Raman spectroscopy of four epitaxial graphene layers: Macro-island grown on 4H-SiC 0001¯ substrate and an associated strain distribution

    Raman Spectroscopy of four epitaxial graphene layers: Macro-island grown on 4H-SiC (0001) substrate and an associated strain distribution A. Ben Gouider Trabelsi, A. Ouerghi, O.E. Kusmartseva, F.V. Kusmartsev, M. Oueslati PII: DOI: Reference:

S0040-6090(13)00908-5 doi: 10.1016/j.tsf.2013.05.093 TSF 32153

To appear in:

Thin Solid Films

Received date: Revised date: Accepted date:

15 October 2012 16 May 2013 17 May 2013

Please cite this article as: A. Ben Gouider Trabelsi, A. Ouerghi, O.E. Kusmartseva, F.V. Kusmartsev, M. Oueslati, Raman Spectroscopy of four epitaxial graphene layers: Macro-island grown on 4H-SiC (0001) substrate and an associated strain distribution, Thin Solid Films (2013), doi: 10.1016/j.tsf.2013.05.093

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ACCEPTED MANUSCRIPT Raman Spectroscopy of four epitaxial graphene layers: macro-island grown on 4H-SiC (000 1 ) substrate and an associated strain distribution

- Unité de Nanomatériaux et Photoniques, Faculté des Sciences de Tunis, Campus Universitaire, Elmanar, 2092 Tunis, Tunisie 2 - CNRS- Laboratoire de Photonique et de Nanostructures (LPN), Route de Nozay, 91460 Marcoussis, France

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A. Ben Gouider Trabelsi (1,3), A. Ouerghi (2), O. E. Kusmartseva (3), F. V. Kusmartsev (3) and M. Oueslati (1)

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- Department of Physics, Loughborough University, Loughborough, LE11 3TU, UK

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ABSTRACT

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Using Raman spectroscopy, we have characterised the optical and mechanical properties of large macro-island area (150µm2) of four layer epitaxial graphene grown on 4H-SiC (000 1 ) substrate.

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Local Raman mapping showed inhomogeneously stressed macro-island. There, the 2D and G

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Raman modes revealed a large frequency red-shift in this island with decreasing temperature. An unexpected change appeared in the Raman spectra due to the inhomogeneous strain effect which

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Graphene; four layers – macro-island; Raman spectroscopy; strain; Gruneisen

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KEYWORDS:

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was described in detail. Uniaxial and biaxial strains have been identified.

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Corresponding author. Fax: + 216 71 88 50 73. E-mail address: [email protected]

(A. Ben Gouider Trabelsi).

ACCEPTED MANUSCRIPT 1. Introduction Graphene ranks highly as a promising material for future nanoelectronics devices due to

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its exceptional electron transport properties. It appears as material of choice for future electronic and optic applications, including conventional components such as high frequency analog devices,

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and devices in emerging fields such as spintronics, terahertz oscillators, and single-molecule gas sensors [1,2]. However, a major factor hindering the development of large-scale graphene-based

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nanoelectronic devices remains the high-quality of uniform graphene layers grown on SiC

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substrates. Epitaxial graphene produced by sublimating Si from SiC heated to high temperatures is sensitive to the surface quality of the SiC substrates. Recent approaches have been developed

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to obtain higher-quality films involve heating in argon at atmospheric pressure [3] or supplying excess Si. These approaches lead to significant improvement in the domain size and electronic

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properties compared to vacuum graphitization [3].

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The study of mechanical properties and in particular the local strain can be used to tailor the electronic properties of epitaxial graphene [4,5]. Moreover, some strain configurations are

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equivalent to a magnetic field [6], even comparable to the highest field reachable in the worldleading laboratories [7]. Raman spectroscopy is a useful method to study monitoring of doping, defects, disorder, chemical modifications, edges, number of layers and the associated strain [8-14]. The dependence of these properties to the strain effect can alter its electronic band structure. For instance, inducing uniaxial strain on graphene may result in a band gap opening [15]. Thus, different characterisation technique was developed for its analysis, such as local Raman mapping that represents an efficient tool to study a non uniform local strain distribution. The study of strain effect could be helpful to develop the graphene based electronics.

ACCEPTED MANUSCRIPT Raman spectroscopy of graphene materials is based on the investigation of its Raman spectra, the so-called G and D peaks, located typically around 1580 and 1360 cm−1. The G-peak

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is associated to the E2g phonon at the Brillouin zone (BZ) centre (the Γ - point). The D-peak

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originates from the breathing of six-C atoms forming the hexagon, i.e. this corresponds to the transverse optic (TO) phonon arising at K- point of the BZ. It is activated by an intervalley

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scattering process and for its activation lattice distortions or a defect is needed [16, 17]. The 2D-

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peak is associated to two-phonons, i.e. the second order of the D- peak. Being a single peak in a monolayer - it splits into four bands in bilayer and to different numbers of bands according to the

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thickness of graphene, reflecting the change in the band structure [18]. Generally, the Raman spectrum shows also other less intensive peaks such as the D′ and the second order, 2D′ bands,

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around 1620 cm−1 and 3240 cm−1. While D’ could be activated by any intravalley process, i.e.,

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connecting two points belonging to the same cone around K (or K'). Its second order peak, called the 2D′ peak, does not require the inter-valley momentum for its activation and may be also very

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useful tool as the G and 2D peaks.

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In the present paper, several graphene features have been determined. The layer number has been identified using the Raman intensity ratio of G and 2D bands (IG/I2D) correlated with the 2D band full width at half maximum (FWHM). The disorder degree has been determined via the D band intensity. The in-plane vibration of carbon atoms has been studied using the G-band position and shape variation. While, the face terminated of SiC substrate has been determined with (D + G) band intensity changes. In fact, here we will focus mainly on the change of G and 2D bands to describe the optical and mechanical properties of epitaxial graphene grown on 4H-SiC (000 1 ). The strain effect induced by the substrate on the graphene layer has been studied using a local mapping of Raman spectra. Phonon associated G and 2D peaks have been identified

ACCEPTED MANUSCRIPT for different location of the laser spot on the macro-island and a possible interpretation of their origin and their properties has been given in detail. Uniaxial and biaxial strains on this macro-

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island of the epitaxial graphene have been detected.

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2. The setup of experimental measurements and Raman mapping method Graphene on 4H-SiC substrates has been epitaxiated into semi vacuum (1.33 10-3 Pa) by

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electron-bombardment heating at 1300°C. Prior to graphene epitaxy, the sample has been etched

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in a hydrogen ambience at 1500°C at (2 102 Pa) for 15 min in order to remove any damage caused by surface polishing and to form a step-ordered structure on the surface. Epitaxial Graphene has

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been produced on a 4H-SiC (000 1 ), as described in detail elsewhere for epitaxial growth [19]. Briefly, the substrates were first annealed under a Si flux at 900°C to remove the native oxide in

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Ultra high vacuum (P = 2 10−8 Pa). Graphene growth was carried out in a chamber equipped by

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Si source and Low Electron Energy Diffraction. To obtain epitaxial graphene, substrates have been annealed at 1300 - 1400°C. The sample is characterized by Micro-Raman Spectroscopy

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technique as well as optically. Using optical image a large homogeneous area has been chosen.

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Raman spectra have been obtained with a high-resolution micro-Raman Jobin Yvon HR LabRAM in backscattering confocal configuration at 300K and 79K. The temperature has been controlled by Linkam’s THMS600 system under liquid-nitrogen stream, ensuring elimination of all contact inside the cold-hot cell. To be sure of the temperatures stability we waited for few minutes after reaching the required temperature. The excitation source is an Ar+ laser at the wavelength of 488 nm and the laser power was controlled at 8.5 mW on the sample surface. We have used 100X objective lens for focussing the laser beam on the surface and collecting the scattered light at room-temperature measurements from different local spots forming a pixel pattern. The spatial resolution of the image is 1µm while the spectral resolution is less than 0.35 cm-1.

ACCEPTED MANUSCRIPT 3. Results obtained and discussion

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3.1. Study of surface morphology and the macro-island

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A surface of the epitaxial graphene sample grown on 4H-SiC (000 1 ) substrate has been first investigated with optical microscope at room temperature. Then the large homogeneous area

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has been chosen that was associated to a macro-island whose image is presented in Fig. 1 (the

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inset a). The macro-island is useful object for epitaxial graphene, where graphene become visible in optical microscope. However, the size of the found macro-island is larger than the size usually

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obtained even with other growth technique. It is important to note that this island was produced intrinsically during the epitaxial growth, as present an excellent tool to study both tensile and

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biaxial strains. Especially, that previous studies of mechanical properties of epitaxial graphene don't give a precise description of the strain variation due to the hard location of the graphene

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layers. This finding may open a door to future study of epitaxial growth similar to the ones

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reported recently for exfoliated graphene, where the graphene configurations of different shapes

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such as bubbles represent an excellent tool to study both tensile and biaxial strains [20,21]. First, the optical contrast obtained for the epitaxially grown graphene macro-island is very high compared to ordinary graphene; a visible darker flake of brown colour appears in the centre surrounded by a lighter area from outside, see Fig. 1a. This optical image shows clearly the dimension of the graphene macro-island that was identified using interference colour observed in the optical microscope. To confirm the formation of macro-island, we represented the image of the sample obtained with the local mapping of intensity and spectral position of graphene Raman active modes associated to the D, G and 2D bands (see, in insets on Fig. 1 (b, c and e)). We observed a large macro-island covering 400 x 150 µm2 that looks similar to the brown part of the sample distinguished under the optical microscope (see, Fig.1(inset a)). All Raman spectra

ACCEPTED MANUSCRIPT exhibit a particular behaviour at the centre of this macro-island. They indicate a signature of four layer graphene in the macro-island. The G band has a high intensity, especially at the centre and

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so the 2D band becomes broader. This was confirmed by the full width at half maximum (FWHM)

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measurements of the 2D band correlated with the intensity ratio of G and 2D band (IG/I2D) that will be discussed later.

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To study the strain distribution in the macro-island the Raman measurements were

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carried out regularly in locations with small step of 50µm along horizontal and vertical directions across the macro-island flake to ensure that all changes in graphene modes will be detected.

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During such mapping the Raman spectra have been checked at each point of the sample surface using an auto focusing adjustment of the laser beam acquisition. There the Raman mapping

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analysis reveals a visual identification of large homogeneous area of high quality epitaxial

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graphene of which the macro-island has been made as well as the various graphene layers outside

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this island.

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3.2. Mapping of Raman spectra to the sample surface

As we described above the Raman spectrum characterising graphene layer exhibit a set of first and second order Raman modes between 1000 and 3000 cm-1. We represent the obtained features using Raman mapping spectra at room temperature; the regions- SZ1 and SZ2 indicates the flakes of various sizes, where SZ1 correspond to the macro-island (see, for example, Fig.1). We will focus our discussion on the central flake which has the largest area and form the macroisland. The first defect Raman mode usually called as D band located at 1360 cm-1 (see, the Fig.1). The second G band located at 1587 cm-1 is the E2g in-plane vibration modes [4,22]. There are many other features displayed in the Raman spectra mapping which are originated from other

ACCEPTED MANUSCRIPT second order Raman modes. We have observed such modes as G*, 2D and (D + G) bands and studied their changes depending on the position on the macro-island (see, Fig.1). The G* band

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appearing at 2447 cm-1 corresponds to an intervalley process involving one TO and one

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longitudinal acoustic phonons [23,24]. The 2D band located about 2720 cm−1 represents a double resonant excitation of two phonons having opposite wave vectors at K point in the Brillouin zone

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[25]. The (D + G) band observed at 2946 cm-1 activated by the presence of defects in the

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graphene layers. The graphene Raman lines taken on the macro-island have been manifested with high intensities in the spectrum SZ1 (see, the Fig. 1). They look similar to the spectra obtained

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for suspended layer of graphene despite the binding of the graphene layers to the substrate. This occurs due to the weak contribution of the second order Raman mode of SiC substrate and the

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high quality of macro-island graphene layer. The layer number n of epitaxial graphene grown on

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4H-SiC has been identified using the full width at half maximum (FWHM) of the 2D band, and the intensity ratio of the G and 2D bands (IG/I2D). The FWHM of the 2D band across the

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investigated macro-island shows an order of 90 cm-1 (see, the Fig. 2. a). Previous work has been

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reported in Ref. [26, 27, 28]. There was shown that, the IG/I2D ratio less than 0.5 corresponds to a single layer, in the range [0.5 - 1] - to bi-layers of graphene and greater than 1.8 (n> 5) - to graphene multilayers. Here, we found that the intensity ratio of the G and 2D bands (IG/I2D) in the studied macro-island is equal to 1.5 (see, the Fig. 1. d). Using these methods, we have determined that the number of graphene layers, n, in the studied macro-island is equal to four layers [26,27].

3.2.1 Strain effect

As clearly shown in Fig.1-SZ1, the main flake of the macro-island exhibited Raman spectrum similar to that of isolated graphene layer despite the good binding of the graphene to the substrate,

ACCEPTED MANUSCRIPT as discussed above. The bands associated to the second-order Raman modes of the SiC substrate on this epitaxial macro-island are either absent or dominated by graphene modes existed as in

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exfoliated or suspended graphene, where the influence of the substrate vanishes. This is a

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signature of the high quality of the epitaxial graphene of which the macro-island has been made. Instead, Fig.1-SZ2 taken outside the macro-island shows several Raman bands associated with SiC

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modes having the frequencies in the range [1400-1500 cm-1]. They are all less Raman intense than

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the G band [29,30]. Most of graphene papers showed a domination of the G band of epitaxial graphene with the second order Raman modes of SiC substrate that coexist in this spectral region

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[22]. Thus many authors subtract the contribution of SiC substrate into the Raman spectra to get information on G band [19]. In our case, the obtained Raman spectrum proves the high quality of

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the graphene layer forming this macro-island, where the substrate Raman modes disappeared (see,

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Fig. 1-SZ1).

Indeed, the Raman mapping analysis is a good tool for elastic strain characterization,

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especially for the four layers of epitaxial graphene of which the macro-island is made. Thus, we

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will focus our discussion on the most notable features obtained with Raman mapping and characterising the graphene G, and 2D bands measured at room temperature on the macro-island. The adjustment of the 2D band using a Lorentzian curve within the main area of this island gives a FWHM values in the range of [87- 94 cm-1] (see, Fig. 2-a). These FWHM values are correlated with the intensity ratio of the G and 2D bands. This represents a clear signature of the four graphene layers, as discussed above. These determined FWHM values are very homogeneous in the centre of the macro-island although there is still their small variation. The bands became broader in the vicinity of the foundations of the island. For different foundation sides of this island the strain is inhomogeneous (see, the dark red colour regions in the Fig.2a indicating the larger FWHM and at the same time on the island foundations). The Figure 2-b shows the mapping of 2D

ACCEPTED MANUSCRIPT peak frequency, which is located within the range [2732 - 2716 cm-1]. We note a blue shift for both 2D (see, Fig. 2-b) and G (see, Fig. 2-c) bands, respectively, of the value approximately, 16

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and 10 cm-1. The blue shift is increasing from the centre of the main flake to the edge of the

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investigated island area [3]. To make a detailed analysis of these spectral variations, we have represented a line scan of 2D band spectrum given in the Fig. 2-d. There a long y axes is taken in

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the spatial interval from -194 µm to 194 µm. The all data were taken for the fixed x- position, i.e.

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x= -27 µm in the main flake area of this island. Due to the high symmetry observed in Raman modes, the mapping of FWHM and other various properties of the 2D band along this island have

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been thoroughly and reliably done and are given in the Fig. 2. The Raman spectra of 2D band obtained for all investigated points (see, Fig. 2-d) illustrate the changes observed in the described

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mapping. The map displays a symmetric behaviour from both sides of a big uniform area located

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at the centre of this island (see, Fig. 1-a), even in spite of the small variation of the central position of the frequency for each Raman band observed inside this area (see, the Spectrum 2- taken in the

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following location spots: A3, A4, A5, A6). But, we notice that a significant frequency blue shift

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appears as far as we move from the central area of the island on both sides (see the Raman Spectrum presented on the Fig. 2 taken in the following location spots, A1, A2, A7, A8). Here, the influence of the substrate arises and plays a role of the extra negative pressure. Therefore, we expect some decompression to arise. The frequency of the 2D Raman band across this island changes from 2710 cm-1 to 2739 cm-1 (see, Fig. 2-f). This blue shift behaviour differed from that usually observed for graphene grown on SiC face termination C, where the high decoupling between graphene layer and substrate induced a decrease of the strain effect [31]. This blue shift could not be attributed to charge transfer from the substrate that decreases with increasing the graphene layer number. Indeed, it was argued that due to the high electron concentration for a single layer of graphene a Raman shift of 7 cm-1 for G band appears [25,32-36]. Thus, a

ACCEPTED MANUSCRIPT decreasing Raman shift is expected with increasing layer number, due to the reduction of the electron concentration in the graphene sheets. This confirms our results discussed above

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eliminating the charge transfer effect as origin of the high blue shift that is 7 cm -1, especially with

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that our macro island is made of four graphene layers. Likewise, the large 2D band shift verifies also this condition revealing the weak amount of charge transfer in this island. The known results

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for the charge transfer even for the single layer of graphene show that their influence on the blue

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shift is negligible.

We have made a detailed comparison of our results to those of four layers of exfoliated

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graphene. There, similar blue shifts have appeared for both G and 2D bands. The G band peak is located at 1582 cm-1 and the 2D band peak is located at 2682 cm-1 [25]. The bands have a blue

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shift of 5 cm-1 and 38 cm-1 for each mode, respectively. The high blue shift obtained here confirms

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that the behaviour observed here is mainly due to the strain effect arising at the formation of this large epitaxial island. Our results are consistent with previous work, where strain effects in

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epitaxial graphene were attributed to the observed blue shifts of 2D and G bands. This is in a

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contrast to the exfoliated graphene, where the frequency shifts of the Raman modes and strain effects are significantly weaker [25]. The obtained values for Raman band shifts are close to ones reported in previous work [25]. They found similar effects for epitaxial graphene grown on 6HSiC face terminated Si, that is on samples very different from our ones [31]. Note that our sample is grown on 4H-SiC substrate but on face terminated C. The origin of this similarity has been investigated using the Raman intensity ratio for D and G peaks, ID/IG. Especially, this becomes clear after we observed a similar behaviour of isolated Raman spectrum in the main flake of which the macro-island is made of (see, Fig. 2-e). The ratio (ID/IG) on this island is about 0.6. This value is close to the one of epitaxial graphene grown on 6H-SiC terminated Si, revealing the good quality of graphene layers on the island elaborated here. Thus, the origin of the blue shift obtained

ACCEPTED MANUSCRIPT for both Raman modes could only be attributed to mechanical properties of four layers of graphene and strain effect arising at the formation of the macro-island. They have originated from the

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graphene-substrate interaction which arises at the areas of the island foundations.

3.2.2. Temperature effect on a formation of strain in epitaxial graphene

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We found that the changes in the shape of the Raman spectra which we ascribed to the strain

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effects in the macro-island have also strong temperature dependence and a high sensitivity on the layer number. It was also found earlier that the temperature coefficients are strongly affected for

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the in-plane G and 2D graphene modes [37]. To understand this temperature behaviour, we present in Fig. 3-a the mapping of the 2D band frequency taken on the macro-island at lower temperature,

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77K. The temperature decrease from 300K to 77K induces a blue shift of the peak frequency and

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the FWHM increase of the 2D band as shown in Fig. 3-a and b, respectively. This is similar to the case for exfoliated graphene, where the strain effect increases with the temperature [38,39]. That

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may arise here only due to the thermal expansion or more precisely the graphene contraction

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arising when the temperature decreases. More details are revealed on the Fig 3-c, which presents a line scan of 2D Raman band taken on the main flake along y axes in the interval [-194, 194] µm for the same position of x = -27 µm and at the same, T = 77K. Here one may clear see that both Raman frequency blue shift and FWHM of the G band increases as the temperature decreases. In fact we found a linear temperature dependence of the frequency position of G and 2D Raman bands where the negative temperature–frequency shift coefficients, χG = - 0.022 cm-1 K-1 and χ2D = -0.030 cm-1 K-1, have been also determined. We noticed that χG is smaller than one observed in monolayer and bilayer of exfoliated graphene, which is χG (bilayer exfoliated) = -0.0154 cm-1 K-1, we expect a decrease of G band shift coefficients with increasing the layer numbers. While χ2D is larger with respect to a small number of graphene layer, where χ2D of bilayer of exfoliated

ACCEPTED MANUSCRIPT graphene χ2D

(bilayer exfoliated)

= -0.066 cm-1 K-1 [37-40]. Thus, the phonon frequency shift with

varying temperature is associated here to the strain and could be attributed primarily to the thermal

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expansion of the four-layer’s graphene in the macro-island. Various factors may contribute also

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such as: graphene-substrate interaction, electron-phonon coupling and an-harmonic phononphonon interactions [37]. For the G band, some effects could be neglected like the anharmonic

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contribution which is small in the temperature range [77-300 K] [37]. Thus with correlation to the

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strain analysis, we conclude that the negative thermal expansion coefficient cannot be the only origin of the negative sign for the frequency shift, see also the Ref. [37]. Thus, this negative sign

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could be attributed to both Gruneisen parameter and thermal expansion coefficient [37]. On the other hand, the value χ2D of our epitaxial graphene is larger in comparison to that of exfoliated

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graphene bilayer. Therefore, the blue shift of the 2D bands observed with decreasing temperature

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could be attributed likewise to the thermal expansion effect of both substrate and the four graphene layers (see also the discussion in the Ref. [37]). In the same way, we have also measured the

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FWHM temperature coefficient for both G and 2D bands. The value τG is negative (τG = -0.004

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cm-1 K-1) while τ2D of 2D band is positive (τ2D = 0.011 cm-1 K-1). 3.3. Estimation of the strain effect on graphene modes

In order to detail the mechanical properties variation of epitaxial graphene, we have determined the strain effect on Raman modes using a theoretical model calculation. In previous work the strain of graphene materials, ε for both Raman modes 2D and G, has been calculated using the following expressions [30, 35, 41]:

   2 D     02 D

  /  2D  

(1)

ACCEPTED MANUSCRIPT    G     0G

 /G  

(2)

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where ω02D (ω0G) is the frequency for the peak of the 2D (G) bands of exfoliated graphene, the

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value ∆ω is the difference between the Raman frequency (of the peak) of the epitaxial graphene under the strain effect and of the graphene free of strain (it was taken for the exfoliated suspended

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graphene), γ2D (γG) is the Gruneisen parameter of 2D (G) band of graphite (with γ2D = 2.7 and γG =

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1.8) [35]. We have represented on the Figs 4 and 5, respectively, the 2D and G bands mapping of strain effects. It is given in a percentage with respect to a suspended graphene. The corresponding

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mapping of the 2D band shows different ranges of strain variation between [0.2- 0.6 %]. From the mapping two areas could be distinguished. One is showing a big homogeneous flake of the macro-

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island (see the blue colour at the centre of the Figure 4). It is surrounded by this island foundation-

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boundaries (see, the light blue colour on the Figure 4) and other similar areas outside the island, which shown to be inhomogeneous with the strain. Interesting that from this estimation we see that

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there is always an increase of the strain value at the edge of the main flake that is an obvious

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influence of the substrate. The strain homogeneity in the central main flake confirms the high quality of elaborated graphene in the macro-island. The strain variation outside of the main central area of this flake could be assigned to graphene-substrate interaction that originates from to the difference between the lattice constants of the graphene layer and the SiC substrate where the graphene of the island and the substrate are bound. That is especially different at the synthesis temperature [22]. The high quality of graphene layers elaborated here presents an advantage for an investigation of strain effects associated with the G band. The graphene layers show high intensity of G line in the central area of the main flake, where no second order Raman mode of SiC substrate coexisted with G band observed despite their low intensity presence at the edges. This

ACCEPTED MANUSCRIPT confirms the formation of high quality of epitaxial graphene island, where the foundation in the surrounded area between the brown area and the lighter area from outside is under some stress.

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The appearance of the substrate mode at the edge, i.e. at this island foundation could explain the

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variation of the mechanical properties of graphene layers arising when we move from the centre. It’s possible that local anisotropy appears for epitaxial growth due the substrate effect that affects

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its mechanical properties with inducing a biaxial strain. As consequence a small splitting and an

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increase of the FWHM of the G band is expected, but no effect on Raman shifts could be observed for such applied strain. To see these effects on the G band, we have studied its variation using the

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same mapping position of 2D band as discussed above. We observe a G band splitting that depends highly on the mapping position. Thus, we choose to keep the same line scan of 2D band

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that we used for the G band: below we present the set of Raman spectra taken along y axes from

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the position y = -194 µm to the position y= 194 µm for an arbitrary chosen coordinate x: x=-27 µm of the main flake studied here (see, the Fig. 5-a). For all investigated points taken from

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the set the Raman spectra exhibit a weak split at the centre (see, the spectra presented in the Fig. 5

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taken at the positions A3, A4, A5, A6, see Fig. 5c). This effect became more pronounced at the edge of the flake (see, the spectra presented in the Fig. 5c taken at the positions A1, A2, A7, A8). To determine the strain variation on the sample associated with the G band position changes at each mapping point, we have used the theoretical model developed previously (see, the equation (2)). The Raman mapping with this band shows a big blue area of this island at the centre identical to the one obtained with the use of the 2D band for the main graphene flake (see, the Fig. 5-b). The strain range and the Raman intensity variation obtained for the G band differ to the strain data obtained with 2D band. This difference is due to simplicity of our model, which is still good enough to describe our results qualitatively. Note that the 2D band spectrum is more sensitive for a

ACCEPTED MANUSCRIPT strain variation. However, the G band investigation still represents a good scale for the strain effect determination.

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The analysis of the Raman mapping on the graphene surface showed that the G band is

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more broadened at this island boundary well identified on the main flake. We have fitted the data set associated with the Raman mapping of the G band with the two Lorentzian curves where the

E 2g

and parallel

E2g modes

which are split due to the applied strain

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respectively to perpendicular

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two split bands noted as G+ and G- have been observed. The bands, G+ and G-, correspond

[31]. We present in Fig. 5-c the intensity mapping of G- (blue colour) and G+ (magenta colour)

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bands. The obtained results show similar behaviour to that obtained in theoretical study. The central island zone of the main flake shows clearly a domination of G+ band which is identical to

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G band without any splitting. The distinguished behaviour of the two bands G+ and G- indicates

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respectively the presence of biaxial strain in the central area of the flake and uniaxial strain. This could be linked to the mechanical properties that change at the edge of this clear island of epitaxial

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graphene and the slide contribution of the substrate at the edge. The Raman spectra in the main

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island area of the flake (points A3, A4, A5 and A6) showed similar behaviour (see, Fig. 5-c) confirming the presence of biaxial strain in the central island zone of the main flake. The spectra measured at different points at the edge of the central island zone of the graphene sample (see, Fig. 5, where spectra have been measured at the points A1, A2, and A8) showed that G- band became more pronounced and verifies the calculated value. This indicated the creation of the uniaxial compressive strain, where the sp2 bonds became shorter to the direction of the applied strain. This is in contrary to perpendicular bonds that are not too much affected. This reveals a good agreement between the two studied Raman mappings and especially the benefits of the investigation for the G+ and G- band changes. That helps to specify the value of the strain for epitaxial growth and

ACCEPTED MANUSCRIPT confirms the above results. In summary, our results showed a strain relaxation in the centre of the large graphene flake forming the macro-island; while at the edge a strong contribution of the

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substrate effect on the mechanical properties of the graphene appeared.

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4. Conclusion

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To summarize, it has been shown in this work that Raman mapping investigation represents a good tool for four layers epitaxial graphene – macro-island characterization. The

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strain range variation obtained for the G and 2D band shows a good agreement with the used

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theoretical model and confirms the high quality of graphene layers elaborated here. The good location of such large macro-island of epitaxial graphene allows to a close determination of the

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mechanical properties variation of graphene as well as the effect induced from the substrate. This can open a door for further study of localised epitaxial graphene layers, like it was reported

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recently in Ref 20, 21 for exfoliated graphene bubbles. Thus, we believe, that our obtained here

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results on the properties of large flakes of epitaxial graphene will further contribute into the fast

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developing graphene-based technology.

ACCEPTED MANUSCRIPT Figure captions: Figure 1: Raman spectra, SZ1 and SZ2 of graphene layers taken inside (Z1) and outside (Z2) areas

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of the main flake. Inset: (a) Optical microscopy image of graphene layers grown on 4H-SiC, (b) Mapping Raman Intensity (MRI) of G band, (c) MRI of 2D band, (d) Mapping Raman Intensity

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(MRI) of the ratio of G /2D band, i.e. IG/I2D ratio, (e) MRI of D band of the graphene flakes.

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Figure 2: The mapping of the Raman spectra to the surface of the sample measured at room temperatures: a- the mapping of the FWHM of the 2D band, b- the mapping of frequency

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associated with the peak of the 2D band, c- the mapping of peak frequency of the G band, d- the evolution of 2D band shape obtained for a line scan taken along vertical, y direction at the

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coordinate, x = -27 µm, e- the mapping of peak intensity ratio, i.e. ID/IG ratio, f- the variation of a

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frequency associated with the 2D band peak for a line scan taken along y direction at the value x

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= -27 µm.

Figure 3: Raman mapping - The spectroscopic map of the central position and the bandwidth of

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the 2D band measured at various points on the surface of the central epitaxial graphene flake at 77K: (a)- the Raman frequency mapping for the 2D peak taken with high resolution in regular positions on a lattice is indicating a smooth variations, (b)- the same procedure is applied to obtain the FWHM mapping , (c)- Evolution of the Raman shift for the 2D band taken on the scan along y-direction at the fixed value x = -27 µm, (d)- Evolution of the shape and the position of the 2D band measured on the scan along y-direction at the fixed value x = -27 µm.

Figure 4: The Raman 2D band mapping of the strain (in percents) of graphene grown on 4H-SiC (000 1 ). The lowest strain is in the centre of the flake while tensions arise near the edges.

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Figure 5: a)- The mapping of Raman spectrum of the G band (precisely speaking, the intensity of

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the G band has been put in a correspondence to the points on the surface of the graphene flake)-

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for darker spot the band shift is larger, b)- G band strain mapping, in percent, on graphene grown on 4H-SiC (000 1 ) substrate- for darker spot the strain is smaller, c)- the mapping intensity and

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Raman spectra of G+ and G- bands measured at the following points, (A1, A2, A3, A4, A5, A6, A7

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and A8 , along y- direction at some fixed coordinate x, see, Fig. a).

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1. Finding giant graphene macro-islands.

4. Temperature dependence of strain in epitaxial graphene.

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5. Theoretical approach of strain effects.

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3. Discovery of various strain effects on the four-layer islands.

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2. Mapping Raman spectroscopy of the macro-island surface.