Topography of the graphene/Ir(111) moir{é} studied by surface x-ray diffraction
Fabien Jean, Tao Zhou, Nils Blanc, Roberto Felici, Johann Coraux, Gilles Renaud
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J un Topography of the graphene/Ir(111) moir studied by surface x-ray diffraction
Fabien Jean,
1, 2
Tao Zhou,
2, 3
Nils Blanc,
1, 2
Roberto Felici, Johann Coraux,
1, 2 and Gilles Renaud
2, 3 CNRS, Inst NEEL, F-38042 Grenoble, France Univ. Grenoble Alpes, Inst NEEL, F-38042 Grenoble, France CEA, INAC-SP2M, Grenoble, F-38054, France European Synchrotron Radiation Facility, Boˆıte Postale 220, F-38043 Grenoble Cedex 9, France (Dated: August 22, 2018)The structure of a graphene monolayer on Ir(111) has been investigated in situ in the growthchamber by surface x-ray diffraction including the specular rod, which allows disentangling theeffect of the sample roughness from that of the nanorippling of graphene and iridium along themoir-like pattern between graphene and Ir(111). Accordingly we are able to provide precise esti-mates of the undulation associated with this nanorippling, which is small in this weakly interactinggraphene/metal system and thus proved difficult to assess in the past. The nanoripplings of grapheneand iridium are found in phase, i.e. the in-plane position of their height maxima coincide, but theamplitude of the height modulation is much larger for graphene (0 . ± .
044 ˚A) than, e.g. , for thetopmost Ir layer (0 . ± .
002 ˚A). The average graphene-Ir distance is found to be 3 . ± .
04 ˚A.
Graphene, a monoatomic layer of carbon atomsarranged in a honeycomb lattice, has been investi-gated thoroughly in the past ten years because ofits exceptional properties, which hold promises fornumerous applications. Transition metal surfacesform a broad family of substrates for the growthof large area, high quality graphene. New proper-ties can be induced in graphene through the interac-tion with the substrate, e.g. electronic bandgaps, spin-polarization and superconductivity. In mostgraphene-on-metal systems, the interaction is mod-ulated at the nanoscale, due to lattice mismatch be-tween graphene and the metal, which results in two-dimensional patterns with periodicity of the orderof nanometers, often referred to as ”moirs”, follow-ing an analogy with the beating of optical wavesthrough two mismatched periodic lattices ( e.g. tis-sue veils). Knowledge on the topographic propertiesof these moirs, i.e. the average graphene-metal dis-tance, and the perpendicular-to-the-surface ampli-tude of the graphene and metal undulations acrossthe moir, is desirable in view of characterizing theinteraction and rationalizing the other properties.The topography is however hard to grasp atsuch small scales. Most efforts that have relied onscanning tunnelling microscopy have faced the is-sue of the entanglement of the structural and lo-cal density of state which is inherent to the tun-nelling effect. A striking illustration has beenthe debate on the amplitude and sign of themoir-related undulation in graphene/Ru(0001) andgraphene/Ir(111), respectively. Atomic force mi-croscopy has proven to be a valuable alternative,provided it is performed with care, especially withrespect to the possible chemical interaction between
FIG. 1. Sketch of the reciprocal space, the hexagonalgrid shows the partition of its ( H , K ) plane accordingto the 10-on-9 commensurability. H , K and L are inreciprocal lattice unit of the moir (superlattice) surfaceunit cell. In gray are shown the measured CTRs fromthe iridium, with circles to highlight the positions of thedifferent Bragg reflections. The graphene rods are shownin black. The specular CTR ( H = K =0) is shown in red.Each is labeled with its ( H , K ) position in the 10-on-9moir surface supercell. tip and sample. Scattering techniques, such aslow-energy electron diffraction (LEED), surface X-ray diffraction (SXRD), and X-ray standing waves(XSW), are free of such probe-induced perturba-tions of the systems. To the expense of com-plex calculations in the framework of the dynam-ical theory of diffraction, LEED was used to as-sess the topography of graphene/Ru(0001) and IG. 2. Experimental structure factors F H,K ( L ) of irid-ium CTRs and graphene rods from SXRD measurementsof the first sample in black with the error bars. The solidred lines represent the best fit with the Fourier model. Inblue with the rods is the contribution of a flat graphenelayer alone, to highlight the effect of the roughness andundulations on the rods. The specular rod (0,0) from thesecond sample is reported in the bottom right in blackwith error bars. The solid red line represents the final fit,the green one the contribution of the iridium alone andin blue the contribution of a flat graphene layer alone. graphene/Ir(111). SXRD was used to analyze thetopography of graphene/Ru(0001), as was done byXSW for graphene/Ir(111). Confirming and refin-ing the results obtained with these approaches isof prime importance in order to set reliable pointsof reference for first principle calculations, whichare cumbersome in essence in such systems due tothe importance of non-local ( e.g. van der Waals)interactions. Here, we address the model graphene/Ir(111) sys-tem, typical of a weak graphene-metal interaction.Its moir topography only slightly deviates from theflat case and is thus difficult to characterize. Withthe help of two techniques, SXRD and extended x-ray reflectivity (EXRR), the latter not having beenemployed to characterize monolayer graphene on asubstrate before, we deduce an average 3 . ± .
04 ˚A distance between graphene and Ir(111), and deter-mine, with an uncertainty as low as with scanningprobe microscopy, a 0 . ± .
044 ˚A amplitude ofthe graphene undulation. Besides, we are able to es-timate the undulation of the Ir layers, which is usu-ally not accessible to other techniques, 0 . ± . z axis diffractometers at the BM32 andID03 beamlines of the European Synchrotron Ra-diation Facility. Details on the chambers and thebeam are given in Ref. 15. The non-specular crys-tal truncation rods (CTRs) were measured on BM32and the specular rod, 00 L , was measured by EXRRon ID03. The x-ray beam energy was set at 11 keV.The reciprocal space scans of the scattered inten-sity presented below are all normalized to the in-tensity measured with a monitor placed before thesample. For the SXRD measurements, the intensityalong the Ir(111) crystal truncation rods (CTRs)and along the graphene rods was measured witha Maxipix two-dimensional detector in stationarymode for the upper range of the out-of-plane scat-tering vector component ( i.e. large values of theout-of-plane reciprocal space coordinate L ), and byperforming sample rocking scans for low L -values. The amplitude of the structure factors F H,K ( L ) - thesquare root of the measured intensity - for the dif-ferent CTRs and graphene rods, corresponding eachto different values of the in-plane reciprocal spaceparameters H and K , were extracted and processedwith the PyRod program described in Ref. 16. Py-Rod was also used to simulate the structure factorsusing the model described below, and to refine thestructural parameters of this model with the help ofa least squares fit of the simulation to the data. Thetotal uncertainty on the experimental structure fac-tors is dominated by the systematic error estimatedto be 6.1%, according to Ref. 16; the statistical errorbeing everywhere smaller than 1 %.The Ir single crystals were cleaned according to aprocedure described in Ref. 15 allowing for consid-erably reducing the concentration of residual carbonin bulk Ir(111). Graphene was grown in two steps,first by 1473 K annealing of a room-temperature-adsorbed monolayer of ethylene, second by exposureto 10 − mbar of ethylene the surface held at 1273K. This growth procedure allows for selecting a well-defined crystallographic orientation of purely single-layer graphene with respect to Ir(111). Comparedto the samples studied in Refs. 8 and 11, the sur-face coverage is larger (100%) in our case. Ourgrowth procedure is similar to that used to prepare2he 100%-coverage graphene studied in Ref. 18, yetthe temperatures which we chose for each step aredifferent, actually identical to those used for prepar-ing one of the samples addressed in Ref. 15. We notethat both the graphene coverage and growth temper-ature have been argued to influence the structure ofgraphene, and thus its properties. Two sampleswere prepared, one in each of the UHV chambers in-stalled at the BM32 and ID03 beamlines where theSXRD and EXRR experiments were performed re-spectively. The hexagonal lattice unit cell of theiridium surface has a lattice parameter of 2.7147 ˚Aat room temperature. The graphene unit cell has ameasured lattice parameter of 2.4530 ˚A. The ratiobetween the two lattice parameters, 0.903, is closeto 0.9. Therefore, in the following we assume thatthe system is commensurate, with a (1010) graphenecell coinciding with a (99) iridium one. In the fol-lowing, the in-plane unit cell of reciprocal space isthe moir one. This corresponds to H or K indexesmultiples of 9 and 10 for Ir CTRs and graphene rods,respectively (Fig. 1).Figure 2 shows the Ir CTRs and graphene rods.As expected for a (essentially) two-dimensional layersuch as graphene, the graphene rods are basicallyfeatureless. Qualitatively, because the undulationsof the graphene and top substrate layers are ex-pected to be small, the main features are i ) thepronounced interference effect on the specular rod F , ( L ) related to the average distance dz Gr betweenIr and graphene, expected to be larger than the bulkdistance of 2.2 ˚A; ii ) the decrease of the otherwisefeatureless CTRs in between Bragg peaks, relatedto the substrate roughness ; and iii ) the decrease ofthe graphene rods with increasing L , dominated bythe undulation of the graphene layer, as shown withthe simulated graphene rods for a flat graphene layeralone in Fig. 2. This decorrelation between rough-ness and undulation allows these parameters to bedetermined with high accuracy.In order to achieve a quantitative characteriza-tion of the topography of the system, we introducea simple model. A limited set of parameters (seeFig. 3), including the average interplanar distances, the actual roughness, and the amplitude of undu-lation of each layer, seems to be a reasonable op-tion for a simple modeling of the system. In orderto approach this description, we introduce a latticemodel based on a Fourier series, such as the one pro-posed for graphene/Ru(0001). In this model, thedisplacement in the direction i ( i = { x,y,z } ) of anatom with x , y and z coordinates, with respect tothe corresponding position in a flat layer, is given FIG. 3. Sketch of the parameters studied. In black isthe graphene and in blue, red and green are the surfacelayers of iridium. The amplitudes of their corrugationare shown by arrows in the middle. The start of thebulk iridium is sketched with the dotted black line. Thegray dashed lines represents the expected bulk positionsfor the different atomic layers without corrugation. Thez-axis on the left is a reference to the linear dependencyof the iridium corrugation amplitude. byd r i = X s,t A is,t × sin[2 π ( sx + ty )]+ B is,t × cos[2 π ( sx + ty )](1)where the sum runs over the different orders ofthe series. Due to the crystal symmetry of grapheneand Ir(111), the displacements must respect a p m i.e. they must fulfillR j − { d r [R j ( r )] } = R j { d r [R j − ( r )] } (2)with j ∈ [0,5]. R is the identity matrix, R andR correspond to the ±
120 rotations and the lastthree to the mirror planes.R = (cid:18) (cid:19) , R = (cid:18) (cid:19) , R = (cid:18) ¯1 1¯1 0 (cid:19) , R = (cid:18) (cid:19) , R = (cid:18) ¯1 10 1 (cid:19) , R = (cid:18) (cid:19) (3)These symmetry constraints impose that not all Fourier coefficients in Eq. (1) are independent.3heir relationships are given in Table I.In the following we further simplify the modelby limiting the Fourier development to first order,which is legitimate due to the fact that no significantdiffraction data is measurable beyond first order (adiffraction experiment is actually a measurement of the Fourier transform of the electronic density, thus,to a good approximation, of the shape of graphene).Besides, we assume that the undulations of all Irlayers are in phase, as found in density functionnaltheory (DFT) calculations. In this framework, the x , y and z displacements simply write:d r x = A x × (2 × sin(2 πx ) + sin(2 πy ) + sin(2 π ( x − y )))+ B x × (2 × cos(2 πx ) − cos(2 πy ) − cos(2 π ( x − y ))) (4)d r y = A x × (sin(2 πx ) + 2 × sin(2 πy ) − sin(2 π ( x − y )))+ B x × (cos(2 πx ) − × cos(2 πy ) + cos(2 π ( x − y ))) (5)d r z = A z × (2 × sin(2 πx ) − × sin(2 πy ) − × sin(2 π ( x − y )))+ B z × (2 × cos(2 πx ) + 2 × cos(2 πy ) + 2 × cos(2 π ( x − y ))) (6)Thus, only two variables per atomic plane, A x and B x , are needed to describe the in-plane displace-ments. The model is applied to graphene/Ir(111),with three iridium layers and one graphene layer.Each of these layers is characterized by four Fouriercoefficients ( A x , B x , A z and B z ), plus another pa-rameter corresponding to an average z displacementof the layer from its equilibrium position in the bulk.This distance between metal planes parallel to thesurface is known to vary, in some cases by as muchas few percents and in a non monotonous manneracross the few topmost layers of metal surfaces . Inorder to reduce the number of free parameters how-ever, we assume a linear dependence of the distancebetween Ir(111) planes, thus of of A z and B z ), as afunction of depth. This assumption complies withthe results of the DFT simulations (cf. Table II,where the topographic parameters of the model arelisted).The Fourier model was used to fit the SXRD data.The expected in-plane displacements (Fig. 4), below0.01 ˚A according to first principle calculations, haveno noticeable influence on the Ir CTRs and graphenerods, and are discarded in the simulations. Thebest fit lead to a χ value of 3.5 and the resultsare shown in Table II. We find a 98 ±
2% graphenecoverage. The graphene is found to have a meandistance of dz Gr = 3 . ± .
28 ˚A with its substrateand a corrugation of ∆ z Gr = 0 . ± .
044 ˚A. Thegraphene distance with its substrate is close to theinterlayer spacing in graphite, 3.36 ˚A. As explainedabove, the benefit of the SXRD analysis of both graphene and Ir contributions is to provide an ac-curate value of the amplitude of the graphene un-dulation perpendicular to the surface, as comparedto other techniques. The interlayer Ir spacings arefound to be 2 . ± .
012 ˚A, 2 . ± .
007 ˚A and2 . ± .
002 ˚A from top to bottom. The topmostlayer of iridium has an undulation of 0 . ± .
002 ˚A,the second layer has an undulation of 0 . ± . . ± .
001 ˚A. Finally, theroughness of the iridium substrate is found to be0 . ± .
20 ˚A, following a simple β -model. Thissmall value may be linked with the small coherencelength of the X-ray beam (corresponding to about10 flat Ir terraces separated by atomic step edges)on the BM32 beamline.
FIG. 4. Cut of the 10-on-9 commensurability to repre-sent the corrugations and displacements of the atomiclayers. Carbon atoms of the graphene are black circles,the iridium atoms are in blue, red and green to show theABC stacking of the different layers. The three coinci-dence regions of graphene with the substrate as well asthe corrugations and interlayer spacing are denoted.
The best fit between simulations and SXRD datais achieved for an iridium undulation in phase with4he graphene one, with a smaller amplitude though.This finding is at variance with that obtained in ear-lier scanning probe microscopy measurements per-formed in specific imaging conditions, and supportsthe picture progressively assembled through otherreports, based on scanning probe microscopies, XSW, and first principle calculations. The main limitation of this SXRD analysis isthe rather large uncertainty on the dz Gr distance.This motivated complementary measurements of thespecular rod on the second sample, using the ID03setup as the extended reflectivity was not accessiblein the BM32 setup. The EXRR result is shown inFig. 2 together with the best fit and simulated andgraphene specular rods. The best fit of the specularrod, yielding a χ value of 1.064, was done with asimplified model, in which the undulations of boththe iridium or graphene were fixed at the values ob-tained from the SXRD analysis. It yields a valueof dz Gr = 3.38 ˚A, very close to that determined onthe other sampler by off-specular SXRD, but with amuch better accuracy, ± ±
2% graphene coverage. In addition, the spacingsbetween the topmost Ir planes, found to be 2.203 ± ± ± This finding is consistent with the p -doping foundfor graphene which implies electron transfers fromgraphene to Ir(111). The corresponding higher elec-tronic density in Ir(111) is expected to counterbal-ance the surface relaxation in bare Ir(111). The sub-strate roughness in this case is found to be 1.1 ± e.g. around 1000 atomic steps of the substrate scatterthe beam coherently.This is the first study of a sample with a completegraphene coverage, thus the deviations from previ-ous studies can be explained due to strains in the fulllayer that can relaxe in graphene island. This couldalso be explained by the difference in the growthprocess (temperature, methods...) and Busse et al. showed that the undulation varies depending on thegraphene coverage. Moreover, the undulation couldalso be affected by the growth methods (full/partialgrowth, chemical vapor deposition, temperature pro-grammed growth...) and growth temperature as ithas been reported that these parameters affect thegraphene lattice parameter and its commensurabil-ity with the substrate. The iridium undulations are also found larger than those deduced from aLEED study. This might be due to some limita-tion of LEED to analyse layers below the grapheneone, because of the small electron mean free path.The graphene-metal distance which we obtain isin good agreement with values deduced by XSW,LEED, and AFM (see Table II). The undulation ofthe graphene which we obtain is also in agreementwith that found by LEED and AFM. It is howeversmaller than that deduced from XSW. The differ-ence might originate from two effects. First, werecently found that the in-plane lattice parameterof graphene varies as a function of the preparationmethod, which is different in Refs. 8 and 11, severalTPG cycles at 1420 K for different coverages andone TPG at 1500 K respectively, and in the presentwork, TPG at 1473 K followed by CVD at 1273 K forcomplete coverage. Given that the strain is closelyrelated to the graphene buckling (undulation), weindeed expect different undulations in each of thesereports. Second, the strain (and thus buckling) ofgraphene was argued to depend on the fraction ofedge atoms in graphene, i.e. on graphene coverage. Our results, unlike those in Refs. 8 and 11, addressclose-to-full layer graphene.The Fourier model was also tested to fit the dis-placements obtained by the DFT calculations de-scribed in Ref. 8. The model was in very good accor-dance with the DFT calculations results, in particu-lar the iridium top layer and graphene, thus confirm-ing that the first order Fourier component is enoughto describe the system, as shown in Fig 5. More-over, it also confirmed that A z and B z of the threeiridium layers have an almost linear dependence asa function of depth. From the DFT simulation, thecorrugations of the iridium surface layers from topto bottom are 0.015 ˚A, 0.012 ˚A and 0.04 ˚A whilethe graphene one is 0.35 ˚A, which are close to theexperimental results.In fact, this analysis has a limite too, as our start-ing hypothesis on the structure of the supercell, a(1010) graphene cell coinciding with a (99) irid-ium, may have an impact on the results. It wasreported previously that this system cannot be con-sider fully commensurate, as it is really a compo-sition of commensurate domains with incommensu-rate boundaries and that the thermal history of thesample effects it. Here, the 9.03 ratio indicatesthat there should be a combinaison of (1010)/(99),(2121)/(1919) and incommensurate domains. How-ever, despite the complexity of the sample, the start-ing hypothesis of the problem allows to extract agood approximation of the actual structure.To conclude we have employed SXRD to deter-5ine with high resolution, on the basis of a simplestructural model, the structure of a weakly scatter-ing atomically thin membrane, graphene, in weakinteraction with a metallic substrate made of strongscatterers, Ir atoms. We determine the undula-tion of graphene across the moir-like superstructureformed between graphene and Ir(111), 0 . ± . . ± .
002 for the topmost Ir layer, and are characteristic of a weakC-Ir bonding having a slight covalent character insome of the sites of the moir. The use of SXRD forother two-dimensional membranes, such as transi-tion metal dichalcogenides, boron nitride, or mono-layer silica, should allow for constructing a compre-hensive picture of the nanomechanics of atomicallythin membranes under the influence of substrates.We thank Olivier Geaymond, Thomas Dufraneand the staff members of the ID03 and BM32beamlines, Nicolae Atodiresei for the DFT calcu-lations data and the French Agence Nationale dela Recherche for funding (Contract No. ANR-2010-BLAN-1019-NMGEM). K. Novoselov, V. Fal’ko, L. Colombo, P. Gellert,M. Schwab, K. Kim, et al., Nature , 192 (2012). H. Tetlow, J. De Boer, I. Ford, D. Vvedensky,J. Coraux, and L. Kantorovich, Phys. Rep. , 195(2014). I. Pletikosi´c, M. Kralj, P. Pervan, R. Brako,J. Coraux, A. N’Diaye, C. Busse, and T. Michely,Phys. Rev. Lett. , 056808 (2009). A. Varykhalov, J. 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Relationships between the Fourier coefficients A is,t and B is,t ( i = { x , y , z } )SXRD (1 st sample) EXRR (2 nd sample) DFT Ref. 8 Ref. 11 dz Gr . ± .
28 3 . ± .
04 3 .
43 3 . ± .
04 3 . ± . z Gr . ± .
044 0 .
46 0 . ± . . ± . . ± . dz Ir . ± .
012 2 . ± .
010 2 .
190 2 . dz Ir . ± .
007 2 . ± .
008 2 .
175 2 . dz Ir . ± .
002 2 . ± .
004 2 .
184 2 . z Ir . ± .
002 0 .
015 0 . z Ir . ± .
001 0 .
012 0 . z Ir . ± .
001 0 .
004 0 ρ . ± .
20 1 . ± . O Gr ±
2% 89 . ±
1% 100% 39% Partial63%TABLE II. Topographic parameters for the two samples, the DFT calculations data from Ref. 8 and results fromRef. 8 (XSW) and (LEED + AFM). dz Gr is the mean distance between the graphene and its substrate; ∆ z Gr isthe graphene undulation amplitude; dz Ir , dz Ir and dz Ir are the interlayer distances of the iridium surface layersand ∆ z Ir , ∆ z Ir and ∆ z Ir are their undulation amplitudes; ρ is the roughness of the sample surface; O Gr is thegraphene coverage in percent. All the parameters are in ngstrms (˚A) except the coverage.FIG. 5. Sketches of the graphene out of plane variations from (a) the Fourier model used on the experimental dataand (b) the DFT calculations results and the out of plane variations of the topmost iridium layer from (c) the Fouriermodel used on the experimental data and (d) the DFT calculations results. with the DFT calculations results shownin left half-discs and the Fourier series fit in right half-discs The out of plane corrugation is shown with a colorgradient, with the scales in ˚A.is thegraphene coverage in percent. All the parameters are in ngstrms (˚A) except the coverage.FIG. 5. Sketches of the graphene out of plane variations from (a) the Fourier model used on the experimental dataand (b) the DFT calculations results and the out of plane variations of the topmost iridium layer from (c) the Fouriermodel used on the experimental data and (d) the DFT calculations results. with the DFT calculations results shownin left half-discs and the Fourier series fit in right half-discs The out of plane corrugation is shown with a colorgradient, with the scales in ˚A.