week ending
PHYSI CAL REVI EW LETTERS
PRL 97, 187401 (2006) 3 NOVEMBER 2006
Raman Spectrum of Graphene and Graphene Layers
A. C. Ferrari,1,* J. C. Meyer,2 V. Scardaci,1 C. Casiraghi,1 M. Lazzeri,3 F. Mauri,3 S. Piscanec,1 D. Jiang,4
K. S. Novoselov,4 S. Roth,2 and A. K. Geim4
1
Cambridge University, Engineering Department, JJ Thompson Avenue, Cambridge CB3 0FA, United Kingdom
2
Max Planck Institute for Solid State Research, Stuttgart 70569, Germany
3
IMPMC, Universités Paris 6 et 7, CNRS, IPGP, 140 rue de Lourmel, 75015 Paris, France
4
Department of Physics and Astronomy, University of Manchester, Manchester, M13 9PL, United Kingdom
(Received 9 June 2006; published 30 October 2006)
Graphene is the two-dimensional building block for carbon allotropes of every other dimensionality.
We show that its electronic structure is captured in its Raman spectrum that clearly evolves with the
number of layers. The D peak second order changes in shape, width, and position for an increasing
number of layers, reflecting the change in the electron bands via a double resonant Raman process. TheG
peak slightly down-shifts. This allows unambiguous, high-throughput, nondestructive identification of
graphene layers, which is critically lacking in this emerging research area.
DOI: 10.1103/PhysRevLett.97.187401 PACS numbers: 78.67.Bf, 63.20.Dj, 63.20.Kr, 78.30. j
The current interest in graphene can be attributed to [1,4]), in practice, it is only possible to distinguish between
three main reasons. First, its electron transport is described one and two layers by AFM if films contain folds or
by the Dirac equation and this allows access to quantum wrinkles [1,4]. This poses a major limitation to the range
electrodynamics in a simple condensed matter experiment of substrates and is a setback for the widespread utilization
[1 5]. Second, the scalability of graphene devices to nano- of this material. Here, we show that graphene s electronic
dimensions [6 10] makes it a promising candidate for structure is uniquely captured in its Raman spectrum.
applications, because of its ballistic transport at room Raman fingerprints for single layers, bilayers, and few
temperature combined with chemical and mechanical layers reflect changes in the electron bands and allow
stability. Remarkable properties extend to bilayer and unambiguous, high-throughput, nondestructive identifica-
few-layers graphene [4 6,8,11]. Third, various forms of tion of graphene layers, which is critically lacking in this
graphite, nanotubes, buckyballs, and others can all be emerging research area.
viewed as derivatives of graphene and, not surprisingly, Here the samples are prepared by micromechanical
this basic material has been intensively investigated theo- cleavage [1]. To provide the most definitive identification
retically for the past 60 years [12]. The recent discovery of of single and bilayers (beyond the AFM counting proce-
graphene [1] at last allows us to probe it experimentally, dure) we perform transmission electron microscopy (TEM)
which paves the way to better understanding the other on some of the samples to be measured by Raman spec-
allotropes and to resolve controversies. troscopy. Samples for TEM are prepared following a simi-
Graphene can be obtained using the procedure of lar process to that previously used to make freestanding
Ref. [1], i.e., micromechanical cleavage of graphite. and TEM-compatible nanotube devices [14]. In addition,
Alternative procedures, such as exfoliation and growth, this allows us to have freestanding layers on a grid easily
so far only produced multilayers [6,8,13], but it is hoped seen in an optical microscope, facilitating their location
that in the near future efficient growth methods will be during Raman measurements, Fig. 1(a). Electron diffrac-
developed, as happened for nanotubes. Despite the wide tion is done in a Zeiss 912 microscope at a voltage of
use of the micromechanical cleavage, the identification and 60 kV, and high-resolution images are obtained with a
counting of graphene layers is a major hurdle. Monolayers Philips CM200 microscope at 120 kV. A high resolution-
are a great minority amongst accompanying thicker flakes. TEM analysis of foldings at the edges or within the free-
They cannot be seen in an optical microscope on most hanging sheets gives the number of layers by direct visual-
substrates. They only become visible when deposited on ization, since at a folding the sheet is locally parallel to the
oxidized Si substrates with a finely tuned thickness of the beam, Figs. 1(b) 1(e). Edges and foldings of one or two
oxide layer (typically, 300 nm SiO2) since, in this case, layers are dominated by one or two dark lines, respectively.
even a monolayer adds to the optical path of reflected light The number of layers is also obtained by a diffraction
to change the interference color with respect to the empty analysis of the freely suspended sheets for varying inci-
substrate [1,4]. Atomic force microscopy (AFM) has been dence angles, and confirms the number of layers from the
so far the only method to identify single and few layers, but foldings, Figs. 1(d) and 1(e). In particular, the diffraction
it is low throughput. Moreover, due to the chemical con- analysis of the bilayer shows that it is A-B stacked (the
trast between graphene and the substrate (which results in intensity of the 11 20 diffraction spots (outer hexagon) is
an apparent chemical thickness of 0.5 1 nm, much bigger roughly twice that of the 1 100 (inner hexagon), Fig. 1(h),
of what expected from the interlayer graphite spacing in agreement with diffraction simulations obtained by a
0031-9007=06=97(18)=187401(4) 187401-1 © 2006 The American Physical Society
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PHYSI CAL REVI EW LETTERS
PRL 97, 187401 (2006) 3 NOVEMBER 2006
nent peak always observed in graphite samples [15]. TheG
peak is due to the doubly degenerate zone centerE2g mode
[16]. On the contrary, theG0 band has nothing to do with
the G peak, but is the second order of zone-boundary
phonons. Since zone-boundary phonons do not satisfy the
Raman fundamental selection rule, they are not seen in first
order Raman spectra of defect-free graphite [17]. Such
phonons give rise to a peak at 1350 cm 1 in defected
graphite, calledDpeak [16]. Thus, for clarity, we refer to
(a)
FIG. 1. (a) TEM of suspended graphene. The grid is also
visible in optical microscopy. (b) High-resolution image of a
(b) (c)
folded edge of a single layer and (c) a wrinkle within the layer.
(d) Folded edge of a two layer, and (e) internal foldings of the
two layer. The amorphous contrast on the sheets is most likely
due to hydrocarbon adsorbates on the samples that were cracked
by the electron beam. (f) Electron diffraction pattern for close to
normal incidence from single layer and (g) from two layers.
Weak diffraction peaks from the supporting metal structure are
also present. (h) Intensity profile plot along the line indicated by
the arrows in (f),(g). The relative intensities of the spots in the
two layer are consistent only with A-B (and not A-A) stacking.
Scale bars: (a) 500 nm; (b e) 2 nm.
Fourier transform of projected atomic potentials. This
(e)
(d)
confirms our multilayer graphene has the same stacking
as graphite.
Raman spectra are measured on single, bi, and multi-
layers on Si SiO2. Some are then processed into free-
hanging sheets, as described above, and measured again
after TEM. The measurements are performed at room
temperature with a Renishaw spectrometer at 514 and
633 nm, with notch filters cutting at 100 cm 1. A
100 objective is used. Extreme care is taken to avoid
sample damage or laser induced heating. Measurements
are performed from 4 to 0:04 mW incident power. No
FIG. 2 (color online). (a) Comparison of Raman spectra at
significant spectral change is observed in this range. The
514 nm for bulk graphite and graphene. They are scaled to
Raman spectra of suspended and on-substrate graphene are
have similar height of the 2D peak at 2700 cm 1. (b) Evolu-
similar, the main difference being a small D peak in the
tion of the spectra at 514 nm with the number of layers. (c) Evo-
TEM samples. We also measure the reference bulk graph-
lution of the Raman spectra at 633 nm with the number of layers.
ite used to produce the layers.
(d) Comparison of the D band at 514 nm at the edge of bulk
Figure 2(a) compares the 514 nm Raman spectra of
graphite and single layer graphene. The fit of the D1 and D2
graphene and bulk graphite. The two most intense features
components of the D band of bulk graphite is shown. (e) The
are theGpeak at 1580 cm 1 and a band at 2700 cm 1, four components of the 2Dband in 2 layer graphene at 514 and
historically named G0, since it is the second most promi- 633 nm.
187401-2
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PHYSI CAL REVI EW LETTERS
PRL 97, 187401 (2006) 3 NOVEMBER 2006
the G0 peak as 2D. Figure 2(a) shows that no D peak is degenerate modes of theGpeak in SWNTs [21], resulting
observed in the center of graphene layers. This proves the inG andG peaks.
absence of a significant number of defects. As expected, a We now explain why graphene has a single 2Dpeak, and
D peak is only observed at the sample edge, Fig. 2(d). why this splits in four components in bilayer graphene.
Figure 2(a) shows a significant change in shape and inten- Several authors previously attempted to explain the double
sity of the 2Dpeak of graphene compared to bulk graphite. structure of the 2Dpeak in graphite [15,17 20,24], how-
The 2Dpeak in bulk graphite consists of two components ever they always neglected the evolution of the electronic
2D1 and 2D2 [15,17], roughly 1=4 and 1=2 the height of bands with the number of layers, which is, on the contrary,
theGpeak, respectively. Here we measure a single, sharp the key fact. The 2D peak in graphene is due to two
2D peak in graphene, roughly 4 times more intense than phonons with opposite momentum in the highest optical
the G peak. Notably, the G peak intensity of single layer branch near the K (A0 symmetry at K) [16,25,26]. Figure 2
1
and bulk graphite is comparable [note that Fig. 2(a) is shows that this peak changes in position with varying
rescaled to show a similar 2Dintensity] and theGposition
excitation energy. This is due to a double resonance (DR)
is 3 5 cm 1 higher than bulk graphite. This upshift is
process, which links the phonon wave vectors to the elec-
partially due to chemical doping. The change in shape of
tronic band structure [27].
the 2Dband is nicely confirmed in Fig. 2(d), which com- Within DR, Raman scattering is a fourth order process
pares the D peak of the graphite edge with that of the
involving four virtual transitions: (i) a laser induced exci-
graphene edge. The graphene D peak is a single sharp
tation of an electron-hole pair [a!bvertical transition in
peak, while in graphite is a band consisting of two peaks
Fig. 3(a)]; (ii) electron-phonon scattering with an ex-
D1 andD2 [15]. Figures 2(b) and 2(c) plot the evolution of
changed momentum q close to K (b!c); (iii) electron-
the 2Dband as a function of layers for 514.5 and 633 nm
phonon scattering with an exchanged momentum q (c!
excitations. These immediately indicate that a bilayer has a
b); (iv) electron-hole recombination (b!a). The DR
much broader and up-shifted 2D band with respect to
condition is reached when the energy is conserved in these
graphene. This band is also quite different from bulk
transitions. The resulting 2DRaman frequency is twice the
graphite. It has 4 components, 2D1B, 2D1A, 2D2A, 2D2B;
frequency of the scattering phonon, with q determined by
two of which, 2D1A and 2D2A, have higher relative inten- the DR condition. For simplicity, Figs. 3(a) and 3(b) ne-
sities than the other two, as indicated in Fig. 2(e).
glect the phonon energy and do not show the equivalent
Figure 2(b) and 2(c) show that a further increase in layers
processes for hole-phonon scattering. In addition, we only
leads to a significant decrease of the relative intensity of
consider the dispersions along K M K0 .
the lower frequency 2D1 peaks. For more than 5 layers the
The transitions within this line correspond to the peaks in
Raman spectrum becomes hardly distinguishable from that
the phonon distribution fulfilling DR [19], once the trigo-
of bulk graphite. Thus Raman spectroscopy can clearly
nal warping is considered [28].
distinguish a single layer, from a bilayer from few (less
than 5) layers. This also explains why previous experi-
a) Monolayer:
q = exchanged
ments on nanographites, but not single or bilayer graphene,
phonon momentum
q
did not identify these features [18,19]. In particular, it was
Ä„*
noted from early studies that turbostratic graphite (i.e.,
b c
without AB stacking) has a single 2D peak [20].
µL
However, its full width at half maximum (FWHM) is
a
50 cm 1 almost double that of the 2D peak of graphene
Ä„
µL = Laser energy Fermi level
and up-shifted of 20 cm 1. Turbostratic graphite also often
has a first orderDpeak [20]. Single wall carbon nanotubes
b) Bilayer:
(SWNTs) show a sharp 2Dpeak similar to that measured
q1B
here for graphene [21]. The close similarity (in position
q1A
and FWHM) of our measured graphene 2D peak and the
2D peak in SWNTs of 1 2 nm diam [22] implies that
µL
curvature effects are small for the 2Dpeak for SWNTs in
this diameter range, the most commonly found in experi-
q2A
ments. This questions the assumption that the 2Dpeak in
SWNT should scale to the up-shifted average 2D peak q2B
position in bulk graphite for large diameters [22]. Thus
µL
the scaling law relating diameter and 2D peak position,
often used to derive the inner diameter in double wall tubes
[22,23], needs to be revisited. Despite the similarities, there
are major differences between graphene and SWNT
“ K M K'
Raman spectra, which allow us to easily distinguish
them. Indeed, confinement and curvature split the two FIG. 3. DR for the 2D peak in (a) single layer and (b) bilayer.
187401-3
Electron energy
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PHYSI CAL REVI EW LETTERS
PRL 97, 187401 (2006) 3 NOVEMBER 2006
TABLE I. Relative splitting of 2D components in bilayer
associated to the 2 less intense optical transitions [not
graphene (in cm 1). In each case, we show the shift with respect
shown in Fig. 3(b)], are associated to momenta almost
to the average frequency of the two main peaks. The four
identical to q1B, q1A, q2A, q2B and almost (within
columns of the bilayer correspond to processes q1B, q1A, q2A,
0:2 cm 1) identical Raman shifts. These wave vectors
q2B, respectively. The theoretical values are obtained by multi-
correspond to phonons with different frequencies, due to
plying the DR q vectors determined from the DFT electronic
the strong phonon dispersion around K induced by the

bands by dw=dq 645 cm 1 A. Here dw=dq is the ratio be-
electron-phonon coupling [26]. They produce four differ-
tween the measured shift of the 2Dpeak frequency with the laser
ent peaks in the Raman spectrum of bilayer graphene.
energy in graphene ( 99 cm 1=eV), and the corresponding
variation of the DRq 2kcomputed from the DFT bands. Table I reports the expected splittings and shows that
they compare very well with experiments.
514.5 nm
In conclusion, graphene s electronic structure is
Experimental 44 10 10 25 uniquely captured in its Raman spectrum, that clearly
Theory 44 11 11 41
evolves with the number of layers. Raman fingerprints
for single-, bilayer, and few-layer graphene reflect changes
633 nm
in the electronic structure and electron-phonon interactions
Experimental 55 10 10 30
and allow unambiguous, high-throughput, nondestructive
Theory 44 9 9 41
identification of graphene layers.
A. C. F. acknowledges funding from EPSRC No. GR/
S97613, The Royal Society, and The Leverhulme Trust;
C. C. acknowledges funding from the Oppenheimer Fund.
Consistent with the experimental observation of a single
component for the 2D peak in single layer graphene,
Figs. 3(a) and 3(b) only shows the phonon satisfying DR
conditions with momentumq>K, along the K M
*Electronic address: acf26@eng.cam.ac.uk
direction (K[1] K. S. Novoselov et al., Proc. Natl. Acad. Sci. U.S.A. 102,
nons, withq10 451 (2005).
bution to the Raman intensity. In fact, the q[2] K. S. Novoselov et al., Nature (London) 438, 197 (2005).
involves a smaller portion of the phase space because of the
[3] Y. Zhang et al., Nature (London) 438, 201 (2005).
band-structure trigonal warping (see Figs. 3,4 of Ref. [28] [4] K. S. Novoselov et al., Science 306, 666 (2004).
[5] K. S. Novoselov et al., Nature Phys. 2, 177 (2006).
and related discussion) and the q K phonon has a zero
[6] Y. Zhang et al., Appl. Phys. Lett. 86, 073104 (2005).
electron-phonon coupling for this transition, as discussed
[7] N. M. Peres et al., Phys. Rev. B 73, 125411 (2006).
in Ref. [26] (see footnote 24, for q K, 00 0) and
[8] C. Berger et al., J. Phys. Chem. B 108, 19 912 (2004).
Ref. [24]. This differs from the model of Ref. [24], which
[9] K. Wakabayashi, Phys. Rev. B 64, 125428 (2001).
predicts 2 similar components for theDpeak even in single
[10] K. Nakada et al., Phys. Rev. B 54, 17 954 (1996).
layer, in disagreement with the experiments of Fig. 2.
[11] J. Scott Bunch et al., Nano Lett. 5, 287 (2005).
We now examine the bilayer case. The observed 4 com-
[12] P. R. Wallace, Phys. Rev. 71, 622 (1947).
ponents of the 2Dpeak could in principle be attributed to
[13] L. M. Viculis, J. J. Mack, and R. B. Kaner, Science 299,
two different mechanisms: the splitting of the phonon
1361 (2003).
branches [15,17,20,29], or the spitting of the electronic [14] J. C. Meyer et al., Ultramicroscopy 106, 176 (2006);
Science 309, 1539 (2005).
bands [25]. To ascertain this we compute the phonon
[15] R. P. Vidano et al., Solid State Commun. 39, 341 (1981).
frequencies [26] for both single and bilayer graphene
[16] F. Tuinstra and J. Koenig, J. Chem. Phys. 53, 1126 (1970).
(stackedAB, as indicated by TEM), at theqcorresponding
[17] R. J. Nemanich and S. A. Solin, Phys. Rev. B 20, 392
to the DR condition for the 514 and 633 nm lasers. The
(1979).
splitting of the phonon branches is <1:5 cm 1, much
[18] L. G. Cancado et al., Phys. Rev. Lett. 93, 047403 (2004).
smaller than the experimentally observed 2D splitting.
[19] L. G. Cancado et al., Phys. Rev. B 66, 035415 (2002).
Thus, this is solely due to electronic bands effects. In the
[20] P. Lespade et al., Carbon 22, 375 (1984).
bilayer, the interaction of the graphene planes causes the
[21] A. Jorio et al., Phys. Rev. B 66, 115411 (2002).
and bands to divide in four bands, with a different [22] A. G. Souza Filho et al., Phys. Rev. B 67, 035427 (2003).
[23] R. Pfeiffer et al., Phys. Rev. B 71, 155409 (2005).
splitting for electrons and holes, Fig. 3(b). According to
[24] J. Maultzsch, S. Reich, and C. Thomsen, Phys. Rev. B 70,
the density functional theory (DFT) dipole matrix ele-
155403 (2004).
ments, amongst the 4 possible optical transitions, the inci-
[25] A. C. Ferrari and J. Robertson, Phys. Rev. B 61, 14 095
dent light couples more strongly the two transitions shown
(2000).
in Fig. 3(b). The two almost degenerate phonons in the
[26] S. Piscanec et al., Phys. Rev. Lett. 93, 185503 (2004).
highest optical branch couple all electron bands amongst
[27] C. Thomsen and S.Reich, Phys. Rev. Lett. 85, 5214 (2000).
them. The resulting four processes involve phonons with
[28] J. Kurti et al., Phys. Rev. B 65, 165433 (2002).
momentaq1B,q1A,q2A, andq2B, as shown in Fig. 3(b). The
[29] A. C. Ferrari and J. Robertson, Phil. Trans. R. Soc. A 362,
four corresponding processes for the holes, and those 2267 (2004).
187401-4


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