Charged nano-domes and bubbles in epitaxial graphene.

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Charged nano-domes and bubbles in epitaxial graphene

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Nanotechnology Nanotechnology 25 (2014) 165704 (16pp)

doi:10.1088/0957-4484/25/16/165704

Charged nano-domes and bubbles in epitaxial graphene A Ben Gouider Trabelsi1,2 , F V Kusmartsev2 , B J Robinson3 , A Ouerghi4 , O E Kusmartseva2 , O V Kolosov3 , R Mazzocco3 , Marat B Gaifullin2 and M Oueslati1 1

Unité des Nanomatériaux et Photonique, Faculté des Sciences de Tunis, Université de Tunis El Manar Campus Universitaire, El Manar, 2092 Tunis, Tunisia 2 Department of Physics, Loughborough University, Loughborough LE11 3TU, UK 3 Department of Physics, Lancaster University, Lancaster LA1 4YB, UK 4 Laboratoire de Photonique et de Nanostructures (LPN-CNRS), Route de Nozay, 91460 Marcoussis, France E-mail: [email protected] Received 1 November 2013, revised 3 February 2014 Accepted for publication 3 March 2014 Published 28 March 2014

Abstract

For the first time, new epitaxial graphene nano-structures resembling charged ‘bubbles’ and ‘domes’ are reported. A strong influence, arising from the change in morphology, on the graphene layer’s electronic, mechanical and optical properties has been shown. The morphological properties of these structures have been studied with atomic force microscopy (AFM), ultrasonic force microscopy (UFM) and Raman spectroscopy. After initial optical microscopy observation of the graphene, a detailed description of the surface morphology, via AFM and nanomechanical UFM measurements, was obtained. Here, graphene nano-structures, domes and bubbles, ranging from a few tens of nanometres (150–200 nm) to a few µm in size have been identified. The AFM topographical and UFM stiffness data implied the freestanding nature of the graphene layer within the domes and bubbles, with heights on the order of 5–12 nm. Raman spectroscopy mappings of G and 2D bands and their ratio confirm not only the graphene composition of these structures but also the existence of step bunching, defect variations and the carrier density distribution. In particular, inside the bubbles and substrate there arises complex charge redistribution; in fact, the graphene bubble–substrate interface forms a charged capacitance. We have determined the strength of the electric field inside the bubble–substrate interface, which may lead to a minigap of the order of 5 meV opening for epitaxial graphene grown on 4H-SiC face-terminated carbon. Keywords: graphene, bubbles, domes, charge density distribution, UFM, Raman spectroscopy S Online supplementary data available from stacks.iop.org/Nano/25/165704/mmedia (Some figures may appear in colour only in the online journal)

Introduction

devices [1–9]. Epitaxial graphene can be grown by annealing SiC substrate surfaces at high temperatures, with different approaches developed to obtain higher-quality graphene films on SiC involving heating in argon at atmospheric pressure [10] or supplying excess Si. These new approaches have led to a significant improvement in the domain size and electronic properties in comparison to vacuum graphitization [10].

Due to its well-documented physical properties, graphene is a promising material not only for fundamental studies but also for future electronic and optical applications, such as field-effect transistors, ultra-sensitive chemical detectors, high-speed analogue electronics, interconnects and spintronic 0957-4484/14/165704+16$33.00

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c 2014 IOP Publishing Ltd

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Nanotechnology 25 (2014) 165704

A B G Trabelsi et al

However, the uniformity of the graphene grown on large SiC substrates, as well as its optical identification, are still the major hurdles hindering the development of technology for the large-scale production of graphene-based nanoelectronic devices. Atomic force microscopy (AFM) is widely used to understand the surface morphology of graphene and related materials at the nanometre scale, whilst force modulation microscopy (FMM) [11–14] may be used to extract limited nanomechanical data. However, it has been shown that ultrasonic force microscopy (UFM) is capable of accurately mapping the mechanical responses as well as subsurface features, such as the graphene–substrate interface, of these very stiff materials with nanometre resolution [15, 16]. Raman spectroscopy is a non-destructive investigative technique widely used to study the defects, disorder, chemical modifications, edges, number of layers, strain effects and doping [17–23] of graphene-based materials. The graphene Raman spectra show different first-order (D and G bands) and second-order (G∗ , 2D and (D + G) bands) phonon modes. The D band corresponds to the transverse optical (TO) phonon arising at K-point of the Brillouin zone (BZ), indicating the breathing mode of the six C atoms forming the hexagon. It is activated by an intra-valley scattering process and requires lattice distortions or defects to be observable [24, 25]. The G band is associated with the E 2g phonon at the BZ centre (the 0-point). The G∗ band corresponds to an inter-valley process involving one TO phonon and one LA (longitudinal acoustic) phonon [26, 27]. The 2D-peak is assigned to two phonons, i.e. the second order of the D-peak, reflecting the evolution of the band structure [28, 29]. The (D + G) band depends strongly on the presence of defects in the graphene layers. Here, graphene doping has been determined using the Raman method, originally introduced by Ferrari et al [30], where a blue shift of the G mode associated with a decrease in the full-width at half-maximum for both electron and hole doping and an intensity dependence of the 2D band on doping assigned to the influence of electron–electron interactions on the total scattering rate of the photo-generated electrons and holes were observed. Due to the doping, an increase in screening and, consequently, a narrowing of the bandwidth occurs. However, here, agreement with these previous results is observed only in some areas of the epitaxial graphene bubbles—those where we have observed high doping. Additionally, for single-layer graphene the highest intensity ratio of the 2D and G peaks, I2D /IG , and its associated areas, A2D /AG , reach a maximum for zero doping and decrease with increasing doping; hence, Raman spectroscopy can be used both to determine separately or concurrently the native strain and charge doping in graphene, [31]. For graphene deposited on SiO2 /Si substrates, Raman analysis shows different shifts of the G and 2D bands for strain and doping; in particular, the hole doping induced by electrical gating leads to a quasi-linear dependence, where (1ω2D /1ωG )hole = 0.75 ± 0.04. For biaxial strained graphene, either compressive or tensile, many groups reported large experimentally determined ratios of (1ω2D /1ωG )εbiaxial of 2.45 [32], 2.63 [33] and 2.8 [34]. Although theory predicts slightly smaller values

of 2.25 [35] and 2.48 [36], it is still significantly larger that the ratio shifts due to doping. Detailed analysis [31] shows that this strong difference in the shift ratios may be useful for fast and reliable characterization of strain and excess charges in graphene when both doping and strain are present. Indeed, applying similar analysis, we found that within our bubbles we have very small strain fluctuations, i.e. very similar to the ones observed in [31]. In fact, the latest reference reported for graphene deposited on SiO2 where, due to the presence of the substrate, an in-plane strain occurs randomly between −0.2% and 0.4%, the material undergoes modest compression (−0.3%) and significant hole doping due to thermal treatments appears. Here, based on the recent development of the Ferrari method [30, 31], we use the Raman spectral mapping as an efficient way to characterize the nonuniform local strain change and local graphene charge density distribution. The latter could be clarified by studying the graphene–substrate interface, where strong coupling between plasmons and substrate phonons occurs [37]. For graphene, the collective charge excitations of the electron–hole gas, i.e. plasmons, originate from the chemical potential fluctuations induced by an external electromagnetic field. The plasmon density variations increase in the vicinity of the Dirac point of the electron spectrum [38], where the density of charge carriers vanishes. In this case, the position of the chemical potential or the Fermi energy (E F ) is very important. For an E F located in the gap of the Dirac spectrum, mini-polaritons having a long enough lifetime may be Bose-condensed [39]. Otherwise, these polaritons may have a strong damping due to a high coupling with electron–hole Landau quasi-particles [40]. In this paper, for the first time, new structures, i.e. ‘bubbles’ and ‘domes’, on the SiC epitaxially grown graphene have been identified. Their clear images, their freestanding nature and stiffness have been determined using UFM. Raman mode (G and 2D lines) mappings of the graphene show similar behaviour to the UFM measurement, where different bubbles separated by uniform terraces have been located. We also show that these structures lead to the modification of the electronic properties of epitaxial graphene grown on 4H¯ Possible charge transfer due to substrate–graphene SiC(0001). electrostatic interactions in the graphene bubble has been discussed, where we have estimated the free electron carrier concentration across the chosen bubble. This effect has been investigated in detail by means of local Raman mapping of the intensity ratio of the 2D and G bands, i.e. I2D /IG . The total system of the graphene and substrate is charge neutral; therefore, using this charge neutrality, an intrinsic doping of the substrate surface layer has been determined, identifying a new charge redistribution effect arising between the positively charged substrate and negatively charged graphene bubble. This doping effect, or redistribution of the charge between the substrate and graphene, has been also independently determined using methods presented in [19]. This finding allows us to develop, also for the first time, a new non-invasive method for determining the electronic distribution in complex graphene bubble–substrate systems and describing its variation across the bubble surface; the electric field inside the bubble and the quantum capacitor, as well as the charge accumulated 2



Figure 1. Image obtained using an optical microscope in the different graphene areas ‘GA’: (a) GA1 (100×), (b) GA2 (50×) and (c) GA3

(100×).

at the substrate–graphene interface, have been determined. Finally, we have investigated the gap opening for the bubbles and there revealed the presence of a small minigap, which is probably also associated with impurities affecting the single-layer graphene.

simultaneously recording the topography of the sample in the standard AFM way. Sample mounts are composed of a glass cover slip bonded to the top face of the piezoceramic disc (PI Piezomaterials) with cyanoacrylate. The sample was attached to the glass cover slip using salol (phenyl salicylate) heated to above 45 ◦ C prior to re-crystallization [43], resulting in almost perfect coupling of the longitudinal and shear ultrasonic vibrations at frequencies up to several tens of MHz.

1. Material preparation and the experimental setup

¯ via an epitaxial route Graphene was grown on 4H-SiC(0001) −10 in UHV (P = 2 × 10 mbar) by electron-bombardment heating, as described in detail elsewhere [41]. Initially, the epitaxial substrate was etched in a hydrogen atmosphere at 1500 ◦ C at 200 mbar for 15 min in order to remove all the damage induced by the surface polishing and form a step-ordered structure on the surface. Then, the substrate was degassed at 700 ◦ C for several hours and annealed under a Si flux at 900 ◦ C to remove the native oxide. Subsequently, the sample was annealed at different temperatures between 1100 and 1300 ◦ C in a UHV chamber equipped with a Si source. Finally, the presence of graphene was confirmed by XPS experiments (Kratos Analytical System) using an Al Kα monochromatic (1486.6 eV) source with an overall energy resolution of ∼350 meV. Raman spectra have been obtained with a high-resolution micro-Raman instrument (Jobin Yvon HR LabRAM) in a backscattering confocal configuration at 300 K. We use an Ar+ laser at a wavelength of 488 nm as an excitation source. The laser power was controlled at 5 mW on the sample surface. We have used a 100× objective lens to focus the laser beam on the surface and collect the scattered light for room-temperature measurements from different local spots forming a pixel pattern. The spatial resolution of the image was 1 µm, while the spectral resolution was about 1.65 cm−1 . Contact mode AFM was used to study the topography and friction (torsional) response of the graphene samples. All measurements were performed in ambient laboratory conditions using standard contact mode cantilevers (Contact-G, Budget Sensors, k = 0.2 N m−1 ). Subsurface imaging and nanomechanical mapping were conducted using UFM via a modification to a commercial AFM system (in this case a Nanoscope IIIa, Bruker AXS) reported in detailed elsewhere [42, 15]. Detection of the UFM signal allows the effective mapping of nanomechanical properties with nanoscale resolution, while

2. Results and discussion 2.1. Surface morphology: identification of epitaxial graphene nano-domes and macro-bubbles

The sample surfaces of epitaxial graphene grown on 4H¯ substrates were initially investigated using SiC(0001) room-temperature optical microscopy, identifying various non-typical surface morphologies (see figures 1(a)–(c)), the main, representative morphologies of which are denoted GA1 , GA2 and GA3 . The optical images obtained in these areas imply morphological differences (see figure 1) investigated using AFM, UFM and Raman methods. Figure 2 shows the AFM topography obtained in contact mode, clearly highlighting the different features in GA3 in comparison to GA1 and GA2 . In GA1 , curved atomic terraces (500 nm wide, uniform height of 10 nm between the adjacent terraces) have been distinguished (see figure 2(a)). GA2 shows terraces with a different orientation from GA1 and smaller regular terraces (250 nm wide, 10 nm height between adjacent terraces) arranged with equidistant steps (see figure 2(b)). The uniform step height along the terraces indicates an identical stacking sequence of Si–C bilayers in this area, as discussed in detail previously [44, 45]. The corresponding main mechanism is attributed to the repulsive step interaction through the minimization process of the total surface energy; however, the presence of equidistant step structures as well as the step bunching of macro-steps could be assigned to an asymmetrical step kinetics mechanism that allows the varied stepped morphology, as reported in GA2 . Here, the terrace heights in GA1 and GA2 are significantly larger than one would usually expect for a graphene layer, i.e. about 5 nm. In fact, generally speaking, the height of the graphene terraces is between approximately a half to a few unit cells of the 4H-SiC 3



Figure 2. Atomic force microscopy (AFM) images obtained in the investigated graphene areas ‘GA’ with different scales. (a) GA1 , (b) GA2 ,

(c) GA3 .

substrate, i.e. 0.5–2 nm [46]. These terraces reach a maximum height for face-terminated C. But, for high-quality 4H-SiC wafers the terrace height decreases and becomes comparable to those on face-terminated Si [47, 48]. Likewise, we noted the appearance of nanometre-size structures even at low resolution for both studied areas. The AFM shows quite different behaviour in GA3 (see figure 2(c)); the result obtained here does not agree with previously reported measurements [48, 49] obtained for epitaxial graphene grown on C or Si face-terminated SiC, or other SiC polytypes. In this area, the sample surface shows large uniformly distributed terraces (500–600 nm, 5 nm between adjacent terraces) and equidistant steps are observed. We note the presence of unusual, AFM scan-independent, circles in the stepped morphology, extending over a few terraces. These circles could not be attributed to the simple roughness of the surface, i.e. 0.5–2 nm, commonly observed for epitaxial graphene grown on 4H-SiC substrates [46, 50, 51], or defects due to their large size and location, far from terrace intersections. These features were further studied by supplementing AFM topography with simultaneous UFM nanomechanical

mapping (figure 3), where the lateral resolution is maintained at approximately 2 nm. A brighter response in the UFM images corresponds to mechanically stiffer areas, whilst darker areas correspond to less mechanically stiff areas—areas with no UFM signal correspond to negligible or zero mechanical contact between the sample and the substrate. We assume that the uniformly distributed dark, hence lower rigidity, regions correspond to localized epitaxial graphene structures (EGS), which could be identified as domes and/or bubbles, respectively, in GA(i=1, 2) and GA3 . In some areas, these EGS show lighter contrast (light brown colour, see figure 3), indicating the different widths and heights that the domes and bubbles may have. However, all show a backbone oriented almost parallel to the surface, with roofs of different forms, i.e. circular and elliptical, dependent on their location on the sample surface. We noted an important difference in the size of the graphene structures obtained and denote those of nanometric size (≈150–200 nm) as ‘domes’ and those of several micrometres in size (≈2 µm) as ‘bubbles’. The measurements indicate a height of 5–12 nm for EGS in both GA1,2 and GA3 . UFM analysis indicates a complex 4



Figure 3. Ultrasonic force microscopy (UFM) images obtained in the studied graphene areas ‘GA’ with different scales. (a) GA1 . (b) GA2 . (c) GA3 .

mechanical response for the epitaxial graphene surface, where some domes show good mechanical stiffness in the centre (see in figure 3(a) the dome highlighted in a white square), indicating a partially supported centre with a decoupled ‘skirt’ around the perimeter (see in figure 4 a representation of this EGS shape). The supported centre is higher (12 nm) and stiffer, corresponding to Si droplet/pillar contamination below the graphene layer, discussed in detail below. However, the many smaller domes, which do not show a stiffer centre, appear completely delaminated from the substrate (see in figure 3(a) the domes highlighted inside the blue square and in figure 4(b) the representation of this EGS shape) with a UFM response corresponding to a lower stiffness than the surrounding material. Topography shows that the large circular regions in figures 2(c) and 3(c) are approximately 0.5–1 nm lower than the surrounding stiffer material. Also, we note large numbers of truly suspended features concentrated within the bubble regions, with diameters of up to 500 nm and heights of approximately 8 nm. We see the highest ‘stiffness’ for regions between the circular features, i.e. bubbles, then a drop of approximately 20% in the nonlinear response, indicating

that either the material comprising the bubbles is not as stiff or, if the same, the mechanical contact is not quite as good (see the blue line in figure 3(c)). There is a further drop over the suspended features to virtually zero—hence these are true delaminations or ‘freestanding nano-domes’ inside the bigger bubble. With increasing nano-dome density, we would expect a decrease of bubble stiffness arising from the more porous structure, i.e. a high density of ‘freestanding nano-domes’ on the bubble surface. Moreover, the EGS observed here differ from exfoliated graphene bubbles reported previously [43] in a number of important ways; firstly, the identification of the exfoliated bubbles was done using optical microscopy with the use of Newton rings; however, due to the lower height of our EGS compared to the bubbles reported in [51, 52], the Newton rings cannot be observed. Secondly, the characteristic dimensions of our EGS are smaller and orders of magnitude lower in height (≈1%) than those described in [52, 32]. However, the advantages of our epitaxial graphene bubbles compared to the other bubbles, which were CVD grown on Pt, are their different sizes, shapes and locations, which are randomly distributed 5



Figure 4. (a) Image of epitaxial graphene structures (EGS) having a supported centre with a decoupled ‘skirt’ around the perimeter, as discussed in the text. (b) Image of epitaxial graphene structures (EGS) completely delaminated or ‘freestanding’. (c) UFM images taken in ¯ substrate. GA2 , proving the presence of the step bunching of the 4H-SiC(0001)

across the sample surface. Analysis of the variation of the mechanical responses, in a comparison with those CVD grown on Pt [53], elucidates the time-dependent development of the epitaxial graphene growth. The low density of Pt bubbles, which are limited to the edges of the graphene flakes, arises from the easy decoupling of the monolayer graphene of the Pt substrate edges.

of the constant temperature lines. These lines, randomly oriented, intersect with those coming from the next closest defects and, therefore, when the temperature around the defect increases the number of constant temperature lines, which are separated by small fixed temperature intervals, also increases. This temperature gradient may induce the appearance of small-sized graphene nano-structures such as ‘nano-domes’, as observed in GA1 and GA2 . The other type of graphene structure may originate from volume defects located in the SiC substrate. These defects are characterized by a temperature lower than that associated with the surface defects when compared at the same experimental conditions. In this case, the intersection of the constant temperature lines is reduced and broad graphene-bubble structures, i.e. ‘macro-bubbles’, appear. Such bubbles are similar to those presented in GA3 . On the other hand, the step bunching imposes different orientations of the terraces, which originate from the substrate terrace itself. Therefore, the step bunching affects the local temperature gradient already imposed by the defect nature across the sample surface, and changes the shape of the graphene surface into the bubble- and dome-shaped structures. Note that the mechanism of EGS formation due to the defects described here becomes clearer when we recognize that these defects coexist with step bunching. There, the distribution of the constant temperature lines is also a result of step bunching and, thus, also affects the graphene layer shape. On the other hand, the Si nano-droplets and nano-pillars play an important role in the presence of some domes inside the bubble. Typically, the bubbles of small size (less then 1 µm) are empty, while the bubbles of larger size (more than 1 µm) have smaller Si nano-droplets and nano-pillars inside; mostly located on the sides and in the foundation of the bubble. In fact, these inclusions support the graphene layer (roof of the big bubble). Of course, in the area of support the bubble is elastically stiffer and the Raman signal stronger. Their porous structure provides lower stiffness than its surrounding substrate. The difference in thermal expansion between graphene and the substrate plays an additional role in the appearance of these structures. In fact, it is responsible for different surface features, such as wrinkles or ripples [57]. In fact, due to the development of our growth process, we can divide the obtained bubbles into three types: (1) bubbles with

2.2. Mechanism for the formation of epitaxial graphene domes and bubbles

Different hypotheses may explain the growth process and the origin of the different sizes and shapes of the EGS. Typically, the growth temperature steps are the main factor inducing such variation in the graphene layer morphology; however, here, this is unlikely due to the precise control of the growth temperature. Therefore, we assume a more general mechanism of the EGS formation which does not depend on particular experimental conditions. Previous works reported the location of small bonded features in the terraces with different shapes, such as triangular protrusions or hexagonal patterned holes, that could derive from etching effects or extended stacking faults and screw dislocations or micro-pipes, respectively [47–49, 54]. However, no mechanical reason has been observed for these etching structures [47–49, 54]. Therefore, the etching effect may not be the origin of such structures. Thus, using a careful study of our EGS, we found that there are mainly three hypotheses able to explain the creation of such structures: (1) the defects, (2) step bunching in the 4H-SiC substrate, and (3) Si nano-droplets and nano-pillars. In fact, these factors show a great complementarity. First, defects have a strong effect on the graphene layers—indeed, defects create a temperature gradient across the sample surface, decreasing from the centre of the defect to the surrounding area, inducing the appearance of constant temperature lines in the graphene layers that become deeper depending on changes in the local defects and the surface morphology. This morphology change requires the presence of different types of defects, which must always be present, namely surface defects and volume column defects [55, 56]. The first type is mainly attributed to the graphene layer; the temperature increases in the central defect area, which enhances the appearance 6



the complementarity of the step bunching and the defect origin of domes and bubbles, as discussed above, we have represented the observed step bunching in GA2 using an optical microscope, UFM measurements and the Raman mapping intensity of the 2D and D bands (see figure 6). In order to verify the first hypothesis, we analysed the optical image of the sample surface (see, figure 1(b)). There, we distinguished large areas in the centre surrounded by two other regions with different contrast and orientation, assigned to the step bunching in 4H-SiC. Additionally, the step bunching was also clearly observed with lateral force (friction) measurements (see figure 4(c)). Moreover, Raman mapping clearly shows the edges between two areas as identified by UFM (see figure 4(c)). A low intensity appears in the upper area (a) that decreases in the lower area (b), respectively for the D and 2D bands (see, figures 6(d) and (e)). The increase of defect density in the lower part of the figure could be attributed to ripples originating from the step bunching. Proof of the existence of Si pillars and droplets obtained using Raman analysis is given in detail in supplementary material (see, supplementary material 1: Raman analysis of Si droplets and/or Si pillars presence available at stacks.iop.org/Nano/25/165704/ mmedia). The detailed analysis of the AFM, UFM and Raman spectroscopy measurements demonstrates the unambiguous mechanism of bubble and dome growth associated with different defects, step bunching and Si pillars and droplets.

a flat graphene layer surface above the nano-domes (here the nano-domes are not high and present with a weak density), (2) bubbles with a small number of nano-domes mostly reside at the edges, and (3) bubbles with many nano-domes randomly distributed across the graphene layer surface (see figure 3(c)). The Si droplets originate during the epitaxial graphene growth process, a solid state evaporation (sublimation process), where Si leaves the SiC bulk sample. Here, due to the relatively low growth temperature and the high Si vapour pressure, it may be difficult for Si atoms to leave the interface, leaving some contamination behind. In fact, on the surface of SiC, there is probably a microscopic phase separation of Si and C. Due to strong sp2 bonding the carbon atoms are self-organized into graphene (single or/and multilayer). The Si atoms leave the SiC sample, until they encounter an obstacle in the form of a graphene layer (probably a flake); when the graphene flake is created at high temperatures (1400 ◦ C), it experiences a pressure from the flux of these Si atoms (Si‘gas’). Under this pressure, the nearly created graphene layer (flake) may form a bubble (although not the final bubbles which we observed). At this stage, the effective pressure under the decoupled graphene layer is greater than above the layer, and the resulting induced tension in the monolayer contributes in addition to the Si atoms released from the SiC bulk, which are now trapped under the graphene layer and form Si droplets or Si pillars. This features exactly the phase separation of SiC into C (graphene flake, nano-dome) and Si (nano-clusters) arising on the surface of the SiC substrate. Inside this bubble there will be nucleated small flakes of the new layer, identically, they are self-organized in nano-domes. Post-growth, the graphene layer relaxes to some equilibrium position where the areas of graphene decoupled from the substrate partially lie back down to form big bubbles, which in turn contain nano-domes. These Si pillars and droplets are the posts on which the newly formed domes and bubbles reside. Importantly, the lifetime and stability of these structures represents a significant advantage. The large bubbles are stable; however, when the size of the bubbles decreases, i.e. nano-domes, their stability is far less clear. They are probably stable at very low temperatures. However, when the temperature rises, thermal fluctuations may change their shape. Therefore, we assume that large bubbles have long lifetimes compared with small structures such as nano-domes. Figure 5 summarizes the growth process of the epitaxial graphene bubbles and domes as described above. To characterize the structures found we have used both inclined platform optical microscopy, to aid with sample transparency, and Raman spectroscopy analysis. Figures 6(a) and (b) show the images obtained with the optical microscope in GA3 , where we observe white columns going from the back of the samples to the graphene surface—a signature of volume defects. Many white points randomly distributed at the surface have been observed in GA1 and GA2 respectively (see figure 6(c)), which correspond to surface defects. We also note the presence of small white points next to each column (figures 6(a) and (b)); these are not surface defects as reported in GA1 and GA2 , but correspond to reflections of the columns observed in the upper face of the sample arising from the interference phenomenon. Moreover, to prove

3. Mapping of Raman spectra on the sample surface

The optical properties of the graphene structures were investigated using local intensity mapping of the graphene Raman active modes associated with the D and 2D bands and the intensity ratio IG /I2D respectively in the areas GA1 , GA2 and GA3 (see insets to figures 7(a)–(c) and (e)). Due to the similarity between GA1 and GA2 , we present here a Raman study of the area GA1 only, as this is typical. Raman measurements were carried out in periodic locations (0.5 µm horizontal and vertical step sizes) across the flake and checked at each point using an auto-focusing adjustment. Two different behaviours have been distinguished in the studied areas. Firstly, the Raman mapping intensity of the 2D band in GA1 shows small flakes of lower intensity surrounded by brighter areas of different shapes, which, from the UFM study, we identify as nano-domes, the dimensions of which exceed the limit of our beam scale (see figure 7); hence with Raman mapping we observe only the areas associated with the agglomeration of many domes. It should be noted that the 2D Raman mapping in the area GA3 shows remarkable circular structures of high intensity and different radii separated by darker homogeneous terraces (see figure 7); these structures look similar to the macro-bubbles identified independently using UFM measurements. The mapping intensity ratio of IG /I2D obtained in areas GA1 and GA3 showed similar behaviour to the 2D band, where the graphene domes and bubbles are clearly seen. These structures also displayed a low intensity ratio IG /I2D , which we ascribed to a signature of the low graphene layer number. Thus, the analysis of optical and Raman mapping data confirms the epitaxial graphene structures identified by UFM; 7



Figure 5. Detail of the formation of graphene bubbles and domes in comparison with the ordinary growth of epitaxial graphene: (a) 4H-SiC substrate. (b) Ordinary epitaxial graphene growth. (c), (d) and (e) Sublimation of the Si in the bilayer Si–C from the substrate and the accumulation of the carbon atoms in three steps, respectively, as a function of the temperature lines induced by the surface and volume (column) defects, until the formation of the graphene layer. (e) Formation of the epitaxial graphene bubbles and domes. (f) Cross section of the substrate, showing the end of the silicon (Si) sublimation and the organization of carbon (C) on the graphene layer. (g) Clear image of the step (e and f) showing the growth of different types of bubbles and domes, as given in detail in the main text. Here, the pink colour that fills some EGS corresponds to Si droplets and/or pillars originating from some sublimated Si atoms left below the graphene layer. The small features located in some large bubbles (similar to those located in the blue circle) correspond to the nano-domes. The transparent EGS are empty (similar to those located in the orange circle), while EGS without a high density of nano-domes grown above Si pillars are similar to those located in the sky-blue circle.

it is especially illustrative for the larger dimension structures, i.e. bubbles. Raman mapping has clearly imaged a large bubble-containing homogeneous area of epitaxial graphene and has, for the first time, provided a visual identification of the graphene terraces that allow interactions with the substrate and bubble structures on these terraces. Also, our observations identified nano-size graphene domes and presented a visual identification of macro-bubbles of epitaxial graphene and their boundaries. The optical, mechanical and electrical properties of these structures will be discussed below.

Table 1. Main characteristics of the graphene Raman spectra (D, G, G∗ , 2D, (D + G) modes) observed respectively in Z 1 and Z 2 .

Spectra

D (cm−1 )

G (cm−1 )

SZ1 SZ2

1366 1368

1590 1589

Raman modes G∗ 2D (cm−1 ) (cm−1 ) 2450 2449

2722 2726

(D + G) (cm−1 ) 2954 2962

spectra all the first-order graphene Raman modes, such as the D and G bands [58, 59], and the second-order modes G∗ , 2D and (D + G) (see table 1). The graphene Raman lines manifest high intensities for both Z 1 and Z 2 (figure 7), similar to those of isolated layer of graphene similar to exfoliated suspended graphene [26]. This occurs due to the weak contribution of the second-order Raman mode of the SiC substrate and also due to the freestanding nature of the graphene layer in EGS. This also shows the high quality of the graphene from which the EGS are made. Focussing on GA3 , where the graphene

3.1. The analysis of Raman mapping of the epitaxial graphene ‘bubbles’

The Raman spectra of the graphene layers exhibit a set of first- and second-order Raman modes in the frequency range (1000–3000 cm−1 ). The Raman spectrum Z 1 corresponds to the agglomeration of nano-domes, while the spectrum Z 2 corresponds to the bubbles (see figure 7). We see in these 8



Figure 6. Images obtained using an optical microscope slightly inclined with respect to the microscope platform (and its negative): (a) (a1 ),

(b) (b1 ) Volume defect. (c) (c1 ) Surface defect. (d), (e) Raman mapping intensity of the D and 2D bands proving the step bunching observed in GA2 .

bubbles are clearly identified, we observe an area with a highly homogeneous 2D band intensity. It is surrounded by another area with low intensity. We also see long terraces separating the bubbles, which are associated with lower intensity. Thus, the Raman spectra within the bubbles show comparable properties to those in the suspended exfoliated graphene [60]. This result is remarkable and has not, to the best of our knowledge, been previously reported for epitaxial graphene.

exhibits behaviour similar to suspended graphene. As the bubbles showed different micrometric sizes we chose to focus on one typical bubble, of size 5 × 4 µm2 , which is in good correlation with our high-resolution beam focusing scale limit; we note that the shape and size are also in good agreement with the UFM measurements. The Raman spectra show a high intensity, especially at the centre, for both the G and 2D bands. The growth process here reveals the existence of three possible types of bubbles, therefore different Raman responses are expected. Predominantly, the nano-dome locations depend on their density and their presence on the extended graphene layer surface above. The UFM measurements show that the majority of these domes have diameters less than 500 nm and, due to their different sizes, we expect to localize a high Raman signal in the area of their agglomerations, where the signal arises from many nano-domes (as we have observed in GA1

3.1.1. Raman spectra of single epitaxial graphene bubbles.

In order to investigate the properties and formation of epitaxial graphene bubbles we have imaged the sample surface using the local intensity mapping and spectral position of the graphene Raman active modes associated with the D and 2D bands and the IG /I2D and I2D /IG ratios (see insets to figures 8(a)–(d)). The entire Raman spectrum inside the bubble 9



Figure 7. Raman spectra, Z 1 and Z 2 , of graphene layers taken in GA2 and GA3 . Inset: (a), (d) Mapping Raman Intensity (MRI) of the 2D band, (b), (e) MRI of the ratio of the G to 2D bands, i.e. IG /I2D . (c), (e) MRI of the D band obtained in GA2 and GA3 respectively.

Figure 8. Raman spectrum on the bubble and Raman mapping intensity of: (a) the ratios I2D /IG and (b) IG /I2D ; (c) the D band; (d) the 2D band; (e) FWHM of the 2D band; (f) Raman shift of the 2D band; (g), (h) Raman shift variation in X = 1 and X = −1, respectively, along the Y axes (Y [−5, 5]) across the bubble.

10



field arising inside this capacitor; due to such a field a gap opening may arise [39, 67]. Graphene properties depend highly on the substrate type. In fact, the intrinsic charge impurities of the substrate may act as a gate voltage and provide a local doping [19], resulting in a charge transfer from the graphene to the substrate and the epitaxial graphene layer being naturally n-doped. This induces strong Coulomb forces and a transverse electrical field in the substrate–graphene system, in the same way as in the plate capacitor. Thus, in epitaxial graphene the capacitance effect appears. Moreover, such charge redistributions between graphene and the substrate could modify the optical properties, dielectric constants and the Raman spectra [19]. Indeed we observe a change of both the Raman spectra of the graphene and the substrate. Using Raman spectroscopy on epitaxial graphene bubbles, we give here, for the first time, a description of a strong Coulomb coupling of the graphene layer with the substrate and the associated charge redistribution. In fact, here, due to the development of the epitaxial graphene bubble grown, we found a possible field variation inside the bubble due to a doping effect where the new charge redistribution appears. Compared to previous work, we found possible field creation due to a doping effect, not only due to a strain effect. In fact, [53] reported a field determination of Pt bubbles arising under a giant strain effect created with decreasing temperature, due to the difference in the thermal expansion of Pt and graphene. This differs from our case, where our epitaxial graphene bubbles arise during the growth process at high temperatures, where all practical strain effects are relaxed.

and GA2 samples, above). Indeed, we see two cases: of low and high densities of domes. Here, the Raman mapping shows a flat graphene layer associated with the bubble surface above the nano-domes. We note a high intensity in the centre of the bubble, assigned to the presence of a Si droplet underneath. In fact, for C-face grown graphene, the layers may be electronically or even spatially decoupled, as reported in [61, 62]. Therefore, we can not rule out this possibility here and we have to study the low-energy interlayer Raman mode, which for the bilayer is about 42 cm−1 [63]. The layer number n of the epitaxial graphene bubble has been identified using the full-width at half-maximum (FWHM) of the 2D band correlated with the intensity ratio of the G and 2D bands (IG /I2D ). We have determined the FWHM of the 2D band across the bubble, which is on the order of 38–63 cm−1 ; such a value indicates single-layer graphene [59] (see figure 8(e)), which we confirm through investigation of the intensity ratio (IG /I2D ). As reported in the literature [64–66], a ratio less than 0.5 corresponds to single-layer graphene, 0.5–1 to a bilayer and 1.8 and above to multilayers (n > 5). In the area surrounding the bubble centre we observe intensity ratios of the G and 2D bands (IG /I2D ) of approximately 0.7 and 1.5 in the centre and on the edges of the bubble (see figure 8(a)). In fact, the correlation between the two methods indicates a signature of single-layer graphene. Here, we noted a low intensity ratio IG /I2D occurs at an intermediate position between the centre and edge of the bubble, while it reaches high intensity in the centre and the bubble edges. Indeed, the low intensity ratio (IG /I2D ) could be attributed to the high doping effect reported previously [19] and is a possible explanation for the variation observed in the behaviour of the intensity ratio (IG /I2D ) relative to the 2D band FWHM recorded in some sample areas. However, it may arise from other factors, including the weak contribution of the substrate at the bubble edges. Thus, using these methods, we have determined the graphene layer, numbers n, to single layers of graphene [64, 65]. The origin of the dispersion or broadening of the 2D band, i.e. the high value of the FWHM and the intensity ratio, IG /I2D , is attributed to the doping effect. Here, the strain is very small across the bubble and, therefore, can be neglected (for details, see supplementary material 2: strain effect investigation available at stacks.iop.org/Nano/25/165704/mmedia.

4.1. Electron density distribution on epitaxial graphene bubbles

To determine the charge distribution between the substrate and the graphene layer, we have used the Geim group method of the corresponding dependence between the charge density of the graphene and the intensity ratio of the 2D and G bands (I2D /IG ) (see figure 1 in [19]). Using this correspondence and the mapping of the intensity ratio of the 2D and G bands (I2D /IG ) of the surface we have determined the charge density distribution in the graphene layer and observed a homogeneous charge density distribution in the bubbles. Here, the ratio I2D /IG reaches a small value in the roof as well as in the foundation of the bubble. In spite of there being large areas with a homogeneous charge density distribution, the intensity ratio (I2D /IG ) varies from 0.5 to 1.5, and its change from point to point taken on different homogeneous areas indicates a different local carrier density in each of them (see figure 9(a)) [19]. Using the method given in [19], we have determined the corresponding charge density in each of these areas. Figure 9(b) represents the respective electron density distribution across the bubble and the surrounding area. We found an electron concentration variation between 0.75 × 1013 and 3 × 1013 cm−2 (see figure 9(b)). Our results clearly show that there is a strong electron doping of the epitaxial graphene layer, as mentioned above [19]. The determined electron concentration in the graphene bubble exhibits a large variation, reflecting the inhomogeneous substrate behaviour.

4. Capacitor formation on epitaxial graphene bubbles

Here we have investigated the charge redistribution between the graphene layer, naturally n-type doped, and the substrate, using the Raman mode variation. This intrinsic doping affects the near-surface area of the substrate, and the surface, in the volume near the surface a new charge density distribution could appear. Therefore, the graphene bubble together with the charged area of the substrate form a layered charged system which can be considered as a plate capacitor and therefore described by an effective total capacitance, C. We must therefore consider the charge on the graphene layer, the charge density distribution of the substrate and the electric 11



Figure 9. (a) Raman mapping of the intensity ratio I2D /IG . (b) Electron density distribution mapping. (c) Mapping of the Fermi energy variation across the bubble. (d) Electric field distribution mapping.

signal will be very small compared with the Raman scattering from the graphene–substrate charged system from which the bubble is made. Such a graphene bubble–substrate interface forms a charged capacitance (for details, see supplementary material 3: Quantum capacitance available at stacks.iop.org/ Nano/25/165704/mmedia).

Here, in the graphene–substrate interface, phonon–plasmon coupling occurs which is strongly enhanced due to the formation of the charged capacitor. Thus, for non-intentionally produced bubbles, we have determined the electron density distribution in the graphene layer. Consequently, due to the charge neutrality of the whole system, a thin layer of SiC substrate is highly charged with the opposite charge to the bubble graphene layer. Due to the negative charge of the graphene layer, assigned to the electron doping, a positive charge in the SiC substrate appears. As a result, the total charge of the system is zero and the neutrality condition is verified. Thus, the graphene bubble and the substrate form a highly active ‘capacitor’ system, which accumulates charge. It arises due to charge redistribution between graphene and the substrate. This capacitor behaves as a resonance cavity for plasmon excitations as well as acting as a mirror, which limits and screens the penetration of electromagnetic radiation from outside to the uncharged volume of the SiC substrate. Actually, we will not determine the precise number of Si–C bilayers involved in the capacitance system. The charged capacitor forms a mirror or a filter for such radiation. In fact, we have used the 488 nm line of an Ar-ion laser as the exciting probe. Knowing that Raman spectroscopy is not a surface probe, we were able to characterize the charge distribution in an area of the substrate a few µms thick. To achieve this, here we have used a high-resolution confocal arrangement of the Raman spectrometer. This leads to probing a typical depth of 1–2 µm, after which most of the incident radiation will be stopped. Although we expect that a small fraction of this radiation will penetrate deeper than 1–2 µm, its contribution to the Raman

4.2. Gap opening

Graphene properties show a strong dependence on the type of substrate and are especially pronounced for samples thermally evaporated, such as epitaxial graphene [60]. One of the important effects of the substrate is the band gap opening in the graphene Dirac spectrum which arises due to symmetry breaking between the transverse lattice distortions of the A and B sub-lattices associated with the graphene–substrate interaction [39]. Suspended graphene shows no gap or intervalley splitting associated with the Dirac K and K 0 points of the Brillouin zone under a transverse lattice distortion [39]. These points remain invariant for any symmetry breaking between up and down displacements. However, the presence of the substrate may induce additional forces—for example, a van der Waals force—that acts with different strengths on atoms located in up and down transverse lattice displacements. In [39] it was shown that such symmetry breaking between the A and B distorted sub-lattices arising due to a substrate may lead to gap opening. The effect may arise for epitaxial graphene with the substrate in the form of the 4H-SiC face-terminated carbon. There is controversy in recent studies regarding the gap opening for epitaxial graphene face-terminated carbon [68], 12



Figure 10. The flatness change of the graphene layer grown on a 3C-SiC (100) substrate to nano-bubbles, imaged using AFM and UFM

measurements: (a) AFM image of the sample surface. (b) AFM image of the nano-bubbles. (c) UFM image of the nano-bubbles.

The intrinsically grown bubbles may help to develop many applications for graphene electronics which require a deliberate change of the graphene charge density. In fact, the formation of the gap is very important, since only in this case may one produce the basic elements required for graphene-based quantum devices such as transistors [70]. The existence of charge density puddles has a strong influence on the transport, electron mobility and conductivity in graphene and their identification is very important at the earliest stages of graphene characterization. Our finding shows that the location of domes and bubbles with the Raman mapping presents an independent non-invasive method to identify the spatial variation of the charge carrier concentration [71].

where the different results may be related to the absence of a buffer layer in some samples. To investigate the possibility of the gap opening here, we first estimate the value of electric field existing inside the charged total capacitor. The electrostatic field is given as: E=

en Gr ; ε

ε = εr ε0

where ε is the dielectric constant of the substrate. We take the range of the values found for the charge density of the graphene layer n Gr = 0.75 × 1013 –3 × 1013 cm−2 and the dielectric constant of the Si–C substrate εr = 10. Here, we found the range of variation of the electrostatic field from 0.14 to 0.54 × 109 V m−1 . Then, the value for the gap may be estimated using the following equation:

5. Conclusions

1 = 2ea E

To summarize, we have presented, for the first time, experimental proof of epitaxial bubbles and domes existing on graphene intrinsically grown on 4H-SiC face-terminated carbon. New graphene structures have been located using optical microscopy, AFM, UFM and Raman mapping. Using AFM measurements, the surface morphology changes have been imaged. Here, we gave a clear description of the behaviour of the surface morphology of the samples and identified areas with new graphene structures. However, the limitation of AFM sensitivity to non-surface-dominated features meant we were unable to precisely characterize the nature of the new graphene structure, which required additional UFM measurements to be implemented. The use of UFM also helped us to measure the nanomechanical stiffness of these dome and bubble structures. Due to the nanometric size of the domes, which is significantly smaller than the focussed area of the Raman beam, we limited our Raman studies to the micrometric bubble sizes. Our Raman analysis showed pronounced differences between epitaxial graphene bubbles on the 4H-SiC face-terminated carbon found here and those of exfoliated graphene bubbles deposited on oxidized silicon substrate (Si/SiOx ), recently reported in [52, 32]. Here, epitaxial graphene bubbles show no dependence on the strain effect. Moreover, we have noted strong charge redistribution between the graphene layer and the rest of the substrate. For the first time, we give in detail the doping

where a = 0.5 Å is the quantum buckling of the graphene layer [39]. The estimated value of the gap opening due to the existing electric field is very small, about 1.4–5.4 meV (see figure 10(d)). The gap value obtained here is very small in comparison with what was determined for epitaxial graphene grown on the face-terminated Si. Thus, we showed the presence of a minigap opening here for a different type of epitaxial graphene. Recently, studies of epitaxial graphene face-terminated silicon attributed the gap opening to the buffer layer [69], but for face-terminated carbon no buffer layer could be present. This is also an additional effect in the bubble structures that are formed in a freestanding way on the substrate. This freestanding nature of the graphene comprising the central part of the bubbles has been verified using Raman spectroscopy. The Raman spectra obtained show behaviour similar to isolated graphene layers and no second-order Raman mode of the substrate has been observed. Therefore, with our finding we propose an alternative route towards minigap opening. Two other important factors could also explain the presence of gap opening of the type we observe: strain or impurity effects. However, here, as discussed above, no strong strain effect could be identified, thus the only factor left is related to the impurity effect. These impurities change the properties of the substrate and even help to induce the phonon–plasmon effects that were observed in the substrate. 13



distribution inside the intrinsically grown epitaxial bubbles. Interestingly, the charge distribution inside the bubbles is also inhomogeneous. In particular, we found a high charge distribution in the roof and in the foundation of the bubbles compared with their sides, where it decreases. The detachment of the graphene layer in bubbles from the substrate surface arises together with the formation of the complex charged nano-structures. We have shown that due to the charged nature of these domes and bubbles there may arise a local minigap in the electronic spectrum. The existence of the minigap may be important for various applications (e.g. graphene transistors [72]). The minigap may also influence electron mobility. Here, we found, in particular, that the modification of the graphene layer due to formation of bubbles and domes strongly affects the electronic properties commonly known for epitaxial graphene face-terminated carbon; namely by inducing a gap opening. The electronic properties of the epitaxial graphene nanostructures studied here should have some similarities to the periodically modulated graphene reported recently in [70]. In our case the weak periodic modulation arises due to terraces, which also play an important role in the bubble formation. The usage of the epitaxial graphene bubbles or domes found here can open a door to successful graphene-based technology and might be used in novel designs in graphene quantum devices [72], extraordinary magneto-resistance [73] or for studies of relativistic Brownian motion [74]. The local charge density strongly affects the transport, electron mobility and conductivity in graphene; our results demonstrate how to use several non-invasive methods, such as optics, AFM, UFM and Raman spectroscopy, to identify the spatial variation of the charge carrier concentration locally within the domes and graphene bubbles, as well as other inhomogeneous structures in graphene. Our finding of the charged domes and bubbles in graphene itself may be very useful for graphene electronics and many future graphene applications [71]. Although, in the present paper, we have focused our study on epitaxial graphene nano-structures grown on 4H-SiC substrates, the results obtained are very general. We have also noticed the existence of similar nano-structures in other SiC polytype used for epitaxial graphene growth, such as ‘3C-SiC (100)’, (see, for example, figure 10, where we have reported some AFM and UFM measurements for other 3C-SiC polytypes). Thus, our results show that under specific conditions of its growth, the flatness of graphene can be disturbed in a controlled way and that different nano-structures may occur, suggesting a method for the possible control of the epitaxial graphene surface different from that observed for exfoliated graphene [52, 32]. This may open doors for the investigation of the optical, electronic and mechanical variation of epitaxial graphene layers for the different used polytypes as well as the influence of their face termination.

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Acknowledgments

OVK acknowledges support from EPSRC grants EP/ G015570/1, EP/K023373/1 and EU FP7 grants GRENADA and FUNPROBE. 14



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Observing high-pressure chemistry in graphene bubbles.

Exceptional ballistic transport in epitaxial graphene nanoribbons.

Magnetoplasmons in quasineutral epitaxial graphene nanoribbons.

Single-molecule junctions with epitaxial graphene nanoelectrodes.

Localization and electron-electron interactions in few-layer epitaxial graphene.

Terahertz and mid-infrared reflectance of epitaxial graphene.

SiC interfaces: photon excitation and probing.

Epitaxial graphene on SiC{0001}: advances and perspectives.

Electroburning of few-layer graphene flakes, epitaxial graphene, and turbostratic graphene discs in air and under vacuum.

Asymmetric Electron-Hole Decoherence in Ion-Gated Epitaxial Graphene.

Epitaxial B-Graphene: Large-Scale Growth and Atomic Structure.

Scanning Tunneling Spectroscopy of Proximity Superconductivity in Epitaxial Multilayer Graphene.

Electronic cooling via interlayer Coulomb coupling in multilayer epitaxial graphene.

Atomic structure of epitaxial graphene sidewall nanoribbons: flat graphene, miniribbons, and the confinement gap.

Low carrier density epitaxial graphene devices on SiC.

Gateless patterning of epitaxial graphene by local intercalation.

Epitaxial growth of asymmetrically-doped bilayer graphene for photocurrent generation.

Chemically resolved interface structure of epitaxial graphene on SiC(0001).

Chemical gating of epitaxial graphene through ultrathin oxide layers.

Growth of Epitaxial Oxide Thin Films on Graphene.

Rotationally Commensurate Growth of MoS2 on Epitaxial Graphene.

Epitaxy of MgO magnetic tunnel barriers on epitaxial graphene.

mica.

Hot carriers in epitaxial graphene sheets with and without hydrogen intercalation: role of substrate coupling.