Strain superlattices and macroscale suspension of Graphene induced by corrugated substrates
Antoine Reserbat-Plantey, Dipankar Kalita, Laurence Ferlazzo, Sandrine Autier-Laurent, Katsuyoshi Komatsu, Chuan Li, Raphaël Weil, Zheng Han, Sandrine Autier-Laurent, Arnaud Ralko, Laetitia Marty, Sophie Guéron, Nedjma Bendiab, Hélène Bouchiat, Vincent Bouchiat
SStrain superlattices and macroscale suspension of Grapheneinduced by corrugated substrates
Antoine Reserbat-Plantey, ∗ Dipankar Kalita, Laurence Ferlazzo, SandrineAutier-Laurent, Katsuyoshi Komatsu, Chuan Li, Rapha¨el Weil, ZhengHan, Sandrine Autier-Laurent, Arnaud Ralko, Laetitia Marty, SophieGu´eron, Nedjma Bendiab, H´el`ene Bouchiat, and Vincent Bouchiat Univ. Grenoble Alpes, CNRS, I. Neel, F-38000 Grenoble, France Laboratoire de photonique et de Nanostructures, CNRS, Marcoussis, France Laboratoire de Physique des Solides,Universit´e Paris-Sud-CNRS, Orsay, France (Dated: 11 novembre 2018)
R´esum´e
We investigate the organized formation of strain, ripples and suspended features in macrosco-pic CVD-prepared graphene sheets transferred onto a corrugated substrate made of an orderedarrays of silica pillars of variable geometries. Depending on the aspect ratio and sharpness of thecorrugated array, graphene can conformally coat the surface, partially collapse, or lay, fakir-like,fully suspended between pillars over tens of micrometers. Upon increase of pillar density, ripplesin collapsed films display a transition from random oriented pleats emerging from pillars to rippleslinking nearest neighboring pillars organized in domains of given orientation. Spatially-resolvedRaman spectroscopy, atomic force microscopy and electronic microscopy reveal uniaxial strain do-mains in the transferred graphene, which are induced and controlled by the geometry. We proposea simple theoretical model to explain the transition between suspended and collapsed graphene.For the arrays with high aspect ratio pillars, graphene membranes stays suspended over macrosco-pic distances with minimal interaction with pillars tip apex. It offers a platform to tailor stress ingraphene layers and open perspectives for electron transport and nanomechanical applications. a r X i v : . [ c ond - m a t . m e s - h a ll ] A p r . INTRODUCTION Graphene, the two-dimensional honeycomb carbon lattice, has unique mechanical proper-ties such as strong in-plane rigidity together with a huge elasticity range as it can withstandup to 25% elastic deformation . It is today the only atomically-thin material that routinelyprovides stable and self-supported membranes, allowing a wide range of applications rangingfrom nanoelectonic and optomechanical devices to biology : among notable recents resultsinvolving graphene membrane as its critical component, one can cite high electronic mobilitydevices showing fractional quantum hall effect , nano-electromechanical systems , leak-proofmembrane , offering promising materials for water filtration and DNA sequencing .The development of graphene growth over centimeter scale area and the improvement oftransfer techniques make it all the more important to control the shape and geometry ofgraphene once transferred onto the destination substrate. Indeed, the possibility of growingcontinuous monolayer graphene onto sacrificial catalytic layers has enabled manipula-tion of large areas of graphene and makes possible its transfer onto surfaces of arbitraryshape and composition. Once transferred on a flat surface, or further suspended , gra-phene membranes always display unwanted ripples that affect its electrical , thermal andmechanical properties. Wrinkles (reminiscent as the one occurring in hanging draperies)that develop in doubly-clamped graphene membranes under uniaxial stress induce additio-nal damping in electromechanical systems , whereas ripples in graphene-based transistorsare known alter the electrical conductivity . Nevertheless these mechanical-induced defectscan be sometimes desirable as a means to engineer a controlled level of stress either togenerate an electrical gap or to induce strong pseudo-magnetic fields .Before reaching such a stage of control, it appears necessary to understand the interactionprocess between a polycrystalline graphene membrane and the destination substrate ontowhich it is wet-transferred. In this paper, we investigate the formation process of strainripples and suspended features in graphene layers obtained by chemical vapor deposition oncopper and transferred onto a corrugated substrate formed by an array of SiO nano-pillars.We show how to engineer the formation of graphene ripples using an ordered corrugatedsubstrate which defines self-organized strain domains forming sets of parallel ripples linking2he pillars. By tuning the aspect ratio of the pillars from the array and its apex sharpness,we show that different membrane shape regimes can be reproducibly found. We explore bothlimits of low density arrays where graphene exhibits ripples domains and of very dense arraysfor in which graphene does not ripple, but on the contrary stays fully suspended, fakir-like,over a dense array of nano-pillars (cf. 1). II. SAMPLE PREPARATION ba a n m n m SiO Si graphene a = μ m c Figure Transferred Graphene on nano-pillars. a : Schematic view of graphene membranedeposited onto SiO nano-pillar array. b : Atomic force micrograph of graphene deposited on SiO nano-pillars. c : cartoon of graphene (in black) transferred onto nano-pillars array (in blue). Fordense array ( a < a ∗ ), we observe fully suspended graphene over large areas. At low array density( a > a ∗ ), graphene fits the substrate and forms highly symmetric ripples. The graphene sheets are obtained by chemical vapor deposition (CVD) growth on asacrificial copper foil as described in our previous work . This growth method produces ho-mogeneous mono-layer graphene sample at the centimeter scale, with no second layer andpolycrystalline film with perfectly stitched crystal grain of typical size 20 microns. The detai-led fabrication process of nano-pillar array is presented in the supplementary informations.A PMMA coating film is used as a flexible and supporting layer to carry the graphene anddeposit it onto the structured substrate, after acid etching of the copper catalyst (cf. Supp.3nfo.). The transfer is then realized by slowly picking up from below the PMMA/Graphenelayer with the clean nano-pillar substrate, followed by a natural drying in air for one hour.Because residual liquid may be trapped under graphene, and to increase the chance of sti-cking onto the substrate, the whole sample was soft-baked before removing PMMA usingacetone. The final structure consists of a monolayer graphene sheet on a SiO nano-pillar ar-ray of variable lattice parameter a . Each nano-pillar is about 260 nm high, and the distance a between two pillars varies from 250 nm to 3 µ m (cf. 1). Our method differs significantlyfrom the one reported by another study which involved suspension of graphene over pillararrays after transfer, by in-situ releasing the polymer membrane using etching through thegraphene layer. Similar systems of graphene on pillars have been studied previously mostly using pillar arrays with flat, mesa-like ends. In the work of Tomori et al , a cros-sed network of ripples merging each other at pillar centers is observed. This different ripplepattern (ie. a second set of parallel ripples) is most probably attributed to the fabricationprocess which involve the in situ formation of pillar array and suspension after transfer byselectively dissolving the underlying substrate. In contrast, our fabrication process relies onthe interaction of the free graphene layer in a fluidic environment with the prefabricatedpillar array and avoids contamination or alteration of the graphene since it is transferred atthe last step and not exposed to electron beam (see 7 Supp. Info.). In our studies, we mainlyfocused on sharp pillars with variable lattice parameter a . III. STUDY OF RIPPLE DOMAINS FORMATION AND TRANSITION TO-WARDS SUSPENDED GRAPHENE. nano-pillars with a largelattice spacing a (typically a ∼ µ m). In such cases, the graphene sheet always fully collapseon its entire surface, forming a conformal capping layer on the corrugated sample with manyfrowns called ”ripples” that will be further analyzed using SEM and Raman spectroscopy.The graphene ripples linking pillars are clearly visible, reminiscent to what can be observedon a cloth covering a non-flat surface, and its ordering becomes more apparent as the pillararray density increases. It is worth noting that depending on the array parameters (pillarsheight and spacing, 2a) the graphene hugs the pillars tight or hangs more loosely around thepillars in other cases (2b-d), leading to partially suspended features. In 2a-b, tears in the4 bdc Figure Graphene sheets deposited on corrugated substrates with increasing pillardensity.
Series of SEM micrographs showing the behavior of transferred graphene membrane forincreasing density of 270-nm-height silicon pillars. From a to d , the spacing between pillars isrespectively equal to 2.3, 1.5, 1.4, and 0.25 µ m. For sharp and low-density-packed pillar arrays( a ), ripples do not join neighboring pillar but rather show a preferential direction presumablyreminiscent of the copper surface step edges on which the graphene has grown (see graph 8).Orientational order of ripples along the symmetry axes of the pillar network starts to appear for1.5 µ m pitch ( b ). At about the same density, partial suspension along symmetry lines could beobserved ( c ), while for 250 nm spacing between pillars (i.e. for an aspect ratio about 1), ( d ) themembrane becomes fully suspended in between pillars. Scale bars represent 2 µ m. graphene are visible, appearing as straights dark stripes and are attributed to correspond tograin boundaries preexisting in the CVD grown graphene membrane. Different morphologiesof ripple formations are observed experimentally : i) the graphene exactly coats the pillarsin a conformal fashion (cf. 2a), or ii) is locally suspended around the pillars, leading to a5ent-like feature (cf. 2b-d). In some cases, for instance as indicated by the arrow in 2b, thegraphene ripples tend to be oriented parallel to the direction of the underlying pillar array(in such case, linking 1 st nearest neighbors). Experimentally, this collective behavior occursif the tip of the pillar is sufficiently small compared to the curvature radius of the typicalripples observed ( ie. ∼
42 nm, cf. 5b) and only in the same graphene grain boundary. Othercases are possible, for example, when the inter-pillar distance is too large, the ripples froma pillar extend radially and point towards various directions (as indicated by the red arrow(2a)) r i pp l e ) l n (
642 3.02.52.01.51.0
Ripple density : e j-1 (a -1 ) Figure Statistical analysis of the distribution of ripples in graphene membrane.a : Graphene ripples distribution as a function of the graphene ripples density e − j for differentgeometrical configurations (1 st , 2 nd , 3 rd neighbor, etc). The notation e j is introduced at the 2(Supp. Info.). The experimental data have been extracted from a single square lattice (parameter a = 1 . µ m). st , 2 nd , 3 rd and 4 th neighbors. The closerneighbor configuration (ie. lower ripple density) is clearly dominant. These observationsraise questions about the formation of graphene ripples, and their resulting geometricalconfiguration. In particular, on has to understand what is the driving force which leadgraphene ripples to be aligned along high symmetry axes of the square lattice of nano-pillars.When graphene is deposited onto the patterned substrate, its area is smaller than the area6f the patterned specific surface of SiO because of the 3D character of the nano-pillars.In other terms, there is an topological mismatch between two surfaces as an unstrainedgraphene membrane cannot fit the substrate exactly. There are two competing interactionsare at work : i) the sum of all attractive interactions (Van der Waals, electrostatic, etc)which tend to force graphene to collapse onto the substrate and ii) the repulsion between π orbitals of graphene which causes internal rigidity of the graphene sheet forcing it to remainas flat as possible .In order to describe the competition between these antagonist interactions, we note E c theenergy density for the attractive interactions and E r the energy needed to create a grapheneripple. Following the notation introduced by Tersoff , we consider a graphene ripple as ahalf cylinder, E r = c R S , where c is an elastic constant for curvature out of the plane ( c = 1.4eV), R the ripple radius (see Supp. Info.), and S = 2 πLR the surface of a cylinder(a ripple is viewed as two half cylinders of opposite curvature). In first approximation, wesimplify the integral (cid:82) E c ( (cid:126)r ) d r as S c E c . A simple equilibrium condition can be written as :∆ E = S c E c − E r N r = 0 (1)where N r is the number of graphene ripple contained in a surface L , and S c is the surfaceof graphene which is in contact with the substrate. Regarding 1, if ∆ E >
0, the energy costto bend graphene remains smaller compared to the total attraction energy. In that case, thetransferred graphene membrane collapses and fits the substrate except at some particularpositions, forming 1D ripples. If ∆
E <
0, the energy cost to bend graphene is now higherthan the total attraction energy, and the transferred graphene membrane stays flat, restingfakir-like on top of the nano-pillars.To connect the 1 to our experimental parameter a , we introduce the ripple density ae j ,where e j is the characteristic distance between two parallel 1D graphene ripples (see supp.info.). Therefore, the number of ripples of size L in a given surface L is N r = Le j . Meanw-hile, the surface of graphene in contact with the substrate is S c = e j L − S susp , where S susp is the fraction of suspended graphene at the pillar edge and at the ripple. Introducing thesenotations in 1, we obtain a critical value of a ∗ satisfying ∆ E = 0 (cf. Supp. Info.). This valueof a ∗ separates the two regimes of fully suspended graphene from collapsed and rippled gra-phene. Interestingly, expression of a ∗ derived in 5 (see Supp. Info.) qualitatively explains thetwo main observations of our work : i) the reduction of a leads to a full suspension of gra-7hene when a < a ∗ , and ii) ripple orientation is statistically in favor of the nearest neighborconfiguration found in the low ripple density regime. In addition, the critical parameter a ∗ also show dependance in E c which is related to the physisorption properties of the substrate.Thus, this result has a crucial importance in order to engineer the corrugated substrate topre-determine the transferred graphene properties. These properties are governed by thegenerated stress and doping in the two different regimes ( a < a ∗ or a > a ∗ ). Both stress anddoping are now probed by Raman spectroscopy. IV. RAMAN ANALYSIS OF COLLAPSED AND SUSPENDED MEMBRANES :CONTROLLED STRESS I S i / I a b a Figure Raman map of TO-silicon peak intensity.
Raman map of the intensity of theSi-TO mode at 521 cm − before ( a ) and after ( b ) the graphene transfer. The configuration of thetransferred graphene is likely to be similar to the case presented in 2b-c. Scale bars represent 3 µ m. In order to have an estimation of the generated stress depending on the different configu-rations, we use Raman spectroscopy which is a powerful tool to reach this goal and allow usalso to approach the critical value a ∗ . First of all, we need to precisely locate the position ofthe nano-pillars before analyzing the Raman response of deposited graphene. For this pur-pose, we investigate the silicon TO Raman active peak (Si-TO) at 520.7 cm − . The Ramanspatial map in 4a shows that the intensity of Si-TO peak follows the nano-pillars periodicity.We find that the top of a nano-pillar exhibits higher Raman intensity I Si than the bottomplane. This phenomenon is explained by optical interference enhancement . We considerthe optical cavity made by a silicon mirror and a semi-transparent SiO layer of thickness8arying from 300 nm at the pillar base, to 560 nm at the pillar top. The height of the pillaris therefore approximately half the wavelength of the scattered light ( ie.
270 nm). Due tooptical interference between scattered beams, the collected Raman signal is modulated whenthe SiO thickness varies by λ/ (2 n ) (where n is the optical index of SiO ). Therefore, inter-ference conditions are different from the top to the basis of one nano-pillar, which explainthe modulation of the collected Raman scattered light along the substrate. When grapheneis deposited on top of the nano-pillars array, I Si still indicates the position of the nano-pillars(cf. 4b). It is worth noting that the optical focus depth is about 700 nm, thus greater thanthe pillar height, excluding any defocusing effect in that I Si modulation. Nevertheless, at apillar position, optical conditions differ since the top part of the optical cavity is now thegraphene layer, absorbing 2.3 % of light and defining new optical interference conditions .Note that 4b yields informations on the polycristallinity of the graphene layers, made up ofgrains of different sizes. These grain boundaries are easily identified on the I Si Raman mapbecause the silicon Raman signal is higher where there is no graphene. In both cases, beforeand after graphene deposition, the frequency of the Si-TO peak (see Supp. Info.) does notvary along the nano-pillars array. The analysis of Raman signal of the Si-TO peak is thus agood mean to determine the position of the nano-pillars and consequently is helpful for theinterpretation of the graphene Raman response.The Raman response of monolayer graphene always shows G and 2D peaks which areshifted in frequency in the presence of strain . For large strain ( (cid:15) > + and G − peak.However, the Raman signature of graphene is also very sensitive to doping or thermaleffects . Because of the bimodal dependence of both G and 2D band to strain and doping,it is rather complex to distinguish those two effects. Nevertheless, correlations between thefrequency of G and 2D bands give a clear signature of the importance of doping and strain .During this experiment, laser power is kept at 500 µ W. µ m − in order to avoid heating effects,that are observed at higher laser power. Moreover, we carefully correlate the position of thenano-pillars with the position of the observed shift on the graphene Raman signature.5 shows confocal Raman maps in the plane of the substrate. The two arrows in 5a point todomains where Raman signatures of the G and 2D peaks are non-uniform and oriented alonga single direction, forming parallel lines. Knowing the exact position of the nano-pillars fromthe Si-TO peak, we assign the domain pointed to by the blue (green) arrow to be constituted9 I G ( a . u . ) I D ( a . u . ) ν G ( r e l . c m - ) ν D ( r e l . c m - ) a bdc e e Figure Strain domains in graphene deposited on SiO nano-pillars. a-b : Raman mapsof the G band intensity ( a ) and frequency ( b ). The blue and green arrows show strain domainswith 1 st and 2 nd nearest neighbors configuration, respectively (cf. insets where black dots symbolizethe position of the nano-pillars and dashed lines represent the 1D graphene ripples. NB : sketchscale is different from data scale). The distance e i between two consecutive ripples is representedin red. c-d : Raman maps of the 2D band intensity ( c ) and frequency ( d ). The configuration ofthe transferred graphene is likely to be similar to the case presented in 2b-c. Laser wavelength is532 nm. Scale bars represent 3 µ m.
10y graphene ripples linking the 1 st (2 nd ) nearest neighbors. The angle between the ripplesaxis on these two domains is equal to 45 ◦ , in agreement with this assignment. Grapheneripple lines are observed in the intensity signal of the Raman G and 2D bands, but alsoin the frequency mapping - ν G and ν D - of these Raman bands (see 5-b,d). A downshiftof ∆ ν G = -2.8 cm − from a ripple region to a flat one corresponds to a stretching of thegraphene membrane of about 0.1 %. It is worth noting that value may be underestimatedsince the laser spot is about 6 times larger than the ripple diameter (cf. 11-b), thereforethe Raman signals of both flat unstrained graphene and highly strained graphene rippleare averaged. Even if I D map exhibits ripples lines, the frequency of the 2D band - ν D -is mainly correlated to the nano-pillars position. 5d shows that ν D is minimum on top ofeach nano-pillar. Previous experiments have shown a similar effect on the frequency of the2D band of locally suspended graphene. This frequency downshift can be attributed to thedecrease of electrostatic interaction between graphene and the substrate, which occurs inregions where graphene is locally suspended as suggested by 2-b,c. It is worth noting thatsuch decrease of the 2D peak frequency can be attributed to the stress within the graphenesheet when it is pinned at the top of a pillar. Both effects, electrostatic doping and stress, canreasonably be considered at the pillar position. High spatial resolution Raman investigation,such as TERS, and cross polarization Raman analysis would give insights to discriminatebetween these two effects.Until now, we have examined low pillar density ( ie. a > µ m) case, in which graphene islying on substrate and forms aligned ripples. However if the pillars lattice parameter a ≤ a ∗ ,the system should not be considered in the intermediate regime where the attractive andrepulsive interactions are almost equilibrated since the bending of graphene is no longer morefavorable at that scale (cf. Supp. Info.). We observe that below a critical value a ≤ a ∗ , thedeposition leads to fully suspended graphene over large areas (cf. 6-ab). We have determineda upper and lower boundary for the value of the critical lattice parameter a ∗ : 250 nm < a ∗ < µ m. Raman spectra of the G band for suspended and supported graphene on a flat region(outside the nano-pillar lattice) are shown in 6-c. In the suspended case, the G band frequencyshows a downshift of about ∆ ν G = -11.9 cm − with respect to the supported case as wellas a reduction in width (∆Γ G = -3 cm − ). Considering that the electrostatic influence ofthe substrate ( ie : charge impurities) strongly weakens when graphene is suspended, thissoftening observed on the G band is interpreted as a consequence of the decrease of charge11 uspended Graphene SiO pillars ab c Supported GrapheneSuspended GrapheneRamp N o r m a li z e d I n t e n s i t y Raman shift (rel. cm -1 ) cm -1 (10.9) 1581.4 cm -1 (13.6)1584.5 cm-1 (13.9) SuspendedSupportedRamp -1 Figure Full suspension of graphene on top of high-aspect ratio pillar arrays. a-b :SEM micrographs of suspended graphene membrane on top of nano-pillars square lattice ( a =250 nm). Scale bars represent 1 µ m. Note the presence of tears at graphene grain boundaries (a),which are consistent with previous Raman maps (cf. 5). c : Raman spectra (G band) of monolayergraphene suspended on top of nano-pillars square lattice (red line), collapsed on the substrate (blueline), and at suspended ramp region (dark line) for comparison. The frequency (width) of the Gband is indicated on the graph. transfer between the graphene and the substrate . Analysis of the 2D band (cf. Supp.Info.) also confirm that graphene is less doped in the suspended case than in the supportedone. According to ref the increase in carrier density between the suspended case andthe supported one is about 8 . cm − . This confirms the reduction of doping for suchmacroscopic suspended graphene sheet. Nevertheless, contribution of residual strain due topinning graphene at the top of nano-pillars array would also downshift the G band frequency.By comparison between the strained graphene on the ramp and the low-doped suspendedgraphene, a rough estimation of this strain can be obtained, and is about 0.1 %, which isquite similar to the strain value extracted at a pillar position in the case where a > a ∗ .12ote that this estimation is an average value because our spatial resolution is bigger thanthe inter-pillar distance. Moreover, no G band splitting has been observed in the suspendedregion (cf. 13), as it is expected in case of strong uniaxial stress, which confirm that stresscontribution to the change on the Raman response is not major in that particular case.Note that doping alone cannot explain all the Raman feature (G and 2D) observed in thesupported region. It is therefore likely that the suspended graphene is less strained than thesupported one. To summarize, when macroscopic graphene sheet is suspended on top of thenano-pillars, both stress and doping are decreased in comparison with supported graphene.This might be an important feature for future integration of high mobility electronic devices.So far, we have examined a square lattice of nano-pillars. Considering now another type ofpillars lattice, for example a random lattice, the ripple propagation should then be impossiblebecause of absence of high symmetry axis to maintain the ripple propagation. In such case,the average distance between N pillars distributed over an area S would be a r = (cid:112) S/N andthe critical value to get fully suspended graphene would be lower than the square lattice case a ∗ r < a ∗ . A recent study highlights the effect of pillars density (made from randomly depo-sited nanoparticles) on graphene ripples formation. These authors show AFM measurementsleading to a critical pillars density for which graphene ripples form a percolating network.In addition to the present work, this is therefore a first step towards large areas of fullysuspended graphene. Devices made of macroscale suspended graphene are of interest bothfor fundamentals investigations (role of periodic potential created by the pillars, collectivelow energy vibration mode, ...) and for applied science (high mobility transparent electrodes,batch fabrication of mechanical resonators, ...) V. CONCLUSION
In conclusion, using a set of prefabricated substrates with pillar arrays of variable aspectratio, we have provided a platform to study the formation of suspended graphene membranesover tens of micrometers and the transition from this suspended state to a collapsed onewhich exhibit organized domains of parallel ripples joining the pillars. Depending of thearray geometry and pitch, graphene films can tightly coat the surface, partially collapse,or lay, ”fakir-like”, suspended for an array parameter below 1 µ m (pillar height of 260 nm).Different cases allow to illustrates the competition between adhesion and membrane rigidity.13ollapsed films display set of parallel ripples organized in domains, thus forming straindomains of different configurations. These ripples are oriented along high symmetry axesof the pillars lattice. Such collective behavior is qualitatively described taking into accountthe ripples density and the corresponding bending energy. Stress domains are then observedby Raman spectroscopy mapping and correspond to parallel ripples regions. Typical stressat the graphene ripple is about 1 GPa. Raman spectroscopy appears as a reliable and noninvasive investigation tool to quantify stress, discriminate strained domains and identifyorder in the strain organization.. In addition to controlling the stress of a graphene oncetransferred onto a substrate (control of ripple formation, and local strain), we have shownthat, by increasing the aspect ratio of the pillar, a transition towards a macroscale suspendedgraphene membrane takes place. In that latter case, the interaction with the substrate isbecoming minimal and offer a promising way to test the influence of suspended graphenewhich periodic substrate interaction. ACKNOWLEDGMENTS
This work was supported by the Agence Nationale de la Recherche (ANR projects :MolNanoSpin, Supergraph, Allucinan and Trico), European Research Council (ERC advan-ced grant no. 226558), the Nanosciences Foundation of Grenoble and Region Rhˆone-Alpesand the Graphene Flagship. Authors thanks Edgar Bonet and Jo¨el Moser for stimulatingdiscussions.
VI. SUPPLEMENTARY MATERIALVII. FABRICATION TECHNIQUES
Graphene is grown by CVD process on copper. In short words, 25 µ m thick Cu foil isloaded in a quartz tube under 1 mbar total pressure, and 1000 ◦ C annealing for 1 hour wasapplied. Keeping the same temperature, graphene growth was performed with 2 sccm CH and 1000 sccm H , while the total pressure was changed into 25 mbar. After 10 min growth,H and CH is shut down immediately, instead 500 sccm Ar is injected, and the setup iscooled down to room temperature in 3 hours. The result graphene are in hexagonal shape.Note that there are wrinkles or ripples within the graphene layer, due to the mismatch of14hermal expansion coefficient of Cu and graphene (corrugated graphene was inevitably foldedinto wrinkles when transferred onto substrate), as previously reported . Graphene shownin 2 b,d comes from CVD graphene supermarket ( http://graphene-supermarket.com/ ).Nano-pillars substrate fabrication is schematically described in 7. One 300 nm-thick layerof PMMA is spin-coated onto a oxidized silicon wafer with 560 nm of SiO . The nano-pillarspattern is designed by electron-beam lithography. After development, 50 nm of Ni or Almetal are deposited, which constitute the mask to create the nano-pillars by plasma etching(RIE) of the silicon oxide. Al and Ni masks lead to different apex shape and sharpness asAl is partially etched during RIE while Ni is not. The remaining metal (Ni) is dissolved inHNO3 solution.The transfer of graphene onto nano-pillars starts by spin-coating the graphene on Cuwith PMMA. Graphene on the back-side of the Cu foil was etched by oxygen plasma andthen the PMMA/graphene/Cu stack was floated on Ammonium persulphate ((NH ) S O )diluted with DI water (0.02 mg/ml) for 24 hours. Once all Cu is removed, the samplePMMA/Graphene is carefully washed in fresh DI water for at least 10 times. The transfer isthen realized by slowly picking-up from below the PMMA/Graphene layer with clean nano-pillar substrate, followed by a natural drying in air for one hour. To increase the chance ofsticking onto substrate, the whole sample was soft-baked on a hotplate at 120 ◦ C for 5 min.The PMMA layer is eventually removed with acetone and dried from an IPA rinse.
VIII. RAMAN SPECTROMETER SETUP
The setup consists of a confocal microscope with a 320 nm spot size for λ laser = 532 nm.Confocality of the system is ensured by a 50 µ m optical fiber for both injection and collectionof light. The elastically scattered light from the sample is filtered out by an edge filter, whilethe inelastically scattered light is collected and sent to a spectrometer with resolution lessthan 0.9 cm − . Spectrum acquisition is performed by a CCD camera, cooled down to -65 ◦ Cby Peltier cooling. A typical Raman spectrum is acquired in 1-10s. To avoid laser heating,laser power is kept below P laser = 0 . .µ m − . The Raman spectrometer (WITec alpha500) is equipped with a piezoelectrical stage, allowing to make 3D confocal maps of thesample. 15 raphene c de f μ m n m n m SiO Si n m PMMA n m e - b e a m a b Figure Fabrication process of the sample. a : electron-beam lithography of pilars. b : 50nm Ni or Al deposition. c : RIE etching (SF /CHF ). d : Metal (Ni) dissolution in HNO to obtainnano-pillars of SiO . e : Transfer of CVD graphene onto the nano-pillars array. f : graphene layerlying on top of nano-pillars. IX. NEIGHBORS INDEXING
Each set of parallel ripple is defined by m j and n j which are integer indexes for the j th nearest neighbor nano-pillar configuration. For instance, ( m j , n j ) = (0 ,
1) represents the firstneighbor configuration ( e = a ), and (1 ,
1) the second neighbor configuration ( e = a/ √ e j = a (cid:113) m j + n j , (2)These indexes follow two selection rules : i) e j > e j +1 , and ii) n j m j (cid:54) = n j m j ∀{ ( m j , n j ) } ∈{ m j + n j = A } (where A is an integer). The first condition imposes that the j th nearestneighbor is always closer to the initial position than the ( j + 1) th one. The second condition16
50 nm0 nm T o p o g r a p h y μ m a
10 nm0 nm T o p o g r a p h y μ m b Figure AFM topography of graphene on PMMA, just before the transfer.a-b :topography mirographies of graphene attached on PMMA layer, corresponding of the snapshotof step e in 1. Graphene wrinkles are observed, probably due to the finger print of Cu-terrasses.Orientation of those wrinkles may vary from one end to the other of the chip. μ m 2 μ m a b Figure Role of the nano-pillar tip. a-b : SEM micrographs of graphene transferred ontop of large area nano-pillar (tip area ∼ µ m , tip radius ∼ . µ m. No collective behavior ofripple propagation is observed. However, ripples point towards multiple directions from one pillar,confirming the hypothesis about destruction of ripple coherence (and propagation) when nano-pillartip is larger than ripple natural radius ( ∼
42 nm). avoids double counting of neighbors and includes the degeneracy of the ripples configuration.As an example (1,1) and (2,2) both correspond to the same ripple while (3,1) and (1,3)are characterized by the same density of ripples. Note that the degeneracy of the rippleconfiguration depends on j (as an example 1 st and 2 nd are doubly degenerate, while 3 rd X. DERIVATION OF THE CRITICAL PARAMETER a ∗ This parameter corresponds to the critical value of the inter pillar distance a ∗ that leadsto a transition from fully suspended to partially collapsed graphene.Starting from 1 : ∆ E = S c E c − E r N r = 0 , ( Le j − LR − πh tan θ ) E c − E r Le j = 0 (3)Where R is the radius of a ripple which has been experimentally determined by SEM (cf.11-b), h the pillar height and θ the angle between the graphene and the pillar as depictedin 10. The surface S c = e j L − S susp correspond to the surface of graphene in contact withthe substrate (cf. 10a). Therefore, it is equal to difference of the surface separating twoconsecutive ripples ( e j L ) and the total suspended area S sups = 2 LR + πh tan θ . To estimate S sups , we take into account the fraction of graphene that is not in contact with the substratealong a ripple (2 LR ), and the fraction of suspended graphene (conical shape with angle θ )hanging around a pillar of height h . In addition, it is worth noting that the term E c variesalong the position of graphene as the distance to the substrate may change locally .The critical parameter a ∗ corresponds to the case where ∆ E = 0. Considering the lowestripple density (ie. first neighbor configuration), e j = a and L = a . The previous equationcan be rewritten as : a − aR − (cid:18) πh tan θ + E r E c (cid:19) = 0 (4)Only the positive solution of 4 has physical meaning : a ∗ = R + (cid:113) (2 R ) + 4 πh tan θ + 4 E r E c a ∗ with the pillar height, ii) thedependance with the ripple width, iii) full suspension of graphene for a < a ∗ and iv) predo-minance of first neighbor configuration. On can derive four qualitative results.– As h increases, the distance separating graphene from substrate increases as well. Thislead to a decrease of the total attraction energy between graphene and substrate, andtherefore, a ∗ would increase. 18 Wider ripples ( R large) can be explained as a consequence of a high bending energy.This is in favor of fully suspended graphene, without ripples. Therefore, for a given setof parameters, a ∗ increases with R , as predicted in 5.– Experimentally, when a is large, we observe ripple formation. Decreasing a leads to astructural transition where graphene remains fully suspended. This suggest existence ofa critical parameter a ∗ . We have shown that equation X can be written as a polynom of a having a positive quadratic term. Therefore, as a is decreasing, there is a mathematicalsolution for ∆ E = 0 at a = a ∗ . This value of a ∗ separates the regime where ∆ E >
E < n j and m j leads to another critical value a ∗ j . We find that a ∗ j +1 > a ∗ j . Thissuggests that for a ∈ [ a ∗ ; a ∗ ...a ∗ j ], the system prefers the most favorable configuration : a ∗ which correspond to the first neighbors.Experimentally, we can determine a set of parameters such as a ∗ = 250nm, R = 42nm (cf.11b), θ = 26 ◦ (cf. 10c), h = 260 nm (cf. 1) and we can calculate E r = c R S , where c is anelastic constant for curvature out of the plane ( c = 1.4eV). We obtain an adhesion energyaround 5 mJ.m − , which is two orders of magnitude smaller than the value of 450 mJ.m − measured by Koenig et al for monolayer graphene on SiO . This discrepancy could beexplained by our overestimation of the ripple radius using SEM contrast images (cf. 11b.Generalization of 5 taking into account other neighbors leads to : a ∗ j = d j R + (cid:113) d j (2 R ) + 4 πh tan θ + 4 E r d j E c a ∗ j as a function of the neighbors. XI. STATISTICAL MODELING OF RIPPLES DOMAIN FORMATION
In order to gain insights about the ripple formation and the fact that low ripple densitiesare dominant, we have developed the following toy model. In such model, we make thefollowing hypothesis : i) a ripple propagates along one direction and is parallel to anotherripple located at a distance e j , ii) the energy to create a ripple costs E r , iii) we only considera system of a fixed number of ripples N , and therefore the contribution for attractive19 L2Rd suspended graphenegraphene on Si θ ab angle (°) c E = E c on t a c t - E r i pp l e inter-pillar distance : a s t n e i g h b o r n d r d a *1 a *2 a *3 d Figure
Geometry of the graphene ripple.a : Top-view sketch of graphene transferredon nano-pillars and showing ripples. Green regions represent the surface where graphene is not incontact with the substrate. Around each nano-pillar, the graphene remains suspended and makesa tent-like conical shape. b : SEM micrograph of a typical case of graphene around a nano-pillar.Locally, suspended graphene can be modeled as a cone having an angle θ . c : Statistical distributionof θ measured on 66 ripples. Mean value is θ = 26 ◦ . d : qualitative evolution of ∆ E with theparameter a for different neighbors. We observe that a ∗ j +1 > a ∗ j . For the first neighbor configuration,if a > a ∗ , graphene shows ripples and stays in contact with the substrate (blue region). If a < a ∗ ,graphene is fully suspended (red region). interaction with the substrate is a constant, and iv) the lattice parameter is above criticalvalue : a > a ∗ . For a system containing N ripples, the total energy is then E T = E r N . Wenow consider a system of size L , containing N ripples of length L . It is worth noting thatthe ripples inside the system of size L are not independent as we consider a set of parallelripples. Therefore, the two indexes ( n j , m j ) govern the configuration state. N is given by thelength of the system divided by the inter-ripple distance, ie. N = L √ n j + m j a . Combining the20recedent equations, the total energy of such system is : E T = E r La (cid:113) n j + m j = E r Le j (7)By analogy with the ideal monoatomic gas model, and within the continuum limit, we define E T = E r La D , where D is a distance in the phase space. The hypersphere containing all themicro-ensembles has a radius D and dimension 2, as the number of ripple is only given bythe indexes ( n j , m j ) (ie. one only needs these two indexes to describe a single µ -state). Thenumber Ω of µ -states is therefore :Ω = V tot V µ = π Γ(2) (cid:18) E T E r La (cid:19) V µ (8)In phase space, the volume of a µ -state, V µ , is given by the distance between two consecutiveneighbors j and j (cid:48) : V µ = ( m j − m j (cid:48) ) ( n j − n j (cid:48) ) = 1 (9)This leads to : Ω = π Γ(2) (cid:18) E T E r La (cid:19) (10)It is therefore possible to define an entropy S , introducing the constant k : S = k ln(Ω) = 2 k ln( E T ) + k ln (cid:20) πE r L Γ(2) a (cid:21) (11)Following Boltzmann theory, an analogue of micro-canonical temperature Θ is defined as :1Θ = ∂ S ∂E T = 2 kE T (12)Therefore, for a given effective temperature Θ, there is a fixed energy E = 2 k Θ for a rippledistribution. Note : k Θ may be seen as the energy contribution for the fluctuations of thecurvature of the grapheme flake. Also, k Θ can be seen as a ripple distribution in everydirection.Therefore, it is possible to define the Bolztmann distribution : P ( E T ) = Λ e − βE T C = Λ e − β ErLej C (13)where β = ( k Θ) − , Λ is the degeneracy of the j th ripple density configuration, C is thepartition function normalizing the probability. Statistical analysis of SEM micrographs of21ample with the same pillars lattice parameter a leads to the distribution of ripple lines lin-king 1 st , 2 nd , 3 rd , . . . neighbors (cf. 11 a). This distribution reveals the probability P ( E T ) / Λ j for each given ripple density e − j . Experimental results shown in 11a are in agreement withthe numerical fit using 13 (dashed line) ; thus indicating that formation of graphene ripplesonto periodic nano-pillars array is governed by pillars density as suggested by our model. Ripple radius (nm) a b r i pp l e ) l n (
642 3.02.52.01.51.0 e v e n t s Ripple density : e j-1 (a -1 ) Figure
Statistical analysis of the distribution of ripples in graphene membrane.a : Graphene ripples distribution as a function of the graphene ripples density e − j for differentgeometrical configurations (1 st , 2 nd , 3 rd neighbor, etc). The experimental data has been extractedfrom one single nano-pillars square lattice (parameter a=1 µ m). Red dashed line is a fit of datausing 13. b : Graphene ripples diameter distribution. Data recorded from SEM micrographs. Thecentral value is 42 nm (gaussian fit), and the distribution width is about 21 nm. Inset : sketch ofa ripple cut. Graphene ripple is viewed as two half cylinders of opposite curvature. I S i ( a . u . )
522 519 ν S i ( r e l . c m - ) μ m μ m I S i ( a . u . )
522 519 ν S i ( r e l . c m - ) a cdb μ m μ m Figure
Raman response of the silicon mode before and after graphene transfer.
Raman map of the intensity ( a ) and of the frequency ( b ) of the Si-TO mode before the graphenetransfer. After graphene transfer, the intensity ( c ) of the Si-TO mode is lower except at the graphenegrain boundaries, which leaves the silicon surface exposed. The frequency ( d ) of the Si-TO modeis unchanged. N o r m a li z ed I n t en s i t y Raman shift (rel. cm -1 ) SuspendedSupportedRamp
Figure
Raman 2D band for suspended and supported graphene.
Spectra of 2D bandcorresponding to the spots shown in 6-c. Spectra are fitted with two lorentzian functions, as sug-gested in reference , due to the coexistence of resonant inner and outer 2D processes. Fit resultsare presented in I. uspended case (cm − ) Ramp (cm − ) Supported (cm − ) ν D − F W HM D − ν D + F W HM D + Table I.
2D band fit results.
2D band profile fitted with two lorentzian functions, as suggestedin reference . Raman spectra are shown in 13. XII. ADDITIONAL DATA ∗ Present address : ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860Castelldefels (Barcelona), Spain. Changgu Lee, Xiaoding Wei, Jeffrey W Kysar, and James Hone. Measurement of the elastic pro-perties and intrinsic strength of monolayer graphene.
Science (New York, N.Y.) , 321(5887) :385–8, July 2008. Xu Du, Ivan Skachko, Fabian Duerr, Adina Luican, and Eva Y. Andrei. Fractional quantumhall effect and insulating phase of dirac electrons in graphene.
Nature , 462(7270) :192–195, 112009. Arend M. Van Der Zande, Robert a. Barton, Jonathan S. Alden, Carlos S. Ruiz-Vargas,William S. Whitney, Phi H. Q. Pham, Jiwoong Park, Jeevak M. Parpia, Harold G. Craighead,and Paul L. McEuen. Large-Scale Arrays of Single-Layer Graphene Resonators.
Nano Letters ,page 101116125413000, November 2010. JS Bunch and SS Verbridge. Impermeable Atomic Membranes from Graphene Sheets.
Nano. . . , pages 3–7, 2008. R. R. Nair, H. A. Wu, P. N. Jayaram, I. V. Grigorieva, and A. K. Geim. Unimpeded permeationof water through helium-leak–tight graphene-based membranes.
Science , 335(6067) :442–444,2012. S Garaj, W Hubbard, a Reina, J Kong, D Branton, and J a Golovchenko. Graphene as a ubnanometre trans-electrode membrane. Nature , 467(7312) :190–3, September 2010. Xuesong Li, Weiwei Cai, Jinho An, Seyoung Kim, Junghyo Nah, Dongxing Yang, Richard Piner,Aruna Velamakanni, Inhwa Jung, Emanuel Tutuc, Sanjay K Banerjee, Luigi Colombo, andRodney S Ruoff. Large-area synthesis of high-quality and uniform graphene films on copperfoils.
Science (New York, N.Y.) , 324(5932) :1312–4, June 2009. Keun Soo Kim, Yue Zhao, Houk Jang, Sang Yoon Lee, Jong Min Kim, Kwang S Kim, Jong-Hyun Ahn, Philip Kim, Jae-Young Choi, and Byung Hee Hong. Large-scale pattern growthof graphene films for stretchable transparent electrodes.
Nature , 457(7230) :706–10, February2009. Zheng Han, Amina Kimouche, Adrien Allain, Hadi Arjmandi-Tash, Antoine Reserbat-Plantey,S´ebastien Pairis, Val´erie Reita, Nedjma Bendiab, Johann Coraux, and Vincent Bouchiat. Sup-pression of Multilayer Graphene Patches during CVD Graphene growth on Copper.
Arxivpreprint arXiv : , 2012. Libo Gao, Wencai Ren, Huilong Xu, Li Jin, Zhenxing Wang, Teng Ma, Lai-Peng Ma, ZhiyongZhang, Qiang Fu, Lian-Mao Peng, Xinhe Bao, and Hui-Ming Cheng. Repeated growth andbubbling transfer of graphene with millimetre-size single-crystal grains using platinum.
Naturecommunications , 3 :699, January 2012. Wenzhong Bao, Feng Miao, Zhen Chen, Hang Zhang, Wanyoung Jang, Chris Dames, andChun Ning Lau. Controlled ripple texturing of suspended graphene and ultrathin graphitemembranes.
Nature nanotechnology , 4(9) :562–6, September 2009. Jannik C. Meyer, A. K. Geim, M. I. Katsnelson, K. S. Novoselov, T. J. Booth, and S. Roth.The structure of suspended graphene sheets.
Nature , 446(7131) :60–63, 03 2007. A. Fasolino, J. H. Los, and M. I. Katsnelson. Intrinsic ripples in graphene.
Nat Mater , 6(11) :858–861, 11 2007. Guang-Xin Ni, Yi Zheng, Sukang Bae, Hye Ri Kim, Alexandre Pachoud, Young Soo Kim, Chang-Ling Tan, Danho Im, Jong-Hyun Ahn, Byung Hee Hong, and Barbaros Ozyilmaz. Quasi-periodicnanoripples in graphene grown by chemical vapor deposition and its impact on charge transport.
ACS nano , 6(2) :1158–64, February 2012. Chun-Chung Chen, Wenzhong Bao, Jesse Theiss, Chris Dames, Chun Ning Lau, and Ste-phen B Cronin. Raman spectroscopy of ripple formation in suspended graphene.
Nano letters ,9(12) :4172–6, December 2009. Wenzhong Bao, Kevin Myhro, Zeng Zhao, Zhen Chen, Wanyoung Jang, Lei Jing, Feng Miao,Hang Zhang, Chris Dames, and Chun Ning Lau. In situ observation of electrostatic and thermalmanipulation of suspended graphene membranes.
Nano letters , 12(11) :5470–4, November 2012. Hugues Vandeparre, Miguel Pi˜neirua, Fabian Brau, Benoit Roman, Jos´e Bico, Cyprien Gay,Wenzhong Bao, Chun Lau, Pedro Reis, and Pascal Damman. Wrinkling Hierarchy in Constrai-ned Thin Sheets from Suspended Graphene to Curtains.
Physical Review Letters , 106(22) :3–6,June 2011. Vitor M. Pereira, A. H. Castro Neto, and N. M. R. Peres. Tight-binding approach to uniaxialstrain in graphene.
Phys. Rev. B , 80 :045401, Jul 2009. F. Guinea, M. I. Katsnelson, and a. K. Geim. Energy gaps and a zero-field quantum Hall effectin graphene by strain engineering.
Nature Physics , 6(1) :30–33, September 2009. L Covaci and F M Peeters. Nano-engineered non-uniform strain in graphene.
Arxiv preprint ,1204.6371, 2012. N Levy, S a Burke, K L Meaker, M Panlasigui, A Zettl, F Guinea, a H Castro Neto, andM F Crommie. Strain-induced pseudo-magnetic fields greater than 300 tesla in graphene nano-bubbles.
Science (New York, N.Y.) , 329(5991) :544–7, July 2010. M. Neek-Amal and F. Peeters. Strain-engineered graphene through a nanostructured substrate.II. Pseudomagnetic fields.
Physical Review B , 85(19) :1–6, May 2012. H Tomori, A Kanda, H Goto, and Y Ootuka. Introducing Nonuniform Strain to Graphene UsingDielectric Nanopillars.
Arxiv preprint arXiv : , 2011. Jung Min Lee, Jae Woong Choung, Jaeseok Yi, Dong Hyun Lee, Monica Samal, Dong Kee Yi,Chul-ho Lee, Gyu-chul Yi, Ungyu Paik, John A Rogers, and Won Il Park. Graphene HybridLight Emitting Diodes.
Nano , pages 2783–2788, 2010. Chongmin Lee, Byung-Jae Kim, Fan Ren, S. J. Pearton, and Jihyun Kim. Large-area suspendedgraphene on GaN nanopillars.
Journal of Vacuum Science & Technology B : Microelectronicsand Nanometer Structures , 29(6) :060601, 2011. J Tersoff. Energies of fullerenes.
Physical Review B , 46(23) :546–549, 1992. Wenjuan Zhu, Tony Low, Vasili Perebeinos, Ageeth a Bol, Yu Zhu, Hugen Yan, Jerry Tersoff,and Phaedon Avouris. Structure and electronic transport in graphene wrinkles.
Nano letters ,12(7) :3431–6, July 2012. JH Parker Jr, DW Feldman, and M Ashkin. Raman scattering by silicon and germanium. hysical Review , 155(3), 1967. H S Skulason, P E Gaskell, and T Szkopek. Optical reflection and transmission properties ofexfoliated graphite from a graphene monolayer to several hundred graphene layers.
Nanotech-nology , 21(29) :295709, July 2010. P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang, R. Yang, T. J. Booth, andA. K. Geim. Making graphene visible.
Applied Physics Letters , 91(6) :063124, 2007. G. a. N. Connell, R. J. Nemanich, and C. C. Tsai. Interference enhanced Raman scatteringfrom very thin absorbing films.
Applied Physics Letters , 36(1) :31, 1980. Antoine Reserbat-plantey, Svetlana Klyatskaya, Olivier Arcizet, Mario Ruben, Nedjma Bendiab,and Vincent Bouchiat. Time- and Space-Modulated Raman Signals in Graphene-based OpticalCavities. arXiv :1306.3462 , pages 1–12, 2013. Antoine Reserbat-Plantey, La¨etitia Marty, Olivier Arcizet, Nedjma Bendiab, and Vincent Bou-chiat. A local optical probe for measuring motion and stress in a nanoelectromechanical system.
Nature nanotechnology , 7(3) :151–5, March 2012. R R Nair, P Blake, A N Grigorenko, K S Novoselov, T J Booth, T Stauber, N M R Peres,and A K Geim. Fine structure constant defines visual transparency of graphene.
Science (NewYork, N.Y.) , 320(5881) :1308, June 2008. Otakar Frank, G Tsoukleri, J Parthenios, and K Papagelis. Compression behavior of single-layergraphenes.
ACS nano , 4(6) :3131–3138, 2010. Otakar Frank, Georgia Tsoukleri, Ibtsam Riaz, Konstantinos Papagelis, John Parthenios, An-drea C Ferrari, Andre K Geim, Kostya S Novoselov, and Costas Galiotis. Development of auniversal stress sensor for graphene and carbon fibres.
Nature communications , 2 :255, January2011. Mingyuan Huang, Hugen Yan, Tony F Heinz, and James Hone. Probing strain-induced electronicstructure change in graphene by Raman spectroscopy.
Nano letters , 10(10) :4074–9, October2010. M Mohr, J Maultzsch, and C Thomsen. Splitting of the Raman 2D band of graphene subjectedto strain.
Physical Review B , 82(201409), 2004. Duhee Yoon, Young-woo Son, and Hyeonsik Cheong. Strain-dependent Splitting of DoubleResonance Raman Scattering Band in Graphene.
Physical Review Letters , 106(155502) :5,March 2011. A. C. Ferrari, A. K. Sood, A. Das, S. Pisana, B. Chakraborty, S. Piscanec, S. K. Saha, U. V.Waghmare, K. S. Novoselov, H. R. Krishnamurthy, and A. K. Geim. Monitoring dopants by Ra-man scattering in an electrochemically top-gated graphene transistor.
Nature Nanotechnology ,3(4) :210–215, 2008. I. Calizo, F. Miao, W. Bao, C. N. Lau, and a. a. Balandin. Variable temperature Ramanmicroscopy as a nanometrology tool for graphene layers and graphene-based devices.
AppliedPhysics Letters , 91(7) :071913, 2007. Ji Eun Lee, Gwanghyun Ahn, Jihye Shim, Young Sik Lee, and Sunmin Ryu. Optical separationof mechanical strain from charge doping in graphene.
Nature communications , 3 :1024, January2012. St´ephane Berciaud, Sunmin Ryu, Louis E Brus, and Tony F Heinz. Probing the intrinsicproperties of exfoliated graphene : Raman spectroscopy of free-standing monolayers.
Nanoletters , 9(1) :346–52, January 2009. Mahito Yamamoto, Olivier Pierre-louis, Jia Huang, and Michael S Fuhrer. Princess and the Peaat the nanoscale : Wrinkling and unbinding of graphene on nanoparticles. arXiv :1201.5667v1 ,2012. Xuesong Li, Carl W. Magnuson, Archana Venugopal, Rudolf M. Tromp, James B. Hannon,Eric M. Vogel, Luigi Colombo, and Rodney S. Ruoff. Large-area graphene single crystals grownby low-pressure chemical vapor deposition of methane on copper.
Journal of the AmericanChemical Society , 133(9) :2816–2819, 2011. Mikhail Katsnelson.
Graphene : carbon in two dimensions . Cambridge edition, 2012. Steven P. Koenig, Narasimha G. Boddeti, Martin L. Dunn, and J. Scott Bunch. Ultrastrongadhesion of graphene membranes.
Nature Nanotechnology , 6(9) :543–546, August 2011. S Berciaud, Xianglong Li, Han Htoon, and LE Brus. Intrinsic Line Shape of the Raman 2D-Modein Freestanding Graphene Monolayers.
Nano . . . , pages 1–8, 2013., pages 1–8, 2013.