= C(EL)

La, (8)

where the empirical constant C(EL) depends on EL. It shouldbe noticed that equation (8) is only valid in the limit La � �D,in which the crystallite borders can be approximated as perfectedges. Structural variabilities of the crystallite borders canbe responsible for different relations between ID/IG and La.

14


Figure 19. (a) Plot of the intensity ratio ID/IG for nanographite samples as a function of 1/La using five different laser excitation energies,as indicated in the legend. (b) All curves shown in part (a) collapse onto the same curve in the (ID/IG)E4

L versus (1/La) plot. Adapted withpermission from [53]. Copyright 2006, AIP Publishing LLC.

Although the dependence of the constant C(EL) on EL hasbeen known since 1984 [70], the quantitative determination ofC(EL) was achieved with experimental data obtained fromnanographites with different La values [53]. Figure 18(a)shows Raman spectra obtained from a sample with La =35 nm, for five different EL values. It is clear from the graphsthat the ID/IG ratio increases with decreasing EL. Figure 18(b)shows the Raman spectra obtained from samples of differentcrystallite sizes La using the same excitation laser energy EL =1.92 eV. All spectra in panels (a) and (b) were normalized tothe G band intensity, and the La sizes were determined by usingboth STM and x-ray diffraction measurements [53].

Figure 19(a) shows the plot of (ID/IG) as a function of1/La for all samples shown in figure 18(b). Figure 19(b) showsthe plot of the product (ID/IG)E4

L as a function of 1/La. Alldata shown in part (a) collapse onto the same curve in panel(b), proving that the proportionality constant C(EL) betweenID/IG and 1/La scale with the fourth power of the excitationlaser energy. From the linear fit (solid line) presented infigure 19(b), the authors obtained a relation to estimate La

from the Raman spectrum of polycrystalline graphitic samples

with La � 10 nm using any laser line in the visible range [53]:

La(nm) = 560

E4laser

(ID

IG

)−1

= (2.4 × 10−10)λ4L

(ID

IG

)−1

,

(9)where the laser excitation is given in terms of EL (eV), or thecorresponding wavelength λL (nm).

In [59], the differential Raman cross section of the D, G,D′, and 2D bands of nanographites was obtained as a functionof both excitation laser energy and crystallite size. The G bandcross section was shown to be proportional to the fourth powerof the excitation laser energy EL, as predicted by the Ramanscattering theory. For the D, D′, and 2D bands, which originatefrom double-resonance processes, the differential cross sectiondid not show a considerable dependence on EL. Together, thesetwo measurements explained the strong dependence of the ratioID/IG on EL. The Raman scattering efficiency has also beenmeasured in single layer graphene samples, and similar resultswere achieved for the G and 2D bands [71].

15


4. Raman characterization of doping in graphene

At its foundation, the importance of semiconductor materialsin modern technology stems from the tunability of the electricalproperties, such as carrier concentration, carrier mobility, andconductivity. Controlling these aspects of semiconductors hasgiven rise to transistors, p-n junctions, and free-electron gases.Similarly, much of the interest in graphene originates fromthe tunability of the electrical properties. In fact grapheneis far more sensitive to changes in carrier concentration thansemiconductors such as silicon, which can be understood fromthe linear electronic dispersion in graphene. Sketches of theDirac cone with no doping, hole doping, and electron dopingare shown in figure 20. Since the conduction and valenceband intersect at the Dirac point, intuitively the Fermi levelmust be extremely sensitive to the carrier concentration. Thissensitivity can be clearly seen by comparing the dependence ofFermi level, EF, on the carrier concentration, n, for grapheneand a two-dimensional free electron gas (2DEG), as shown infigure 21(a). For SLG, EF = hvFπ

√n, where vF is the Fermi

velocity. In bilayer graphene (BLG) EF ∝ n, which meansBLG is far less sensitive to doping than SLG at the achievablevalues of n. Therefore, any property of graphene that relieson the carrier concentration, such as the optical conductivity[72] and the carrier mobility [17], can be widely tuned (seefigures 21(b) and (c)). For large enough doping levels inter-band transitions are forbidden due to Pauli blocking. In thiscase, a transparency window in the absorption opens and intra-band processes are more easily observed [73]. An importantexample of this are plasmons in graphene [72]. For plasmons,doping is even more significant since the carrier concentrationdetermines the plasma frequency of a material [74], and allowsthe plasma frequency in graphene to be tuned [72]. Themethods for altering the electrical properties of graphene arebroadly referred to as doping techniques. In the followingsection, Raman characterization of doped graphene as well asseveral doping methods are discussed.

4.1. Raman characterization of doped graphene

While there are several methods for measuring the dopinglevel in graphene, this article focuses on Raman spectroscopy.As discussed earlier, there are three main Raman featuresin graphene: the G, 2D, and D band. Since the D bandrequires a defect to be Raman active, it is generally notused to characterize doping. The G and 2D bands are bothstrongly influenced by the carrier concentration and theyhave been extensively studied for doping characterization[17, 31, 75, 76]. For additional information, [24] also reviewsRaman spectroscopy of doping in graphene.

The width and position of the G band change with doping.These changes are related to electron–phonon coupling andthe Kohn anomaly. The frequency of the G band reaches aminimum when the Fermi level is at the Dirac point and theRaman shift increases as the concentration of holes or electronsincreases, as shown in figure 22(a). The G band widthdecreases symmetrically as the concentration of electrons orholes increases (figure 22(b)).

Hole Doping Electron Doping

(a) (b) (c)

No Doping

EF

EF

EFk

E

Figure 20. Sketch of the Fermi level in graphene for (a) no doping,(b) hole doping (p-doped), and (c) electron doping (n-doped).

There are two effects that determine the position of the Gband. The lattice constant increases (decreases) for electron(hole) doping resulting in a stiffening (softening) of the phononenergy. The second effect is related to the Kohn anomalyat the � point in the phonon dispersion (see figure 1). Asdiscussed in section 2, the Kohn anomaly originates fromstrong electron–phonon interactions and the strength of thoseinteractions depends on the Fermi level. Figures 23(a) and(b) show sketches of the phonon renormalization process viathe creation of virtual electron–hole pairs. Increasing EF

inhibits the creation of electron–hole pairs, which suppressesthe perturbation of electrons and phonons. Due to the linearelectronic dispersion in graphene, this term is symmetric withrespect to EF, and for large doping levels the frequency shiftis ∝ |EF|. The contribution from the change in the latticeconstant is asymmetric with respect to EF and the combinationof the two terms leads to the profile shown in figure 22(a).

The doping dependence of the G band width is also causedby the electron–phonon coupling, which is expected sincethe G band width is predominately determined by electron–phonon scattering. Phonon–phonon scattering adds only asmall contribution [24]. Electron–phonon scattering resultsin G band phonons decaying into electron–hole pairs. As theFermi level increases, Pauli exclusion reduces the number ofelectronic states that are available as decay pathways, whichresults in G band narrowing. The G band width reaches aminimum once the Fermi energy exceeds half the phononenergy, as shown in figure 23(b). At room temperature thenarrowing is smooth. However, at low temperature the G bandwidth is constant for |EF| < hωG and above |EF| > hωG thereis zero damping due to the phonons decaying into electron–hole pairs [30, 32].

The position of the 2D band also depends on EF. However,unlike the G band the contribution is only due to changes inthe lattice constant. While there is a Kohn anomaly at theK-point as well, the iTO phonons involved in the 2D bandprocess are too far from the K-point for the Kohn anomaly tocontribute. The 2D band position increases (decreases) as thehole (electron) concentration increases, as in the case for thelattice constant term in the G band position [17].

In addition to the changes in the width and position of thebands, the relative intensity of the G to 2D bands also changes,as shown in figure 22(d). At low doping levels the G bandintegrated intensity is independent of EF, while the 2D bandintensity decreases as |EF| increases. Since all the intermediatestates of the 2D band are resonant with electronic levels(see figure 4), its intensity is sensitive to electron–phonon

16


0 1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Electron Concentration (x1013 cm−2 )

Fer

mi E

nerg

y (e

V)

Graphene

2DEG

(a) (b)

Mob

ility

(cm

2 V

–1 s

–1)

105

104

103

102

6420n (×1012 cm–2)

–2–4

00

0.2

0.4

0.6

0.8

1.0

1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000

ω (cm –1)

1 (π

e2 /

2h)

σ

71 V

54 V

40 V

28 V

17 V

10 V

0 V

(c)

Figure 21. (a) Carrier concentration versus Fermi level for graphene and a two-dimensional electron gas (2DEG). (b) Mobility versuscarrier concentration for a top gated (dashed red) and backgated (solid blue) device. Adapted with permission from [17]. Copyright 2008Macmillan Publishers LTD: Nature Nanotechnology. (c) Optical conductivity as a function of gate voltage. Adapted with permissionfrom [73]. Copyright 2008 Macmillan Publishers LTD: Nature Physics.

coupling. The 2D band scattering rate has an electron–phononand an electron–electron contribution. The electron–phononscattering rate is independent of carrier concentration since theprocess is far from the Kohn anomaly, but the electron–electronscattering rate does depend on EF (γee ∼ 0.07|EF|) [77].Therefore, by tuning EF and measuring the integrated intensityof the 2D band, the electron–phonon scattering rate, γep, can bedetermined [76]. While measuring absolute Raman intensitiescan be difficult [59, 71], the electron–phonon scattering ratecan also be determined from the ratio of the 2D and G peakareas, A(G)/A(2D), using the equation,

√A(G)/A(2D) ∝ γep + γee ∝ γep + 0.07|EF|. (10)

It is important to note that the independence of A(G) on EF

and equation (10) are only valid for low doping levels [78],which will be discussed shortly.

4.1.1. Raman decay pathways and quantum interference.Earlier, G band narrowing for increased doping was presentedas the result of decay pathways being removed. While this isa valid description, it fails to take into account any potentialinterference effects between the different G band scatteringpathways. The impact of quantum interference on Ramanscattering in graphene was theoretically investigated in [79]and experimentally in [80]. In [80] the graphene flake was

strongly doped using an ion-gel gate, which is described below,and the flake was illuminated with a continuous-wave laserwith excitation energy of Eex = 1.58 eV. As EF was increased,the integrated intensity of the G band, A(G), remained constantfor low doping levels, in agreement with [76]. However as|EF| approaches Eex/2, A(G) increases significantly, reachinga maximum at 2|EF| = Eex − hωG/2 (figure 24(a)). Asdiscussed above, the G band has several decay pathways,which are illustrated in figure 24(b). As |EF| increases,pathway II is eliminated, which would result in a decreasein A(G) if there were no interference between paths I andII. Therefore the increase in A(G) is indicative of quantuminterference and suggests that paths I and II are out-of-phaseand destructively interfere, as shown by the phase plot infigure 24(c). For low doping levels the removal of decaypathways results in a narrowing and an amplitude increase ofthe G band, which leads to A(G) being constant. The 2D bandalso shows quantum interference, but in this case the pathwaysare in-phase and interfere constructively. As a result A(2D)

decreases as |EF| increases (figure 24(d)). Figures 24(e) and(f ) show two paths for the 2D and the phase of the Ramanamplitude, respectively. The phases plotted in figures 24(c)and (f ) are the complex phase of the resonance factor, Rk , inthe Raman intensity equation, I = |∑k CkRk|2, where Ck isthe Raman matrix element [80].

17


FW

HM

(G)

(cm

–1)

18

16

14

12

10

8

6

4

Electron concentration (×10 13 cm–2 )

Pos

(2D

) (c

m–1

)

Electron concentration (×1013 cm–2)

–3 –2 –1 0 1 2 3 4

Fermi energy (meV)–703

2,700

2,690

2,670

2,660

2,680

–574 –406 0 406 574 703 811

Electron concentration (×1013 cm–2 )

3.5

3.0

2.5

2.0

1.5I (2D

)/I(

G)

1.0

0.5

Electron concentration (×1013 cm–2)

–3 –2 –1 1 42 30

Fermi energy (meV)–703

1,610

1,605

Pos

(G)

(cm

–1)

1,600

1,595

1,590

1,585

1,580–3 –2 –1 0 1 2 3 4–3 –2 –1 0 1 2 3 4

–574 –406 0 406 574 703 811(a) (b)

(c) (d)

Figure 22. Raman spectra of a doped graphene flake using an electrolyte gel as the top gate. (a) Position and (b) width of the G as afunction of EF. (c) Position of the 2D as a function of EF. (d) Ratio of the 2D to G ratio. Adapted with permission from [17]. Copyright2008 Macmillan Publishers LTD: Nature Nanotechnology.

0

4

8

12

Phon

on li

new

idth

FWH

M (

cm-1

)

(a)

(b)

T=300 KT=70 KT=4 K

-0.6 -0.4 -0.2 0 0.2 0.4 0.6Electron concentration (1013 cm-2)

hωG hωGhωG hωG

Figure 23. (a) Sketch of Pauli blocking of the decay of G bandphonons into electron–hole pairs due to doping. On the left thedecay is allowed, whereas on the right it is blocked. The bluerepresents the states filled with electrons. (b) Theoretical plot of theG band width as a function of EF at three different temperatures:300 K, 77 K, and 4 K. Adapted with permission from [30].Copyright 2006 by the American Physical Society.

4.1.2. Doping of bilayer graphene. Several doping effectshave been observed in BLG. The first is similar to the Kohnanomaly in SLG, and [81] showed that there are singularities

in the phonon energy at EF = hωG, as shown by the dottedvertical lines in figure 25(a). Observing these two anomaliesrequires a uniform carrier concentration, because local chargevariations reduces the depth of the anomalies, �EA. Thesecond effect for the G band is quite different from SLG.The in-plane Raman modes can be in-phase or out-of-phasebetween the sheets, which leads to a symmetric (in-phase)and antisymmetric (out-of-phase) phonon modes. Howeverfor a phonon mode to be Raman active it must change thepolarizability of the material. For the symmetric mode, thevibrations are in-phase, and therefore it is Raman active.However the antisymmetric mode is not Raman active sinceit is centro-symmetric and the polarizability change betweenthe two sheets cancels. For the antisymmetric mode tobecome Raman active the centro-symmetry must be brokenby modifying one sheet with respect to the other. This can beaccomplished by applying an asymmetric doping between thetwo sheets, which results in a doping dependent splitting of theG band (see figures 25(b) and (c)), as shown in [82, 83]. Thesolid lines are the theoretical predictions [84]. The observed Gband splitting can only be observed for even numbers of layers,since odd numbers of layers are mirror symmetric, insteadof centro-symmetric, and the antisymmetric mode is alreadyRaman active [83]. This type of study can be extended to studyinterlayer interactions in BLG by modulating the gate voltagein combination with Raman spectroscopy [85].

18


0.0 0.5 1.0 1.5

0.0

2.5

5.0

7.5

0.0 0.5 1.0 1.5 2.0

0

1

2

3

4

0.0 0.5 1.0 1.5 2.0

1,590

1,600

1,610

1,620

EF

G

GD

D

I IIIII

1.0 1.5 2.0

Pha

se

1.0 1.5–π

–π/2

0

π/2

π

–π

–π/2

0

π/2

π

Pha

se

(a)

(c)(b)

(d)

(f)(e)

2|EF| (eV) 2|EF| (eV)

I G (

a.u.

)

I 2D (

a.u.

) Ek (eV) Ek (eV)

Eex – 2

2|EF| (eV)

G (c

m–1

)

Eex – 2h D

Gh

Figure 24. Measurements of quantum interference of the Raman scattering process for large doping levels. (a) A(G) versus |EF|. Insetshows the dependence of the G band position on |EF|. (b) Sketch of two pathways for the G band process. For low doping levels bothpathways are available. However for high doping levels pathway II is blocked. (c) Phase of the Raman amplitude as a function of the energyof the intermediate state, Ek . The pathways above and below Ek = Eex − h�G/2 are out-of-phase and destructively interfere. (d) A(2D)versus |EF|. (e) Sketch of two pathways for the 2D band process. As with the G band, pathway II is blocked for high doping levels. (f )Phase of the Raman amplitude as a function of the energy of the intermediate state, Ek . In contrast to the G band case, the phase is constant.Adapted with permission from [80]. Copyright 2011 Macmillan Publishers LTD: Nature.

-0.4

1.2

-100 -50 0 50 1001580

1582

1584

8 6 4 2 0 -2 -4 -6

3

6

9

12

15

G b

and

en

erg

y (c

m-1)

V g (V)

∆∆∆∆EA

Gω

n (X1012 cm-2)

G b

and

wid

th (cm

-1)

(a) (b)

(c)

ASS

-0.2 -0.1 0.0

0.8

0.4

0.0

1.6

1.4

1.2

1.0

0.8

0.6

0.4-100 -80 -60 -40 -20 0 20 40 60 80 100

12

8

4

0

-4

16

14

12

10

8

6

4

Figure 25. Doping dependence of the G band for bilayer graphene. (a) G band doping dependence when both graphene layers are dopedsymmetrically. The width is shown in red and the position is shown in blue. �EA is the depth of the phonon anomaly and hωG is theseparation between the two phonon anomalies. Adapted with permission from [81]. Copyright 2008 by the American Physical Society.(b) and (c) Asymmetric doping between the layers in bilayer graphene resulting in the G band splitting into an antisymmetric (AS) andsymmetric (S) mode shown in red and black, respectively. (b) The position and (c) the width of the G band versus EF. The antisymmetric(AS) and symmetric (S) modes are shown in red and black, respectively. The solid lines are the theoretical predictions [84]. Adapted withpermission from [82]. Copyright 2008 by the American Physical Society.

4.1.3. Doping dependence of defective graphene. Asillustrated in the previous sections, Raman spectroscopy hasbeen used extensively to study defects and dopants in graphene.Recently several groups have begun investigating doping

effects in defective samples, which is crucial for understandinggraphene devices [86–88]. In [86, 88] the defected samplesare created by ion bombardment, as in section 3.1, and thedependence of the D band is measured as a function of gate

19


(a) (b)

Gate Voltage (V)

A(D

)/A

(G)

Figure 26. (a) Experimental hyperspectral Raman map of a defective graphene sample as a function of |EF|. A defected graphene flake wascreated by ion bombarded and the Raman bands were measured as a function of gate voltage. Note that the intensity of the D and 2Ddecrease as the gate voltage increases. Adapted with permission from [88]. Copyright 2014 American Chemical Society. (b) A(D)/A(G)as a function of Vg for sp3 defects. In this case the effect is attributed to a chemical functionalization of the graphene. The applied voltagebreaks the water molecules under the graphene flake into H+ and OH− groups which react with the graphene. As Vg increases more watermolecules are split, which results in a stronger reaction and more defects. Adapted with permission from [87]. Copyright 2014 Springer.

voltage. In this case the defect density is predetermined bythe ion bombardment, and Raman measurements are studyingthe dependence of the D band on the Fermi level. In [87] thegate voltage leads to a chemical reaction, which creates thedefects in the graphene flake. In this geometry the Ramanspectroscopy is primarily measuring the density of createddefects opposed to the intrinsic properties of the D band. Theexperiments are discussed in more detail below.

The experiment presented in [88] was conducted byion bombarding a gated graphene sample and measuring thedependence of I (D) as a function of gate voltage for differentdefect densities. Figure 26 shows the measured hyperspectralmap of the Raman bands as a function of EF for a sample witha defect density of nD∼ 4.4 × 1011 cm−2. The dependence ofthe G and 2D bands are in agreement with the results on pristinesamples discussed earlier. The most prominent change in theD band as a function of |EF| is the intensity of the peak. Noticethat a similar intensity change is observed for the D′, 2D, and2D′ (or G′′) bands. These bands are all double resonant (DR)processes and therefore interact more strongly with electronicstates than the G band. Within the DR framework, [88]interprets this behavior as the result of the electron–electronscattering rate γee increasing, since γee ∝ |EF|, as discussedpreviously. Bruna et al [88] builds on the Tuinstra–Koenigrelationship for quantifying defect densities [33], which wasextended to include the dependence on the excitation laserwavelength [40], as discussed in section 3.1. In this caseequation (4) is modified and L2

D can be expressed as,

L2D (nm2) = (1.2 ± 0.3) × 103

E4L

(ID

IG

)−1

E−(0.54±0.04)F .

(11)This model is valid in the regime spanning from crystallinegraphene to nanocrystalline graphene, which is the region ofinterest for graphene applications. Note that ID/IG refers to the

peak intensity, not the integrated area. Liu et al [86] observesthe same behavior for the D band, but the results are interpretedas a quantum interference effect, similar to [80].

The doping dependence of the D band was also studiedin [87]. As mentioned above, in this experiment the gatevoltage creates the defects and therefore as Vg increases the Dband signal increases. and the results are shown in figure 26(b).The proposed mechanism is that the applied voltage leads to sp3

sites in the graphene sheet through an electrochemical reactionbetween the water molecules trapped between the substrate andthe graphene sheet. The electric field disassociates the watermolecules and OH− groups attach to the graphene sheet. Asthe gate voltage increases more water molecules disassociateinto OH− groups that can react with the graphene sheet, whichincreases the density of sp3 defects. The A(D)/A(G) ratio ofthe integrated peak areas are shown in figure 26(b).

4.2. Doping methods

In this subsection we divide doping methods into severalcategories: electrostatic doping, contact doping, chemicaldoping, substitution doping, and optical doping. Inelectrostatic doping the carrier concentration is tuned byexposing the graphene sheet to an electric field that is typicallygenerated by a gate potential. Contact doping is similar, butthe electric field is due to the work function difference betweenthe graphene sample and the contact material. Chemicaldoping involves exposing the graphene flake to gases or liquidsthat adsorb onto the surface. The adsorbed molecules act asdonors/acceptors. In substitutional doping, carbon atoms in thegraphene lattice are replaced with atoms that have a differentnumber of electrons, as is commonly done with conventionalsemiconductors. Finally, several groups have demonstratedrecently that graphene can be doped through a variety of opticalprocesses. It is important to note that chemical and substitution

20


Raman Shift (cm )-11500 1600 2600 2800

(b)

1500 1600 2600 2800Raman Shift (cm )-1

3.0 3.5 4.0 4.5 5.0d

1.0

0.5

0

0.5

EF

eV EF

EF

Al

Ag

Cu

Au

Pt

(d)(c)

Inte

nsity

(ar

b. u

nits

)

Inte

nsity

(ar

b. u

nits

)

----

++++

Metal

Gra

phen

e

d

dz

WM

-q +q

WG

EF EF

W

V(a)

Figure 27. (a) Sketch of the contact doping mechanism. (b) Theoretical calculation of the doping due to different metals as a function of theseparation. (c) and (d) Raman spectra of graphene doping due to Co and Ni substrates. The spectra for the SLG flakes before and after themetal deposition is shown in blue and black, respectively. The doped spectra are inverted to help show the spectral shift due to the doping.(a) and (b) Adapted with permission from [101]. Copyright 2008 by the American Physical Society. (c) and (d) Adapted with permissionfrom [103]. Copyright 2011 AIP Publishing LLC.

doping can change the Fermi level and potentially open abandgap in graphene [89], whereas electrostatic and contactdoping only change the Fermi level. However, electrostaticdoping is tunable and reversible. The various doping methodsare discussed in detail in [90–93].

4.2.1. Electrostatic doping. The most common dopingtechnique is electrostatic doping. The main advantages ofelectrostatic doping are that the doping level is tunable andit can readily be integrated into more complicated devicearchitectures. Generally these devices consist of field-effecttransistors (FETs) made with graphene. The two most commonfabrication methods involve depositing a graphene flake ontoa doped silicon wafer with a ∼300 nm thermal oxide layer.Source-drain electrodes are evaporated onto the grapheneflake, and the silicon substrate is used as the back-gate [6, 94].This approach typically achieves doping levels of �EF ≈0.3 eV [95]. Alternatively, the device can also be top-gatedby applying an electrolyte polymer gel [96, 97]. Since the gelcreates a Debye layer of only a few nanometers, the electricfields are much higher, which results in much higher dopinglevels (�EF ≈ 0.8 eV [17]) and lower gate voltages. Thedependence of carrier concentration on gate voltage can beexpressed as,

VG = hvFπ√

n

e+

ne

C, (12)

where C is the geometrical capacitance. For a thin spacerlayer, like ion-gels and tunneling gaps in scanning tunnelingmicroscopes [98, 99], the first term in equation (12) can add asignificant contribution.

4.2.2. Contact doping. Putting a graphene sheet in contactwith another material results in contact doping. Since grapheneis a single atomic layer it is very sensitive to surface charges.For example, graphene flakes deposited on SiO2 are typicallydoped by ∼1011 cm−2 [75, 100]. This effect can be muchstronger when the graphene flake is in contact with a metalsurface. In this case the work function difference betweenthe graphene and metal leads to an inherent electric fieldat the interface, as shown in figure 27(a). Figure 27(b)shows a theoretical plot of the doping of graphene due tometals with different work functions [101, 102]. Note thatcontact doping also depends on the separation between themetal film and the graphene flake. Metals with a higher(lower) work function p-dope (n-dope) the graphene. This wasexperimentally demonstrated in [103], and the Raman spectrafor graphene deposited on Co and Ni are shown in figures 27(c)and (d), respectively. The spectra of the SLG flakes beforeand after the metal deposition are shown in blue and black,respectively. The doped spectra is inverted to show the spectralshift. It is important to note that the substrate can also strainthe graphene flake, as is the case for gold substrates. Strainalso strongly influences the Raman peaks and therefore care

21


must be taken when calculating contact doping for a grapheneflake [103] based on Raman results.

4.2.3. Chemical doping. Another common type of dopingis chemical doping. In this case a molecule adsorbs ontothe surface and acts as a donor or acceptor, resulting in ann- or p-doped flake. These treatments include acids, metalchlorides, and organic molecules among other methods. Whilea variety of acids have been used, nitric acid is commonly usedto p-dope graphene [104]. In the case of metal chlorides, thedoping is due to the work function mismatch as in the caseof the contact doping discussed above. One draw back to thisapproach is that it reduces the transparency of the grapheneflake. However, this can be avoided by using organic moleculesinstead of metals [93]. Besides the methods highlighted above,graphene can also be p-doped using water [94, 105] or n-doped using ammonia [94, 106] and NO2 [107–109]. Anotherexciting chemical doping technique involves intercolaginggraphene sheets. In [110] graphene sheets were intercolatedwith iron chloride, known as GraphExeter, to produce carrierconcentrations as high as ∼9 × 1014 cm−2 while maintaininga high carrier mobility.

4.2.4. Heteroatom doping. In heteroatom doping some ofthe carbon atoms in the graphene sheet are substituted withother atoms. Generally either nitrogen or boron are useddue to their similar atomic masses, which leads to n- and p-doping, respectively [89, 91]. Nitrogen substitutional dopinghas been accomplished by thermal annealing and chemicalvapor deposition using NH3 [90]. Nitrogen doping is aparticularly active research area, because it can open a bandgapin the graphene, thus allowing it to behave like a conventionaln-type semiconductor with low mobility and conductivity [89].Unfortunately nitrogen doping also tends to introduce defectsin the graphene flake [91]. Therefore Raman spectroscopyis particularly important for characterizing these type ofsamples.

4.2.5. Optical doping. An interesting category of doping thathas been recently demonstrated is optically induced doping.This has been accomplished in several ways. In the first casea material is deposited on the graphene flake and subsequentlyexcited optically. The excited carriers can tunnel into thegraphene flake from the other material, resulting in a Fermilevel shift. Some examples of this are hot electron donationfrom plasmons [111] and holes donated from quantum dots[112] and certain organic molecules [113]. In addition to thesetechniques, it has also been demonstrated that graphene canbe directly doped by exposing it to light [114]. This resultsuggests that Raman spectroscopy is not always a non-invasivemethod for probing the electrical properties of graphene.Photoinduced doping has recently been used in graphene-boron nitride heterostructures to make writable doping features[115]. Both of these techniques rely on defects or charge trapsin the substrate and are not present in suspended graphenesamples. Laser-based techniques have also been used to createnitrogen doped graphene from graphene oxide [116].

5. Importance of defects and dopants for devices

Graphene is being explored for a wide variety of devices andapplications, many of which are discussed in [11, 117, 118].Many of these applications require controlling the electricalproperties of graphene as well as minimizing the defect density,which degrades the electrical properties such as mobilityand conductivity. In the following section several grapheneapplications that require doping or well-characterized defectdensities are reviewed. As will be shown, Raman spectroscopyis an invaluable tool for characterizing these type ofdevices.

5.1. Flexible transparent electronics

Given its mechanical, optical, and electrical properties,graphene is a natural candidate for flexible transparentelectronics, the figures of merit being the sheet resistance andthe transparency. The intrinsic sheet resistance of grapheneis ≈6 k� cm−2 [11]. However, as discussed above this canbe lowered significantly through doping. While the electronicproperties of graphene are excellent, graphene-based deviceshave not surpassed the industry of standard indium-tin-oxide(ITO) films for consumer electronics. Furthermore, in orderto mass-produce devices, either CVD or chemical exfoliationtechniques are required, which are currently of lower qualitythan mechanically exfoliated flakes [117]. However, graphenedoes have an advantage due to it’s material strength andflexibility for applications such as e-paper or wearableelectronics. These types of devices require the graphene tobe highly doped to minimize the sheet resistance and, foroptimum performance, the defect density should be kept ata minimum. The interpolation of graphene with iron chlorideopens up very attractive applications. These materials canhave sheet resistances of >9 � cm−2 and 84% transparency.Konstantin et al [117] discusses many of these applications inmore detail.

5.2. Photonics and plasmonics

Recently graphene has been extensively explored as a platformfor photonics and plasmonics. Due to its unique electrondispersion relation, graphene is inherently broadband and atunable transparency window can be opened by controllingthe doping level [73]. Furthermore, a bandgap can also beopened by nitrogen-doping SLG [89]. In BLG, applying anelectric field creates a tunable bandgap in the mid-infrared[119, 120]. Optical modulators using SLG and BLG havebeen created with bandwidths exceeding 1 GHz [121, 122].Both high-speed and high-efficiency photodetectors havebeen demonstrated in graphene FETs [10, 12, 112]. Theresponsivity is controlled with the carrier concentration definedby the gate voltage. In the case of [112], quantum dots are usedas an absorber to increase the efficiency.

Another area of growing research is graphene plasmonics.According to the Drude model, the plasma frequency isdetermined by the carrier concentration. In conventionalmetals, such as Au, this parameter is fixed. However, asdiscussed above, it is tunable in graphene, which means that

22


the plasmonic characteristics of graphene can be controlled[72, 118, 123]. Unfortunately, due to the limitations onachievable doping levels, currently these applications arerestricted to the infrared. However, graphene plasmonics isideal for terahertz applications and tunable detectors havealready been demonstrated [124]. Researchers have alsodemonstrated visible photodetectors by using graphene inconjunction with metal antennas [111, 125, 126]. Plasmonsin doped graphene have also been directly imaged at the nano-scale [127, 128].

5.3. Electrochemical sensors

As discussed in section 4, chemicals that adsorb onto thesurface of graphene can result in charge transfer, thus dopingthe graphene. Instead of using this as a doping method, it canbe used as a chemical sensor. Given the large surface area andsensitivity to doping, graphene is a logical material for sensingapplications. Electrochemical sensors operate by exposing anelectrode to a gas. The gas reacts at the surface of the electrodeby either oxidizing or reducing, which results in a currentacross the electrodes. By functionalizing the electrode withreagents allows for chemically specific detection [129–132].Graphene has been used in biological applications such asglucose, dopamine, and DNA detection [132, 133]. Grapheneelectrodes have also been used to detect a wide variety ofchemicals, including nitrogen dioxide, hydrogen peroxide,carbon monoxide, water, and ammonia with sensitivitiesas low as a few parts per billion [130]. As with othergraphene-based applications, fabrication cost is important.Currently the most common approach is to use reducedgraphene oxide (rGO), since it can be produced throughchemical exfoliation from graphite [134–137]. Compared toexfoliated or CVD graphene, rGO also has a higher defectdensity, which reduces the conductivity of the grapheneelectrode and increases the number of chemical attachmentsites [130]. The increased number of attachment sites makesrGO more suitable as a chemical sensor than pristine graphene.However, the sp3 defect sites require annealing to removethe adsorbed chemical, opposed to simply removing thegas [137].

5.4. Heterostructures

In addition to graphene, many other 2D materials have beendiscovered and studied, each with unique physical properties.Currently many groups are investigating 2D heterostructures tomake hybrid materials. Perhaps the best example is grapheneon hexagonal boron nitride (hBN), which serves to insulate thegraphene flake from the environment. Recently researchershave also demonstrated hBN encapsulated graphene [138], forwhich defects in hBN become important for device properties.Beyond graphene and hBN, considerable effort has beeninvested in chalcogenides, such as MoS2 and WS2, whichexhibit bandgaps in the visible. Obviously, controlling EF

in graphene is a valuable parameter for fabricating theseheterostructures. Geim and Grigorieva [139] provides anexcellent outlook on this topic.

6. Summary

In this article we have discussed the importance of Ramanspectroscopy for understanding the electrical and structuralproperties of graphene through defects and dopants. Generallyfor graphene devices, defects degrade the beneficial propertieswhile dopants allow for tunability and control of physicalproperties. Nevertheless, in certain applications, such as gas-sensors, defects can also be beneficial. Recently, researchershave begun to explore samples with both defects and dopantsthat will hopefully deepen the understanding of grapheneand allow new types of applications to be explored. Asmore complicated graphene devices are being fabricated inconjunction with other 2D materials, the need for quantitativeRaman characterization will increase. However, there isalso an increasing need for Raman techniques that can probematerial properties at the nano-scale in order to understandthe local behavior of electrons and phonons in graphene. Tip-enhanced Raman spectroscopy (TERS) has been used withgreat success on carbon nanotubes and is now being applied tographene samples. As the resolution of TERS continuous toimprove, it presents a viable way to quantitatively study localmaterial properties.

Acknowledgments

LGC acknowledges financial support from CNPq andFAPEMIG. LN acknowledges the financial support by USDepartment of Energy (grant DE-FG02-05ER46207) and theSwiss National Science Foundation (grant 200021 149433).

References

[1] Cerdeira F and Cardona M 1972 Effect of carrierconcentration on the Raman frequencies of Si and GePhys. Rev. B 5 1440

[2] Chandrasekhar M, Renucci J B and Cardona M 1978 Effectsof interband excitations on Raman phonons in heavilydoped n-Si Phys. Rev. B 17 1623

[3] Olego D and Cardona M 1981 Raman scattering by coupledLO-phonon-plasmon modes and forbidden TO-phononRaman scattering in heavily doped p-type GaAs Phys.Rev. B 24 7217

[4] Avouris P, Chen Z and Perebeinos V 2007 Carbon-basedelectronics Nat. Nanotechnol. 2 605–15

[5] Castro Neto A H 2010 The carbon new age Mater. Today13 12–7

[6] Zhang Y, Tan Y-W, Stormer H L and P Kim 2005Experimental observation of the quantum Hall effect andBerry’s phase in graphene Nature 438 201

[7] Novoselov K S, Jiang Z, Zhang Y, Morozov S V, StormerH L, Zeitler U, Maan J C, Boebinger G S, Kim P andGeim A K 2007 Room-temperature quantum Hall effect ingraphene Science 315 1379

[8] Bolotin K I, Ghahari F, Shulman M D, Stormer H L andKim P 2009 Observation of the fractional quantum Halleffect in graphene Nature 462 196–9

[9] Du X, Skachko I, Duerr F, Luican A and Andrei E Y 2009Fractional quantum Hall effect and insulating phase ofDirac electrons in graphene Nature 462 192–5

[10] Xia F, Mueller T, Lin Y-M, Valdes-Garcia A and Avouris P2009 Ultrafast graphene photodetector Nat. Nanotechnol.4 839–43

23

http://dx.doi.org/10.1103/PhysRevB.5.1440



http://dx.doi.org/10.1038/nnano.2007.300

http://dx.doi.org/10.1016/S1369-7021(10)70029-8

http://dx.doi.org/10.1038/nature04235

http://dx.doi.org/10.1126/science.1137201





[11] Bonaccorso F, Sun Z, Hasan T and Ferrari A C 2010Graphene photonics and optoelectronics Nat. Photon.4 611–22

[12] Mueller T, Xia F and Avouris P 2010 Graphenephotodetectors for high-speed optical communicationsNat. Photon. 4 297–301

[13] Schwierz F 2010 Graphene transistors Nat. Nanotechnol.5 487–96

[14] Reddy D, Register L F, Carpenter G D and Banerjee S K 2011Graphene field-effect transistors J. Phys. D 44 313001

[15] Cancado L G, Pimenta M A, Neves B R A, Dantas M S S andJorio A 2004 Influence of the atomic structure on theRaman spectra of graphite edges Phys. Rev. Lett.93 247401

[16] Ferrari A C et al 2006 Raman spectrum of graphene andgraphene layers Phys. Rev. Lett. 97 187401

[17] Das A et al 2008 Monitoring dopants by Raman scattering inan electrochemically top-gated graphene transistor Nat.Nanotechnol. 3 210

[18] Mohiuddin T M G et al 2009 Uniaxial strain in graphene byRaman spectroscopy: G peak splitting, Gruneisenparameters, and sample orientation Phys. Rev. B79 205433

[19] Lucchese M M, Stavale F, Ferreira E H M, Vilani C,Moutinho M V O, Capaz R B, Achete C A and Jorio A2010 Quantifying ion-induced defects and Ramanrelaxation length in graphene Carbon 48 1592–7

[20] Balandin A A 2011 Thermal properties of grapheneand nanostructured carbon materials Nat. Mater.10 569–81

[21] Chen S, Wu Q, Mishra C, Kang J, Zhang H, Cho K,Cai W, Balandin A A and Ruoff R S 2012 Thermalconductivity of isotopically modified graphene Nat.Mater. 11 203–7

[22] Hao Y, Wang Y, Wang L, Ni Z, Wang Z, Wang R, Koo C K,Shen Z and Thong J T L 2010 Probing layer number andstacking order of few-layer graphene by Ramanspectroscopy Small 6 195–200

[23] Carozo V, Almeida C M, Ferreira E H M, Cancado L G,Achete C A and Jorio A 2011 Raman signature ofgraphene superlattices Nano Lett. 11 4527–34

[24] Ferrari A C 2007 Raman spectroscopy of graphene andgraphite: disorder, electron–phonon coupling, doping andnonadiabatic effects Solid State Commun. 143 47–57

[25] Malard L M, Pimenta M A, Dresselhaus G and DresselhausM S 2009 Raman spectroscopy in graphene Phys. Rep.473 51–87

[26] Jorio A, Dresselhaus M S, Saito R and Dresselhaus G 2011Raman Spectroscopy in Graphene Related System 1st edn(Weinheim: Wiley)

[27] Ferrari A C and Basko D M 2013 Raman spectroscopy as aversatile tool for studying the properties of graphene Nat.Nanotechnol. 8 235–46

[28] Kohn W 1959 Image of the Fermi surface in the vibrationspectrum of a metal Phys. Rev. Lett. 2 393

[29] Piscanec S, Lazzeri M, Mauri F, Ferrari A C and Robertson J2004 Kohn anomalies and electron–phonon interactions ingraphite Phys. Rev. Lett. 93 185503

[30] Lazzeri M and Mauri F 2006 Nonadiabatic Kohn anomaly ina doped graphene monolayer Phys. Rev. Lett. 97 266407

[31] Pisana S, Lazzeri M, Casiraghi C, Novoselov K S, Geim A K,Ferrari A C and Mauri F 2007 Breakdown of the adiabaticBorn–Oppenheimer approximation in graphene Nat.Mater. 6 198

[32] Yan J, Zhang Y, Kim P and Pinczuk A 2007 Electric fieldeffect tuning of electron–phonon coupling in graphenePhys. Rev. Lett. 98 166802

[33] Tuinstra F and Koenig J L 1970 Raman spectrum of graphiteJ. Chem. Phys. 53 1126

[34] Jorio A et al 2002 G-band resonant Raman study of 62isolated single-wall carbon nanotubes Phys. Rev. B65 155412

[35] Cancado L G, Reina A, Kong J and Dresselhaus M S 2008Geometrical approach for the study of G′ band in theRaman spectrum of monolayer graphene, bilayergraphene, and bulk graphite Phys. Rev. B 77 245408

[36] Thomsen C and Reich S 2000 Double resonant Ramanscattering in graphite Phys. Rev. Lett. 85 5214

[37] Saito R, Jorio A, Souza Filho A G, Dresselhaus G,Dresselhaus M S and Pimenta M A 2002 Probing phonondispersion relations of graphite by double resonanceRaman scattering Phys. Rev. Lett. 88 027401

[38] Pimenta M A, Dresselhaus G, Dresselhaus M S,Cancado L G, Jorio A and Saito R 2007 Studying disorderin graphite-based systems by Raman spectroscopy Phys.Chem. Chem. Phys. 9 1276–90

[39] Eckmann A, Felten A, Mishchenko A, Britnell L, Krupke R,Novoselov K S and Casiraghi C 2012 Probing the natureof defects in graphene by Raman spectroscopy Nano Lett.12 3925–30

[40] Gustavo Cancado L, Jorio A, Ferreira E H M, Stavale F,Achete C A, Capaz R B, Moutinho M V O, Lombardo A,Kulmala T S and Ferrari A C 2011 Quantifying defects ingraphene via Raman spectroscopy at different excitationenergies Nano Lett. 11 3190–6

[41] Lespade P, Marchand A, Couzi M and Cruege F 1984Caracterisation de materiaux carbones parmicrospectrometrie Raman Carbon 22 375–85

[42] Casiraghi C, Hartschuh A, Qian H, Piscanec S, Georgi C,Fasoli A, Novoselov K S, Basko D M and Ferrari A C2009 Raman spectroscopy of graphene edges Nano Lett.9 1433–41

[43] Beams R, Cancado L G and Novotny L 2011 Lowtemperature Raman study of the electron coherence lengthnear graphene edges Nano Lett. 11 1177–81

[44] Liu G, Teweldebrhan D and Balandin A A 2011 Tuning ofgraphene properties via controlled exposure to electronbeams IEEE Trans. Nanotechnol. 10 865–70

[45] Hossain M Z, Rumyantsev S, Shur M S and Balandin A A2013 Reduction of 1/f noise in graphene afterelectron-beam irradiation Appl. Phys. Lett. 102 153512

[46] Felten A, Bittencourt C, Pireaux J-J, Van Lier G and CharlierJ-C 2005 Radio-frequency plasma functionalization ofcarbon nanotubes surface O2, NH3 and CF4 treatmentsJ. Appl. Phys. 98 074308

[47] Mafra D L, Samsonidze G, Malard L M, Elias D C,Brant J C, Plentz F, Alves E S and Pimenta M A 2007Determination of LA and TO phonon dispersion relationsof graphene near the Dirac point by double resonanceRaman scattering Phys. Rev. B 76 233407

[48] Calizo I, Bejenari I, Rahman M, Liu G and Balandin A A2009 Ultraviolet Raman microscopy of single andmultilayer graphene J. Appl. Phys. 106 043509

[49] Tsu R, Jesus Gonzalez H and Isaac Hernandez C 1978Observation of splitting of the E2g mode and two-phononspectrum in graphites Solid State Commun. 27 507–10

[50] Venezuela P, Lazzeri M and Mauri F 2011 Theory ofdouble-resonant Raman spectra in graphene: intensity andline shape of defect-induced and two-phonon bands Phys.Rev. B 84 035433

[51] Bernard S, Whiteway E, Yu V, Austing D G and Hilke M 2012Probing the experimental phonon dispersion of grapheneusing 12C and 13C isotopes Phys. Rev. B 86 085409

[52] Teweldebrhan D and Balandin A A 2009 Modification ofgraphene properties due to electron-beam irradiation Appl.Phys. Lett. 94 013101

[53] Cancado L G, Takai K, Enoki T, Endo M, Kim Y A,Mizusaki H, Jorio A, Coelho L N, Magalhaes-Paniago R

24

http://dx.doi.org/10.1038/nphoton.2010.186



http://dx.doi.org/10.1088/0022-3727/44/31/313001

http://dx.doi.org/10.1103/PhysRevLett.93.247401




http://dx.doi.org/10.1016/j.carbon.2009.12.057

http://dx.doi.org/10.1038/nmat3064


http://dx.doi.org/10.1002/smll.200901173

http://dx.doi.org/10.1021/nl201370m

http://dx.doi.org/10.1016/j.ssc.2007.03.052

http://dx.doi.org/10.1016/j.physrep.2009.02.003







http://dx.doi.org/10.1063/1.1674108





http://dx.doi.org/10.1039/b613962k

http://dx.doi.org/10.1021/nl300901a

http://dx.doi.org/10.1021/nl201432g

http://dx.doi.org/10.1016/0008-6223(84)90009-5

http://dx.doi.org/10.1021/nl8032697

http://dx.doi.org/10.1021/nl104134a

http://dx.doi.org/10.1109/TNANO.2010.2087391

http://dx.doi.org/10.1063/1.4802759

http://dx.doi.org/10.1063/1.2071455


http://dx.doi.org/10.1063/1.3197065

http://dx.doi.org/10.1016/0038-1098(78)90382-4



http://dx.doi.org/10.1063/1.3062851


and Pimenta M A 2006 General equation for thedetermination of the crystallite size La of nanographite byRaman spectroscopy Appl. Phys. Lett. 88 163106

[54] Ferrari A C and Robertson J 2001 Resonant Ramanspectroscopy of disordered, amorphous, and diamondlikecarbon Phys. Rev. B 64 075414

[55] Cancado L G, Beams R and Novotny L 2008 Opticalmeasurement of the phase-breaking length in graphene(arXiv:0802.3709v1)

[56] Basko D M 2009 Boundary problems for Dirac electrons andedge-assisted Raman scattering in graphene Phys. Rev. B79 205428–49

[57] Gupta A K, Russin T J, Gutierrez H R and Eklund P C 2009Probing graphene edges via Raman scattering ACS Nano3 45–52

[58] Lazzeri M, Attaccalite C, Wirtz L and Mauri F 2008 Impactof the electron–electron correlation on phonon dispersion:failure of LDA and GGA DFT functionals in graphene andgraphite Phys. Rev. B 78 081406

[59] Cancado L G, Jorio A and Pimenta M A 2007 Measuring theabsolute Raman cross section of nanographites as afunction of laser energy and crystallite size Phys. Rev. B76 064304

[60] You Y, Ni Z, Yu T and Shen Z 2008 Edge chiralitydetermination of graphene by Raman spectroscopy Appl.Phys. Lett. 93 163112

[61] Neubeck S, You Y M, Ni Z H, Blake P, Shen Z X, Geim A Kand Novoselov K S 2010 Direct determination of thecrystallographic orientation of graphene edges by atomicresolution imaging Appl. Phys. Lett. 97 053110

[62] Krauss B, Nemes-Incze P, Skakalova V, Biro L P, vonKlitzing K and Smet J H 2010 Raman scattering at puregraphene zigzag edges Nano Lett. 10 4544–8

[63] Gruneis A, Saito R, Samsonidze Ge G, Kimura T,Pimenta M A, Jorio A, Souza Filho A G, Dresselhaus Gand Dresselhaus M S 2003 Inhomogeneous opticalabsorption around the K point in graphite and carbonnanotubes Phys. Rev. B 67 165402

[64] You Y et al 2008 Visualization and investigation of Si–Ccovalent bonding of single carbon nanotube grown onsilicon substrate Appl. Phys. Lett. 93 103111

[65] Archanjo B S, Fragneaud B, Cancado L G, Winston D,Miao F, Achete C A and Medeiros-Ribeiro G 2014Graphene nanoribbon superlattices fabricated via He ionlithography Appl. Phys. Lett. 104 193114

[66] Taylor P L and Heinonen O 2002 A Quantum Approach toCondensed Matter Physics (New York: CambridgeUniversity Press)

[67] Beenakker C W J and van Houten H 1991 Quantum transportin semiconductor nanostructures Solid State Phys. 441–228

[68] Morozov S V, Novoselov K S, Katsnelson M I, Schedin F,Ponomarenko L A, Jiang D and Geim A K 2006 Strongsuppression of weak localization in graphene Phys. Rev.Lett. 97 016801

[69] Su W and Roy D 2013 Visualizing graphene edges usingtip-enhanced Raman spectroscopy J. Vac. Sci. Technol. B31 041808

[70] Mernagh T P, Cooney R P and Johnson R A 1984 Ramanspectra of graphon carbon black Carbon 22 39–42

[71] Klar P, Lidorikis E, Eckmann A, Verzhbitskiy I A, Ferrari AC and Casiraghi C 2013 Raman scattering efficiency ofgraphene Phys. Rev. B 87 205435

[72] Koppens F H L, Chang D E and Garcıa F J 2011 Grapheneplasmonics: a platform for strong light-matter interactionsNano Lett. 11 3370–7

[73] Li Z Q, Henriksen E A, Jiang Z, Hao Z, Martin M C, Kim P,Stormer H L and Basov D N 2008 Dirac charge dynamicsin graphene by infrared spectroscopy Nat. Phys. 4 532–5

[74] Novotny L and Hecht B 2006 Principles of Nano-Optics(Cambridge: Cambridge University Press)

[75] Stampfer C, Molitor F, Graf D, Ensslin K, Jungen A,Hierold C and Wirtz L 2007 Raman imaging ofdoping domains in graphene on SiO2 Appl. Phys. Lett.91 241907

[76] Casiraghi C 2009 Doping dependence of the Raman peaksintensity of graphene close to the Dirac point Phys. Rev. B80 233407

[77] Basko B M, Piscanec S and Ferrari A C 2009Electron–electron interactions and doping dependence ofthe two-phonon Raman intensity in graphene Phys. Rev. B80 165413–22

[78] Casiraghi C 2011 Raman intensity of graphene Phys. StateSolidi B 248 2593–7

[79] Basko D M 2009 Calculation of the Raman G peak intensityin monolayer graphene: role of Ward identities New J.Phys. 11 095011

[80] Chen C F et al 2011 Controlling inelastic light scatteringquantum pathways in graphene Nature 471 617–20

[81] Yan J, Henriksen E A, Kim P and Pinczuk A 2008Observation of anomalous phonon softening in bilayergraphene Phys. Rev. Lett. 101 136804

[82] Malard L M, Elias D C, Alves E S and Pimenta M A 2008Observation of distinct electron–phonon couplings ingated bilayer graphene Phys. Rev. Lett. 101 257401

[83] Bruna M and Borini S 2010 Observation of Raman G-bandsplitting in top-doped few-layer graphene Phys. Rev. B81 125421

[84] Ando T 2007 Anomaly of optical phonons in bilayergraphene J. Phys. Soc. Japan 76 104711

[85] Saito R, Sato K, Araujo P T, Mafra D L and Dresselhaus M S2013 Gate modulated Raman spectroscopy of grapheneand carbon nanotubes Solid State Commun. 175 18–34

[86] Liu J, Li Q, Zou Y, Qian Q, Jin Y, Li G, Jiang K and Fan S2013 The dependence of graphene Raman D-band oncarrier density Nano Lett. 13 6170–5

[87] Ott A, Verzhbitskiy I A, Clough J, Eckmann A, Georgiou Tand Casiraghi C 2014 Tunable D peak in gated grapheneNano Res. 7 338–44

[88] Bruna M, Ott A K, Ijas M, Yoon D, Sassi U and Ferrari A C2014 Doping dependence of the Raman spectrum ofdefected graphene ACS Nano 8 7432–41

[89] Wei D, Liu Y, Wang Y, Zhang H, Huang L and Yu G 2009Synthesis of N-doped graphene by chemical vapordeposition and its electrical properties Nano Lett. 9 1752–8

[90] Liu H, Liu Y and Zhu D 2011 Chemical doping of grapheneJ. Mater. Chem. 21 3335–45

[91] Guo B, Fang L, Zhang B and Gong J R 2011 Graphenedoping: a review Insciences J. 1 80–9

[92] Wang H, Maiyalagan T and Wang X 2012 Review on recentprogress in nitrogen-doped graphene: synthesis,characterization, and its potential applications ACS Catal.2 781–94

[93] Oh J S, Kim K N and Yeom G Y 2014 Graphene dopingmethods and device applications J. Nanosci. Nanotechnol.14 1120–33

[94] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y,Dubono S V, Grigorieva I V and Firsov A A 2004 Electricfield effect in atomically thin carbon films Science306 666–9

[95] Geim A K and Novoselov K S 2007 The rise of grapheneNat. Mater. 6 183

[96] Sirringhaus H, Kawase T, Friend R H, Shimoda T,Inbasekaran M, Wu W and Woo E P 2000 High-resolutioninkjet printing of all-polymer transistor circuits Science290 2123–6

[97] Dhoot A S, Yuen J D, Heeney M, McCulloch I, Moses D andHeeger A J 2006 Beyond the metal-insulator transition in

25

http://dx.doi.org/10.1063/1.2196057


http://arxiv.org/abs/0802.3709v1


http://dx.doi.org/10.1021/nn8003636



http://dx.doi.org/10.1063/1.3005599

http://dx.doi.org/10.1063/1.3467468

http://dx.doi.org/10.1021/nl102526s


http://dx.doi.org/10.1063/1.2980402

http://dx.doi.org/10.1063/1.4878407


http://dx.doi.org/10.1116/1.4813848

http://dx.doi.org/10.1016/0008-6223(84)90130-1


http://dx.doi.org/10.1021/nl201771h

http://dx.doi.org/10.1038/nphys989

http://dx.doi.org/10.1063/1.2816262



http://dx.doi.org/10.1002/pssb.201100040

http://dx.doi.org/10.1088/1367-2630/11/9/095011





http://dx.doi.org/10.1143/JPSJ.76.104711

http://dx.doi.org/10.1016/j.ssc.2013.05.010


http://dx.doi.org/10.1007/s12274-013-0399-2

http://dx.doi.org/10.1021/nn502676g

http://dx.doi.org/10.1021/nl803279t

http://dx.doi.org/10.1039/c0jm02922j

http://dx.doi.org/10.5640/insc.010280

http://dx.doi.org/10.1021/cs200652y

http://dx.doi.org/10.1166/jnn.2014.9118



http://dx.doi.org/10.1126/science.290.5499.2123


polymer electrolyte gated polymer field-effect transistorsProc. Natl Acad. Sci. USA 103 11834–7

[98] Zhang Y, Brar V W, Wang F, Girit C, Yayon Y, Panlasigui M,Zettl A and Crommie M F 2008 Giant phonon-inducedconductance in scanning tunnelling spectroscopy ofgate-tunable graphene Nat. Phys. 4 627–30

[99] Brar V W 2010 Scanning tunneling spectroscopy of grapheneand magnetic nanostructures PhD Thesis University ofCalifornia, Berkeley

[100] Casiraghi C, Pisana S, Novoselov K S, Geim A K and FerrariA C 2007 Raman fingerprint of charged impurities ingraphene Appl. Phys. Lett. 91 233108

[101] Giovannetti G, Khomyakov P A, Brocks G, Karpan V M,van den Brink J and Kelly P J 2008 Doping graphene withmetal contacts Phys. Rev. Lett. 101 026803

[102] Khomyakov P A, Giovannetti G, Rusu P C, Brocks G,van den Brink J and Kelly P J 2009 First-principles studyof the interaction and charge transfer between grapheneand metals Phys. Rev. B 79 195425

[103] Wang W X, Liang S H, Yu T, Li D H, Li Y B and Han X F2011 The study of interaction between graphene andmetals by Raman spectroscopy J. Appl. Phys. 109 07C501

[104] Kasry A, Kuroda M A, Martyna G J, Tulevski G S and BolA A 2010 Chemical doping of large-area stacked graphenefilms for use as transparent, conducting electrodes ACSNano 4 3839–44

[105] Shim J, Lui C H, Ko T Y, Yu Y-J, Kim P, Heinz T R andRyu S 2012 Water-gated charge doping of grapheneinduced by mica substrates Nano Lett. 12 648–54

[106] Romero H E, Joshi P, Gupta A K, Gutierrez H R, Cole M W,Tadigadapa S A and Eklund P C 2009 Adsorption ofammonia on graphene Nanotechnology 20 245501

[107] Schedin F, Geim A K, Morozov S V, Hill E W, Blake P,Katsnelson M I and Novoselov K S 2007 Detection ofindividual gas molecules adsorbed on graphene Nat.Mater. 6 652–5

[108] Hwang E H, Adam S and Das Sarma S 2007 Transport inchemically doped graphene in the presence of adsorbedmolecules Phys. Rev. B 76 195421

[109] Wehling T O, Novoselov K S, Morozov S V, Vdovin E E,Katsnelson M I, Geim A K and Lichtenstein A I 2008Molecular doping of graphene Nano Lett. 8 173–7

[110] Khrapach I, Withers F, Bointon T H, Polyushkin D K,Barnes W L, Russo S and Craciun M F 2012 Novel highlyconductive and transparent graphene-based conductorsAdv. Mater. 24 2844–9

[111] Fang Z, Wang Y, Liu Z, Schlather A, Ajayan P M,Koppens F H L, Nordlander P and Halas N J 2012Plasmon-induced doping of graphene ACS Nano6 10222–8

[112] Konstantatos G, Badioli M, Gaudreau L, Osmond J,Bernechea M, Pelayo Garcia de Arquer F, Gatti F andKoppens F H L 2012 Hybrid graphene-quantum dotphototransistors with ultrahigh gain Nat. Nanotechnol.7 363–8

[113] Liu H, Ryu S, Chen Z, Steigerwald M L, Nuckolls C andBrus L E 2009 Photochemical reactivity of graphene J.Am. Chem. Soc. 131 17099–101

[114] Tiberj A, Rubio-Roy M, Paillet M, Huntzinger J-R,Landois P, Mikolasek M, Contreras S, Sauvajol J-L,Dujardin E and Zahab A-A 2013 Reversible optical dopingof graphene Sci. Rep. 3 2355

[115] Ju L et al 2014 Photoinduced doping in heterostructures ofgraphene and boron nitride Nat. Nanotechnol. 9 348–52

[116] Guo L, Zhang Y-L, Han D-D, Jiang H-B, Wang D, Li X-B,Xia H, Feng J, Chen Q-D and Sun H-B 2014

Laser-mediated programmable N doping and simultaneousreduction of graphene oxides Adv. Opt. Mater. 2 120–5

[117] Novoselov K S, Fal V I, Colombo L, Gellert P R, Schwab MG and Kim K 2012 A roadmap for graphene Nature490 192–200

[118] Grigorenko A N, Polini M and Novoselov K S 2012Graphene plasmonics Nat. Photon. 6 749–58

[119] Mak K F, Lui C H, Shan J and Heinz T F 2009 Observationof an electric-field-induced band gap in bilayer grapheneby infrared spectroscopy Phys. Rev. Lett. 102 256405

[120] Zhang Y, Tang T-T, Girit C, Hao Z, Martin M C, Zettl A,Crommie M F, Ron Shen Y and Wang F 2009 Directobservation of a widely tunable bandgap in bilayergraphene Nature 459 820–3

[121] Liu M, Yin X, Ulin-Avila E, Geng B, Zentgraf T, Ju L,Wang F and Zhang X 2011 A graphene-based broadbandoptical modulator Nature 474 64–7

[122] Liu M, Yin X and Zhang X 2012 Double-layer grapheneoptical modulator Nano Lett. 12 1482–5

[123] Hwang E H and Das Sarma S 2007 Dielectric function,screening, and plasmons in two-dimensional graphenePhys. Rev. B 75 205418

[124] Ju L et al 2011 Graphene plasmonics for tunable terahertzmetamaterials Nature Nanotechnol. 6 630–4

[125] Echtermeyer T J, Britnell L, Jasnos P K, Lombardo A,Gorbachev R V, Grigorenko A N, Geim A K, Ferrari A Cand Novoselov K S 2011 Strong plasmonic enhancementof photovoltage in graphene Nat. Commun. 2 458

[126] Fang Z, Liu Z, Wang Y, Ajayan P M, Nordlander P and HalasN J 2012 Graphene-antenna sandwich photodetector NanoLett. 12 3808–13

[127] Chen J et al 2012 Optical nano-imaging of gate-tunablegraphene plasmons Nature 487 77–81

[128] Fei Z et al 2012 Gate-tuning of graphene plasmons revealedby infrared nano-imaging Nature 487 82–5

[129] Shao Y, Wang J, Wu H, Liu J, Aksay I A and Lin Y 2010Graphene based electrochemical sensors and biosensors: areview Electroanalysis 22 1027–36

[130] Ratinac K R, Yang W, Ringer S P and Braet F 2010 Towardubiquitous environmental gas sensors: capitalizing on thepromise of graphene Environ. Sci. Technol. 44 1167–76

[131] Llobet E 2013 Gas sensors using carbon nanomaterials: areview Sensors Actuators B: Chem. 179 32–45

[132] Wu S, He Q, Tan C, Wang Y and Zhang H 2013Graphene-based electrochemical sensors Small 9 1160–72

[133] Liu Y, Dong X and Chen P 2012 Biological and chemicalsensors based on graphene materials Chem. Soc. Rev.41 2283–307

[134] Gomez-Navarro C, Thomas Weitz R, Bittner A M, Scolari M,Mews A, Burghard M and Kern K 2007 Electronictransport properties of individual chemically reducedgraphene oxide sheets Nano Lett. 7 3499–503

[135] Becerril H A, Mao J, Liu Z, Stoltenberg R M, Bao Z andChen Y 2008 Evaluation of solution-processed reducedgraphene oxide films as transparent conductors ACS Nano2 463–70

[136] Eda G, Fanchini G and Chhowalla M 2008 Large-areaultrathin films of reduced graphene oxide as a transparentand flexible electronic material Nat. Nanotechnol. 3 270–4

[137] Robinson J T, Keith Perkins F, Snow E S, Wei Z andSheehan P E 2008 Reduced graphene oxide molecularsensors Nano Lett. 8 3137–40

[138] Wang L et al 2013 One-dimensional electrical contact to atwo-dimensional material Science 342 614–7

[139] Geim A K and Grigorieva I V 2013 Van der waalsheterostructures Nature 499 419–25

26

http://dx.doi.org/10.1073/pnas.0605033103

http://dx.doi.org/10.1038/nphys1022

http://dx.doi.org/10.1063/1.2818692



http://dx.doi.org/10.1063/1.3536670

http://dx.doi.org/10.1021/nn100508g


http://dx.doi.org/10.1088/0957-4484/20/24/245501



http://dx.doi.org/10.1021/nl072364w

http://dx.doi.org/10.1002/adma.201200489

http://dx.doi.org/10.1021/nn304028b


http://dx.doi.org/10.1021/ja9043906


http://dx.doi.org/10.1002/adom.201300401






http://dx.doi.org/10.1021/nl204202k



http://dx.doi.org/10.1038/ncomms1464

http://dx.doi.org/10.1021/nl301774e



http://dx.doi.org/10.1002/elan.200900571

http://dx.doi.org/10.1021/es902659d

http://dx.doi.org/10.1016/j.snb.2012.11.014

http://dx.doi.org/10.1002/smll.201202896

http://dx.doi.org/10.1039/c1cs15270j

http://dx.doi.org/10.1021/nl072090c

http://dx.doi.org/10.1021/nn700375n





Documents

Raman characterization of defects and dopants in graphene · Raman characterization of defects and dopants in graphene Ryan Beams1, Luiz Gustavo Canc¸ado2 and Lukas Novotny3