Raman imaging and electronic properties of graphene
aa r X i v : . [ c ond - m a t . m e s - h a ll ] S e p Raman imaging and electronic properties ofgraphene
F. Molitor, D. Graf, C. Stampfer, T. Ihn and K. Ensslin
Laboratory for Solid State Physics, ETH Zurich,8093 Zurich, Switzerland [email protected]
Abstract.
Graphite is a well-studied material with known electronic and opticalproperties. Graphene, on the other hand, which is just one layer of carbon atomsarranged in a hexagonal lattice, has been studied theoretically for quite some timebut has only recently become accessible for experiments. Here we demonstrate howsingle- and multi-layer graphene can be unambiguously identified using Raman scat-tering. Furthermore, we use a scanning Raman set-up to image few-layer grapheneflakes of various heights. In transport experiments we measure weak localizationand conductance fluctuations in a graphene flake of about 7 monolayer thickness.We obtain a phase-coherence length of about 2 µ m at a temperature of 2 K. Fur-thermore we investigate the conductivity through single-layer graphene flakes andthe tuning of electron and hole densities via a back gate. The interest in graphite has been revived in the last two decades with theadvent of fullerenes [1] and carbon nanotubes [2]. In a pioneering series of ex-periments it has become possible to transfer single- and few-layer grapheneto a substrate [3]. Transport measurements revealed a highly-tunable two-dimensional electron/hole gas which mimics relativistic Dirac Fermions em-bedded in a solid-state environment [4, 5]. The term ”relativistic” describesthe linear energy-wave vector relation which gives graphene its exceptionalelectronic properties. Going to few-layer graphene, however, disturbs thisunique system in such a way that the usual parabolic energy dispersion is re-covered. The large structural anisotropy makes few-layer graphene thereforea promising candidate to study the rich physics at the crossover from bulkto purely two-dimensional systems. Turning on the weak interlayer couplingwhile stacking a second layer onto a graphene sheet leads to a branching of theelectronic bands and the phonon dispersion at the K point. Double-resonantRaman scattering [7] which depends on electronic and vibrational propertiesturns out to be an ingenious tool to probe the lifting of that specific degen-eracy. Here we show scanning Raman images of graphene flakes and comparethem with scanning force images. We evaluate the intensity, position andwidth of various Raman lines in order to quantify the numbers of monolayersin a given flake. Furthermore we determine the inelastic mean free path in a
F. Molitor, D. Graf, C. Stampfer, T. Ihn and K. Ensslin few-layer graphene wire and estimate the mobility in a single-layer grapheneflake.
The energy gain and loss of scattered photons is related to the creationand annihilation of phonons at specific points in the phonon spectrum. Forgraphite the electron is excited from the valence band π to the conductionband π * close to the K point in the electronic bandstructure. In graphenethe unit cell is composed of two atoms leading to 6 phonon branches: Threeacoustic branches starting at zero frequency and three optical branches athigher energies. The phonon spectrum of graphite has been calculated (see,e.g., [8]).In Fig. 1(a) we start by presenting an image of a graphene flake takenwith a scanning force microscope (SFM). The flakes were prepared followingthe method described in Ref. [3]. The number of monolayers is marked bya number in the respective flake area. Fig. 2 shows Raman spectra takenwith a laser spot within one of the respective areas corresponding to one andtwo layers of graphene. The Raman spectrum of graphite has four prominentpeaks. For a recent review see Ref. [6]. The G line is a standard Raman signalarising from the E in-plane vibration of the atoms. In first approximationits intensity increases monotonously with the amount of material. The D line(D for defect) usually has a pronounced intensity if a material has defects [10]or is strongly bend like in the case of carbon nanotubes. The absence of theD line in Fig. 2 is already a good indication for the structural quality of ourgraphene flakes. In the case of the D’ line a second phonon excitation insteadof an elastic backscattering is required [7]. The D’ line is highly sensitiveto the underlying energy dispersion. Consequently the D’-line is an idealindicator to discriminate mono- from double layers in a given flake. The twomonolayer areas show a single narrow peak, see Fig. 2, while the double layerarea shows a broadened peak with substructure. The width of the D’ peak or- at high resolution - its splitting into different sub-peaks is explained in theframework of the double-resonant Raman model [7]. A very similar analysisof the Raman lines of few-layer graphene was presented in Ref. [12]. The most prominent difference in the spectra of single-layer, few-layer, andbulk graphite lies in the D’ line: the integrated intensity of the D’ line staysalmost constant, even though it narrows to a single peak at lower wave num-ber at the crossover to a single layer (Fig. 2). The width of the D’ line isplotted in Fig. 1(b) for the same area of the SFM scan in Fig. 1(a). Theoutline of the flake and in particular the difference between the single and aman imaging and electronic properties of graphene 3 m m1 m m (a) m m) I n t en s i t y ( a . u . ) (b) (c) (d) (e) SFMFWHM: D' Intensity: D
21 1
DG / D x10 m m Fig. 1. (a) SFM micrograph of a graphitic flake consisting of one double- and twosingle-layer sections (white dashed line along the boundaries), highlighted in theRaman map (b) showing the FWHM of the D’ line. (c) Raman mapping of theintegrated intensity of the D line: A strong signal is detected along the edge of theflake 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 theG peak (solid line) and pronounced peaks at the steps for the integrated intensityof the D line (dashed line). (e) Spatially averaged D peak for the crossover fromdouble to single layer (disk, dashed line) and from single layer to the SiO substrate(square, solid line). Taken from Ref. [9]. double layer areas can clearly be observed. We conclude that the width ofthe D’ line is an excellent indicator to identify single-layer graphene.From cross-correlating the SFM micrograph in Fig. 1(a) with the Ramanmap of the integrated D line (1300-1383 cm − ) intensity in Fig. 1(c) we inferdirectly that the edges of the flake and also the borderline between sectionsof different height contribute to the D band signal whereas the inner partsof the flakes do not. This is somewhat surprising since for thinner flakes theinfluence of a nearby substrate on the structural quality should be increas- F. Molitor, D. Graf, C. Stampfer, T. Ihn and K. Ensslin
Raman shift (cm-1) I n t en s i t y ( CCD c oun t s ) D G D' G'
Fig. 2.
Raman spectra of (a) single- and (b) double-layer graphene (collected atspots A and B, see Fig. 1(b). Taken from Ref. [9]. ingly important. In the cross-section Fig. 1(d) we see clearly that the D lineintensity is maximal at the section boundaries, which can be assigned totranslational symmetry breaking or to defects. However, we want to empha-size that the D line is still one order of magnitude smaller than the G line.In Fig. 1(e) spatially averaged D mode spectra from the two steps shownin Fig. 1(d) are presented. The frequency fits well into the linear dispersionrelation of peak shift and laser excitation energy found in earlier experiments[11]. In addition, we find that the peak is narrower and down-shifted at theedge of the single layer while it is somewhat broader and displays a shoulderat the crossover from the double to the single layer.
Fig. 3 shows transport measurements through a graphitic flake of several µ mlength, 320 nm in width and about 7 monolayers in height. Ohmic contactsand four in-plane gates as indicated by the gold colored areas were fabricatedby electron beam lithography (SFM scan, Fig. 3(a)). We measured the re-sistance down to temperatures of 1.7 K as a function of back gate voltage(Fig. 3(b)) and side gate voltage (Fig. 3(c)) [13]. All features in the resis-tance traces are reproducible. The metallic in-plane gates basically changethe Fermi energy in a similar way as the homogeneous back gate, however,with a significantly reduced lever arm (Fig. 3(d)). We envision that in-planegates could therefore serve well for the electrostatic tuning of nanostructuresfabricated on graphene.We also measured the resistance as a function of magnetic field and foundwell developed features corresponding to weak localization and conductancefluctuations [13]. The data could be quantitatively analyzed in the frameworkof diffusive one-dimensional metals. We obtained a phase-coherence length ofabout 2 µ m at a temperature of about 2 K. The temperature dependence aman imaging and electronic properties of graphene 5 µm-20 0 2041020 V bg (V) R ( k Ω ) (a)(b)1.7K10K20K50K100K L L R R side gate voltage (V)100 Ω Ω -16-26 bg =30.4V (d)V bg (V) o L i L o R i R Fig. 3. (a) SFM micrograph of a graphite wire resting ona silicon oxide surface witha schematic of the four contacts(iL, iR, oL, oR) and four side gates (L1, L2, R1,R2). Inset: Optical microscope image of the structure. (b) Four-terminal resistanceas a function of back gate for different temperatures. (c) Resistance change as afunction of the side gates L1+L2 (solid line) and R1+R2 (dotted line) at 1.7 K.(d) Resistance change as a function of back gate for different side gate voltages(L1+L2+R1+R2) at 1.7 K. Taken from Ref. [13]. is consistent with carrier-carrier scattering being the dominant dephasingmechanism.Fig. 4 shows the resistance of a single-layer graphene flake. The maximumresistance, i.e. the charge neutrality point, is close to zero back gate voltageindicating that doping is relatively weak. Using a plate-capacitor model wecan infer the electron and hole densities for positive and negative gate volt-ages. We find a maximum mobility of about 7000 cm /Vs. F. Molitor, D. Graf, C. Stampfer, T. Ihn and K. Ensslin -20 0 2024681012 V bg (V) R ( k W ) Fig. 4.
Two-terminal resistance of a single-layer graphene flake as a function ofback gate voltage.
We thank A. Jungen and C. Hierold for a fruitful collaboration during themeasurement of the Raman spectra and L. Wirtz for theoretical support.Financial support from the Swiss National Science Foundation and NCCRNanoscience is gratefully acknowledged.
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