搜档网
当前位置:搜档网 › Spatially Resolved Raman Spectroscopy of Single- and Few-Layer Graphene

Spatially Resolved Raman Spectroscopy of Single- and Few-Layer Graphene

a r X i v :c o n d -m a t /0607562v 1 [c o n d -m a t .m e s -h a l l ] 21 J u l 2006

Spatially Resolved Raman Spectroscopy of Single-and Few-Layer Graphene

Davy Graf,?Fran?c oise Molitor,and Klaus Ensslin

Solid State Physics Laboratory,ETH Zurich,8093Zurich,Switzerland

Christoph Stampfer,Alain Jungen,and Christofer Hierold

Micro and Nanosystems,ETH Zurich,8092Zurich,Switzerland

Ludger Wirtz

Institute for Electronics,Microelectronics,and Nanotechnology (IEMN),

CNRS-UMR 8520,B.P.60069,59652Villeneuve d’Ascq Cedex,France

(Dated:February 4,2008)

We present Raman spectroscopy measurements on single-and few-layer graphene ?https://www.sodocs.net/doc/f712787412.html,ing a scanning confocal approach we collect spectral data with spatial resolution,which allows us to directly compare Raman images with scanning force micrographs.Single-layer graphene can be distinguished from double-and few-layer by the width of the D’line:the single peak for single-layer graphene splits into di?erent peaks for the double-layer.These ?ndings are explained using the double-resonant Raman model based on ab-initio calculations of the electronic structure and of the phonon dispersion.We investigate the D line intensity and ?nd no defects within the ?ake.A ?nite D line response originating from the edges can be attributed either to defects or to the breakdown of translational symmetry.

PACS numbers:Valid PACS appear here Keywords:Raman mapping

The interest in graphite has been revived in the last two decades with the advent of fullerenes 1and carbon nanotubes.2However,only recently single-and few-layer graphene could be transferred to a substrate.3Transport measurements revealed a highly-tunable two-dimensional electron/hole gas of relativistic Dirac Fermions embed-ded in a solid-state environment.4,5Going to few-layer graphene,however,disturbs this unique system in such a way that the usual parabolic energy dispersion is re-covered.The large structural anisotropy makes few-layer graphene therefore a promising candidate to study the rich physics at the crossover from bulk to purely two-dimensional systems.Turning on the weak interlayer coupling while stacking a second layer onto a graphene sheet leads to a branching of the electronic bands and the phonon dispersion at the K point.Double-resonant Raman scattering 6which depends on electronic and vi-brational properties turns out to be an ingenious tool to probe the lifting of that speci?c degeneracy.

We report on Raman mapping of single-and few-layer graphene ?akes resting on a silicon oxide https://www.sodocs.net/doc/f712787412.html,t-eral resolution of 400nm allows to address neighboring sections with various layers of graphene down to a sin-gle graphene sheet,previously determined with the scan-ning force microscope (SFM).We ?nd that the integrated G line signal is directly correlated with the thickness of the graphitic ?ake and is shifted upward in frequency for double-and single-layer graphene compared to bulk graphite.The mapping of the peak width of the D’line shows a strong contrast between single-and few-layer graphene.Such a pronounced sensitivity to the tran-sition to the very last layer o?ers an optical and non-destructive method to unambiguously detect single-layer

graphene.In addition,we locally resolve the structural quality of the ?ake by investigating the D band,which is related to elastic backscattering.The map of the in-tegrated D line signal of a graphitic ?ake with double-and single-layer sections shows that the inner part of the ?ake is quasi defect free,whereas edges and steps serves as scatterers.Finally,we explain the splitting of the D’line as a function of the number of graphene layers within the double-resonant Raman model.6The compar-ison between experimental data and theory con?rms the qualitative validity of the double-resonant Raman model,but demonstrates quantitative di?erences between theory and experiment.In particular,the model,when based on ?rst-principles calculations,predicts a much smaller splitting of the peaks.

The graphite ?lms were prepared by mechanical ex-foliation of highly oriented pyrolytic graphite (HOPG)and subsequent transfer to a highly doped Si waver with 300nm SiO 2(atomic oxidation process)cap layer.3,7The combination of optical microscopy using phase contrast and SFM makes it possible to locate ?akes with various thicknesses down to a monolayer with lateral extensions in the micrometer range.The Raman spectra were ac-quired using a laser excitation of 532nm (2.33eV)deliv-ered through a single-mode optical ?ber,whose spot size is limited by di?https://www.sodocs.net/doc/f712787412.html,ing a long working distance focusing lens with a numerical aperture NA=0.80we ob-tain a spot size of about 400nm.With a very low incident power of 4-7μW heating e?ects can be neglected.The Raman spectrum of graphite has four prominent peaks (Fig.3-for a recent review see Ref.8).The peak around 1582cm ?1,commonly called G line,is caused by the Raman active E 2g phonon,(in-plane optical mode)

2

1

1

2

6

64

(a)

2 mm

Lateral position (mm)

(c m -1)

n s i t y (a .u .)

S F M h e i g h t (n SFM

(c)

Intensity G

(e)

FWHM D'

FIG.1:(a),(b)SFM micrograph and cross-sectional plot (in-dicated with the white dashed arrow;lateral average over 400nm)of a few-layer graphene ?ake with central sections down to a single layer.Raman maps (dashed square corresponding to the SFM image in (a))showing (c)the integrated intensity of the G line and (e)the FWHM of the D’line.The related cross sections (d),(f)are aligned (vertical dashed lines)with the height trace.

close to the Γpoint.The D line around 1350cm ?1exhibits two remarkable features:its position shifts to higher frequencies with increasing incident laser excita-tion energies 9and its relative signal strength (compared to the G line)depends strongly on the amount of disorder in the graphitic material.9,10The associated overtone D’around 2700cm ?1is pronounced even in the absence of a D signal.Finally,the overtone of the G line,the G’line,is located at 3248cm ?1,which is more than twice the energy of the G line.The di?erent experimental ?ndings related to the dispersive D,D’bands could be explained by Thomsen and Reich within the framework of double resonant Raman scattering,6which was extended to other phonon branches by Saito et al.11The electronic and vi-brational properties of graphite are dominated by the sp 2-nature of the strong intraplane covalent bonds.The relatively weak inter-layer coupling causes the high struc-tural anisotropy.Raman spectra for multiple graphene layers can be compared qualitatively and quantitatively while investigating ?akes with sections of various thick-nesses.In Fig.1(a)the SFM micrograph of a graphite ?ake with di?erent layers is presented:The bare SiO 2(in-dicated by ’0’)is surrounded by single-layer sections with steps of up to two,six and four layers.The di?erent step heights are clearly depicted in Fig.1(b),where a cross section of Fig.1(a)(see white dashed arrow)is shown.Scanning the ?ake and collecting for each spot the com-

0.8μm

1μm

(a)

Lateral position (μm)

(b)

(c)

Raman shift (cm -1)

A

B

SFM

FWHM: D'

Intensity: D

2

1

1

0.8μm

FIG.2:(a)SFM micrograph of a graphitic ?ake consisting of one double-and two single-layer sections (white dashed line along the boundaries),highlighted in the Raman map (b)showing the FWHM of the D’line.(c)Raman mapping of the integrated intensity of the D line:A strong signal is detected along the edge of the ?ake and at the steps from double-to single-layer sections.(d)Raman cross section (white dashed arrow in (c)):Staircase behavior of the integrated intensity of the G peak (solid line)and pronounced peaks at the steps for the integrated intensity of the D line (dashed line).(e)Spatially averaged D peak for the crossover from double to single layer (?,dashed line)and from single layer to the SiO 2substrate ( ,solid line).

plete Raman spectrum we can subsequently ?lter speci?c spectral data for spatially resolved data point and con-struct false-color 2D plots.In Fig.1(c)the intensity of the G peak is integrated from 1537to 1622cm ?1.We ?nd a remarkable correlation with the SFM graph:Brighter regions correspond to thicker sections.The cross section in Fig.1(d)shows a step-like behavior,perfectly corre-lated with the topographical changes shown in Fig.1(b).In Fig.1(e)we plot the FWHM (full width at half max-imum)of the D’line.It shows the narrowing at the transition to a single-layer (see e.g.Fig.3)and gives an evident contrast between single-and few-layer graphene sections.The quasi digital change from about 60to 30cm ?1shown in Fig.1(f)suggests that the width of the D’line can be used as a detector for single-layer graphene resting on a substrate.Raman spectroscopy can therefore be used to count the layers of a thin graphite stack and to discriminate between single and double https://www.sodocs.net/doc/f712787412.html,bined with the double-resonant Raman scattering mechanism an optical setup using light in the visible range turns out to be an alternative to scanning force microscopy,which requires stacking folds as height references.

Transport measurements show that the quality of the

3

Raman shift (cm -1)

I n t e n s i t y (C C D c o u n t s )

FIG.3:Raman spectra of (a)single-and

(b)double-layer graphene (collected at spots A and B,see Fig.2(b)).

?nite graphitic ?akes on the silicon oxide matrix obtained with the technique explained above is remarkable:elec-tronic mobilities up to 15’000cm 2(Vs)?1were estimated from transport experiments.4,5We point out that also the Raman spectroscopy reveals quasi defect free graphitic sheets via the absence of a D band signal.First exper-iments have related the intensity of the D band to the structural coherence of the graphite material.In fact it is inversely proportional to the crystallite grain size.10The appearance of the D band can,however,be related to the occurrence of defects and disorder in general,as shown in experiments with boron-doped and electrochemically ox-idized HOPG.12With micro-Raman mapping we are able to localize the spatial origin of the defects.From cross-correlating the SFM micrograph in Fig.2(a)with the Raman map of the integrated D line (1300-1383cm ?1)intensity in Fig.2(c)we infer directly that the edges of the ?ake and also the borderline between sections of dif-ferent height contribute to the D band signal whereas the inner parts of the ?akes do not.This is somewhat sur-prising since for thinner ?akes the in?uence of a nearby substrate on the structural quality should be increasingly important.In the cross-section Fig.2(d)we see clearly that the D line intensity is maximal at the section bound-aries,which can be assigned to translational symmetry breaking or to defects.However,we want to emphasize that the D line is still one order of magnitude smaller than the G line.In Fig.2(e)spatially averaged D mode spectra from the two steps shown in Fig.2(d)are pre-sented.The frequency ?ts well into the linear dispersion relation of peak shift and excitation energy found in ear-lier experiments.9In addition,we ?nd that the peak is narrower and down-shifted at the edge of the single-layer while it is somewhat broader and displays a shoulder at the crossover from the double to the single layer.

In Fig.3(a)and (b),we compare the Raman spec-tra of the double-and single-layer graphene shown in Fig.2(b)and labeled with A and B.The Raman signal is signi?cantly altered when peeling o?the penultimate layer:the G peak decreases strongly in intensity and shifts towards higher wave numbers.In connection with Fig.1(b)we already stated that the integrated G line

# layer

R e l. i n t e n s i t y G /D '

# layer

G p e a k (c m -1)

FIG.4:(a)Plot of the ratio of the integrated intensities of the G and D’peak versus number of stacked layers (average value and standard deviation).(b)G line frequency versus number of stacked layers (average value and standard deviation).(c)G peak for HOPG (upper peak),double-(middle peak)and single-layer (lower peak)graphene.The vertical dashed line indicates the reference value for bulk graphite.

signal is monotonously increasing with increasing ?ake thickness.In order to compare data of di?erent ?akes and measurement runs we turn our attention to the ratio of the integrated intensities of the G and D’line,plotted in Fig.4(a).Most of the changes can be attributed to the decrease of the G line,since the spectral weight of the D’band changes only slightly.The intensity ratio increases almost linearly from one to four layers.In Fig.4(b)the dependence of the G peak position on the layer number is investigated.Spectral data of various sections on dif-ferent ?akes were averaged.The frequency shifts towards higher wave numbers at the crossover to the double-and especially to the single-layer graphene.However,in the case of single-layer graphene,it is accompanied by an im-portant statistical spread of the collected data.In Fig.4(c)representative G peak spectra for single-,double-layer graphene and HOPG are presented.It is important to note that in contrast to the G line,the corresponding overtone band,the G’line,does not change its spectral position as a function of the number of layers.

The most prominent di?erence in the spectra of single-layer,few-layer,and bulk graphite lies in the D’line:the integrated intensity of the D’line stays almost constant,even though it narrows to a single peak at lower wave number at the crossover to a single layer (Fig.3).The width of the D’peak or -at high resolution -its splitting into di?erent sub-peaks (Fig.5)is in the following ex-plained in the framework of the double-resonant Raman model.6The model explains the D’line in the following way (see Fig.6(a)):An electron is vertically excited from point A in the πband to point B in the π?band by ab-sorbing a photon.The excited electron is inelastically scattered to point C by emission of a phonon with mo-mentum q .Since the energy of this phonon (≈150meV)is small compared with the photon energy of 2.33eV,we have drawn the line horizontally,for simplicity.Inelastic backscattering to the vicinity of point A by emission of another phonon with momentum ≈q and electron-hole recombination lead to emission of a photon with an en-ergy about 300meV less than the energy of the incident photon.In principle,two other double-resonant Raman

4

Raman shift (cm-1)

FIG.5:D’peaks for an increasing number of graphene lay-ers along with HOPG as a bulk reference.The dashed lines show the Lorentzian peaks used to?t the data,the solid lines are the?tted results.The single peak position for the single-layer graphene is at2678.8±1.0cm?1.The peak position of the the two inner most peaks for double-layer graphene are 2683.0±1.5and2701.8±1.0cm?1.On the left the value for the splitting from double-layer graphene up to HOPG is pre-sented.All peaks are normalized in amplitude and vertically o?set.

processes,involving the phonons q′and q′′

,are possible as well.However,it was argued in Ref.13that their weight is very low.14

In Fig.6,we compare the electronic band structure of the single layer with the ones of the double layer and of bulk graphite.All three dispersion relations were calcu-lated from?rst-principles,using density-functional the-ory in the local density approximation.15In the double-layer,theπandπ?bands split into two bands each.This gives rise to four di?erent possible excitations.We have calculated the corresponding oscillator strengths16and found that for the excitation energy of2.33eV,tran-sitions1–3and2–4have negligible weight,while tran-sitions1–4and2–3(displayed in Fig.6(b))have almost equal weight.For each of the two dominant vertical tran-sitions,there are two possible horizontal transitions.The corresponding electron-phonon coupling matrix elements for the phonons q0to q3are almost equal.17In theory, we therefore expect a splitting of the D’band into four peaks of almost equal height.Our experimental data (Fig.5)shows indeed that the D’line for the double layer can be decomposed into four peaks.However,the outer two peaks(corresponding to the phonons q0and q3)have very low weight in the experimental data.We calculated

0.400.2

0.4

0.2

K

M

ΓM

-2

-1

1

2

E

(

e

V

)

-2

-1

1

2

E

(

e

V

)

single layer

-2

-1

1

2

E

(

e

V

)

(a)

(b)

(c)

FIG.6:Electronic band structure along the high-symmetry linesΓ-K and K-M:(a)single-layer graphene,(b)double-layer graphene,and(c)bulk graphite.For bulk graphite,we display the band structure in the direction parallel to the graphene planes for di?erent values of the transverse momentum k z. Vertical arrows denote vertical transitions by2.33eV from a valence(π)band to a conductance(π?)band.Horizon-tal arrows denote transitions between two states of almost equal energy by coupling to a phonon of momentum q i(the corresponding phonon frequencies are displayed in Table I). Dashed horizontal lines denote transitions with considerably less weight than the solid horizontal lines(see text).

from?rst principles15the phonon-frequenciesν1andν2, corresponding to the momenta q1and q2.The frequen-cies of the highest optical branch are given in Table I. Due to the weak inter-layer coupling the degeneracy of this branch is lifted.However,the frequency di?erence remains weak(<1cm?1)and does not signi?cantly con-tribute to the experimentally observed splitting about19 cm?1of the D’line(see Fig.5).Table I furthermore gives the value for2(ν2?ν1).We note that the value obtained from our?rst-principles calculation is only half as large as the experimentally observed splitting of about19cm?1. This discrepancy is related to the fact,that the double-resonant Raman model based on ab-initio calculations also predicts a value for the dispersion of the D’line with incident laser energy that amounts only to about half of the experimentally observed value of99cm?1/eV.18 We conclude therefore that the double-resonant Raman model can qualitatively explain the fourfold splitting of the D’line in the double-layer,but the amount of the splitting and the relative heights of the peaks are not

5

ν2/cm?12(ν2?ν1)/cm?1 bulk1402.9/1403.119.4/19.0

1395.6/1395.6

single layer1398.1-TABLE I:Frequencies of the optical phonons involved in the double-resonant Raman model.The corresponding phonon momenta q1and q2are determined from the ab-initio elec-tronic band structures of Fig.6.The splitting of the fre-quencies in the double-layer and bulk is due to the(weak) inter-layer interaction.

properly described within this model.19

In bulk graphite,theπandπ?bands split into a con-

tinuum of bands,i.e.,they disperse in the direction k z perpendicular to the layer.In Fig.6(c),we display the

bands for three di?erent values of k z.In the joint-density of states,the vertical transitions for k z=0have the

dominant weight and are thus considered in our calcu-lations.Since the splitting between the bands is much

more pronounced than for the double-layer,the value for 2(ν2?ν1)is about a factor of two higher than for the double layer.This is in agreement with the experimen-tal data,see Fig.5,where the splitting increases likewise

by about a factor of two between the double layer and

bulk graphite.As in the case of the double layer,there are quantitative di?erences between theory and experi-ment for graphite as well:First-principles calculations of the oscillator strengths and of electron-phonon cou-pling matrix elements predict an almost equal height of the peaks whereas the experiment shows that the lower-frequency peak has a strongly reduced weight.The peaks corresponding to the horizontal transitions q0and q3are missing altogether in the experimental spectrum.

Even though some quantitative di?erences remain,the

double-resonant Raman model explains well the observed di?erences in the D’line as we go from the single-layer via few-layer systems to the bulk limit.The quantitative dif-ferences may be an indicator that some essential e?ects are not properly included in the model. E.g.,the role of quasi-particle e?ects(electron-electron interaction)20 and of excitonic e?ects(electron-hole interaction)in the double-resonance process remains to be understood.The importance of these e?ects has been recently demon-strated for electronic excitations in carbon nanotubes (both semiconducting and metallic).21,22A similar im-portance may be therefore expected for processes that involve electronic excitations in graphite.23

In conclusion,Raman mapping reveals to be a pow-erful tool to investigate single-and few-layer graphene ?akes.It turns out that the width of the D’line is highly sensitive to the crossover from single-to double-layer graphene,which is explained by a peak splitting follow-ing the double-resonant Raman model together with ab initio electronic band structure calculations.A remain-ing open question is the decrease of the G line intensity with decreasing layer number compared to the almost constant spectral weight of the D’line and the accompa-nied upshift of its frequency for double-and single-layer graphene.The structural quality of the?akes is studied by analyzing the D line intensity:no defects are detected in the inner part of the?ake.The D line signal from the boundaries of the individual sections of the?ake suggest that they act as elastic scatterer.

The authors are grateful to Hubert Heersche for useful advices on sample preparation.We acknowledge stimu-lating discussions with A.Rubio and https://www.sodocs.net/doc/f712787412.html,zzeri.Cal-culations were performed at IDRIS(project061827). Financial support from the Swiss Science Foundation (Schweizerischer Nationalfonds)is gratefully acknowl-edged.L.W.acknowledges support from the French Na-tional Research Agency.

?Electronic address:grafdavy@phys.ethz.ch

1H.W.Kroto,J.R.Heath,S.C.Obrien,R.F.Curl,R.E. Smalley,Nature318,162(1985)

2S.Iijima,Nature354,56(1991)

3K.S.Novoselov,A.K.Geim,S.V.Morozov,D.Jiang,Y. Zhang,S.V.Dubonos,I.V.Grigorieva,A.A.Firsov,Sci-ence306,666(2004)

4K.S.Novoselov,A.K.Geim,S.V.Morozov,D.Jiang,M.I. Katsnelson,I.V.Grigorieva,S.V.Dubonos,A.A.Firsov, Nature438,197(2005)

5Yuanbo Zhang,Yan-Wen Tan,Horst L.Stormer,Philip Kim,Nature438201(2005)

6C.Thomsen and S.Reich,Phys.Rev.Lett.85,5214(2000) 7K.S.Novoselov,D.Jiang,F.Schedin,T.J.Booth,V.V. Khotkevich,S.V.Morozov,and A.K.Geim,PNAS102, 10451(2005)

8S.Reich and C.Thomsen,Phil.Trans.R.Soc.Lond.A 362,2271(2004)

9R.P.Vidano,D.B.Fischbach,L.J.Willis,T.M.Loehr, Solid State Commun.39,341(1981)10F.Tuinstra and J.L.Koenig,J.Chem.Phys.53,1126 (1970)

11R.Saito,A.Jorio,A.G.Souza Filho,G.Dresselhaus,M.

S.Dresselhaus,and M.A.Pimenta,Phys.Rev.Lett.88, 027401(2002)

12Y.Wang, D.C.Alsmeyer,and R.L.McCreery,Chem.

Mater.2,557(1990)

13A.C.Ferrari,J.C.Meyer,V.Scardaci,C.Casiraghi,M.

Lazzeri,F.Mauri,S.Piscanec,Da Jiang,K.S.Novoselov, S.Roth,and A.K.Geim,cond-mat/0606284(2006)

14The process involving q′(a phonon very close to the K-point)does not occur because the corresponding electron-phonon coupling matrix element is approximately0(see footnote[24]of Ref.24).And the process involving q′′has a low weight because due to the“trigonal warping”

e?ect,the corresponding phase space volume in the two-dimensional Brillouin zone is small compared to the phase space volume for process involving q.

15We use the code ABINIT:X.Gonze et al.,Comp.Mat.Sci.

25,478(2002).

6

16We use the computer code SELF written by A.Marini (http://www.?sica.uniroma2.it/?self/).

https://www.sodocs.net/doc/f712787412.html,zzeri,private communication.

18We note that Ferrari et al.13overcome this di?culty by using the semiempirical parameter dω/dq(caption of Ta-ble I of Ref.13)which is?tted to the experimental dis-persion of the D’peak.We have avoided the use of this semiempirical parameter in order to assess the quantita-tive validity of the double-resonant Raman model based on ?rst-principles calculations.The good agreement between experimental and theoretical D peak dispersion in Ref.6 is based on a corresponding?t of the hopping parameter in the tight-binding band-structure.

19For an exact quantitative evaluation of the peak heights, an integration in the two-dimensional Brillouin zone for all transitions of energy?E=2.33eV would have to be performed.

20For a calculation of the quasiparticle bandstructure of graphite in the GW approximation see:S.G.Louie,in Top-

ics in Computational Materials in Science,edited by C.Y.

Fong(World Scienti?c,Singapore,1997),p.96.

21C.D.Spataru,S.Ismail-Beigi,L.X.Benedict,and S.G.

Louie,Phys.Rev.Lett.92,077402(2004).

22E.Chang,G.Bussi,A.Ruini,and E.Molinari,Phys.Rev.

Lett.92,196401(2004).

23We note that the picture of independent electron-hole pair excitations has been quantitatively very successful for the assignment of nanotube spectra to the chiral indices(m,n).

However,this success was based on the use of tight-binding band-structures with correspondingly?tted parameters.

A parameter-free,?rst-principles,calculation of the opti-

cal spectra of carbon nanotubes must take into account electron-electron and electron-hole interaction,and we sug-gest that this may be true for graphite as well.

24S.Piscanec,https://www.sodocs.net/doc/f712787412.html,zzeri,F.Mauri,A.C.Ferrari,and J.

Robertson,Phys.Rev.Lett.93,185503(2004).

相关主题