Direct evaluation of CVD multilayer graphene elastic properties

Abstract

The rolling of semiconductor thin films with graphene layers on top is carried out to integrate distinct material classes. Tubular structures obtained can span from the nanometer to the micrometer range, providing controlled and homogeneous curvature on few-layer CVD graphene systems. Scanning electron microscopy measurements reveal an increase in the tube radius for larger amounts of stacked/rolled graphene sheets. The relation between the retrieved radii for different layered configurations and total layer thickness is fitted with continuum elasticity theory, directly providing elastic parameters such as Young modulus and Poisson's ratio for few-layer graphene systems. X-ray diffraction and Raman spectroscopy evidence that surface modifications due to the transferring methods are negligible and that layer-to-layer registry (graphitization) is not observed. The concept of rolling up layered materials for direct evaluation of elastic properties can be extended to other two-dimensional systems.

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Introduction

Two-dimensional materials have attracted increasing scientific interest due to their unique physical properties as well as their potential future applications.^1,2 Graphene, a monolayer of sp²-hybridized carbon atoms arranged in a two-dimensional (2D) lattice, is the most investigated system of this material class and regarded as a model system to address properties of more complex 2D compounds.^3–5 In single and multilayer graphene, the atomic lattice, the electronic structure and the strength of carbon–carbon bonds provide conditions favorable for unique mechanical properties such as enhanced strength (large Young modulus)^6,7 and low friction coefficient.^8,9 In many practical applications graphene-based nanocomposites are present as multilayer graphene rather than on its monolayer form.^10,11

For example, large area graphene sheets synthesized by Chemical Vapor Deposition (CVD) can be transferred into diverse substrates and surfaces, where physical interactions impact on both structural and electronic properties.^12,13 Perfect registry of graphene lattice in adjacent sheets is not expected for transferred large area systems, implying in configurations which usually lead to different responses with respect to graphite AB stacking.¹⁴

Works from different groups have addressed the structural properties of graphene layers (GLs).^15–17 Recently it was shown by indentation tests, directly carried out on grain boundaries, that in CVD graphene the elastic stiffness is identical to that of pristine graphene.¹⁵ However, since the vast majority of experiments are carried out using scanning probe microscopy techniques. Hereby, the use of local probes cannot be extended to evaluate homogeneity in areas larger than few micrometers or under capping layers.^16,17

The use of graphene layers supported or encapsulated by polymeric substrates consists in another type of experiment that must be examined in particular. In such case a controlled bending or curvature is imposed to the GLs^18,19 and Raman shifts are used to evaluate the Young modulus. As shown previously²⁰ the strain phenomena observed in such systems is ascribed to stretching due to the formation of local atomic bonds between GLs and the polymers. Finally, the evaluation of graphene shear modulus through torsional strain²¹ experiments reveal a striking difference between single- and multilayered graphene films. This difference is found to have its origin in the distinct impact on the shear restoring force of intralayer covalent interactions and interlayer van der Waals interactions.

In view of the scenario depicted above, the development of techniques that directly address structural and elastic properties with a flexible degree of scalability is mandatory. Curving graphene layers is a valuable tool to evaluate elastic properties, especially if a nonlocal curvature (extending homogeneously over a large area) is relevant for the integration of graphene with other systems such as semiconductors and metals, where lithographic processes and material deposition take place over an extent area of several micrometers and can induce bending/bowing of 2D materials.

We have shown recently that the scalability of rolled-up hybrid membranes^22–24 is an elegant way to study elastic properties of single layered graphene on mesoscopic scale.²⁰ Hereby, we take advantage that the diameter of rolled-up tubes only depends on the elastic modulus, the layer thickness and the inherent strain of the rolled-up nanomembrane^25,26 and can be completely described by continuum elasticity models down to the nanometer scale.^27,28

Here, we seek for changes on mechanical properties of GLs grown by CVD and stacked into few-layer systems. The rolling-up is used as non-destructive platform for structural studies in any two-dimensional system.²⁰

One, two and three GLs were rolled-up with InGaAs/Cr layers deposited on top of a GaAs (001) substrate. The analysis of X-ray diffraction (XRD) measurements, as well as continuum elasticity theory simulations allow retrieving the strain status of the systems and the deduction of graphene elastic constants for single and few-layer stacks. Combining XRD and Raman results ensure the effectiveness of mechanical assumptions for elasticity analysis, which provides a direct evidence of the absence of plastic deformation or unusual strain state of the rolled-up InGaAs/Cr layers. The retrieved values for Young modulus and Poisson's ratio are in good agreement with values found from other techniques.^6,19,29 Our results provide evidence that the lattice of stacked GLs is uncorrelated, as the elastic constants remain unchanged for one, two or three graphene layers. Finally, Raman measurements show no significant shift of any of the typical graphene Raman bands. This result indicates that the influence of strain is minimized in our system and can be substrate-dependent in measurements from other groups.¹⁹

Experimental methods

CVD graphene layers were grown on polycrystalline Cu foils with 25 μm thickness. The deposition procedure consists in heating the Cu foil at 1000 °C under a 60 sccm flux of H₂ at 730 mTorr, followed by a 40 minutes annealing at this temperature. After this step, a mixture of CH₄ and H₂ (1 : 2) was inserted into the tube at 330 mTorr for 2.5 hours.³⁰ Finally, the sample was quenched to room temperature under CH₄ : H₂ atmosphere. Single graphene layers were then released from the Cu and transferred into hosting substrates using poly-methylmethacrylate (PMMA),³¹ as depicted in Fig. 1(a). Chemical etching of Cu was obtained by immersion on ammonium persulfate ((NH₄)₂S₂O₈), which does not degrade graphene's mechanical properties [Fig. 1(c)].¹⁵ The resulting PMMA/graphene membrane was washed with de-ionized water to be lifted by other substrate. In our case, single GLs were transferred to the top of GaAs(substrate)/AlAs/InGaAs/Cr systems. For multiple GLs a stacking procedure that avoids the use of PMMA (and consequently its presence) between layers was employed. In fact, one must point out here that the procedure underlined below results on direct physical contact between successive graphene layers (uncovered with any type of polymeric layer or photoresist), resulting in graphene/graphene interfaces free of residues. The released graphene sheet was lifted by another Cu foil where graphene CVD growth was carried out, leading to a few-layer graphene stack as represented in Fig. 1(b). The amount of transferred layers was then determined by repeating subsequent Cu etching and transfer procedures. Multilayer graphene films were then placed on top of GaAs/AlAs/InGaAs/Cr films and the PMMA removed by acetone. This final step minimizes the upper surface contamination by PMMA residues.

Fig. 1 Sketch of the processing steps to produce rolled-up tubes with multiple graphene layers. (a) CVD graphene is produced on Cu foils and a PMMA layer is deposited on one substrate side to protect and support the graphene layer. (b) For multilayer graphene stacking graphene one makes use of graphene foils supported on PMMA, that are pressed against the top of Cu substrates with graphene. (c) Cu is removed using [(NH₄)₂S₂O₈], leaving a PMMA/graphene membrane that is lifted by other substrate (additional Cu foils with graphene can be used to produce a stack of graphene layers). (d) GLs transferred to the top of a Cr/InGaAs/AlAs heterostructure grown on GaAs (001). A first optical lithography step, followed by O₂ plasma etching is performed to define areas with and without graphene. (e) Another round of optical lithography and etching (with H₃PO₄ : H₂O₂ : H₂O solution) procedures leave the AlAs layer exposed. The AlAs is then selectively etched using a diluted HF solution. (f) A rolled-up tube with embedded GLs and well-defined radius is formed due to strain relaxation of the InGaAs layer. (g) Optical microscopy image with a single tube rolled with 2 graphene layers inside (left panel) and a general view of the substrate with several rolled tubes (right panel).

In order to fabricate rolled-up tubes, a semiconductor–metal system^24,26,32 was used. It consisted of a GaAs (001) substrate in which 28.1 nm of AlAs were grown, followed by 9.6 nm of an In_0.27Ga_0.73As layer [thickness and composition studied by XRD, Fig. 3(a)]. This heterostructure was grown by Metallorganic-CVD (Brolis semiconductors). On top of these layers, Cr thin films were thermally evaporated, with different thickness, ranging from 7 to 27 nm. The deposited Cr induces a thermal strain, which in our particular conditions (InGaAs thickness and composition) determines the final radius of the tubes without graphene.^19,26 Localized tubes were obtained by lithographic definition of Cr areas (stripes, 100 μm width). Above all layers previously described, graphene foils were placed and their lateral dimensions defined by optical lithography and oxygen plasma, matching the Cr stripe size [see Fig. 1(d)]. Fig. 1(g) shows optical microscopy images of tubes containing 2 GLs (single tube on the left panel and overview of all tubes on the right panel). All tubes produced in this work had 100 μm length and were separated from neighbor tubes by 50 μm in both directions, resulting on ensembles with reduced amount of defects and cracks (present in approximately 2% of tubes).

Scanning Electron Microscopy (SEM) images shown in this work were obtained on a FEI Inspect F50 microscope, operating at 10 kV. X-ray diffraction (XRD) measurements were carried out at the XRD2 beamline of the Brazilian Synchrotron (LNLS, Campinas, Brazil), using λ = 0.12335 nm and a Pilatus 100K area detector that allows to acquire a 4° interval of scattering angles (2θ).³³ Our XRD results are expressed in momentum transfer vector units q_r = (4π/λ)[sin(2θ/2)].

Results and discussion

Inserting additional GLs on our tubes causes a modification of their radii. Fig. 2(a)–(d) show SEM (scanning electron microscope) images of the opening of tubes with 0, 1, 2 and 3 GLs.

Fig. 2 Scanning electron microscopy images of In_0.27Ga_0.73As (9.6 nm)/Cr (24.2 nm) (a), and In_0.27Ga_0.73As (9.6 nm)/Cr (24.2 nm)/graphene (b–d) tubes. Tube openings with zero, one, two and three GLs are shown in panels (a)–(d), respectively.

In this figure, one observes that successive windings are compact and graphene foils are visible in regions near the tubes openings. An increase in the inner radius is found as the number of GLs increases. The tubes shown in Fig. 2 were produced with the same Cr layer thickness (24.2 nm) and represent the average radius for each configuration (openings of 50 or more tubes were measured for each Cr/graphene configuration).

It is known that GLs have a large Young modulus^15,29,34 and one must verify if the increase in tube radius of our tubes takes place within the limits of continuum elasticity or if defects are generated. Measuring the strain status of the single-crystalline InGaAs layer is mandatory to indicate the occurrence of elastic (non-plastic) processes. XRD measurements of the flat (as-grown) semiconductor layers were obtained by carrying out longitudinal scans with the sample-detector coupling on perfect Bragg condition, as sketched in Fig. 3(a).^33,35 De-tunning Bragg's condition by 10° allows the observation of diffraction from the rolled InGaAs layer only [situation depicted in Fig. 3(b)],^33,35 allowing for a direct evaluation its strain status. The analysis of such measurements using a kinematical diffraction model (due to limited thickness of the semiconductor layers)³⁵ and provides the elastic conditions of the tube walls due to the presence of GLs.

Fig. 3 Diffraction geometries for measuring the strain status of the flat (unrolled) layer (a) and for retrieving the strain status of rolled-up tubes (b). (c) XRD measurements (dots) and semi-kinematical fit near the (004) GaAs reflection for the flat InGaAs/AlAs/GaAs system (upper curves) and the rolled InGaAs layer (lower curve).

XRD results are shown in the Fig. 3(c). A longitudinal scan carried out for the flat layers is reproduced on the upper curve (black dots). This profile is fitted with a semi-kinematical model³⁶ (solid red line), allowing the extraction of layer thickness, in composition and pseudomorphic strain. The narrow peak at 44.45 nm⁻¹ corresponds to the (004) GaAs reflection, while the hump at 42.8 nm⁻¹ is ascribed to the diffraction from the InGaAs layer. Short period oscillations observed along all measured q-range are originated by the diffraction of the AlAs layer. The measurement shown on the lower curve (blue dots) is retrieved due to the diffraction from the tubes (detuned Bragg condition), evidencing the relaxation of pseudomorphic strain of the InGaAs film after rolling. Although the used X-ray beam (1 mm × 3 mm) illuminates several tubes, similar experiments performed previously^33,37 revealed that the average strain status of the tube ensemble does not differ from the strain of a single tube on lithographic structures.

XRD measurements (dots) shown in Fig. 4(a), (c), (e) and (g) were carried out near the (004) InGaAs reflection for tubes with 0, 1, 2 and 3 GLs, respectively, for a fixed Cr thickness of 18.8 nm. These measurements were analyzed considering that the layers forming the tube and the GLs are well described by linear elasticity models. We also consider that polycrystalline Cr and graphene layers are isotropic, while the InGaAs elastic constants used, specifically take into account the rolling and relaxation directions (i.e. Young modulus and Poisson's ratio dependence along the in-plane 〈100〉 direction). The single peak profiles observed these figures indicate that only the InGaAs layer is epitaxial (previous works used epitaxial GaAs instead of Cr) and are simulated using the radial lattice parameter distribution and a kinematical model (solid lines).³⁵ The radial and tangential lattice parameter distributions are depicted in Fig. 4(b), (d), (f) and (h) for the inner tube turn. One observes a monotonic drift of the radial lattice parameter profiles and a consequent shift of the center of the fitted peaks towards lower values of q_r for larger amounts of GLs. This indicates a less effective relaxation upon rolling, since the average radial InGaAs lattice parameter a_r (out-of-plane lattice on flat layers) increases as more GLs are inserted into the tube. The kinematical model makes use of the inner radius retrieved by SEM measurements and is able to depict the InGaAs lattice relaxation for each layer turn inside the tubes,³⁸ since fits of Fig. 4(a), (c), (e) and (g) result from the incoherent addition of three InGaAs layer turns. Each turn is represented as a dotted line curve. The inner layer diffraction signal is always located at larger q_r values, meaning a smaller a_r, as a consequence of more effective strain relaxation and reduced rolling radius (the sensitivity of these fits is addressed at the ESI of this work†). The distinct intensities for each winding indicate the spread of average orientation of each turn during the formation of our tubes. In other words, the inner layer of the InGaAs/Cr tube contributes to the XRD profile of Fig. 4(a) as the most intense diffraction component, indicating that the first winding is better aligned along the [100] direction. Additional turns slightly de-tune the tube layers from the perfect Bragg condition. For 1, 2 and 3 GLs, shown in Fig. 4(c), (e) and (g), the outer layer scatters with more intensity, indicating the occurrence of a mosaic of rolling directions which is larger at the first winding but lower when more turns are performed. Hence, in tubes with graphene a higher alignment quality is retrieved after some turns. One also notices that as the amount of graphene layers increase the center of mass of the diffraction peak shifts towards larger q_r values (smaller average radial lattice parameter), meaning that the InGaAs relaxation is less effective in such conditions. The lattice parameter distribution obtained from the XRD analysis provides a signature of the elastic energy stored in the InGaAs layers. The lattice profiles of Fig. 4(b), (d), (f) and (h) represent the first turn of each tube (successive turns exhibit slightly distinct profiles³⁵) for 0, 1, 2 and 3 GLs (respectively). The triangular area formed on the right of the crossing point between the a_r (radial) and the a_t (tangential) lattice profiles is larger for more relaxed InGaAs layers, indicating a reduction of stored elastic energy. As the amount of graphene increases, the energy stored on the InGaAs layers tends to be released less effectively, due to the large Young modulus of graphene.

Fig. 4 X-ray diffraction results and simulations for the InGaAs layer lattice inside rolled-up tubes with and without graphene. Panels (a), (c), (e) and (g) show measured XRD data (dots) and fits (solid lines for the overall scattering and dotted lines for the simulated InGaAs XRD of each tube turn) for tubes rolled with 0, 1, 2 and 3 GLs, respectively. Fits with a kinematical model are used to retrieve the radial and tangential lattice parameter profiles, shown here for the inner turn of each tube type in panels (b), (d), (f) and (h).

The scenario discussed above is compatible with increasing tube radii for the introduction of more GLs due to incomplete in-plane relaxation of the InGaAs layers during the rolling process, driving the system elastically into different rolling radii. Plotting, in Fig. 5, the results of a continuum elasticity model and the observed tube radii data as a function of the Cr layer thickness and the amount of GLs²⁰ allows a quantitative estimation of the average radius for each sample configuration (details are provided at the ESI of this work†). For the Cr thickness range and amount of GLs used the tube radius was found to vary between 500 nm (thinnest Cr layer, no graphene) and 2200 nm (thickest Cr layer, 3 added GLs). The homogeneous tube curvature obtained by the variation of the Cr thickness for a fixed amount of GLs allows for an evaluation of the strain on the InGaAs/Cr system as well as the elastic constants of the GLs. The observed InGaAs/Cr tube radius dependence on Cr thickness for tubes without graphene is depicted by the star-shaped dots at the lowest curve of Fig. 5, for 6 different Cr coverages, resulting in a series of tubes with distinct radii. By using this dataset and the elasticity theory depicted in ref. 27 and 28 the lowest curve of Fig. 5 is fitted (solid line). At the semiconductor/metal interface, both XRD analysis and continuum elasticity model points to an in-plane biaxial thermal strain of 2.03%, with a Cr Young modulus E_Cr = 109(5) GPa and Poisson's ratio ν_Cr = 0.28(1) (E_InGaAs and ν_InGaAs were fixed to reference values of 71 GPa and 0.32, respectively). The obtained strain is compatible with the InGaAs/GaAs mismatch for a 29% In composition, evidencing that the Cr layers approximately preserve the pseudomorphic strain induced by the GaAs substrate.^26,32 Finally, the values of the tangential (in-plane) InGaAs lattice parameter profiles (a_t), shown in Fig. 4(b), (d), (f) and (h), shift towards lower values as more graphene layers are added to the tubes. Hence, if bonds between the InGaAs/Cr heterostructure and the graphene layers are formed strain differences should be noticed and directly scale with variations in a_t.

Fig. 5 Analysis of tube radii as a function of the Cr layer thickness and the number of GLs. Symbols in this plot correspond to average radius of tubes with Cr (stars), 1 graphene layer (1G – solid circles), 2 GLs (2G – open squares) and 3 GLs (3G – open circles). Error bars are smaller than symbol sizes in both axis. Solid lines are fits using the continuum elastic theory of ref. 27 and 28.

With the introduction of GLs the tube radii shift towards larger values, as depicted by the data points for the tubes with 1 (filled circles), 2 (open squares) and 3 (open circles) GLs. In these additional datasets an increase of the Cr layer thickness also induces a larger tube radius. The radii of the tube series with a single rolled GL are fitted with a model that considers a 0.4 nm thick GL without interfacial strain (no registry with respect to the Cr layer), with Young modulus E_1G = 800(30) GPa and Poisson's ratio ν_1G = 0.20(2).²⁷ For 2 and 3 GLs the fit considers that the stacked system does not present any registry among layers. This last consideration is related to the weak van der Waals interactions between graphene layers, which do not generate strong built-in interfacial strain. In both cases we retrieved E_Stacked-G = 700(40) GPa and ν_Stacked-G = 0.20(4), for 0.8 nm (2 layers) and 1.2 nm (3 layers) total graphene thickness. Both values are close to results reported on CVD graphene, extracted with different methods.^15,29,34

The values retrieved above must be compared to previous reports from experimental and theoretical groups. One must mention that the elastic properties of CVD graphene are only identical to that of pristine graphene if postprocessing steps avoid structural damage or the formation of ripples. The Young modulus value, which is often reported to be as large as 1 TPa,¹⁵ may have been found to be smaller here due to rippling of some regions of the GLs during the rolling up of our tubes. Our Poisson's ratio value is placed within the range reported in the literature.^7,19,39–41 The figures retrieved by other groups are quite scattered, ranging from between the 0.16 (for free-standing single layers) and 0.36 (the case of ideal contact between GLs and substrate). Although a clear justification of the value retrieved here cannot be directly drawn, we must mention some particularities of our system that may impact on our result. Firstly, the layers are not bonded to the substrate, as indicated by the absence of strain (usually denoted by peak shifts) in our Raman spectroscopy results. Secondly, although geometrical constraints are imposed to GLs in the radial and tangential direction, due to the tube wall contact after successive windings, no constraint is imposed along the tubes axis (longitudinal direction). Therefore, ν_1G = 0.20(2) probably represents an average value from distinct in-plane strain processes. Finally, in our case GLs are in contact with a metallic (Cr) and a semiconductor (InGaAs) surface (placed between both films), differently from indentation processes where GLs lie on a flat substrate or are suspended. Such specificity may imply in surface interactions that also lead to the value retrieved.

In the case where any kind of registry or partial registry would be found among the stacked GLs one would expect a larger Young modulus, shifting towards the asymptotic value of 1000 GPa of AB graphite.^42,43 Our results suggest that the lack of registry between 2 or 3 GLs also produces a lubrication effect on the system. In such scenario, the successive tube windings can slide on graphene–graphene interfaces, producing more compact tubes and leading to the slightly reduced values of E_Stacked-G. This is indirectly evidenced by our continuum elasticity model, since the use of E = 800 GPa (retrieved for a single graphene layer) for 2 and 3 GLs leads to larger calculated tube radii. At this point of our analysis, one may also demand whether anticlastic effects may take place in our geometrical configuration. This is generally the case for indentation procedures, where GLs are held by few and well-defined fixed points during mechanical essays (including graphene support edges, as well as scanning probe microscopy tips).¹⁶ Tubular structures present an inherent advantage with respect to such scenarios, since a large plane area is homogeneously bent with a well-defined curvature radius. We believe anticlastic deformation would be preferentially noticed as a modified bending regime at the tube openings, which is not observed on our SEM measurements. Anticlastic effects may be minimized in our system and should be considered less relevant as the number of GLs increase (due to the possibility of layer slipping discussed above). It may play a minor role, however, on the difference of Young modulus found between one and few GLs.

For all tubes studied in Fig. 5, micro-Raman measurements were carried out for positions on top and outside the tubular structures. The Raman spectra for these conditions are shown in Fig. 6. This technique provides direct evidence of the presence in-plane strain on graphene layers, that could be induced by variation in the tube radius and tangential lattice parameter profile. One notices that the position, width and relative intensity of G and G′ Raman peaks from rolled graphene layers remain consistent with those of flat single- or multiple-GLs, indicating that no out-of-plane registry is observed on stacked GLs and that negligible in-plane strain is induced due to the rolling process. As discussed in our previous work for a single rolled graphene layer,²⁰ this also indicates the formation of strain free interfaces, and a maximum detected strain (maximum Raman shift) below 0.4%.^19,20

Fig. 6 Raman scattering measurements showing the D, G and G′ bands for flat regions (outside tubes, red curves) and rolled regions (inside tubes, black curves) for samples with 1 (upper panel), 2 (middle panel) and 3 (lower panel) graphene layers. All curves show the maximum shift observed from the flat regions to the rolled regions denote the presence of a very reduced strain (less than 0.4%, according to ref. 19).

Conclusions

In summary, we show a direct, large area and nondestructive approach for integrating few-layer graphene systems with semiconductor/metal thin films. Besides the potential application of graphene heterostructure interfaces, we established a method for retrieving elastic properties of atomically thin layers using XRD and continuum elasticity theory. In particular, our results point out that graphene's Young modulus and Poisson's ratio for CVD transferred layers are independent of the amount of stacked material. The mild interaction among adjacent graphene sheets keeps their elastic properties unchanged and our experimental results are fitted by increasing the overall graphene thickness and reducing the Young modulus with respect to the single layer sample. The addition of GLs does not induce local strain due to absence of chemical interactions between adjacent layers or with semiconductor/metal surfaces as shown in our Raman results. XRD allows measuring the strain status of our semiconductor layers, showing that the relaxation of the InGaAs film is affected by the presence of graphene, which partially counterbalances the rolling driving force and produces tubes with larger radii. The properties discussed here are statistically compatible with large-area 2D systems, as e.g. multilayer graphene, relevant for future applications.

Acknowledgements

The authors acknowledge the CNPq, FAPEMIG, CAPES and INCT-Carbon for financial support. The use of the Electron Microscopy Laboratory at LNNano/CNPEM and the XRD2 beamline at the LNLS/CNPEM is also greatly acknowledged.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra22588h

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