Scanning Raman spectroscopy of graphene antidot lattices: Evidence for systematic p-type doping
S. Heydrich, M. Hirmer, C. Preis, T. Korn, J. Eroms, D. Weiss, C. Schüller
aa r X i v : . [ c ond - m a t . m e s - h a ll ] J un Scanning Raman spectroscopy of graphene antidot lattices: Evidence for systematicp-type doping
S. Heydrich, M. Hirmer, C. Preis, T. Korn, J. Eroms, D. Weiss, and C. Sch¨uller ∗ Institut f¨ur Experimentelle und Angewandte Physik,Universit¨at Regensburg, D-93040 Regensburg, Germany (Dated: June 19, 2018)We have investigated antidot lattices, which were prepared on exfoliated graphene single layers viaelectron-beam lithography and ion etching, by means of scanning Raman spectroscopy. The peakpositions, peak widths and intensities of the characteristic phonon modes of the carbon lattice havebeen studied systematically in a series of samples. In the patterned samples, we found a systematicstiffening of the G band mode, accompanied by a line narrowing, while the 2D mode energies arefound to be linearly correlated with the G mode energies. We interpret this as evidence for p-typedoping of the nanostructured graphene.
PACS numbers: 63.20.kd 63.22.Rc 78.30.-j
Since the first report about the preparation ofgraphene single layers via mechanical exfoliationtechnique , the interest in this seemingly ideal two-dimensional system has grown enormously. For themost part, this is motivated by the vision that the two-dimensional carbon system is potentially a promisingcandidate for future electronic devices . Scanning Ra-man spectroscopy has proven to be a powerful techniquefor the characterization and investigation of graphenesamples. It enables a fast and nondestructive investiga-tion of the electronic and structural properties of layeredand laterally-structured samples with sub-micron spatialresolution. Via Raman spectroscopy, e.g., one is able toidentify the number of layers in a sample , to charac-terize the edge chirality or to probe strain . Most im-portantly for this work, it was shown that the doping ingraphene can be monitored by Raman spectroscopy ,even in the case of unintentional doping due to chargedimpurities . The most prominent phonon modes intwo-dimensional carbon lattices are: (i) The G band,which stems from inplane LO phonons with E g sym-metry at the center of the Brillouin zone, and which iscentered around 1580 cm − in intrinsic graphene. (ii)The D mode (around 1340 cm − ), which is attributed toinplane TO phonons from around the K or K’ points ofthe Brillouin zone, and which is forbidden due to wave-vector conservation. It requires a defect-induced scatter-ing process to be observable, and appears in high-qualitygraphene layers at the edges, only . (iii) The 2D mode,which is an overtone of the D mode. Due to the two-phonon nature of this mode, it is wave-vector conserv-ing. Finally, (iv), the D’ band, which is again thoughtto be a defect-induced mode from the maximum of theLO phonon dispersion between Γ and K. In this work,we have investigated systematically the Raman modesin a series of graphene samples, on which periodic holelattices, i.e., so called antidot lattices, were prepared byelectron-beam lithography and subsequent ion etching.Recently, in transport experiments on similar structurestwo of the authors observed pronounced weak localiza- i n t en s i t y ( a r b . un i t s ) Raman shift (cm -1 )D G D· 2D (a) 5 m m
100 nm(b)(c)(d)AB R Region ARegion BRegion R(Reference)
FIG. 1: (a) Microscope image of a graphene flake. The dashedrectangles mark the regions, where antidot lattices were pre-pared. (b) Scanning electron micrograph of region B, and, (c)of region A. (c) Representative Raman spectra of regions A,B, and R on the sample. tion due to strong intervalley scattering at the antidotedges and found a transport gap by analyzing thermallyactivated transport around the Dirac point. Here, wefind in our Raman experiments a strong correlation ofthe energetic positions of the G modes and 2D modesin all antidot samples, from which we conclude that thenanoscale patterning produces a p-type doping. We havefound doping levels in the range of 3 − × cm − .The graphene samples were prepared on Si wafers with300 nm SiO cap layers by the well-known mechanicalexfoliation technique . On selected single layer flakes,antidot lattices with periods of 80 nm, 100 nm, 200 nm,and 400 nm were prepared using electron beam lithogra-phy and oxygen reactive ion etching. The hole diametersare between about 50 nm and 60 nm. In this series ofsamples, we have intentionally deposited no metal con-tacts in order to avoid unwanted additional doping due tothe presence of metals on the samples . We use below,however, measurements on a gated graphene referencesample for estimates of the hole densities. The Ramanexperiments were performed at room temperature witha 532 nm diode-pumped solid state laser and a micro-scope setup. The samples were mounted on a motor-ized x-y translation stage with minimal step sizes of 100nm, the laser-spot diameter was 800 nm. Raman spec-tra were recorded with a TriVista triple Raman system,equipped with a nitrogen-cooled CCD detector. Figure1a shows an optical microscope image of one of the in-vestigated samples. In the regions A and B, indicated bydashed rectangles in Fig. 1a, antidot lattices with a pe-riod of 80 nm were prepared. The holes in region A havea slightly larger diameter ( ∼
60 nm, see Fig. 1c) thanthe holes in region B ( ∼
50 nm, see Fig. 1b). RegionR is an un-patterned part of the sample. Note that onthe left edge of region A and on the upper right edge ofthe reference region R, there are multi-layer areas, visi-ble by the much darker contrast in the microscope image(Fig. 1a). Typical Raman spectra of the three regions,A, B and R, are displayed in Fig. 1d. In the antidotregions, A and B, pronounced D peaks are observable,along with D’ peaks. We interpret this to be dominantlycaused by the introduction of additional edges into thesample due to the creation of the holes, and not by ad-ditional defects or disorder, which might be caused bythe preparation process. The reason for this interpreta-tion is evident from the scanning Raman images, shownin Fig. 2. Figure 2 shows false color plots of data, ob-tained from scanning Raman experiments on the samesample, as shown in Fig. 1. In these measurements, in-dividual Raman spectra were taken with lateral spatialresolution of about 800 nm, in steps of 500 nm in x and ydirections. From the raw spectra, peak positions, intensi-ties and linewidths of the phonon modes were extracted.The image of the G mode intensity (Fig. 2a) essentiallyreproduces the topology of the whole flake. The inten-sity of the G mode increases from region A, which con-tains the larger holes, to region B, with smaller holes,to the un-patterned reference region R. A maximum in-tensity is visible in the multi-layer part, left of regionA. On the other hand, a pronounced intensity of the Dmode is observed in the antidot areas A and B, only, withhigher intensities in A, which contains the larger holes,i.e., with longer edges (Fig. 2b). Interestingly, the ener-getic position of the G mode is systematically higher inthe antidot lattices than in the reference part (see Fig.2c). While the G mode energy in the reference part isbetween about 1589 and 1590 cm − , it is in regions Aand B upshifted to about 1592 to 1594 cm − . Evidencefor the high crystalline quality of the prepared samplescan be deduced from the image of the linewidths of the Gmode, displayed in Fig. 2d. The linewidths are over the (a) A AAB BB min. min.max. max. AB µ Intensity G (b)Intensity D(c)Position G (d)FWHM G
R RR R
FIG. 2: False color plots of scanning Raman experiments onthe same sample as in Fig. 1. Displayed are measured imagesof (a) the intensity of the G mode, (b) the intensity of the Dmode, (c) the energetic position of the G mode, and, (d) thelinewidth of the G mode. The numbers at the scale bars in(c) and (d) are given in cm − . whole single-layer region between about 9 and 11 cm − ,comparable to pristine graphene samples , and to plaingated graphene outside the Landau-damping region (seebelow Fig. 3b). For significantly disordered samples onewould expect linewidths in the range of several tens ofwavenumbers . This clearly excludes the interpretationthat the observed stiffening of the G mode in the antidotsample is caused by disorder. The narrow and almostunchanged linewidths indicate that doping is the reasonfor the upshift, caused by the nonadiabatic removal ofthe Kohn anomaly (see below) . The most importantresults of the present work are shown in Fig. 3. Figure3a displays a summary of the most relevant data fromthe whole series of investigated antidot samples. If weplot, sample by sample, the positions of the observed 2Dmodes versus the positions of the G modes, we find an ap-proximately linear correlation (Fig. 3a). The linewidthsof the observed G modes in the different samples tenta-tively decrease with increasing G mode energy (inset ofFig. 3a). The correlation between G mode and 2D modepositions was recently investigated systematically on alarge number of graphene samples, both, in as-depositedand in gated samples . It was reported that while the2D mode position decreases with increasing G mode po-sition in n-doped samples, it increases with increasing Gmode position in p-doped graphene . The dashed linein Fig. 3a indicates, for the range of G mode energies rel-evant for our work, the slope of the approximately linearcorrelation, as reported in Ref. for p-doped graphene.In stark contrast, for n-type doping the slope should benegative. One can see a fairly good agreement of thedata, extracted from our measurements on the antidotsamples, with the dashed line in Fig. 3a. Please note
80 nm80 nm(s)100 nm100 nm(s)200 nm400 nmplain D - pea k po s i t i on ( c m - ) G-peak position (cm -1 ) G-peakposition(cm -1 ) G F W H M ( c m - ) (b)(a) gate voltage (V) G - pea k po s i t i on ( c m - ) G - pea k F W H M ( c m - ) FIG. 3: (a) Plot of the energetic positions of the observed2D modes versus the positions of the G modes of all inves-tigated antidot samples. The legend indicates the periods ofthe investigated antidot lattices. The diameter of the holesis approximately 60 nm. The label (s) means slightly smallerholes ( ∼
50 nm). The inset shows the linewidths of the Gmodes versus energetic position. (b) Plot of the energetic po-sitions of the G mode and its linewidth versus gate voltage,as measured in a plain, gated graphene sample. that the 2D mode energies in our experiments are slightlylower than in Ref. , since we measured with a 532 nmline (514 nm line in Ref. ): The 2D mode energy in-creases with decreasing laser wavelength due to the dou-bly resonant intervalley scattering process . Therefore,the dashed line in Fig. 3a is rigidly shifted by about 17cm − to lower energies as compared to 2D mode ener-gies in Fig. 3 of Ref. . Obviously, our data in Fig. 3asuggest a p-type doping of the antidot lattices. We notehere, that in previous Raman investigations of grapheneedges, also indications of a stronger doping in close vicin-ity to the edges, as compared to the bulk of the samples,were found . Based on this, and on our observations,we suspect that the doping effect reaches up to a max-imum distance of a few tens of nanometers around theedges of the holes. Hence, the amount of p doping ap-pears to increase systematically with the ratio of etchedto unetched graphene area, which is tentatively verified by the data in Fig. 3a. As a result, the plain referencesample regions are not affected by the doping. In orderto quantify the amount of p doping, we have comparedour results to measurements on an un-patterned gatedsample, where doping can be introduced electrostatically(cf. Refs. ). Figure 3b shows the observed G mode posi-tions and linewidths versus applied gate voltage for elec-trostatic p doping. The gate voltage where the Fermienergy is at the Dirac point is indicated by a verticalblue dashed line. The G mode is Landau-damped due todecay into vertical electron-hole excitations, and hencehas a larger linewidth, as long as the Fermi energy issmaller than half of the G mode energy (gray-shaded re-gion in Fig. 3b) . In accordance with Ref. , the observedG mode energy in the gated sample increases almost lin-early with increasing negative gate voltage (indicated bydashed black line in Fig. 3b) due to the nonadiabaticremoval of the Kohn anomaly at the Γ point . In thelow-density range, within the Landau-damped region, thedisorder potential dominates the charge state , leaving anonzero average doping, and, hence, an almost constantG mode energy. From transport experiments on similarsamples we know that the relation between hole (elec-tron) density and applied gate voltage, measured withrespect to the Dirac point, is p ∼ . × cm − × V gate [V]. From this and the measured slope of G mode energyversus gate voltage in Fig. 3b, we conclude that the Gmode energy increases by 1 cm − in the graphene samplesper ∼ . × cm − increase in hole density, starting ata G mode energy of 1580 cm − at zero density. Of course,this relation holds for densities > × cm − , abovethe disorder-dominated regime, only. With this calibra-tion we can assign hole densities between about 3 × cm − (400 nm sample in Fig. 3a) and 7 × cm − (80nm sample in Fig. 3a) to our investigated antidot samplesin Fig. 3a.In conclusion, we have investigated antidot graphenesamples by scanning Raman spectroscopy. The overallcrystalline quality of the antidot lattices is as good asthat of the as-deposited layers. An observed systematicstiffening of the G mode in the antidot samples, accompa-nied by a similar increase in 2D mode energy lead to theconclusion that the introduction of the antidot latticescauses a p-type doping. In all likelihood, the observed pdoping is a consequence of the patterning process here,and not a result of the specific antidot pattern.We acknowledge financial support by the DFG viaGRK 1570 and SPP 1459. ∗ Electronic address: [email protected] A. K. Geim and K. S. Novoselov, Nat. Mater. , 183 (2007). e.g., M. Y. Han et al., Phys. Rev. Lett. , 206805 (2007). A. C. Ferrari et al., Phys. Rev. Lett. , 187401 (2006). L. M. Malard et al., Phys. Rev. B , 201401 (2007). Y. You et al., Appl. Phys. Lett. , 163112 (2008). C. Metzger et al., Nano Lett. , 6 (2010). S. Pisana et al., Nat. Mater. , 198 (2007). J. Yan et al., Phys. Rev. Lett. , 166802 (2007). C. Casiraghi et al., Appl. Phys. Lett. , 233108 (2007). C. Stampfer et al., Appl. Phys. Lett. , 241907 (2007). C. Casiraghi, Phys. Status Solidi RRL , 175 (2009). C. Casiraghi et al., Nano Lett. , 1433 (2009). J. Eroms and D. Weiss, New J. Phys. , 095021 (2009). A. Das et al., Nat. Nanotechnol. , 210 (2008). M. Lazzeri and F. Mauri, Phys. Rev. Lett.97