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

Spatially Resolved Raman Spectroscopy

of Single-and Few-Layer Graphene

D.Graf,*,?F.Molitor,?K.Ensslin,?C.Stampfer,?A.Jungen,?C.Hierold,?and

L.Wirtz§

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

Nanosystems,ETH Zurich,8092Zurich,Switzerland,and Institute for Electronics,

Microelectronics,and Nanotechnology(IEMN),CNRS-UMR8520,B.P.60069,

59652Villeneu V e d’Ascq Cedex,France

Received July21,2006;Revised Manuscript Received October7,2006

ABSTRACT

We present Raman spectroscopy measurements on single-and few-layer graphene flakes.By using 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 different peaks for the double-layer.These findings 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 find no defects within the flake.A finite D line response originating from the edges can be attributed either to defects or to the breakdown of translational symmetry.

The interest in graphite has been revived in the last two decades with the advent of fullerenes1and carbon nanotubes.2 However,only recently,single-and few-layer graphene could be transferred to a substrate.3Transport measurements revealed a highly tunable two-dimensional electron-hole gas with a linear energy dispersion around the Fermi energy embedded 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 recovered. 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 vibrational properties,turns out to be an ingenious tool to probe the lifting of that specific degeneracy. We report on Raman mapping of single-and few-layer graphene flakes resting on a silicon oxide https://www.wendangku.net/doc/676339517.html,teral resolution of400nm allows one to address neighboring sections with various layers of graphene down to a single graphene sheet,previously determined with the scanning force microscope(SFM).We find that the integrated G line signal is directly correlated with the thickness of the graphitic flake and is shifted upward in frequency for double-and single-layer graphene compared to that of 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 transition to the very last layer offers an optical and nondestructive method to unambigu-ously detect single-layer graphene.In addition,we locally resolve the structural quality of the flake by investigating the D band,which is related to elastic backscattering.The map of the integrated D line signal of a graphitic flake with double-and single-layer sections shows that the inner part of the flake is quasi-defect-free,whereas edges and steps serve as scatterers.Finally,we calculate the splitting of the D′line as a function of the number of graphene layers by following the recent work of Ferrari et al.,7who explained the splitting within the double-resonant Raman model.6The comparison between experimental data and theory confirms the qualitative validity of the double-resonant Raman model but demonstrates quantitative differences between theory and experiment.In particular,the model,when based on first-principles calculations,predicts a much smaller splitting of the peaks.

The graphite films were prepared by mechanical exfolia-tion of highly oriented pyrolytic graphite(HOPG)and subsequent transfer to a highly doped Si wafer with a300 nm SiO2(atomic oxidation process)cap layer.3,8The combination of optical microscopy using phase contrast and SFM makes it possible to locate flakes with various thick-nesses down to a monolayer with lateral extensions in the micrometer range.The Raman spectra were acquired using

*Corresponding author.E-mail:grafdavy@phys.ethz.ch.

?Solid State Physics Laboratory,ETH Zurich.

?Micro and Nanosystems,ETH Zurich.

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

NANO LETTERS

2007 Vol.7,No.2 238-242

a laser excitation of 532nm (2.33eV)delivered through a single-mode optical fiber,whose spot size is limited by https://www.wendangku.net/doc/676339517.html,ing a long working distance focusing lens with a numerical aperture NA )0.80,we obtained a spot size of about 400nm.With a very low incident power of 4-7μW,heating effects can be neglected.

The Raman spectrum of graphite has four prominent peaks (Figure 3:for a recent review,see ref 9).The peak around 1582cm -1,commonly called the G line,is caused by the Raman active E 2g phonon (in-plane optical mode),close to the Γpoint.The D line around 1350cm -1exhibits two remark-able features:its position shifts to higher frequencies with increasing incident laser excitation energies 10and its relative signal strength (compared to the G line)depends strongly on the amount of disorder in the graphitic material.10,11The 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 different experi-mental findings 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.12The electronic and vibrational properties of graphite are dominated by the sp 2nature of the strong intraplane covalent bonds.Raman spectra for multiple graphene layers can be compared qualitatively and quantitatively while investigating flakes with sections of various thicknesses.In Figure 1a,the SFM micrograph of a graphite flake with different layers is presented:the bare SiO 2(indicated by “0”)is surrounded by single-layer

sections with steps of up to two,four,and six layers.The different step heights are clearly depicted in Figure 1b,where a cross section of Figure 1a (see white dashed arrow)is shown.By scanning the flake and collecting for each spot the complete Raman spectrum,we can subsequently filter specific spectral data for a spatially resolved data point and construct false-color 2D plots.In Figure 1c,the intensity of the G peak is integrated from 1537to 1622cm -1.We find a remarkable correlation with the SFM graph:brighter regions correspond to thicker sections.The cross section in Figure 1d shows a steplike behavior,perfectly correlated with the topographical changes shown in Figure 1b.In Figure 1e,we plot the fwhm (full width at half-maximum)of the D ′line.It shows the narrowing at the transition to a single-layer (see,e.g.,Figure 3)and gives an evident contrast be-tween single-and few-layer graphene sections.The two discrete levels in the fwhm of the D ′line shown in Figure 1f related to a single layer (～30cm -1)and two and more layers (～60cm -1)suggest that the width of the D ′line can be used as a detector for single-layer graphene.Raman spectro-scopy can therefore be used to count the layers of a thin graphite stack and to discriminate between single and double https://www.wendangku.net/doc/676339517.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 finite graphitic flakes on the silicon oxide matrix obtained with the technique explained above is remarkable:electronic mobilities up to 15000cm 2(Vs)-1were estimated from transport experiments.4,5We point out also that the Raman spectroscopy reveals quasi-defect-free graphitic sheets via the absence of a D band signal.First experiments 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.11The 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 oxidized HOPG.13With micro-Raman mapping,we are able to localize the spatial origin of the defects,which can have important consequences for the electronic properties.14From cross-correlating the SFM micrograph in Figure 2a with the Raman map of the integrated D line (1300-1383cm -1)intensity in Figure 2c,we infer directly that the edges of the flake and also the borderline between sections of different heights contribute to the D band signal,whereas the inner parts of the flakes do not.This is somewhat surprising because,for thinner flakes,the influence of a nearby substrate on the structural quality should be increasingly important.In the cross-section in Figure 2d,we see clearly that the D line intensity is maximal at the section boundaries,which can be assigned to translational symmetry breaking or to defects.However,we want to emphasize that the D line is still 1order of magnitude smaller than the G line.In Figure 2e,spatially averaged D mode spectra from the two steps shown in Figure 2d are presented.The frequency fits well into the linear dispersion relation of peak shift and excitation energy

found

Figure 1.(a,b)SFM micrograph and cross-sectional plot (indicated with the white dashed arrow;lateral average over 400nm)of a few-layer graphene flake 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.

in earlier experiments.10In addition,we find that the peak is narrower and downshifted 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 parts a and b of Figure 3,we compare the Raman spectra of the double-and single-layer graphene shown in Figure 2b and labeled with A and B.The Raman signal is significantly altered when peeling off the penultimate layer:the G peak decreases strongly in intensity and shifts toward higher wave numbers.In connection with Figure 1b,we already stated that the integrated G line signal is monotonic-ally increasing with increasing flake thickness.To compare data of different flakes and measurement runs,we turn our

attention to the ratio of the integrated intensities of the G and D ′line,plotted in Figure 4a.Most of the changes can be attributed to the decrease of the G line because the spectral weight of the D ′band changes only slightly.The intensity ratio increases almost linearly from one to four layers.In Figure 4b,the dependence of the G peak position on the layer number is investigated.Spectral data of various sections on different flakes were averaged.The frequency shifts toward 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 important statistical spread of the collected data.In Figure 4c,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 difference 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 a lower wave number at the crossover to a single layer (Figure 3).The width of the D ′peak or,at high resolution,its splitting into different subpeaks (Figure 5)is explained in the following in the framework of the double-resonant Raman model.6,7The model explains the D ′line in the following way (see Figure 6a):an electron is vertically excited from point A in the πband to point B in the π*band by absorbing a photon.The excited electron is inelastically scattered to point C by emission of a phonon with wave vector q .Because the energy of this phonon (≈150meV)is small compared with the photon energy of 2.33eV,we have drawn the line horizon-tally for simplicity.Inelastic backscattering to the vicinity of point A by emission of another phonon with wave vector ≈q and electron -hole recombination leads to emission of a photon with an energy about 300meV less than the energy of the incident photon.In principle,two other double-resonant Raman processes,involving the phonons q ′and q ′′,are possible as well.However,it was argued in ref 7that their weight is very low.15

In Figure 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

calculated

Figure 2.(a)SFM micrograph of a graphitic flake 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 flake 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 (disk,dashed line)and from single layer to the SiO 2substrate (square,solid

line).

Figure 3.Raman spectra of (a)single-and (b)double-layer graphene (collected at spots A and B,see Figure

2b).

Figure 4.(a)Plot of the ratio of the integrated intensities of the G and D ′peak vs number of stacked layers (average value and standard deviation).(b)G line frequency vs 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.

from first principles,using density-functional theory in the local density approximation.16In the double layer,the πand π*bands split into two bands each.This gives rise to four different possible excitations.We have calculated the cor-responding oscillator strengths 19and found that,for the excitation energy of 2.33eV,transitions 1-3and 2-4have negligible weight,while transitions 1-4and 2-3(displayed in Figure 6b)have almost equal weight.For each of the two dominant vertical transitions,there are two possible hori-zontal transitions.The corresponding electron -phonon cou-pling matrix elements for the phonons q 0to q 3are almost equal.20In theory,we therefore expect a splitting of the D ′band into four peaks of almost equal height.Our experi-mental data (Figure 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 q 0and q 3)have very low weight in the experimental data.We calculated from first principles 21the phonon frequencies ν1and ν2,corresponding to the wave vectors q 1and q 2.The frequencies of the highest optical branch are given in Table 1.Because of the weak interlayer coupling,the degeneracy of this branch is lifted.However,the frequency difference remains weak (<1cm -1)and does not significantly contrib-ute to the experimentally observed splitting of about 19cm -1of the D ′line (see Figure 5).Table 1furthermore gives the value for 2(ν2-ν1).We note that the value obtained from

our first-principles calculation is only half as large as the experimentally observed splitting of about 19cm -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 of 99cm -1/eV.25We 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 properly described within this model.26

In bulk graphite,the πand π*bands split into a continuum of bands,i.e.,they disperse in the direction k z

perpendicular

Figure 5.D ′peaks for an increasing number of graphene layers along with HOPG as a bulk reference.The dashed lines show the Lorentzian peaks used to fit the data,the solid lines are the fitted results.The single peak position for the single-layer graphene is at 2678.8(1.0cm -1.The peak position of the two innermost peaks for double-layer graphene are 2683.0(1.5and 2701.8(1.0cm -1.On the left,the value for the splitting from double-layer graphene up to HOPG is presented.All peaks are normalized in amplitude and vertically

offset.

Figure 6.Electronic band structure along the high-symmetry lines Γ-K and K -M:(a)single-layer graphene,(b)double-layer graph-ene,and (c)bulk graphite.For bulk graphite,we display the band structure in the direction parallel to the graphene planes for different values of the transverse wave vector k z .Vertical arrows denote vertical transitions by 2.33eV from a valence (π)band to a conduc-tance (π*)band.Horizontal arrows denote transitions between two states of almost equal energy by coupling to a phonon of wave vector q i (the corresponding phonon frequencies are displayed in Table 1).Dashed horizontal lines denote transitions with consider-ably less weight than the solid horizontal lines (see text).Table 1.Frequencies of the Optical Phonons Involved in the Double-Resonant Raman Model a

ν1/cm -1

ν2/cm -12(ν2-ν1)/cm -1

bulk

1393.2/1393.61402.9/1403.119.4/19.0double layer 1395.6/1395.61400.0/1400.6

8.8/10.0

single layer

1398.1

a

The corresponding phonon wave vectors q 1and q 2are determined from the ab initio electronic band structures of Figure 6.The splitting of the frequencies in the double-layer and bulk is due to the (weak)interlayer interaction.

to the layer.In Figure6c,we display the bands for three dif-ferent 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 calculations.Because the splitting between the bands is much more pronounced than for the double layer, the value for2(ν2-ν1)is about a factor of2higher than for the double layer.This is in agreement with the experimental data,see Figure5,where the splitting increases likewise by about a factor of2between the double layer and bulk graph-ite.As in the case of the double layer,there are quantitative differences between theory and experiment for graphite as well:First-principles calculations of the oscillator strengths and of the electron-phonon coupling 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 both missing in the experimental spectrum. Even though some quantitative differences remain,the double-resonant Raman model explains well the observed differences in the D′line as we go from the single-layer via few-layer systems to the bulk limit.The quantitative differ-ences may be an indicator that some essential effects are not properly included in the model.e.g.,the role of excitonic effects during the electron-hole pair excitation in the double-resonance process remains to be understood.The importance of these effects has been recently demonstrated for electronic excitations in carbon nanotubes(both semiconducting and metallic).27,28A similar importance may be therefore expected for processes that involve electronic excitations in graphite.29 In conclusion,Raman mapping is a powerful tool to investigate single-and few-layer graphene flakes.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 following the double-resonant Raman model together with ab initio electronic band structure calculations.A remaining 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 accompanied upshift of its frequency for double-and single-layer graphene.The structural quality of the flakes is studied by analyzing the D line intensity:no defects are detected in the inner part of the flake.The D line signal from the boundaries of the individual sections of the flake suggest that they act as an elastic scatterer. Acknowledgment.We are grateful to A.Geim for the stimulation to start working on graphene and H.Heersche for useful advice on sample preparation.We acknowledge stimulating discussions with M.Haluska,A.Rubio,and M. Lazzeri.Calculations were performed at IDRIS(project 061827).Financial support from the Swiss Science Founda-tion(Schweizerischer Nationalfonds)is gratefully acknowl-edged.L.W.acknowledges support from the French National Research Agency.

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