Raman Spectroscopic Characterization of Graphene

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Raman Spectroscopic Characterization of

GrapheneBo Tang

a, Hu Guoxin

a& Hanyang Gao

b

aSchool of Mechanical and Power Engineering, ShangHai JiaoTong

University, Shanghai, China

b School of Environmental Science and Engineering, ShangHai

JiaoTong University, Shanghai, China

Version of record first published: 13 Apr 2010.

To cite this article: Bo Tang , Hu Guoxin & Hanyang Gao (2010): Raman Spectroscopic

Characterization of Graphene, Applied Spectroscopy Reviews, 45:5, 369-407

To link to this article: http://dx.doi.org/10.1080/05704928.2010.483886

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Applied Spectroscopy Reviews, 45:369–407, 2010

Copyright © Taylor & Francis Group, LLC

ISSN: 0570-4928 print / 1520-569X online

DOI: 10.1080/05704928.2010.483886

Raman Spectroscopic Characterization of Graphene

BO TANG,1 HU GUOXIN,1 AND HANYANG GAO2

1School of Mechanical and Power Engineering, ShangHai JiaoTong University,

Shanghai, China2School of Environmental Science and Engineering, ShangHai JiaoTong

University, Shanghai, China

Abstract: The recent progress using Raman spectroscopy and imaging of graphene is

reviewed. The intensity of the G band increases with increased graphene layers, and the shape of 2D band evolves into four peaks of bilayer graphene from a single peak of monolayer graphene. The G band will blue shift and become narrow with both electronand hole doping, whereas the 2D band will blue shift with hole doping and red shift with electron doping. Frequencies of the G and 2D band will downshift with increasingtemperature. Under compressed strain, the upshift of the G and 2D bands can be found. Moreover, the strong Raman signal of monolayer graphene is explained by interference

enhancement effect. As for epitaxial graphene, Raman spectroscopy can be used toidentify the superior and inferior carrier mobility. The edge chirality of graphene canbe determined by using polarized Raman spectroscopy. All results mentioned here areclosely relevant to the basic theory of graphene and application in nanodevices.

Keywords: Raman spectroscopy, graphene, doping, strain, FWHM

Introduction

Graphene, a strictly two-dimensional material with a honeycomb lattice of sp2-bonded

carbon atoms, has attracted extensive study since being experimentally discovered by

Novoselov et al. in 2004 (1). In physical structure, graphene is the basic building block of

carbon nanomaterials, including one-dimensional carbon nanotubes and zero-dimensional

fullerenes. For the electronic bands structure, the conduction and valence band touch each

otherattheKandK points in the Brillouin zone. Graphene exhibits an unusual linear energy

dispersion relationship (the electron energy has a linear relationship with wave vector near

K and K points), which make the electrons like the massless relativistic Dirac fermions

with a vanishing density of states at the Fermi level (2, 3). In the last 5 years, some novel

properties of graphene were discovered, such as the quantum spin hall effect (4, 5), electron

mobility as high as 120,000 cm2 /Vs (the charge carriers mobility of graphene is higher

than any other semiconductor at room temperature) (1, 6, 7), ballistic transport at room

temperature (8–12), enhanced coulomb interaction (13–17), high mechanical strength (18),

high thermal conduction (19–22), and suppression of weak localization (23, 24). These

unique properties of graphene make it a candidate for theoretical study and potential device

Address correspondence to Hu Guoxin, School of Mechanical and Power Engineering, ShangHaiJiaoTong University, No. 800 Dong Chuan Road, Shanghai City, 200240, China. E-mail: [email protected]

369



370 B. Tang et al.

applications (4, 25–29). Furthermore, the application of graphene in the spin device has

attracted interest (the spin relaxation length reaches ∼2 µm).

In order to fabricate this potentially exciting material, some methods including mi-

cromechanical cleavage of graphite (MG) (1), chemical vapor deposition (CVD) (30, 31),

epitaxial growth on an SiC surface (32–34), and reduction of graphite oxides (35–39)have been developed. The charge carrier mobility of epitaxial graphene growth on SiC is

lower, whereas numerous functional groups always remain on the surface of the reduced

graphene. Micromechanical cleavage of graphite is the most frequently used method to

produce graphene but with a small size (<1,000 µm2). Recently, larger-scale (<1 cm2)

graphene has been fabricated by CVD (30). Characterizing graphene is another major area

of study because the results are closely relevant to the application of graphene. Some

modern measurement technologies are used to characterize graphene, including scanning

electron microscopy (SEM) (30, 40), transmission electron microscopy (TEM) (30, 40,

41), atomic force microscopy (AFM) (41), and Raman spectroscopy (40–47). SEM and

TEM can be used to obtain physical morphology, but the graphene may be damaged during

the complicated measurement process. The precise depth of graphene can be determinedby AFM but can be time consuming. Moreover, measuring the electronic properties of

graphene is beyond the ability of these three techniques.

Raman spectroscopy is not only a versatile tool (number of graphene layers, doping

level, and edge chirality of graphene can be obtained at the same time) but is a rapid

and nondestructive method to study graphene. Raman spectroscopy is widely used to

characterize electronic properties and microstructure of graphite materials (48–51). As a

nondestructive technique, a considerable amount of work on graphene has been performed

by Raman spectroscopy (46, 47). According to the electronic characteristics of graphite

materials, it is well known that the common features of graphene in Raman spectroscopy are

in the wavelength region of 800–3,000 cm−

1. Three major peaks are found around 1,580,

1,350, and 2,700 cm−1, so-called G, D, and 2D bands, respectively (52–54). The G band

associates with E2g phonon at the Brillouin zone center (55). The disorder-induced D band

is another fingerprint peak in graphite material with a concentration of defects (56). A 2D

peak is the second order of the D peak and caused by the double resonant Raman scattering

with two-phonon emissions (52, 57). Interestingly, the 2D band, sensitive to the number

of graphene layers, is free of defect and has no D peak (52). It can be fitted with a single

peak of the monolayer graphene and fitted with multiple peaks of multilayer graphene (58).

Doping is a common phenomenon during fabrication of graphene. The peak positions of

the G and 2D bands always shift under doping condition due to electron–phonon coupling

(42, 44). Except that the peak shift of G and 2D band can be used to determine the density

of a charged impurity, the ratio of integrated intensity of the 2D band to the G band I2D /IG isanother method to identify the doping level of graphene (59). The temperature fluctuation

in graphene can also be studied by Raman spectroscopy: a linear red shift of the G and 2D

bands with increasing temperature can be found (60). Quantitative strain study of graphene

results from the substrate can be calculated through Raman curves (61–63).

The organization of this review article is as follows: the details of changes in the G

band (position, intensity, and full width at half maximum [FWHM]) with varied number

of graphene layers, strain, doping level, and fluctuation of temperature in graphene are

described in the next section. In the following section the details of changes in the 2D

band with number of graphene layers, strain, doping level, and fluctuation of temperature

of graphene are described. The integrated intensity ratio I2D /IG is discussed in the next

section. Then, attention is focused on edge chirality, so D band is the major content. Raman



Raman Spectroscopic Characterization of Graphene 371

spectroscopy to study epitaxial graphene (EG) growth on SiC is reviewed in the following

section. Then, an explanation about the strong Raman signal of monolayer graphene is

given based on an interference enhancement model. The graphene analyzed are MG except

special mention. In the final section, a summary is given.

G Band of Graphene

Intensity Change of the G Band with Varied Number of Graphene Layers

An efficient and precise method to identify the number of graphene layers is needed in

characterizing graphene. Graf and and Molitor (64) analyzed the change of G band with

different number of graphene layers. Figure 1 shows that the intensity of the G peak

increases in an almost linear relation with increased layers. This phenomenon can be easily

understood as more sp2 bond carbon atoms being detected by the laser spot with increased

layers of graphene. It is worthy to note that in addition to increasing intensity, the red shiftof the G band takes place with increased number of graphene layers. A peak shift also takes

place when graphene under doping or strain results from substrate, which will be addressed

in the following section (65). It is not an accurate method to determine the number of

graphene layers based on the red shift of the G band. On the other hand, the independence

of G band intensity from doping and strain makes it a good criterion to identify monolayer

and multilayer graphene.

Figure 1. (a, b) SFM micrograph and cross-sectional plot of a few-layer graphene flake with central

sections down to a single layer. (c) Raman maps of the integrated intensity of the G line. (e) The

FWHM of the 2D band. The related cross sections (d, f) are aligned (vertical dashed lines) with the

height trace (64).



372 B. Tang et al.

Peak Position and FWHM of the G Band as a Function of Doping Level

The G band can not only be used to identify the number of graphene layers but can also

determine doping level of graphene on various substrates according to the peak shift and

FWHM. Normally, the MG can always be deposited on SiO2-coated Si substrate (1, 60, 66).

Unintentional doping, as large as ∼1012 /cm2, being induced by the substrate and ambientconditions was reported (67). Doping can have a strong influence upon transport properties

of graphene, and it is important to obtain the doping level of graphene (1, 64).

Stephane et al. (65) abstracted the difference of the G band between the free-standing

monolayer graphene and supported monolayer of graphene on an SiO2 substrate. A

micrometer-sized trench was etched in the SiO2 substrate before the prepared monolayer

graphene was deposited. In Figure 2, spatially resolved Raman spectroscopy is used to char-

acterize these two portions of graphene. Some clear differences can be observed: (1) The

G band frequency of the free-standing portion is red shift (∼7 cm−1) compared to the

supported portion and accompanies a wider FWHM (14 and 6 cm−1, respectively). (2) The

2D band of the suspended graphene is downshifted with respect to the supported portion.

(3) The ratio of integrated intensity of the 2D band to the G band is four times for the

suspended portion compared to the supported portion. (2) and (3) Will be discussed in

succeeding sections; only the G band is discussed here. The frequency of the G band of

the suspended portion is similar to the single crystal of graphite (68) and the FWHM is

similar to the highest value of charge neutrality graphene (69–75). The latter means that

the suspended portion of graphene is almost charge neutral. On the other hand, a stiffening

frequency and narrow FWHM can be observed on the supported portion of graphene. The

7 cm−1 blue shift in the G band frequency means that approximately 6 × 1012 cm−2 carrier

Figure 2. (a) Optical micrograph of an exfoliated graphene monolayer spanning a 300-nm-deep

trench etched in the SiO2 epilayer. (b) Raman spectra recorded on the single-layer graphene sample

of (a), both for the suspended (red solid line) and supported regions (blue dashed line). (c) Raman

spectra in the lower-frequency region (1,270–1,420 cm−1) for the two regions of the sample. (d)

Detailed comparison of normalized spectra for the G mode. The experimental data (red open circles

and blue open squares, for suspended and supported graphene, respectively) are fit with Voigt profiles

(solid lines) (65).




Figure 3. Spatial maps of the Raman features of a single-layer graphene sample, with regions of

free-standing and supported material: (a) the G-mode frequency, ωG; (b) the G-mode line width, G;

and (c) the ratio of the integrated intensity of the D mode to that of the G mode, I D /IG. (d) Correlation

between ωG and G for the suspended (red open circles) and lower supported (blue open squares)

regions, as well as for the defective tip of the sample (gray open triangles) (65).

density resulting from the substrate is reached in the supported portion, which implies a

shift in the Fermi energy of ∼250 meV from the Dirac point (69).

In order to obtain more details, Raman spatial mapping was performed by St ephane

et al. (65). In Figure 3, the suspended portion of graphene can easily be distinguished

from the supported portion through a lower value of frequency of the G band and wider

FWHM. The frequency and FWHM of the G band of supported graphene varies point to

point, which means that inhomogeneous doping occurs. On the contrary, for the suspended

graphene, the frequency and FWHM of the G band is almost homogeneous around the

mean values of ωG = 1,581 cm−1 and G = 13.5 cm−1. In earlier papers, some authors took

the ratio of integrated intensity of the 2D to G peaks as one of the criteria to determine the

number of graphene layers. Inhomogeneity of I2D /IG occurring in Figure 3c indicates thatthe ratio of integrated intensity of the 2D band to the G band is strongly dependent on the

doping level due to substrates. Therefore, it is not a precise method to identify the number

of graphene layers by using the ratio I2D /IG when graphene is deposited on a substrate.

A quantitative discussion about the doping levels in free-standing monolayer graphene

through Raman spectra is needed (73). Both the frequency and FWHM of the G band

are influenced by doping level through the strong electron–phonon coupling (73–75). The

doping level can be measured by the frequency of the G band even at low levels at low

temperature (76, 77). But the frequency of the G band is expected to reach an essentially

constant minimum value for all carrier densities below 6 × 1012 cm−2 at room temperature.

Lazzeri et al. (73) proposed an equation associated with FWHM of the G band with doping

level. They pointed out that the broadening of the G mode is proportional to the statistical

availability for electron-hole pair generation at the G-mode energy, so the line width of the



374 B. Tang et al.

G band can be written as:

G = 0 + [f T (− ωG/2 − EF ) − f T ( ωG/2 − EF )] (1)

Here denotes the maximum phonon broadening from electron-hole pair generation

(Landau damping) as it would occur at zero temperature; f T is the Fermi-Dirac distributionat temperature T ; EF is the Fermi energy relative to the Dirac point in graphene; and 0 is

the contribution to the line width from phonon–phonon coupling and other sources that are

independent of these electronic interactions.

A conclusion can be made from Eq. (1) that the average doping level of suspended

graphene is less than 2 × 1011 cm−2, and the small deviation around the mean value (about

1 cm−1 (65)) of G implies that the inhomogeneity of the low doping level of free-standing

monolayer graphene is less than this level. But the inhomogeneous doping occurs in the

supported portion of grapheme, which means that the interaction of graphene with the

substrate is stronger than an intrinsic property of exfoliated graphene prepared and held

under ambient conditions (65). The possible influence of strain on the graphene samples is

neglected in the above discussion (we will discuss the change of the G band resulting from

the strain in the following part). The isotropic strain can be excluded in a suspended sample

with sample geometry. Polarization Raman was performed to exclude residual uniaxial

stress. The researchers noted that there was no obvious peak shift more than 0.5 cm −1 and

no splitting of the G band occurred (65) (because anisotropic strain would lead to a splitting

of the G band (61)). A residual strain in the free-standing graphene can be estimated to

be less than 0.1% according to the experimentally determined shift ratio (78). Stephane et

al. suggested that the G band frequency reached its lowest value and maximum width for

electrical neutral graphene (65). The supported portion of graphene on SiO2-covered Si

substrate shows increased frequency and reduced FWHM of the G band.

So a blue shift and narrow FWHM of the G band can be used to identify the dopinglevel (in order to exclude the influence of number of graphene layers, the shape of the 2D

bond needs to be considered too, which we will discuss below). It is worth noting that the

blue shift of the G band occurs both in electron and hole doping. In order to distinguish the

doping type, the peak shift of the 2D band needs to considered and will be discussed below.

Temperature Dependence of the G Band

Calizo et al. (60) studied temperature-dependent Raman spectroscopy of monolayer and

multilayer graphene. The temperature ranged from −190 to 100◦C. The downshift of

the G band was observed with increasing temperature. Ci et al. (79) pointed out that the

temperature dependence of Raman spectroscopy of carbon-based materials can be explained

based on the elongation of the C C bond due to thermal expansion or anharmonic coupling

of phonon modes. The relationship between frequency of the G mode with temperature can

be represented as:

ω = ω0 + χ T (2)

where ω0 is the frequency of the G mode when temperature T is extrapolated to 0 K and

x is the first-order temperature coefficient, which defines the slope of the dependence. The

extracted negative value for single-layer graphene is χ = −(1.62 ± 0.20) × 10−2 cm−1 /K

from Figure 4a. Similar measurements were carried out for the bilayer graphene and gave

the value of χ = −(1.54 ± 0.06) × 10−2 cm−1 /K from Figure 4b. The extrapolated ω0

values are 1,584 and 1,582 cm−1 for the single- and bilayer graphene, correspondingly.




Figure 4. Temperature dependence of the G peak frequency for the single- (a) and bilayer (b)

graphene. The insets show the shape of G peak. The measured data were used to extract the temperature

coefficient for G peak (60).

According to the anharmonic terms in the lattice potential energy, the change of phonon

frequency of graphene with temperature can be provided (80). The temperature effects can

be roughly divided into the “self-energy” shift due to the anharmonic coupling of the

phonon modes and the shift contribution due to the thermal expansion of the crystal. The

physical mechanism of the latter is different from the former but related to the change of

the force constants of the material with volume, although the thermal expansion also results

from the anharmonicity. Thus, the measured frequency change ω = ω − ω0 can be shown

as (60):

ω

≡(χT

+χV )T

= dω

dT V

T

+dω

dV T

T

= dω

dT V

T

+dω

dV T

dω

dT P

T

(3)

Here, x T is defined as to be the self-energy shift due to the direct coupling of the phonon

modes and x V as the shift due to the thermal expansion induced volume change. Under con-

stant pressure rather than constant volume, both contributions are reflected in the resulting

Raman spectra of the temperature coefficient, x = x V + x T . Unlike frequency, the FWHM

of the G band of monolayer and bilayer graphene is not sensitive to temperature, which

indicates that the effect of electron–phonon coupling is obviously not with this range of

temperature. This result is in line with the report of the G band of highly oriented pyrolytic

graphite (HOPG) (81).

The possible effect of the substrate (Si coated with 300 nm of SiO2) should be con-

sidered. Although one cannot absolutely exclude the influence from the substrate, the

effect does not strongly affect the value of thermal coefficients (82, 83). This means that

the measured temperature coefficients for the G band are less influenced by the substrate

property.

Relationship between the G Band and Uniaxial Strain in Graphene

As monolayer graphite material, it is predicted that strain resulting from a substrate can

strongly modify the electronic and optical properties of graphene. Moreover, it is possible

to open a band gap on graphene because the strain can break the sublattice symmetry (61,

84). Two kinds of strain can be introduced to graphene through substrate: uniaxial strain

and biaxial strain. Raman curves of tensile strained graphene show an obvious red shift of

the G and 2D bands. Zhen researched the evolution of the Raman pattern of graphene under



376 B. Tang et al.

Figure 5. The G band frequency of single-layer (black squares) and three-layer (red circles) graphene

under uniaxial strain. The black lines are the curve fit to the data. The slope is 14.2 cm−1 /% for single-

layer graphene and 12.1 cm−1 /% for three-layer graphene (62).

uniaxial strain (62). The graphene was deposited on a transparent and flexible substrate,

polyethylene terephthalate (PET) (62).

Tensile strain on single-/three-layer graphene was loaded by stretching the substrate

film in one direction. The value of the strain is determined by dividing the extra length by

the unstrained length of substrate. Although the interaction between graphene and PET is

van der Waals force, it is enough to load the strain to graphene. The frequency of the G band

is red shift with increasing uniaxial strain, which can be understood by the weakened bonds

between carbon atoms and lower vibrational frequency due to raised distance betweencarbon atoms. Figure 5 shows the frequency of the G band as a function of uniaxial strain

for monolayer graphene and three-layer graphene. A linear dependence of the G band

frequency with strain can be seen, and the slope for single-layer and three-layer graphene

are −14.2 ± 0.7 and −12.1 ± 0.6 cm−1 /%, respectively. The linear dependence between

peak shifts with strain can be interpreted on the basis of phonon deformation potentials.

Both uniaxial strain and shear strain are attributed to the change of peak position; the

shear strain can be ignored because of its smaller contribution (85). So the relationship of

frequency with strain can be written as (85, 86):

ω

ω0 = γ · (εxx + εyy ) (4)

where r = 1.24 is the Gruneisen parameter of carbon nanotubes (CNTs) (85); ε xx is the

uniaxial strain; ε yy ≈ −0.186εxx is the relative strain in the perpendicular direction, which

is calculated by using the Poisson ratio of graphene (87); and ω0 is the Raman frequency

of the G band of unstrained graphene.

Therefore, the G band frequency dependence on uniaxial tensile strain is approximately

estimated as:

ω

ε= −ω0 · γ · (1 − 0.186) = −15.9cm−1/% (5)

The value is in accordance with the experimental result of single-layer graphene (−14.2 ±0.7 cm−1 /%). The dependence between uniaxial strain with electronic structure of graphene




Figure 6. (a) Schematic representation of the effect of uniaxial tensile stress on a graphene supercell.

The dashed (solid) lattices indicate the unstrained (strained) graphene. Calculated band structure of

unstrained (b) and 1% tensile strained (c) graphene. A band gap is clearly seen on the band structure

of strained graphene (62).

was calculated by using a first-principle calculation. A band gap appears at the K point

of the Brillouin zone of strained grapheme, which can be attributed to the breaking of

sublattice symmetry (88–90). Quantitatively, a band gap as big as 300 meV can be reachedafter loading 1% uniaxial strain on graphene. The results are shown in Figures 6 and 7.

Figure 7. Band gap of strained graphene with the increase of uniaxial tensile strain on graphene.

The magnitude of the gap is determined by the gap opening of the density of states. The insets show

the calculated density of states (DOS) of unstrained and 1% tensile strained graphene. The dashed

line and red solid dot indicate the calculated band gap of graphene under the highest strain (0.78%)

in our experiment (62).



378 B. Tang et al.

Figure 6(c) indicates the graphene transfer to a semiconductor material with an obvious

band gap of the π band at the K point of the boundary of the Brillouin zone after loading

the uniaxial strain. From Figure 7, an almost linear relationship between uniaxial strain and

band gap can be seen.

Relationship between the G Band and Biaxial Strain in Graphene

Zhen et al. (63) also studied graphene with biaxial strain. The SiO 2 capping layers (5 nm)

were deposited on the top of the graphene by pulsed laser deposition (PLD), followed by

annealing at different temperatures to load the biaxial strain to the graphene.

Figure 8 clearly shows that both the G and 2D bands blue shift with increased annealing

temperature, whereas the intensity of D band decreases. (We only discuss the G band here;

the 2D and Ds band will be discussed later.) The peak shift of the G band is attributed to the

compressive stress on graphene result from SiO2. The capping film becomes denser duringthe process of annealing, so exerted compressive stress loaded in the graphene through van

der Waals force. From the above discussion we know that the effect of doping from the

substrate can modify the frequency of the G band, too. In this case only a small fluctuation (1

cm−1) appears about the FWHM, which indicates that the effect of doping can be ignored

(in the next section we will see that the information of the 2D band further proves this

opinion). The biaxial compressive stress is similar to the biaxial stress at thin film, which

results from the lattice mismatch with substrate. Therefore, the biaxial compressive stress

on graphene can be estimated as follows.

Figure 8. (a) Raman spectra of single-layer graphene coated by 5-nm SiO2 and annealed at different

temperature. (b) The intensity ratio of the D band and G band ( I D / I G) of graphene sheets with one to

four layers (coated with SiO2) after annealing at different temperature. The I D / I G (defects) decreased

significantly upon annealing (63).




For a hexagonal system, the strain ε induced by an biaxial stress can be expressed as

(91, 92)

⎡⎢⎢⎢⎢⎢⎢⎣

εxx

εyy

εzz

εyz

εzx

εxy

⎤⎥⎥⎥⎥⎥⎥⎦

=

⎡⎢⎢⎢⎢⎢⎢⎣

S 11 S 12 S 13

S 12 S 11 S 13

S 13 S 13 S 33

S 44

S 44

2(S 11 − S 12)

⎤⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎣

σ

σ

0

0

0

0

⎤⎥⎥⎥⎥⎥⎥⎦

(6)

with the coordinates x and y in the graphene plane and with z perpendicular to the plane, so

that ε xx = ε yy = (S11 − S12)σ , ε xx = 2S13σ , ε xy = ε yz = εz x = 0. With all shear components

of strain equal to zero, the secular equation of such a system can be written as:

A(εxx + εyy ) − λ B(εxx − εyy )

B(εxx

−εyy ) A(εxx

+εyy )

−λ

= 0 (7)

where λ = ω2σ − ω2

0, with ωσ and ω0 being the frequencies of Raman E2g phonon under

stressed and unstressed conditions. There is only one solution for this equation:

λ = A(εxx + εyy ) = 2Aεxx = 2A(S 11 + S 12)σ (8)

Therefore,

ωσ − ω0 = λ

ωτ + ω0

≈ λ

2ω0

= A(S 11 + S 12)σ

ω0

= ασ (9)

where a = A(S11 + S12)/ω0 is the stress coefficient for Raman peak shift. Using A =−1.44 × 107 cm−2 (91) and graphite elastic constants S11 = 0.98 × 10−12 Pa−1, S12=

−0.16 × 10−12 Pa−1 (93), and ω0 = 1,580 cm−1, the stress coefficient is estimated to

be 7.47 cm−1 /GPa. The estimated stress on single-layer graphene with varies annealing

temperature as shown in Figure 9d. The compressive stress on graphene was as high as

∼2.1 GPa after depositing SiO2 following annealing at 500◦C, and the stress on single-layer

graphene can be fitted by the following formula:

σ = −0.155 + (2.36 × 10−3)T + (5.17 × 10−6)T 2 (10)

where σ is the compressive stress (GPa) and T is temperature (◦C). The appearance of such

large stress is mainly because graphene sheets are very thin (0.335 nm in thickness forsingle-layer graphene) (94), so graphene can be easily compressed or expanded. It has been

reported that even very weak van der Waals interaction can produce large stress on single-

wall carbon nanotubes (95). Tensile stress was introduced onto graphene by depositing a

thin cover layer of silicon. The G band of graphene red shifted by ∼5 cm−1 after silicon

deposition, which corresponds to a tensile stress of ∼0.67 GPa on graphene sheet (63).

Mohiuddin et al. (61) did some detailed research of the G band of graphene under

uniaxial stress. The double degenerate E2g optical mode splits into two components (named

G+ and G−) under a strong enough uniaxial strain. One of the components polarized along

the strain and another polarized perpendicular the strain. Both peaks are red shift with

increasing strain, while the splitting increases. The evolution of the G and 2D bands with

varied strain are shown in Figure 10. The G band split into two components after the strain

reached about 0.5%.



380 B. Tang et al.

Figure 9. The Raman peak frequency of G band (a), D band (b), and 2D band (c) of graphene sheets

with one to four layers (coated with SiO2) after annealing at different temperature. Blue shifts of all the

Raman bands were observed after annealing, which were attributed to the strong compressive stress

on graphene. (d) Magnitude of compressive stress on single-layer graphene controlled by annealing

temperature. The red line is a curve fit to the experimental data (63).

Figure 10. (a) G and (b) 2D peaks as a function of uniaxial strain. The spectra are measured with

incident light polarized along the strain direction, collecting the scattered light with no analyzer. Note

that the doubly degenerate G peak splits into two subbands G + and G−, whereas this does not happen

for the 2D peak. The strains, ranging from 0 to 0.8%, are indicated on the right side of the spectra

(61).




Figure 11. Positions of the (a) G+ and G− and (b) 2D peaks as a function of applied uniaxial strain.

The lines are linear fit to the data. The slopes of the fitting lines are also indicated (61).

Figure 11 was plotted with the linear fit and yield ∂ωG+ / ∂ε ∼ −10.8 cm−1 /%, ∂ωG− / ∂ε

∼ −31.7 cm−1 /%, and ∂ω2D / ∂ε ∼ −64 cm−1 /%. There are two different conclusions

between Mohiuddin et al. (61) and Zhen et al. (62). The first one is about splitting, which

does not occur in Zhen et al. (62), although the strain reached 0.8% (far higher than 0.5%

in Mohiuddin et al. 61). The next one is about the value of ∂ωG / ∂ε and ∂ω2D / ∂ε, −14.2 ±0.7 cm−1 /% and −27.8 ± 0.8 cm−1 /% are from Zhen et al. (62), whereas −31.7 cm−1 /%

(−10.8 cm−1 /%) and −64 cm−1 /% are abstracted in Mohiuddin et al. (61). These big

differences cannot be attributed to inaccuracy of the apparatus. Moreover, two sets of

results are in accordance with each theoretical calculation.

We are more in accord with Mohiuddin et al. (61) than Zhen et al. (62). Firstly,

G band splitting is a common phenomenon of carbon nanomaterial under strain, suchas nanotubes (96, 97). Secondly, the calculation in Mohiuddin et al. (61) is performed

with a more accurate value of Gruneisen parameter r (1.99) on the basis of Grimvall

(98), whereas the value of r (1.24) used in Zhen et al. (62) is the Gruneisen parameter

of CNTs (85). There are at least two reasons that can lead to the small result ( ∂ωG / ∂ε

and ∂ω2D / ∂ε) in Zhen et al. (62): (1) The graphene is not single but multilayer, because

strain is more effectively applied on a thinner graphene sheet. (2) The factual strain in

graphene is less than the value of calculation. The value of ε is calculated directly from

the change of PET (substrate) instead of directly from the change of graphene. If the strain

did not sufficiently load on graphene, the resulting ∂ωG / ∂ε is smaller than the real value.

This may be why the G band did not split even though the strain reached 0.78% in Zhen

et al. (62).



382 B. Tang et al.

Figure 12. Raman spectra of (a) single- and (b) double-layer graphene (collected at spots A and B;

see (b) (64).

2D Band of Graphene

Shape Evolution of 2D Band with Varied Number of Graphene LayersThe 2D peak in Raman spectra of graphene is another useful tool to identify the number of

graphene layers. The prominent difference in the 2D peak between monolayer and bilayer

graphene is shown in Figure 12 according to Graf and Molitor (64). Although the integrated

intensity of the 2D line stays almost constant, it narrows to a single peak at a lower wave

number as a single-layer graphene.

Evolution of the 2D peak width with increased layer count of graphene or, at high

resolution, its splitting into some Lorentzian components (see Figure 13) can be explained

in the framework of the double-resonant Raman model (52, 64, 99). This model explains the

origin of the 2D line in the following way (see Figure 14a): an electron is vertically excited

from point A in the π band to point B in the π∗ band by absorbing a photon. The excitedelectron is inelastically scattered to point C by emission of a phonon with wave vector q.

Inelastic backscattering to the vicinity of point A by emission another phonon with wave

Figure 13. 2D peaks for an increasing number of graphene layers along with HOPG as a bulk

reference (64).




Figure 14. Electronic band structure: (a) single-layer graphene, (b) double-layer graphene, and (c)

bulk graphite (64).

vector q, then electron-hole recombination and emission a photon whose energy is less

than the incident photon. The evolution of the electronic band structure of the monolayer

graphene/double-layer graphene/bulk graphite is shown in Figure 13.

In the case of double layer graphene, the π and π ∗ bands split into two bands each

and give rise to four differently possible excitations (1-4 in Figure 14b). The corresponding

electron-phonon coupling matrix elements for the phonons qo∼q4 are almost equal in

theoretical calculation, which is in line with experimental data (see Figure 13: 2D band

decomposes into four peaks). However, the outer two peaks (corresponding to the phonons

qo andq3) have very low weight which is contradicted with the calculated result. The phonon

frequencies v1 and v2 are corresponding to the wave vectors q1 and q2 by calculation

(100). The values of v1, v2, and 2(v2- v1) corresponding to bulk graphite/double layer

graphene/single layer graphene are given in Table 1 (64). However, the splitting valueobtained from first-principles calculation is only half as large as that of experimental result

(19 cm-1). This discrepancy is related to the fact that the double-resonant Raman model

Table 1

Frequencies of the optical phonons involved in the double-resonant Raman model (64)

v1 (cm−1) v2 (cm−1) 2(v2 − v1) (cm−1)

Bulk 1,393.2/1,393.6 1,402.9/1,403.1 19.4/19.0

Double layer 1,395.6/1,395.6 1,400.0/1,400.6 8.8/10.0Single layer 1,398.1



384 B. Tang et al.

Figure 15. Position of the 2D peak (Pos(2D)) as a function of doping. The solid line is adiabatic

DFT calculation (71).

based on ab initio calculations also predicts a value for the dispersion of the 2D line with

incident laser energy that amounts only to about half of the experimentally observed value

of 99 cm-1 /eV (64). So far, the double-resonant Raman model can qualitatively explain the

fourfold splitting of the 2D line in the bilayer graphene, but the amount of the splitting and

the relative heights of the peaks are not properly described. For the bulk graphite, the π and

π∗ bands split into continued bands, q1 and q2 represent the possible process of 2D mode.

And the splitting between them is lager than double layer graphene, which is in line with

the experimental data (see Figure 13).

Ferrari et al. (52) explained the phenomenon of splitting of the 2D band of bilayer

graphene for the first time. In the bilayer case, the observed four components of the 2D

band could due to two reasons: (1) the splitting of the phonon branches (101, 102) or (2) thesplitting of the electronic bands (103). After calculation (104), the splitting of the phonon

branch is less than 1.5 cm−1, much smaller than the experimental result. So the splitting is

attributed to electronic band effects.

Peak Shifts of the 2D Band as a Function of Doping Level and Type

Frequency shift of the 2D peak takes place when graphene was doped with electron or hole.

Unlike the unique blue shift of the G band with both electron and hole doping (65, 70),

the 2D peak upshifts with hole doping and red shifts with electron doping (67, 71). The

reason for the peak shift of the 2D band with doping can be considered as follows: (1) theequilibrium lattice parameter is modified with a consequent stiffening/softening of the

phonons (105) and (2) due to the onset of dynamic effects beyond the Born-Oppenheimer

approximation that modify the phonon dispersions close to the Kohn anomalies (70, 73).

The excess charge leads to an expansion of the crystal lattice, whereas the excess defect

has a contraction effect. The dependence of the position of the 2D peak on doping can

be investigated by calculation, the Fermi-level shifts on the phonon frequencies within a

density functional theory (DFT) framework. A theoretical model of the Fermi surface shift

due to varied concentrations of electrons in a graphene system was given in Das et al.

(71). Positions of the 2D band of theoretical and experimental results are shown in Figure

15, respectively. Calculations are in qualitative agreement with experiments. Note that the

dynamic effects are neglected in the model because phonons of the 2D peak are far away

from the Kohn anomalies at the K point.




More attention should focus on the right part of Figure 15, although the general

tendency of the 2D band under electron doping condition is the red shift, the initial slight

blue shift with low-density electron doping (lower than 1.5 × 1013 cm−2) may lead to

contrary conclusion. In Stampfer et al. (46), because the concentration of doping is small

(±6 × 10

12

cm−2

), an incorrect conclusion that the 2D line stiffens for both electron andhole doping was made.

The Raman mapping of the 2D band with and without hole doping is shown in Figure 16.

From the (a) and (b) panels we can see that the frequency of the 2D band is lower in the

suspended portion (the area between white lines) than in the supported portion, whereas the

FWHM becomes narrow in the suspended portion. The overall stiffening of the 2D mode

in the supported region indicates that the graphene is hole doped (with low concentration

8 × 1012 cm−2) after being deposited on the SiO2-coated Si substrate (64). Panel b shows

that the 2D peak exhibits a greater width on the supported portion of the graphene (about

+5 cm−1) and a significant upshift in frequency (about+10 cm−1) compared to the response

of the free-standing graphene. This is the first time that the 2D band line width showed a

significant change after doping, which indicates that this change may not be due to dopingonly (64). As far as we know, the resulting wider 2D band may partly be due to the phonon

confinement effect. The tip of the sample (most narrow portion), which was been identified

as a highly doped and disordered region, shows the highest 2D-mode frequency and is

associated with increased and scattered values of the line width.

Correlation between position (2D band) and position (G band) under hole doping with

514.5 and 633 nm laser is shown in Figure 17 (67). The scale of the vertical and horizontal

axes shows that the frequency of 2D peak is more sensitive to hole doping than the G peak,

which is in line with Calizo et al. (60) and Mohiuddin et al. (61).

Figure 16. Spatial maps for the same sample as in Figure 2 but presenting results for the Raman

spectra of the 2D mode: (a) the mode frequency, ω2D; (b) the line width (FWHM), 2D; and (c) the

ratio of the integrated intensity of 2D mode to that of the G mode, I 2D / I G. (d) Correlation between

ω2D and 2D for the suspended (red open circles) and lower supported (blue open squares) regions,

as well as for the defective tip of the sample (gray open triangles) (65).



386 B. Tang et al.

Figure 17. Position of 2D as a function of the position of G at 514 and 633 nm (67).

In brief, the peak position of the G and 2Ds band can serve as a powerful tool to

identify the type and quantity of doping, at least for significant (>5 × 1011 cm−2) carrier

concentration (65). At the same time, the peak width of the 2D line, which has been

recognized as the most striking feature to distinguish single layer from a few-layer graphene,

is insensitive to doping.

Temperature Dependence of the 2D Band

Calizo et al. (60, 106) also studied the temperature dependence of the 2D peak of graphene.Use Eq. (2) from the previous section:

ω2D = ω2D0 + χ T (2)

where x represents the 2D mode temperature coefficient, and ω2D0 is the frequency of the

2D band when the temperature T is extrapolated to 0 K. Figure 18 shows the position of the

2D band of monolayer and bilayer graphene when temperature varies from 113 to 373 K.

It is easy to see in these curves that the 2D band red shifts with the increased temperature.

The reason for the red shift was discussed in the previous section (60).

The calculated values of the temperature coefficients x 2D and zero temperature fre-

quencies x 2D0 for the 2D peak from the curves of monolayer and bilayer graphene are

summarized in Table 2 (106). x 2D is almost three to four times greater than x G, which

indicates that the position of the 2D band is more sensitive than the G band under varied

temperature.

Table 2

Temperature coefficients for the 2D peaks in single-layer and bilayer graphene (106)

Material cm−1 (K) Peak at 0 K (cm−1) Temperature range (K)

Single-layer graphene −0.034 2,687 83–373Bilayer graphene −0.066 2,687 113–373




Figure 18. Raman curves of 2D peak frequency at 113 and 373 K for (a) single layer graphene and

(b) bilayer graphene (106).

Relationship between the 2D Band with Uniaxial Strain and Biaxial Strain in Graphene

Figure 19a presents the 2D frequency of Raman mapping of graphene under various

conditions: (a1) unstrained; (a2) strained 0.18%; (a3) 0.35%; (a4) 0.61%; (a5) 0.78%; and

(a6) relaxed. The scale of these images is from 2,650 to 2,710 cm−1 and darker color

represents lower frequency. It is obvious that with the increased strain, the color becomes

increasingly darker, suggesting that a red shift of the 2D band occurs over the strained

sample. The red shift can be understood by considering the elongation of the C C bonds,

which weakens the bonds and lowers the vibrational frequency. The right-side image of Figure 19a shows the positions of the 2D bands of unstrained, 0.78% strained, and relaxed

graphene, respectively. The resulting curves indicate that the position of the 2D band can

recover after the strain relaxation. Figure 19b shows the 2D frequencies of unstrained,

strained, and relaxed graphene, which can be used to quantify the strain coefficient. The 2D

frequency is plotted as a function of strain and shown as two lines with a slope of −27.8 ±0.8 cm−1 /% for monolayer graphene and −29 ± 1.1 cm−1 /% for three-layer graphene. The

linear dependence of the frequency of the 2D band with strain can be expected by phonon

deformation potentials, which we discussed above (86, 87). The high strain sensitivity of

graphene makes it a potential material as an ultrasensitive strain sensor.

The evolution of the 2D band of graphene with different layers (one to four layers)

under biaxial strain was also studied by Zhen et al. (63). The calculation and theory of the

correlation between strain with peak shift were shown in the previous section. The frequency



388 B. Tang et al.

Figure 19. (a) Two-dimensional frequency Raman images of unstrained (a1), 0.18% (a2), 0.35%

(a3), 0.61% (a4), and 0.78% (a5) strained, and relaxed (a6) graphene. The scale bar of all the images

is 2,650 to 2,710 cm−1. The Raman spectra on the right-hand side are taken from the 2D band SLG

of a1, a5, and a6. (b) The analyzed 2D band frequency of single- (black squares) and three-layer (red

circles) graphene under different uniaxial strain, from the highlighted area of inset figures. The green

square/circle is the frequencies of relaxed graphene. The blue lines are the curve fit to the data. The

slope is 27.8 cm−1 /% for single-layer graphene and 21.9 cm−1 /% for three-layer graphene (62).

of the 2D band blue shift changes with increasing annealing temperature and up to 25 cm −1

after annealing at 500◦C. The result is plotted in Figure 9c and it can be interpreted by

the strong compressive stress on graphene due to the substrate (63). Compared with the G

band (15 cm−1), the blue shift is greater in the 2D band, which suggests that the 2D band

is more sensitive under biaxial stress. It is worth noting that although both uniaxial strain

and biaxial strain lead to a peak shift of the G (2D) band, the uniaxial strain is different

from the biaxial strain. The former would affect the electronic properties of graphene much

more significantly as it breaks the equivalence of sublattice of graphene.

Integrated Intensity Ratio of 2D Band to G Band I2D /IG

In some earlier papers (53, 54), the integrated intensity ratio I2D /IG was suggested to be

used to estimate the number of graphene layers. However, in studies reported by Poncharal

and Ayari (45) and Calizo et al. (76), it was concluded that the variation of I2D /IG in a single

layer graphene deposited on the SiO2 coated Si substrate far exceeds that assigned to the

increase of number of graphene layers, which indicates that this parameter is not a good

criterion to determine the number of graphene layers. On the other hand, similar to the

peak shift of the G and 2D bands, I2D /IG can be used to determine the density of charged

impurity in graphene, particularly on the condition of low charged impurity concentration.

I2D /IG is more sensitive to the presence of charged impurity than the blue shift of the G

band.




Zhen and Ting (59) employed Raman spectroscopy to study the probing charged impu-

rities concentration in suspended graphene. In order to obtain a suspended graphene sample,

a process for fabricating the substrate is needed. First of all, 10-µm-thick photoresist was

spin-coated on SiO2 /Si substrate (the thickness of the SiO2 was 285 nm). Photolithography

was used to pattern holes into the photoresist, following the deep reactive-ion etching. Thenext step was to removal the photoresist. The diameter of the holes wa from 3 to 8 µm.

Graphene samples were prepared by micromechanical cleavage and then deposited on the

fabricated substrate (59).

Figure 20a shows the optical image of graphene where the diameter of the hole on the

substrate is 8 µm. Single-layer graphene can be distinguished from three-layer graphene in

Figure 20b from the FWHM of the 2D band as discussed previously. Panels c and d show the

Raman mapping of the G and 2D bands, respectively. A strange phenomenon can be found:

the intensity of the G band from supported graphene (NSG) is stronger than suspended

gaphene (SG), whereas the intensity of the 2D band from NSG is weaker than NG instead.

Panel f is constructed using the I2D /IG ratio, and the ratio changes obviously from 8.7 for

SG to 3.9 for NSG. For different samples the similar I2D /IG ratio occurred in panels g–i.The integrated intensity difference of the G band between NSG with SG is a result of the

interference enhancement effect, which we will discuss below (107), whereas the difference

between the 2D band arises from doping. First of all, some other potential reasons need to

be excluded. The absence of an obvious D band in both the suspended and the supported

portion means that the samples were high quality and exclude disorder induce the change of

I2D /IG. In order to rule out the influence from strain, the G band frequencies from different

pieces of suspended graphene and supported graphene were recorded by Zhen and Ting (59)

Figure 20. (a) Optical image of a graphene sheet on a patterned substrate covering a hole. (b) Raman

imaging using the 2D bandwidth. The dark strip with a 2D bandwidth of 30 cm−1 is SLG. The bright

area with 2D width of 57 cm−1 is three-layer graphene. Panels c and d are the Raman imaging of G

and 2D band intensity, respectively. (e) Raman spectra of SG and NSG taken from the red and blue

dots in panel d, respectively. (f) Raman imaging of the I 2D /IG ratio. (g–i) Raman images of I2D /IG

ratio of three more samples. The I2D /IG ratios of SG are much higher than those of NSG. The scale

bars in Raman images are 2 µm (59).



390 B. Tang et al.

Table 3

The G band frequencies of SG and NSG from five different samples. The 2D bandwidths

of SG and NSG are also presented (59)

Samples SG NSG SG NSG

1 1,578.7 ± 1.3 1,577.6 ± 1.2 28.1 ± 1.6 31.7 ± 1.8

2 1,579.6 ± 0.8 1,580.2 ± 0.6 29.5 ± 1.1 35.4 ± 1.7

3 1,580.9 ± 0.9 1,581.1 ± 0.4 28.0 ± 0.7 31.8 ± 0.9

4 1,579.2 ± 1.7 1,580.8 ± 1.3 27.6 ± 2.0 29.5 ± 1.8

5 1,582.6 ± 1.2 1,581.4 ± 0.8 26.1 ± 1.3 31.6 ± 1.4

and are shown in Table 3. According to the previous discussion, we know that the frequency

of the G band is sensitive to strain, and the shift coefficient reaches 10–20 cm−1 /%. Butin Table 3 the G frequency of supported single graphene has the same value (within an

experimental error of ∼1 cm−1), which suggests that the strain in suspended graphene can

be ignored (108, 109).

The integrated intensity ratio (G and 2D bands) of SG and NSG are shown in Figure 21.

The ratio of the G band is almost a constant around 0.5, whereas the ratio of the 2D band

has a larger range, from 0.7 to 1.4. Under the interference enhancement model (59), the

intensity ratio of the G band between suspended and supported graphene is ∼0.51. This

indicates that the difference in intensity of the G band between them is only due to different

interference and multiple reflection conditions, though there must be other factors that

contribute to such a discrepancy of the 2D band. Now consider the influence of intensity of

the 2D band from charged impurities.

Figure 21. The G and 2D band integrated intensity ratio of suspended and nonsuspended graphene

(59).




The matrix element of the electron scattering in graphene can be represented as (57,

110):

M

≈v

s0,s1,s2

i| ∧H e−em|s0s0|

∧H e−ph|s1s1|

∧H e−ph|s2s2|

∧H e−em|f

(Ei − E0 + 2iγ )(Ei − E1 + 2iγ )(Ei − E2 + 2iγ ) (12)

where i| and |f are the initial and final states of the process. S0, S1, and S2 are the

intermediate states where an electron-hole pair is created. E i and E0, . . ., E2 are the energies

of these states and 2r is the inverse lifetime of the electron or hole due to collisions or

scattering.

The intensity of the 2D band can be written as:

I 2D

=

(e2c)2v2ω2

in

48π c

2

γ

2 9F 2K

MωK v

2

√ 27a2

4

2

(13)

Here, v is the Fermi velocity, a is the lattice constant of graphene, M is the mass of the

carbon atom, and F K is the coupling constant. ωin and ωK are the frequencies of the incident

laser and the 2D phonon at around the K point, respectively. So I2D is proportional to 1/ r 2,

where 2r is the electron or whole inelastic scattering rate as mentioned above. According to

Eq. (12), it is easy to see that the intensity of 2D band of supported graphene will decrease as

a result of the charged impurities from the SiO2 substrate. On the other hand, the integrated

intensity of G band is insensitive to the doping condition, which we have mentioned above

(57).

Compared with the blue shift (approximately 1012 cm−2 to 1 cm−1) of the G band, the

value of I2D /IG is more sensitive even at low doping concentration. The relation betweendoping level and I2D /IG is presented in Figure 22. The squares in Figure 22 show the

I2D /IG ratios of tens of single-layer graphene (SG and NSG) at different charged impurity

concentrations. The charged impurity concentration in NSG is estimated by the blue shift

of G band (42), and the charged impurity concentration in SG is estimated to be 1010 to

1011 cm−2 (111, 112). The higher the ratio, the lower the concentration of charged impurity

in graphene. The relation between the blue shift of G the band and doping level is also

Figure 22. The G and 2D band integrated intensity ratio of SLG with different CI concentration: blue

and red squares for NSG and SG, respectively. The solid line is a guide for the eye. For comparison,the relation between the G band blue shift and CI concentration is also presented: black and purple

triangles represent NSG and SG, respectively (59).



392 B. Tang et al.

presented in the Figure 22 for comparison. The blue shift of the G band is too small to

distinguish the experimental error when the concentration is low ( <1012 cm−2). It is worth

noting that the excitation laser must invariable when directly comparing the I2D /IG ratio,

because that this value is affected by the excitation laser energy.

Edge Chirality of Graphene

One-dimensional graphene nanoribbon (GNR), which can be produced by traditional lithog-

raphy technique from graphene sheet, have received intense attention (1, 113–116).The

optical and magnetic properties of GNR are strongly dependent on quantum confinement

effect and definite edge chirality (29, 117). Therefore, it is crucial to distinguish two edge

types (armchair and zigzag) of graphene and GNR. Raman spectroscopy is a fast and

nondestructive method to determine the edge chirality. Yu et al. (118) found that a typical

graphene sheet has an angle of n × 30◦ between two adjacent edges, where n is an integer.

The resulting angles are shown in Figure 23. Two adjacent edges have different chirality

when the angle between them is 30◦, 90◦, 150◦. Contrarily, both edges have the samechirality when the angle is 60◦ and120◦.

It is well known that the D band, TO phonons around the K-point of the

Brillouin-zone, is related to double resonance Raman scattering process. Two premises

must be satisfied to active D band: (1) q must from K point to K point, where

q, stands for phonon frequency. (2) Both phonon and edge must back-scatter

with electrons. As defect scattering, the second condition is satisfied automatically. The

wave vector of a phonon must twice that of an electron with opposite direction. A detailed

description was given by Casiraghi et al. (119). The D mode will not appear by a perfect

zigzag edge because the D band requires scattering between two nonequivalent cones; in

other words, scattering (120, 121). Raman spectroscopy is a good tool to identify the zigzag

Figure 23. (a) Optical image of a typical MG sheet and the angles between edges. (b) The statisticalresults of the included angle of adjacent edges. (c) Illustration of the relationship between angles and

the chiralities of the adjacent edges (118).




Figure 24. (A) Raman spectra of one edge measured for different incident polarization at 633 nm.

(B) ID /IG as a function of θ in. Note that ID /IG does not go to zero for perpendicular polarization (119).

and armchair edges, but it is too early to say that a high I D represents armchair edge or a

low ID stands for zigzag edge for the following reasons:

1. The intensity of the D band is strongly dependent on the polarization of incidence laser

because of the backscattering condition (119). The minimum intensity appears when

the angle between laser polarization and graphene edge is 90◦, and up to maximum

intensity when the angle is 0◦.

2. The evolution of the D band of a fixed edge with varied polarization direction is shown

in Figure 24a. The Imin is not zero, which means that the edge of graphene is not ideally

smooth but both of armchair and zigzag segment (118, 119). Figure 24b and Figure 25show ID /IG as a function of θ in. Based on the curves, polarization dependence must be

considered when identifying the average edge orientation. It is wrong to say that high

ID /IG represents armchair edge, simply. The value of ID /IG depends on position of the

laser spot, which indicates that the edge can be mixed and disordered at least on the

laser spot scale.

Figure 25. ID /IG as a function of θ in measured on two edges forming an angle of 90◦ (119).



394 B. Tang et al.

Figure 26. (a)Raman image constructed by the intensity of the G band withthe expected arrangement

in blue. (b) and (c) are images constructed by the D band intensity with horizontal and vertical

polarization, respectively. (d) Raman spectra taken from edge 1 (spectrum a) and edge 2 (spectrum b)

with horizontal laser polarization. Spectra c and d were also collected from edges 1 and 2, respectively,

with vertical laser polarization. (e) The solid and dotted lines represent the D band intensity profile

(solid/dash) plotted along the solid line on (b) and the dashed line on (c), respectively. Spectra a and

b are recorded at edges 1 and 2, respectively (118).

A single-layer graphene with three edges was used by Yu et al. (118). The angle

between edge 1 and 2 is 30◦, and the angle between edge 2 and 3 is 120◦. According

to the previous discussion, edge 1 and 2 have different chirality, whereas edge 2 and 3

have the same chirality. The resulting polarized Raman images are shown in Figure 26.

Panel a shows uniform intensity of the G band over the whole graphene, which indicates

a good quality of sample. Panels b and c show the intensity of the D band with horizontal

laser polarization and vertical laser polarization, respectively. The results prove that these

adjacent edges have different chirality as expected and the D band shows strong polarization

dependence. The D band intensity of edge 1 is 1.7 times of that of edge 2. Edge 1 can be

identified as an armchair edge and edge 2 as zigzag edge. Note that the armchair or zigzag

arrangement mentioned here for edges 1 and 2 is a result of the majority of carbon atomsalong the edge being arranged in one kind of chirality (either armchair or zigzag). A weak

D band observed in curve a of panel d suggests that a small portion of carbon atoms is in

armchair arrangement in edge 2. Curves c and d in panel e are recorded at edges 1 and 2,

respectively, with a vertical laser polarization. Both curves hardly show any D band because

of the polarization effect. Further experimental results are shown in Figure 27 (118). For

30◦ and 90◦ included angles, the adjacent edges have different intensities of the D band,

which indicates that they have different chirality. For the 60◦ and 90◦ included angles, two

adjacent edges show similar D band intensity, which means that they have the same atomic

arrangements at the edge. The ID intensity ratio of adjacent edges with same edges chirality

is around 1, while the value is greater than 1.6 for different edges chirality.

The defect-induced D band at the edges was found to be strongly polarization depen-

dent, which is similar to that of graphite edges. This can make Raman spectroscopy a useful




Figure 27. Raman imaging results from edges with angles (a) 30◦, (b) 60◦ (zigzag), (c) 90◦, and

(d) 60◦ (armchair). The laser polarization is indicated by the green arrows. The superimposed frame-

works are guides for the eye indicating the edge chirality (118).

way to determine the crystallographic orientation of the graphene, which is important for

the study of graphene and graphene-based devices.

Raman Spectroscopy of Epitaxial Graphene

Except for micromechanical exfoliation from HOPG, epitaxial growth from bulk SiC

substrate is another method to fabricate graphene (122). The quality of epitaxial graphene

(EG) is not as good as mechanical exfoliation graphene, as well as the electron mobility. In

order to promote this relatively simple synthesis method, some means are used to improve

the quality of EG. The thickness, strain, doping, and stack between graphene layers play

important roles to determine the EG’s characteristics. Measuring the electronic feature of

EG is a complicated process, such as Hall effect, which always requires further destructive

process. Recently, a simple and fast method to identify superior and inferior carrier mobility

of EG relying on Raman spectroscopy was proposed by Joshua and Maxwell (122). Epitaxial

graphene films EGSi and EGC were grown on the SiC(0001) (Si-face) and SiC(0001) (C-face), respectively. The 2D band can be used to identify the monolayer and multilayer

graphene not only for MG but for EG. The uniformity of the 2D band around the entire

EGSi corresponds to high electronic mobility, whereas the carrier mobility depends strongly

on the stacking order for the EGC.

After growth, a transition layer can be seen between the SiC substrate with EGsi

through TEM. The 2D peak of the Raman curve can be fitted with a single Lorentzian

function of single-layer EGsi and evolves to four Lorentzian functions to bilayer EGsi.

Contrarily, EGC always several layers thick, thus Raman curve shows a similar 2D band to

bulk graphite (generally fit with two Lorentzian functions) (see Figure 28).

It is well known that varied strain appearing in graphene drives from the difference of

lattice parameter of the SiC substrate and graphene. Furthermore, both the substrate not

atomically smooth and the process of sample cooling induces the anisotropic strain. The



396 B. Tang et al.

Figure 28. The 2D Raman peak of epitaxial graphene is used to rapidly identify (a) monolayer and

bilayer graphene on SiC(0001) and layer stacking on SiC (0001). Film thickness confirmed via TEM

(b), (c). Graphene layer stacking is correlated with 2D Raman peak width for EG on SiC (0001) (d)

(122).

EGSi with high carrier mobility exhibits a uniform 2D signature, on the other hand, low

mobility EGSi has a significant variation in the 2D band position (2,690–2,760 cm−1) (see

Figure 29). The value of mobility reaches 1000 cm 2 /vs when the Raman topography map

is uniform over half of the device and over 2000 cm

2

/vs when EGSi is uniform over theentire device. High mobility EGSi exhibits uniform strain with minimal thickness variation,

which is identified in Raman topography by a uniformly distributed 2D peak position.

Low mobility graphene (Figure 29c: Raman topography; Figure 29d: AFM figure) can

Figure 29. Raman topography (a), (c), atomic force microscopy (b), (d), and Hall mobility (e) data

are used to identify the influence of graphene uniformity on carrier mobility of EGSi (122).




Figure 30. The Raman 2D peak width is strongly from a high value of 18,100 to 50 cm2 /Vs (122).

be mono- or bilayer; however, the length scale of the Raman topography uniformity is

significantly smaller than the device length scale. The Raman topography domain size and

Hall mobility from EGSi Hall crosses indicates that the uniformity of strain of the graphene

film significantly influences carrier mobility (Figure 29e). Arrows in Figures 29a and 29b

indicate the location of the SiC terrace step edge.

EGC exhibits better carrier mobility compared with EGSi. But it is difficult to determinethe thickness of EGc through the 2D band of Raman spectroscopy as mentioned. Luckily,

the layer stacking of EGC, which can be extracted from the 2D band, strongly affects the

carrier mobility. The model of layer stacking of EGC is complex in two ways: (1) AB

stacked (Bernal stacked) (2) grows with a high density of rotational faults where adjacent

sheets are rotated relative to each other (123). As rotationally faulted EGC, a narrow 2D

peak fitted with a single Lorentzian function (Figure 28d, top), whereas wider 2D peaks

indicate the AB stacking (Figure 28d, middle and bottom). The single peak of the 2D band

indicates that the AB stacked does not appear in the EGC and shows high carrier mobility.

As the Lorentzian components of the 2D band increase, the mobility decreases strongly

from a high value of 18,100 to 50 cm

2

/vs (122). When the rotationally faulted EGc and ABstacked appear in the EGc at the same time, the 2D peak splits to two Lorenzian components

and follows a low mobility. Note that the correlation between FWHM and mobility only

exists for the device with a uniform EGC film (122). So the 2D band can be used as a

quick way to identify the superior and inferior carrier mobility of EGSi and EGC. In order to

fabricate high-quality EGSi, the uniform stress and thickness are needed. On the other hand,

the rotationally faulted EGC means a high mobility graphene, represented by a narrow 2D

band fitted by a single Lorentzian component in Raman spectroscopy.

Interference Enhancement Model of Raman Signal of Graphene

Laser penetration depth of Raman spectroscopy is around 50–100 nm (514–488 nm

laser). The Raman signal of graphene (single or few layers) should be very weak or even



398 B. Tang et al.

Figure 31. Calculation result of enhancement factor E as a function of thickness of SiO2 (124).

invisible, but the experimental result always contradicts this view. Micromechanical cleav-

age graphene is always deposited on the Si wafer with 300 nm SiO2 capping layer, so the

interference of the laser enhances the Raman signal of graphene. Except the interference

of laser, multi-reflection of Raman light must be taken into account to explain the signal of

single-layer graphene which is comparable to bulk graphite (124). According to Fresnel’s

equations (125, 126), the intensity of the signal depends on the electronic field distribution;

in other words, the resulting interference between all transmitted optical paths in graphene

films (124). The thickness of the SiO2 capping layer is a key factor to determine the intensityof the Raman signal of graphene. The enhancement factor E is a function of the thickness

of SiO2, where E represents the ratio of Raman signal intensity of single-layer graphene

with SiO2 a capping layer to without this capping layer. Figure 31 shows the result of the

calculation (124). When the thickness of SiO2 is satisfied, nSiO2 × dSiO2 / λ ≈ 1/4, 34

, and so

on, the maximum enhancement can be reached. The general selection of the capping layer

and substrate to enhancement the intensity of Raman signal is choosing n 1 n2 n3, at

Figure 32. Schematic of Si/Ag/Al2O3 with graphene on it (127).




the same time n2 × d2 / λ = 1/4, 3/4, and so on, or choosing n1 n2 n3 with n2 × d2 / λ =1/4, 3/4, and so on (n1, n2, n3, and d2 represent refractive indices of graphene, capping

layer, substrate and thickness of capping layer, respectively).

A question may be raised: Does the interference effect influence the relative intensity

ratio of the 2D band to the G band of graphene? It is important to answer this question

because the intensity ratio of the 2D band to the G band is always used as a criterion

to determine the doping level, as mentioned above (59). Duhee, Y. et al. answered this

question. When I2D /IG is used to determine doping level, all graphene samples must be

deposited on Si substrate with the same thickness of the SiO 2 capping layer. If the intensity

ratio data from samples on different thickness of SiO2, the intrinsic intensity ratio of I2D /IG

can be got after factor out the interference effect (66).

Recently, Li et al. (127) proposed a co-enhanced Raman scattering technique to char-

acterize graphene, combining surface enhanced and interference enhanced Raman signals.

An enhancement ratio reaches ∼1,000 by optimizing the substrate structure. The interfer-

ence enhanced Raman scattering (IERS) is mentioned above. Surface enhanced Raman

scattering (SERS) is another technique that combines modern laser spectroscopy with theexciting optical properties of metallic nanostructures and dramatically enhances Raman

signals (128–131). A typical active metal/oxide layer substrate, Si/Ag/Al2O3, was adopted

(shown in Figure 32).

In order to find the optimized substrate structure, the thickness of Ag and Al2O3 are

various to get the strongest Raman signal. When thickness of Ag and Al 2O3 are 50 nm and

72 nm, respectively, the maximum intensity is reached (Figure 33). Figure 34 shows Raman

spectroscopy of graphene on kinds of substrates. The resulting Raman signal intensity of

monolayer graphene is great enhanced on the optimized substrate (Si/50 nm Ag/72 nm

Al2O3 and Si/50 nm Au/72 nm Al2O3) compared with the corresponding IERS substrate

Figure 33. Enhancement effect comparison of graphene on different substrates. (a) Raman spectra

of graphene on an Si substrate with 50-nm-thick Ag film and different thickness of Al 2O3 layers.(b) Raman spectra of graphene on an Si substrate with 72-nm-thick Al2O3 layer and different

thicknesses of Ag film (127).



400 B. Tang et al.

Figure 34. Raman spectra of graphene deposited on kinds of substrates (127).

(Si/72 nm Al2O3), SERS substrate (Si/50 nm Ag), and an original Si substrate (without

oxide layer).

Because of the great enhancement ratio, fine structural information of graphene can be

probed. This technique makes Raman spectroscopy a strong tool to probe tiny structural

changes and surface structure changes of graphene.

Conclusion

In summary, a review of Raman spectroscopy and imaging of graphene has been presented.

Raman spectroscopy is a versatile tool to study graphene. The number of graphene layers

can be determined quickly by using Raman spectroscopy. The intensity of the G peak

increases in an almost linear relation with increased layers, whereas the shape of 2D

band evolves into four components of bilayer graphene from a single peak of monolayer

graphene. The doping level, fluctuation of temperature in graphene, strain, as well as edge

chirality of graphene also can be determined through Raman curve, which are closely

related to frequency, FWHM, and intensity of the G and 2D bands. The G band will blueshift and become narrow with both electron and hole doping, whereas the 2D band will blue

shift with hole doping and red shift with electron doping. The value of I2D /IG decreases with

increased doping level and is sensitive to doping even under low doping level. Frequencies

of bot the G band and 2D band will red shift with increasing temperature, which can

be interpreted according to the elongation of the C C bond due to thermal expansion or

anharmonic coupling of phonon modes. Under compressed strain (both uniaxial and biaxial

strain) the blue shift of the G and 2D bands can be found. All of the experimental results

are provided in Table 4.

The intensity of the D band of polarized Raman spectroscopy is a useful criterion to

determine the edge chirality of graphene. Two adjacent edges have different chirality when

the angle between them is 30◦, 90◦, 150◦. Contrarily, both edges have the same chirality

when the included angle is 60◦ and 120◦. The value of ID /IG depends on the position of



T a b l e 4

C l a s s i fi e d e x p e r i m e n t r e s u l t s

G b a n d

F r e q u e n c y

F W H M

I n t e n s i t y

N u m b e r o f

l a

y e r s

R e d s h i f t w i t h

i n c r e a s e d l a y e r s

( 6 4 )

C o n s t a

n t ( 6 0 , 6

4 )

L i n e a r i n c r

e a s i n g w i t h

i n c r e a s e d

l a y e r s

( 6 4 , 6 5 )

D o p i n g

c o n c e n t r a t i o n

B l u e s h i f t w i t h b o t h e l e c t r o n a n d

h o l e d o p i n g

( 6 5 – 6 7 )

N a r r o w

( 6 5 , 7

0 , 7 6 )

C o n s t a n t ( 6 5 , 7 6 )

T e m

p e r a t u r e

d e p e n d e n c e


i n c r e a s i n g

t e m p e r a t u r e

( 6 0 , 7

0 )

N o t s e n s i t i v e ( 6 0 )

C o n s t a n t

U n i a x i a l s t r a i n

B l u e s h i f t w i t h c o m p r e s s e d s t r a i n

( 6 2 )

N o t s e n s i t i v e ( 6 2 )

C o n s t a n t

B i a

x i a l s t r a i n


( 6 1 , 6

3 )

N o t s e n s i t i v e ( 6 1 )

C o n s t a n t

2 D b a n d

F r e q u e n c y

F W H M

I n t e n s i t y

I 2 D / I G

N u m b e r o f

l a

y e r s

S p l i t t i n g t o s o m e c o m p o n e n t s w i t h

i n c r e a s e d l a y e r s ( 5 2 , 6

4 , 9 9 )

B i g g e r

f o r b i l a y e r t h a n

s i n g l e - l a y e r ( 5 2 , 6

4 )

N o t s e n s i t i v e ( 6 4 ,

1 2 5 )

D e c r e a s i n g w i t h

i n c r e a s e d l a y

e r s ( 6 4 )

D o p i n g

c o n c e n t r a t i o n

B l u e s h i f t w i t h h o l e d o p i n g a n d

r e d s h i f t w i t h e l e c t r o n d o p i n g

( 7 1 )

N o t s e n s i t i v e ( 4 6 , 6 9 ,

7 1 , 7

2 ) , b e c o m e s

n a r r o

w ( 6 4 )

D e c r e a s i n g

w i t h

i n c r e a s e d

e l e c t r o n

c o n c e n t r a t i o n ( 5 9 )

D e c r e a s i n g w i t h

i n c r e a s e d e l e c t r o n

c o n c e n t r a t i o n ( 4 5 , 7

6 )

T e m

p e r a t u r e

d e p e n d e n c e


i n c r e a s i n g

t e m p e r a t u r e

( 6 0 , 7

0 )

N o t s e n s i t i v e ( 6 0 )

C o n s t a n t

—

U n i a x i a l s t r a i n


( 6 2 )

N o t s e n s i t i v e

C o n s t a n t

—

B i a

x i a l s t r a i n


( 6 1 , 6

3 )

N o t s e n s i t i v e

C o n s t a n t

—

401



402 B. Tang et al.

laser spot, which indicates that the edge can be mixed and disordered at least on the laser

spot scale even under a macroscopically smooth condition. The very strong Raman signal

of single-layer graphene, which is comparable to that of bulk graphite, can be explained

by an interference enhancement model. Except for the MG, the Raman spectroscopy of

EG have been discussed, too. The uniform intensity of the 2D band means a high carrier

mobility of EGSi, meanwhile, narrow 2D band of EGC the fast and non-destructive features

make Raman spectra a strong tool to identify the carrier mobility of EG. Further probing

the fine structure of graphene through Raman spectroscopy, for example, the type of defects

in graphene, may attract more attention in the future.

Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No.

50876062).

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Raman Spectroscopic Characterization of Graphene