# Fileset

[ncomms9429.pdf](https://mdr.nims.go.jp/filesets/5673ef48-7031-40d2-b0c2-d1b4ac33a820/download)

## Creator

C. Neumann, S. Reichardt, P. Venezuela, M. Drögeler, L. Banszerus, M. Schmitz, [K. Watanabe](https://orcid.org/0000-0003-3701-8119), [T. Taniguchi](https://orcid.org/0000-0002-1467-3105), F. Mauri, B. Beschoten, S. V. Rotkin, C. Stampfer

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Raman spectroscopy as probe of nanometre-scale strain variations in graphene](https://mdr.nims.go.jp/datasets/0de49969-5e13-4aa5-8865-4162c899308f)

## Fulltext

Raman spectroscopy as probe of nanometre-scale strain variations in grapheneARTICLEReceived 20 May 2015 | Accepted 21 Aug 2015 | Published 29 Sep 2015Raman spectroscopy as probe of nanometre-scalestrain variations in grapheneC. Neumann1,2, S. Reichardt1, P. Venezuela3, M. Drögeler1, L. Banszerus1, M. Schmitz1, K. Watanabe4,T. Taniguchi4, F. Mauri5, B. Beschoten1, S.V. Rotkin1,6 & C. Stampfer1,2Confocal Raman spectroscopy has emerged as a major, versatile workhorse for thenon-invasive characterization of graphene. Although it is successfully used to determinethe number of layers, the quality of edges, and the effects of strain, doping and disorder,the nature of the experimentally observed broadening of the most prominent Raman2D line has remained unclear. Here we show that the observed 2D line width containsvaluable information on strain variations in graphene on length scales far below the laser spotsize, that is, on the nanometre-scale. This finding is highly relevant as it has been shownrecently that such nanometre-scaled strain variations limit the carrier mobility in high-qualitygraphene devices. Consequently, the 2D line width is a good and easily accessible quantityfor classifying the crystalline quality, nanometre-scale flatness as well as local electronicproperties of graphene, all important for future scientific and industrial applications.DOI: 10.1038/ncomms9429 OPEN1 JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, Aachen 52074, Germany. 2 Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich,Jülich 52425, Germany. 3 Instituto de Fsica, Universidade Federal Fluminense, Niterói, 24210-346 Rio de Janeiro, Brazil. 4 National Institute for MaterialsScience,1-1 Namiki, Tsukuba 305-0044, Japan. 5 IMPMC, UMR CNRS 7590, Sorbonne Universités—UPMC Univ. Paris 06, MNHN, IRD, 4 Place Jussieu, Paris75005, France. 6Department of Physics and Center for Advanced Materials and Nanotechnology, Lehigh University, Bethlehem, Pennsylvania 18015, USA.Correspondence and requests for materials should be addressed to C.S. (email: stampfer@physik.rwth-aachen.de).NATURE COMMUNICATIONS | 6:8429 | DOI: 10.1038/ncomms9429 | www.nature.com/naturecommunications 1& 2015 Macmillan Publishers Limited. All rights reserved.mailto:stampfer@physik.rwth-aachen.dehttp://www.nature.com/naturecommunicationsGraphene combines several highly interesting materialproperties in a unique way, promising unprecedentedmaterial functionality. This makes graphene increasinglyattractive for fundamental research as well as industrialapplications1, but, at the same time, stresses the need for non-invasive characterization techniques. In recent years, Ramanspectroscopy has proven to be highly useful as a non-invasivemethod not only to identify graphene2,3 but also to extractinformation on doping4–7, strain8,9 and lattice temperature10,11.Even more insights can be gained when utilizing confocal,scanning Raman spectroscopy to study spatially resolved dopingdomains7,12, edge effects3,13 and position-dependent mechanicallattice deformations, including strain14–16. The spatial resolutionof so-called Raman maps is on the order of the laser spot size(which for confocal systems is typically on the order of 500 nm)and the extracted quantities (such as doping or strain) are ingeneral averaged over the spot size. It is therefore important todistinguish between length scales significantly larger or smallerthan the laser spot size. In particular, we will distinguish betweenstrain variations on a micrometre scale, which can be extractedfrom spatially resolved Raman maps, and nanometre-scale strainvariations, which are on sub-spot-size length scales and cannot bedirectly observed. Especially, nanometre-scale strain variationshave been recently identified as the most important limitation tocarrier mobility in high-quality graphene17, making this quantityincreasingly important18.In this article, we show that the experimentally observedRaman 2D line width is a measure of nanometre-scale strainvariations in graphene on insulating substrates, that is, it containsvaluable information on local (that is, nanometre-scale) flatness,lattice deformations and crystal quality of graphene. Our findingssolve the long-standing question of the nature of the observedbroadening of the Raman 2D line and also link this quantity tothe electronic transport properties of graphene, making it avaluable quantity for classifying the quality of graphene. To provethat the experimentally observed 2D line width depends on sub-spot-size strain variations and lattice deformations, we employthe following strategy.We start by showing that by combining Raman spectroscopywith magnetic fields, electronic broadening contributions forthe Raman G line width can be strongly suppressed. Sincein perpendicular magnetic fields the electronic states ingraphene condense into Landau levels (LLs), the interactionbetween electronic excitations and lattice vibrations becomesB-field dependent. In agreement with existing theory19–22 andexperiments23,24, we demonstrate that by applying aperpendicular B-field of B8T, the G line becomes almostindependent of electronic properties such as charge carrierdoping, screening, or electronic broadening.We observe that, under these conditions, the G line widthnevertheless exhibits strong variations across graphene flakes. Inparticular, we show that the G line width is significantly increasedin regions where the graphene flake features bubbles and folds,that is, in correspondence with increased structural deformations.Finally, we show that at 8 T, there is a (nearly) lineardependence between the G line width and the 2D line width,implying that there is a common source of line broadening.According to the previous points, the broadening must be relatedto structural lattice deformations. This finding is furthersupported by a detailed analysis of the relation between the areaof the 2D peak and its line width. By analysing the relationbetween the G and 2D line width, we find that nanometre-scalestrain variations constitute a dominant contribution to theobserved line broadenings. Importantly, the 2D line has beenshown to only very weakly depend on the B-field25, implying thatno magnetic field is required to extract information onnanometre-scale strain variations from the 2D line width,which makes this quantity interesting for practical applications.ResultsSample characterization. The investigated graphene (Gr) sheet ispartly encapsulated in hexagonal boron nitride (hBN) and partly2,6702,6802,6902,7002,7102,7201,580 1,590 1,6002.2hBN (I) SiO2  (II)1,200 1,600 2,400 2,800Raman shift (cm–1 )cd15 25 3520 3010Counts (a.u.)ghihBN intensity (a.u.) 2,680 2,690 2,700 2,7100102030405051015202501,580 1,585 1,590 1,595�G (cm–1)�2D (cm–1)fGraphene�2D (cm–1)�2D (cm–1)�G (cm–1)�2D (cm–1)SiO2hBNII IIebIIIISiO2-Gr-hBNhBN-Gr-hBNIIIIIntensity (a.u.)daSiO2-Gr-hBN22.7Intensity (a.u.)1,200 1,600 2,400 2,800IIIIII�G (cm–1)hBN-Gr-hBN17.2hBN G 2D Figure 1 | Graphene sample characterization. (a) Schematic representation of cross-section of the investigated sample highlighting the different regions I(hBN-Gr-hBN) and II (SiO2-Gr-hBN). (b) Optical image of a Gr-hBN heterostructure resting partly on hBN and SiO2. Scale bar, 10 mm. (c,d) Ramanspectrum taken on the SiO2-Gr-hBN (c) and hBN-Gr-hBN (d) areas. The positions where the spectra were taken are marked by a blue and a red star,respectively (b). (e) Raman map of the intensity of the hBN peak. The dashed lines mark the regions I and II. (f) GG versus oG recorded on various spots onregions I (blue) and II (red) of the sample. (g) G2D versus o2D recorded on various spots on regions I (blue) and II (red) of the sample. (h) Histograms ofG2D recorded on various spots on regions I (blue) and II (red) of the sample. (i) o2D versus oG recorded on various spots on regions I (blue) and II (red) ofthe sample.ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms94292 NATURE COMMUNICATIONS | 6:8429 | DOI: 10.1038/ncomms9429 | www.nature.com/naturecommunications& 2015 Macmillan Publishers Limited. All rights reserved.http://www.nature.com/naturecommunicationssandwiched between SiO2 and hBN as illustrated in Fig. 1a. Anoptical image of our sample is shown in Fig. 1b. In contrast tographene encapsulated in hBN, graphene flakes supported by SiO2usually feature lower carrier mobilities of around 103–104 cm2/(Vs),indicating a detrimental influence of SiO2 on the electronic prop-erties of graphene. In this regard, our structure gives us theinvaluable capability of probing a single graphene sheet exposed totwo different substrates (regions I and II in Fig. 1a,b). The sample isfabricated with a dry and resist-free transfer process followingWang et al.26 and Engels et al.27, where we pick up an exfoliatedgraphene flake with an hBN flake and deposit it onto the hBN-SiO2transition area of the substrate. A typical Raman spectrum ofgraphene supported by SiO2 and covered by hBN, taken at theposition of the red star in Fig. 1b, is shown in Fig. 1c. Thecharacteristic hBN line as well as the graphene G and 2D lines canbe clearly identified. At first glance, the spectra recorded in thehBN-Gr-hBN area look similar (see Fig. 1d, taken at the positionmarked by the blue star in Fig. 1b). However, it is evident that thefull-width at half-maximum (FWHM) of the 2D line, G2D, issignificantly smaller.The confocal nature of our Raman setup enables us to dospatially resolved measurements. An example of a Raman map isshown in Fig. 1e, where the spatially resolved intensity of the hBNline is depicted. The hBN and SiO2 areas can be clearlydistinguished in the map (see highlighted regions I and II).While analysing the Raman spectra of every point on the map, itis evident that the G lines recorded in the hBN-encapsulated areaare broader than in the SiO2 supported area (compare red andblue data points in Fig. 1f). This is a clear indication of reducedcharge carrier doping induced by the hBN substrate comparedwith SiO2. In fact, at low charge carrier doping, the phonon modecan decay into electron–hole pairs, which results in a broadeningof the G peak5,28. For the 2D line, in contrast, the G2D recorded inthe hBN-encapsulated area is mostly between 17 cm� 1 and20 cm� 1, while it is above 22 cm� 1 in the SiO2 area (see blue andred curves in the histogram of Fig. 1h, respectively). Note thatboth G2D and GG do not depend on the respective frequencieso2D and oG (Fig. 1f,g). In Fig. 1i the position of the G and 2Dlines for every spectrum obtained on the investigated graphenesheet are displayed. For both substrates, the data points scatteralong a line with a slope of 2.2. This slope coincides with the ratioof strain-induced shifts (that is, of the related Grüneisenparameters) of the Raman G and 2D modes29. This indicatesthat there are significant strain variations on both substratesacross the entire graphene layer. Assuming the strain to be ofbiaxial nature, the spread of the data points translates into amaximum, micrometre-scale strain variation of B0.14% (ref. 29).The offset of the SiO2 and hBN data points can be understood interms of the higher charge carrier doping induced by the SiO2substrate, which shifts the data points towards higher values ofoG (ref. 5), and differences in the dielectric screening of hBN andSiO2 that effectively shift the 2D line position30. Since the datastems from a single graphene flake that has undergone identicalfabrication steps for both substrate regions, the difference incharge carrier doping is unambiguously because of the twodifferent substrate materials.Suppressing electronic broadening with a magnetic field. Fora more refined comparison of the Raman spectra on bothsubstrates, we seek to suppress the effects on the G line arisingfrom these differences in charge carrier doping. We thereforeminimize the influence of the electronic system on the Raman Gline by applying a perpendicular magnetic field. In the presence ofa perpendicular magnetic field, the electronic states in graphenecondense into LLs. The coupling of these LLs to the G mode iswell understood19,20 and experimentally confirmed22–24,31–36.When a LL transition energetically matches the G mode phonon,the position of the G line is shifted and its line width increases.An example for the evolution of the Raman G peak with magneticfield, taken on the hBN sandwich area, is shown in Fig. 2a. Theindividual spectra are offset for clarity. For a detailed analysis,single Lorentzians are fitted to every spectrum. The resultingfrequency, oG, and FWHM, GG, are displayed in Fig. 2b,c,respectively. The arrow at B¼ 3.7 T (Fig. 2c) shows a value of themagnetic field where a LL transition is energetically matched withthe phonon, leading to a broadening of the G line. However, atmagnetic fields around 8 T, no LL transition is energetically closeto the G mode, as illustrated in Fig. 2d, where the energies of therelevant LL transitions as a function of magnetic field arecompared with the energy of the G mode phonon. Consequently,at this high magnetic field the influence of the electronic systemon the position and width of the G line is minimized. Note thatthis effect is independent of the charge carrier density and theexact values of the broadening of the LL transitions assuming thatthe latter are within a reasonable range as found by otherstudies24,35. Thus, the residual broadening of the G line is mostlikely determined by phonon–phonon scattering and averagingeffects over different strain values that vary on a nanometre scale.Strain variations within the laser spot. To demonstrate that thisapplies to the entire sample, we first show that the broadening ofthe electronic states is low enough on the entire hBN-Gr-hBNarea. In Fig. 3a,b, we show maps of GG at B¼ 0 and 3.8 T,respectively. On the hBN part, the width of the G line shows the1020301,5801,5851,590�G (cm–1)�G (cm–1)Intensity (a. u.)1,580 1,600a bcRaman shift (cm–1) B (T)100200300Energy (meV)0  02 4 6 80d�ph2 4 6 80Figure 2 | Magneto-Raman spectroscopy. (a) Raman spectra recorded asa function of magnetic field, ranging from 0T (bottom spectrum) to 8.9 T(top spectrum). The spectra are vertically offset for clarity. (b,c) Frequency,oG, and FWHM, GG, of the G peak as a function of magnetic field asobtained from Lorentzian fits to the data shown in a. The arrow (c)highlights a value of the magnetic field at which the phonon is energeticallymatched to a LL transition. (d) Evolution of the energies of LL transitionswith magnetic field. The full lines represent inter-band transitions in whichthe LL index changes by one. The dashed lines represent inter-bandtransitions in which the LL index does not change. The red line representsthe G mode phonon frequency at zero B field. The circled region in (c,d)highlights the region in which no LL transitions energetically match theG mode phonon.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9429 ARTICLENATURE COMMUNICATIONS | 6:8429 | DOI: 10.1038/ncomms9429 | www.nature.com/naturecommunications 3& 2015 Macmillan Publishers Limited. All rights reserved.http://www.nature.com/naturecommunicationsresonant behaviour depicted in Fig. 2c (see also histogram inFig. 3d). This effect happens throughout the entire hBN area,independent of the local doping and strain values and indepen-dent of possible local folds and bubbles. The suppression ofmagneto-phonon resonances on the SiO2 substrate can beattributed to the higher charge carrier density. At higher chargecarrier density the needed LL transitions are blocked by the Pauliprinciple. In the next step, we tune the magnetic field to 8 T,where the electronic influences on the Raman G line are at aminimum. A map of GG over the entire flake at a magnetic field of8 T is shown in Fig. 3c. Distinct features across the whole sampleare visible as regions with increased line width. A comparisonwith a scanning force microscope image of the sample (Fig. 3e)reveals that many of these regions can be associated with foldsand bubbles most likely induced during the fabrication process,some of which even cross the border between the underlying hBNand SiO2 substrate regions.As electronic broadening effects are suppressed at 8 T, theincreased line width of the G line in the vicinity of these latticedeformations arises from enhanced phonon–phonon scatteringand/or an averaging effect over varying nanometre-scale strainconditions.Interestingly, the same features can also be identified in a G2Dmap recorded at B¼ 0 T, shown in Fig. 3f. This strongly suggeststhat the lattice deformations identified at 8 T in GG also cause abroadening of the 2D mode. The same trend is highlighted inFig. 4a, where we show the relation of GG and G2D for all recordedRaman spectra at 8 T. The additional teal data points stem from aGr-SiO2 sample and the orange star originates from a differenthBN-Gr-hBN sandwich structure with all data having beenobtained at 8 T. Notably, the points from all substrate regions lieon one common line. From this linear relation between G2D andGG (Fig. 4a), we conclude that there must be a common source ofline broadening, which is connected to structural deformations.This is mainly due to the fact that at 8 T the G-line broadening isonly very weakly affected by electronic contributions (see above).The range of the presented scatter plot can be extended byincluding data recorded on low-quality graphene samples withsignificant doping, as shown in Fig. 4b. Here, no magnetic fieldbut high doping (corresponding to Fermi energies much higherthan half of the phonon energy ‘oph/2E100meV) is used tosuppress Landau damping of the G mode, leaving GG unaffectedfrom electronic contributions. The coloured data points stemfrom Raman maps (B¼ 0 T) of chemical vapour deposition(CVD)-grown graphene flakes that were transferred onto SiO2 bya wet chemistry-based transfer. These graphene sheets containdoping values of nel43� 1012 cm� 2, which corresponds toFermi energies EF4200meV (Supplementary Figs 1 and 2). Thedata points show the same trend as the values obtained at 8 T(grey data points in Fig. 4b) and even extend the total range of thedependence to higher values of G2D.DiscussionAlthough the linear relation between GG and G2D in Fig. 4a,bshows that structural deformations also broaden the 2D line,it is less straightforward to identify the actual mechanism ofbroadening. In principle, it is possible that the high values of G2Daround folds and bubbles are due to a combination of increasedphonon–phonon scattering, averaging effects over different strainvalues within the laser spot and reduced electronic life times.However, interestingly the slopes in Fig. 4a,b are around 2.2 (seeblack lines). This is a remarkable resemblance to the strain-induced frequency shifts of both modes (compare Fig. 1i). Thisprovides very strong indication that averaging over differentstrain values, which vary on a nanometre scale (see Fig. 4c), playan important role in the broadening of the experimentallyobserved 2D line. This averaging effect broadens the G and 2Dline by the same ratio as their peak positions shift for fixedaverage strain values explaining the slope of 2.2 between GG andhBN0 T10 20 305 15 25 358 T 3.8 TCounts (a.u.)SiO20355B= 0 T1015202530�G (cm–1)b301020hBNHeight (nm)0206040B= 3.8 T B= 8 Ta ce fdSiO2�2D (cm–1)�G (cm–1)Figure 3 | Sample morphology probed by Raman spectroscopy. (a–c) Raman maps of the FWHM of the G peak, GG, taken at different magnetic fields,B¼0T (a), 3.8 T (b) and 8 T (c). The different regions I and II (labelled in Fig. 1a) can be well distinguished in all three panels. (d) Histograms of GG forthe different magnetic fields, B¼0T (blue), 3.8 T (red), B¼8T (grey) and the two substrates hBN (top panel) and SiO2 (bottom panel). (e) SFM image ofthe investigated sample. The scale bar represents 5 mm. (f) Raman map of G2D recorded at 0 T. The arrows highlight mechanical folds visible in theSFM image as well as in the Raman maps (c,e,f). SFM, scanning force microscopy.ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms94294 NATURE COMMUNICATIONS | 6:8429 | DOI: 10.1038/ncomms9429 | www.nature.com/naturecommunications& 2015 Macmillan Publishers Limited. All rights reserved.http://www.nature.com/naturecommunicationsG2D (Supplementary Fig. 3), which we demonstrate with a simpletoy model as shown in Fig. 5. Each individual Raman process thattakes place within the laser spot is subject to a different amount ofstrain since the latter varies across the laser spot. Each of thecorresponding Raman peaks is thus shifted by a different amount(see blue and dashed cyan curves in Fig. 5a). The intrinsicbroadening of each individual Raman process is assumed to beGG¼ 5 cm� 1 and G2D¼ 17 cm� 1. Due to the size of the laserspot, the sum of several of these individual Raman processes isrecorded, with the resulting peak being given by the sum of theindividual peaks (see blue curve in Fig. 5b). Following the dataanalysis of our measurements, the resulting curve is fitted by asingle Lorentzian (red curve in Fig. 5b). To simulate the effect ofthis statistical broadening mechanism on the width of theresulting Raman peak, we simulate statistical strain distributionsfor several laser spots that are subject to different amounts ofstrain variation De in Fig. 5c. For each of the red points, 20 strainvalues were randomly generated. Each set of strain values followsa Gaussian distribution centred at �e¼ � 0.1% with a widthvarying from De¼ 0 to 0.15%. The dashed black line has a slopeof 2.2 and matches the distribution of the red points, illustratingthat averaging over nanometre-scale variations leads to a lineardependence of GG and G2D.We are aware that the low charge carrier densities in thehBN-encapsulated area might result in a narrowing of the 2Dmode by three to four wave numbers37. However, the largedifferences of G2D on the order of 20–30 cm� 1 on both substratescannot be explained by the differences in charge carrierdoping7,37,38.Interestingly, the lowest G2D observed in our experiments arevery close to the value that we compute from first-principles asby Venezuela et al.38 assuming an undoped, defect-free andstress-free sample of graphene (horizontal dashed and dottedlines in Fig. 4a,b). In such an approach, the width of the 2D peakis determined by the anharmonic decay rate of the two phononsinvolved (5.3 cm� 1 according to Paulatto et al.39), and, indirectly,B= 8 T203040505 10 15 20 5 10 15 2020304050a b�2D (cm–1)�2D (cm–1)�2D (cm–1)�2D (cm–1)0 0c2.2152025303540de8 T0 T10100 0.5 1 1.5 2Area2D (a.u.)Area2D (a.u.)0 0.5 1 1.5 21015202530354010�G (cm–1) �G (cm–1)Figure 4 | Nanometre-scale strain variations. (a) GG versus G2D recorded on various points on the hBN part (blue) and SiO2 (red) of the sample at amagnetic field of 8 T. Additional data points from a graphene-on-SiO2 sample (teal) and a second hBN-Gr-hBN sample (orange star) are shown. (b) Thedata points of (a) are depicted in grey. The coloured data are recorded on four different CVD graphene flakes on SiO2 substrate at 0 T. All four sampleshave doping values of nel43� 1012 cm� 2, such that Landau damping of the G line is suppressed. The dashed and dotted lines in (a,b) indicate thecalculated values of G2D from DFT calculations including electron–phonon and phonon–phonon broadening (dotted line) and electron–phonon, electron–eletron and phonon–phonon broadening (dashed line). (c) Two schematic illustrations of nanometre-scale strain variations (top: large variations; bottom:small variations). (d) G2D versus the integrated area of the 2D peak as obtained from single Lorentzian fits for the hBN part (blue) and SiO2 (red) measuredat 8 T. Both data clouds are scaled to an average area2D value of one. (e) Similar plot as in panel (d) but for 0 T. The solid black line is the calculateddependence of G2D and area2D for varying electronic broadening from the first-principles calculations, specified in the text and in Venezuela et al.38. Thedashed and dotted black lines are the same as in (a,b). DFT, density-functional theory.5 10 150152025303540c�2D (cm–1)2.22,650 2,700Intensity (a.u.)Intensity (a.u.)ab2,650 2,700Raman shift (cm–1)Raman shift (cm–1)�G (cm–1)Figure 5 | Illustration of line broadening due to averaging effects.(a,b) Individual Raman processes within the laser spot (a) add up to abroad Raman peak that is recorded (blue peak in b). The red curve in (b) isa Lorentzian fit to the blue line. The dashed cyan lines, representing the twooutmost individual Raman processes, are the same in (a,b) and serve as aguide to the eye. (c) Width of the statistical broadened Raman G and 2Dpeaks as obtained from a simple statistical model. The procedure describedin (a,b) was performed for different sets of strain variations. Each set ofstrain values follows a Gaussian distribution centred at �e¼ �0.1% with awidth varying from De¼0–0.15%. The resulting G and 2D peaks are fittedwith a single Lorentzian with the respective widths represented by a redpoint. The dashed black line has the slope of 2.2. It matches to thegenerated data points indicating that strain variations within the laser spotbroaden the G and 2D lines by this ratio.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9429 ARTICLENATURE COMMUNICATIONS | 6:8429 | DOI: 10.1038/ncomms9429 | www.nature.com/naturecommunications 5& 2015 Macmillan Publishers Limited. All rights reserved.http://www.nature.com/naturecommunicationsby the broadening of the electron and hole, denoted as g inVenezuela et al.38 (see also Basko40). According to ReferenceVenezuela et al.38, the electron–phonon contribution to g is81.9meV for electronic states in resonance with the 2.33 eV laser-light. With such a value of g we obtain a G2D of 12.1 cm� 1(dotted lines in Fig. 4a,b,e). If, following Herziger et al.41, wedouble the value of g to account for the electron–electronscattering, we obtain a G2D of 17.9 cm� 1 (dashed lines inFig. 4a,b,e), in close agreement with the lowest measured values.In principle, the observed increase of G2D with respect to itsminimum value could be attributed to an increase ofthe electronic broadening g, due to doping (increasing theelectron–electron scattering) or to the presence of defects(increasing the electron-defect scattering)38,40,42. Byinvestigating the relation between G2D and the integrated areaof the 2D peak (area2D) we can exclude such a hypothesis.In Fig. 4d,e we show scatter plots of G2D versus theregion-normalized area2D for both B¼ 8 T and B¼ 0 T,highlighting the very weak B-field dependence of G2D. Moreimportantly, we observe that the area of the 2D peak doesnot depend on G2D, contrary to what is expected in presenceof a variation of the electronic broadening g (refs 38,40,42). Inparticular the measured data does not follow the calculateddependence of G2D on area2D, reported in Fig. 4e, obtained in thecalculation by varying electronic broadening g. This dismissesdifferences in the electronic broadening as a main mechanism forthe observed variations of G2D.Finally, our finding that the 2D line depends on nanometre-scale strain inhomogeneities is also in good agreement with high-resolution scanning tunnelling microscopy measurements, whichreveal that graphene on SiO2 forms short-ranged corrugations,while graphene on hBN features significantly flatter areas43.In summary, we showed that by using a magnetic field of 8 T tostrongly suppress the influence of the electronic contributions onthe Raman G line width, the latter can be used as a measurefor the amount of nanometre-scale strain variations. Mostimportantly, we observed a nearly linear dependence betweenthe G and 2D line widths at 8 T independent of the substratematerial, indicating that the dominating source of the spreadof the broadening of both peaks is the same. From the slopeDG2D/DGG of around 2.2, we deduce that averaging effects overnanometre-scale strain variations make a major contribution tothis trend. Since the 2D line width shows only a very weakdependence on the B field, this quantity can even be used withouta magnetic field to gain information on the local strainhomogeneity and thus on the structural quality of graphene.These insights can be potentially very valuable for monitoringgraphene fabrication and growth processes in research andindustrial applications, where a fast and non-invasive control ofgraphene lattice deformations is of great interest.MethodsRaman spectroscopy measurements. The room temperature Raman spectrawere acquired using a commercial Witec system with a laser excitation of 532 nm(2.33 eV) delivered through a single-mode optical fibre, where the spot size islimited by diffraction. Using a long working distance focusing lens with anumerical aperture of 0.80, we obtained a spot size of B400–500 nm. For the low-temperature Raman measurements, we employ a commercially available confocalRaman setup that allows us to perform spatially resolved experiments at a tem-perature of 4.2 K and magnetic fields of up to 9 T. We use an excitation laserwavelength of 532 nm with a spot diameter on the sample of B500 nm. Fordetection, we use a single-mode optical fibre and a charge-coupled spectrometerwith a grating of 1,200 linesmm� 1. All measurements are performed with linearlaser polarization and a � 100 objective.First-principles calculations. For the computation of the double-resonant Ramancross-section we employ an approach based on Fermi’s golden rule generalized tothe fourth perturbative order as described in detail in Reference Venezuela et al.38.In this approach, electron–light, and electron–phonon scattering matrix elementsare explicitly calculated and the phonon and electronic dispersions reproducecalculations based on density-functional theory corrected with GW. Convergedresults are obtained using 480� 480 and 240� 240 grids in the Brillouin zone forthe electron and phonon wave-vectors, respectively. The finite phonon life time istaken into account by broadening the Raman intensity with 5.3 cm� 1 wideLorentzians39. We varied the electron broadening (g in eq. (5) from Venezuelaet al.38) from 16.4 to 344meV and then we determined G2D as a function of area2D.For a laser energy of 2.33 eV, the electron–phonon contribution for the electronicbroadening is 81.9meV, which leads to G2D¼ 12.1 cm� 1. However, when wechoose g to be twice this value, to account for additional electron–electroninteraction41, we obtain G2D equal to 17.9 cm� 1. These values can be understoodas a theoretical expectation of the 2D line width for a perfect graphene latticedisregarding any broadening from averaging effects over different strain valueswithin the laser spot.References1. Novoselov, K. S. et al. A roadmap for graphene. Nature 490, 192–200 (2012).2. Ferrari, A. et al. Raman spectrum of graphene and graphene layers. Phys. Rev.Lett. 97, 187401 (2006).3. Graf, D. et al. Spatially resolved Raman spectroscopy of single- and few-layergraphene. Nano. Lett. 7, 238–242 (2007).4. Ferrari, A. C. Raman spectroscopy of graphene and graphite: disorder, electron-phonon coupling, doping and nonadiabatic effects. Solid State Commun. 143,47–57 (2007).5. Yan, J., Zhang, Y., Kim, P. & Pinczuk, A. Electric field effect tuning of electron-phonon coupling in graphene. Phys. Rev. Lett. 98, 166802 (2007).6. Pisana, S. et al. Breakdown of the adiabatic Born-Oppenheimer approximationin graphene. Nat. Mater. 6, 198–201 (2007).7. Stampfer, C. et al. Raman imaging of doping domains in graphene on SiO2.Appl. Phys. Lett. 91, 241907 (2007).8. Mohr, M., Maultzsch, J. & Thomsen, C. Splitting of the Raman 2D band ofgraphene subjected to strain. Phys. Rev. B 82, 201409 (2010).9. Huang, M., Yan, H., Heinz, T. F. & Hone, J. Probing strain-inducedelectronic structure change in graphene by Raman spectroscopy. Nano. Lett.10, 4074–4079 (2010).10. Calizo, I., Balandin, A., Bao, W., Miao, F. & Lau, C. Temperature dependenceof the Raman spectra of graphene and graphene multilayers. Nano. Lett. 7,2645–2649 (2007).11. Balandin, A. A. et al. Superior thermal conductivity of single-layer graphene.Nano Lett. 8, 902–907 (2008).12. Drögeler, M. et al. Nanosecond spin lifetimes in single-and few-layergraphene-hBN heterostructures at room temperature. Nano Lett. 14,6050–6055 (2014).13. Casiraghi, C. et al. Raman spectroscopy of graphene edges. Nano Lett. 9,1433–1441 (2009).14. Mohiuddin, T. et al. Uniaxial strain in graphene by Raman spectroscopy: Gpeak splitting, Grüneisen parameters, and sample orientation. Phys. Rev. B 79,205433 (2009).15. Zabel, J. et al. Raman spectroscopy of graphene and bilayer under biaxial strain:bubbles and balloons. Nano Lett. 12, 617–621 (2012).16. Yoon, D., Son, Y.-W. & Cheong, H. Strain-dependent splitting of the double-resonance Raman scattering band in graphene. Phys. Rev. Lett. 106, 155502(2011).17. Couto, N. J. et al. Random strain fluctuations as dominant disorder source forhigh-quality on-substrate graphene devices. Phys. Rev. X 4, 041019 (2014).18. Banszerus, L. et al. Ultrahigh-mobility graphene devices from chemical vapordeposition on reusable copper. Sci. Adv. 1, e1500222 (2015).19. Ando, T. Magnetic oscillation of optical phonon in graphene. J. Phys. Soc. Jpn76, 024712 (2007).20. Goerbig, M., Fuchs, J.-N., Kechedzhi, K. & Fal’ko, V. I. Filling-factor-dependentmagnetophonon resonance in graphene. Phys. Rev. Lett. 99, 087402 (2007).21. Kashuba, O. & Fal’ko, V. I. Role of electronic excitations in magneto-Ramanspectra of graphene. New. J. Phys. 14, 105016 (2012).22. Qiu, C. et al. Strong magnetophonon resonance induced triple G-modesplitting in graphene on graphite probed by micromagneto Ramanspectroscopy. Phys. Rev. B 88, 165407 (2013).23. Yan, J. et al. Observation of magnetophonon resonance of Dirac fermions ingraphite. Phys. Rev. Lett. 105, 227401 (2010).24. Neumann, C. et al. Low B field magneto-phonon resonances in single-layer andbilayer graphene. Nano. Lett. 15, 1547–1552 (2015).25. Faugeras, C. et al. Effect of a magnetic field on the two-phonon Ramanscattering in graphene. Phys. Rev. B 81, 155436 (2010).26. Wang, L. et al. One-dimensional electrical contact to a two-dimensionalmaterial. Science 342, 614–617 (2013).27. Engels, S. et al. Impact of thermal annealing on graphene devicesencapsulated in hexagonal boron nitride. Phys. Status Solidi B 251, 2545–2550(2014).ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms94296 NATURE COMMUNICATIONS | 6:8429 | DOI: 10.1038/ncomms9429 | www.nature.com/naturecommunications& 2015 Macmillan Publishers Limited. All rights reserved.http://www.nature.com/naturecommunications28. Casiraghi, C., Pisana, S., Novoselov, K., Geim, A. & Ferrari, A. Raman fingerprintof charged impurities in graphene. Appl. Phys. Lett. 91, 233108 (2007).29. Lee, J. E., Ahn, G., Shim, J., Lee, Y. S. & Ryu, S. Optical separation of mechanicalstrain from charge doping in graphene. Nat. Commun. 3, 1024 (2012).30. Forster, F. et al. Dielectric screening of the Kohn anomaly of graphene onhexagonal boron nitride. Phys. Rev. B 88, 085419 (2013).31. Faugeras, C. et al. Magneto-Raman scattering of graphene on graphite:electronic and phonon excitations. Phys. Rev. Lett. 107, 036807 (2011).32. Faugeras, C. et al. Probing the band structure of quadri-layer graphene withmagneto-phonon resonance. New J. Phys. 14, 095007 (2012).33. Faugeras, C. et al. Tuning the electron-phonon coupling in multilayer graphenewith magnetic fields. Phys. Rev. Lett. 103, 186803 (2009).34. Kossacki, P. et al. Circular dichroism of magnetophonon resonance in dopedgraphene. Phys. Rev. B 86, 205431 (2012).35. Kim, Y. et al. Measurement of filling-factor-dependent magnetophononresonances in graphene using Raman spectroscopy. Phys. Rev. Lett. 110, 227402(2013).36. Leszczynski, P. et al. Electrical switch to the resonant magneto-phonon effect ingraphene. Nano. Lett. 14, 1460–1466 (2014).37. Berciaud, S. et al. Intrinsic line shape of the Raman 2D-mode in freestandinggraphene monolayers. Nano. Lett. 13, 3517–3523 (2013).38. Venezuela, P., Lazzeri, M. & Mauri, F. Theory of double-resonant Ramanspectra in graphene: intensity and line shape of defect-induced and two-phonon bands. Phys. Rev. B 84, 035433 (2011).39. Paulatto, L., Mauri, F. & Lazzeri, M. Anharmonic properties from a generalizedthird-order ab initio approach: theory and applications to graphite andgraphene. Phys. Rev. B 87, 214303 (2013).40. Basko, D. M. Theory of resonant multiphonon Raman scattering in graphene.Phys. Rev. B 78, 125418 (2008).41. Herziger, F. et al. Two-dimensional analysis of the double-resonant 2D Ramanmode in bilayer graphene. Phys. Rev. Lett. 113, 187401 (2014).42. Basko, D., Piscanec, S. & Ferrari, A. Electron-electron interactions and dopingdependence of the two-phonon Raman intensity in graphene. Phys. Rev. B 80,165413 (2009).43. Lu, C.-P., Li, G., Watanabe, K., Taniguchi, T. & Andrei, E. Y. MoS2: choicesubstrate for accessing and tuning the electronic properties of graphene. Phys.Rev. Lett. 113, 156804 (2014).AcknowledgementsWe thank T. Khodkov for support during the measurements. Support by the HelmholtzNanoelectronic Facility (HNF), the Deutsche Forschungsgemeinschaft through SPP1459, the ERC (GA-Nr. 280140) and the EU project Graphene Flagship (contract no.NECT-ICT-604391), are gratefully acknowledged. P.V. acknowledges financial supportfrom the Capes-Cofecub agreement. The work of S.V.R. was partially supported by NSF(ECCS-1509786) and the CORE grant from Lehigh University.Author contributionsC.S., C.N., B.B. and S.V.R. conceived the experiment. C.N. and M.D. carried outthe optical measurements. C.N. fabricated the exfoliated graphene samples. L.B.and M.S. fabricated the CVD graphene samples. K.W. and T.T. synthesized the hBNsamples. P.V. and F.M. performed the first-principles calculations. C.N., S.R. andS.V.R. performed data analysis and theoretical analysis. C.N., S.R., S.V.R., B.B., P.V., F.M.and C.S. co-wrote the manuscript. All authors discussed the results and commented onthe paper.Additional informationSupplementary Information accompanies this paper at http://www.nature.com/naturecommunicationsCompeting financial interests: The authors declare no competing financial interests.Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/How to cite this article: Neumann, C. et al. Raman spectroscopy as probe of nanometre-scale strain variations in graphene. Nat. Commun. 6:8429 doi: 10.1038/ncomms9429(2015).This work is licensed under a Creative Commons Attribution 4.0International License. The images or other third party material in thisarticle are included in the article’s Creative Commons license, unless indicated otherwisein the credit line; if the material is not included under the Creative Commons license,users will need to obtain permission from the license holder to reproduce the material.To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/NATURE COMMUNICATIONS | DOI: 10.1038/ncomms9429 ARTICLENATURE COMMUNICATIONS | 6:8429 | DOI: 10.1038/ncomms9429 | www.nature.com/naturecommunications 7& 2015 Macmillan Publishers Limited. All rights reserved.http://www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationshttp://npg.nature.com/reprintsandpermissionshttp://npg.nature.com/reprintsandpermissionshttp://creativecommons.org/licenses/by/4.0/http://www.nature.com/naturecommunications Raman spectroscopy as probe of nanometre-scale strain variations in graphene Introduction Results Sample characterization Suppressing electronic broadening with a magnetic field Strain variations within the laser spot Discussion Methods Raman spectroscopy measurements First-principles calculations Additional information Acknowledgements References