# Self-limited monolayer graphene growth on SiC with propane-hydrogen CVD

Chiara Mastropasqua, Ahmed El Alouani, Matthieu Paillet, Marc Portail, Mathieu Koudia, Mathieu Abel, Yvon Cordier, Benoît Jouault, Isabelle Berbezier, Sandrine Juillaguet, et al.

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Chiara Mastropasqua, Ahmed El Alouani, Matthieu Paillet, Marc Portail, Mathieu Koudia, et al. Self-limited monolayer graphene growth on SiC with propane-hydrogen CVD. npj 2D Materials and Applications, 2025, 9 (1), pp.32. 10.1038/s41699-025-00554-4. hal-05201892

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# Self-limited monolayer graphene growth on SiC with propane-hydrogen CVD

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Chiara Mastropasqua<fnref n="1" />,², Ahmed El Alouani<fnref n="1" />,³, Matthieu Paillet³, Marc Portail<fnref n="1" />, Mathieu Koudia², Mathieu Abel², Yvon Cordier<fnref n="1" />, Benoît Jouault³, Isabelle Berbezier², Sandrine Juillaguet³ & Adrien Michon<fnref n="1" />✉

Among the different methods to grow graphene on silicon carbide (SiC), the chemical vapor deposition (CVD) in a hydrogen atmosphere has several interesting features arising from the use of this gas. Despite its versatility and its ability to grow graphene with a quality allowing applications in electrical metrology, this synthesis method remains largely understudied. This work is specifically dedicated to this growth technique in conditions leading to the epitaxy of graphene on a buffer layer. We first show that hydrogen has several effects during the cooling down, possibly leading to hydrogen intercalation beneath graphene, or even to graphene etching. Then, we use a specific cooling under argon, allowing the suppression of hydrogen effects, to follow the successive phases of the graphene formation, from the nucleation of islands and ribbons to their coalescence on SiC. Finally, we demonstrate that graphene growth is, in our growth conditions, self-limited to a unique monolayer.

Graphene can be grown on silicon carbide (SiC) simply by heating its surface<fnref n="1" />. This method, known as the annealing or sublimation method, has been first described in the sixties² and rediscovered around 2000³⁻⁵. Beyond its relative simplicity, its main interest lies in the use of the SiC substrate, a wide bandgap semiconductor now widespread in the electronic industry.

In the annealing method, the SiC surface heated under ultra-high vacuum (UHV) or argon atmosphere decomposes into silicon and carbon species, and the difference in vapour pressures allows silicon to go in the gas phase while carbon remains on the surface to form graphene⁶. Depending on the SiC polar face, graphene presents very different properties⁷,⁸. On SiC(0001), also known as the silicon face, the growth starts with the formation of a buffer layer, a carbon layer similar to graphene and oriented at 30° with respect to SiC but containing about 30% of sp³ atoms sharing covalent bonds with SiC⁹. If annealing continues, a new buffer layer can form underneath the first one. At the same time, the upper layer is transformed into a graphene layer with 100% sp² carbon atoms, while keeping its orientation. As a result, graphene on the silicon face can be monocrystalline¹⁰. Experimentally, epitaxial graphene on a buffer layer always has a high electron concentration¹¹, of the order of $n = 10^{13} cm^{-2}$. This doping is thought to be because the buffer layer has a broad and large density of states, which pins the Fermi level and thus n-dopes the graphene by charge transfer. A formalization of this mechanism has been proposed by Kopylov et al.¹². To circumvent the effects of Fermi level pinning, hydrogen can be intercalated at the interface with SiC to transform the buffer layer into a second graphene layer. Similarly, a single buffer layer can be transformed

by hydrogenation into quasi free-standing monolayer graphene (QFMLG)¹³⁻¹⁵. We stress that QFMLG also has residual doping and is p-doped, because of the spontaneous polarization of the SiC substrate¹⁶. On SiC(000-1), known as the carbon face, the weak interaction between graphene and SiC limits the influence of the substrate on the electronic properties¹⁷, but this weak interaction also leads to the presence of graphene domains with various orientations¹⁸. In addition, the graphene growth starts at a lower temperature and is faster than on the silicon face¹⁹, so that graphene on the carbon face is usually multilayer²⁰. Given the monocrystalline nature of graphene and the possibility to control its interface with SiC, silicon face is generally preferred to the carbon face for graphene growth.

Beside SiC annealing, different groups have developed the direct growth of graphene on SiC using external carbon sources using molecular beam epitaxy (MBE)²¹,²² and chemical vapour deposition (CVD) under argon²³,²⁴. A hybrid method also consists of enriching the surface with carbon by polymer deposition before annealing²⁵. All these methods allow the growth of graphene films similar to those obtained by conventional annealing, particularly considering the orientation of graphene on the different polar faces. In parallel, we have developed since 2010 the CVD growth of graphene on SiC in a hydrogen atmosphere which drastically alters the growth process²⁶. First, adding hydrogen in the gas phase allows the formation of many carbonated species, thus facilitating the transfer of carbon to the gas phase⁶. As a result, carbon excess does not occur naturally on the surface, and an external carbon source is required to grow graphene. Second,

<footnote n="1">¹Université Côte d'Azur, CNRS, CRHEA, rue Bernard Grégory, Valbonne, France. ²Aix Marseille Univ., CNRS, IM2NP, Marseille, France. ³Laboratoire Charles Coulomb (L2C), UMR 5221, CNRS-Université de Montpellier, Montpellier, France. ✉e-mail: adrien.michon@crhea.cnrs.fr</footnote>
hydrogen can interfere with the formation of the buffer layer, possibly prohibiting its formation. As a result, it is possible to obtain multilayer graphene with azimuthal disorder (similarly to that obtained on the carbon face) on the silicon face²⁷. Monolayer graphene on a buffer layer can also be obtained²⁷,²⁸, and in intermediate hydrogenation conditions it is possible to obtain directly QFMLG²⁷,²⁸. In these previous works, the formation of the different graphene structures has been interpreted on the basis of mechanisms occurring during the growth step. Finally, from a technological point of view, this method allows the growth of graphene with a high crystalline quality on large surfaces. This allows high precision applications such as quantum Hall resistance standards²⁹, while large area growth is advantageous to develop van der Waals epitaxy³⁰⁻³².

Despite its specificities and potential applications, only a few groups have studied graphene growth using CVD in hydrogen atmosphere³³⁻³⁵. A mobility of around 9000 cm²/V·s at room temperature has been reported³⁴, but detailed explanations of the growth mechanisms are still lacking. We have recently suggested that in specific conditions, thermodynamic equilibrium may favour the formation of a monolayer, and suspected possible effects arising during cooling down³⁶. Here, we study specifically the growth conditions leading to the formation of graphene on a buffer layer at high temperature. In the first part, we describe the effects arising during the cooling process and show how this process can have a strong impact on the graphene properties. In the second part, we use a specific cooling protocol to freeze the surface at intermediate levels of graphene formation, allowing the observation of graphene nucleation, growth and coalescence. Finally, we demonstrate that graphene growth can be self-limited to a single layer, hence explaining why hydrogen CVD allows the growth of uniform graphene films.

## Results

### Evidence of hydrogen effects during conventional cooling

We have grown graphene on SiC(0001) by exposing its surface to a propane flow at a temperature of 1550 °C. SiC was exposed to hydrogen during the

whole process (i.e. from temperature ramp to cooling), and to propane only during the temperature plateau for a duration referred to as growth time. The details of this growth method, referred to as hydrogen CVD, are given in section "Methods", and a typical temperature profile is presented in supplementary material (Supplementary Fig. S1).

With the initial aim of studying the various stages of the formation of graphene, we first prepared samples with growth times ranging from 0 to 15 min and studied them with AFM (Fig. 1) and XPS (Fig. 2). Graphitic peaks are observed in XPS C1s spectra for growth times of 2 min and beyond. For 2 min and 4 min of growth, the formation of graphene is confirmed by AFM images with the presence of wrinkles. In our previous works, the presence of wrinkles has always been correlated to a hydrogenated interface²⁷. This is also the case here, as attested by the XPS spectra decompositions where no interface peaks corresponding to a buffer layer can be found (Supplementary Fig. S2a, b). Besides, we observed pits of a few nanometres deep with irregular shapes on the AFM images for both samples. At 7 min of growth, no more wrinkles are observed, but XPS proves that the interface is still hydrogenated, while pits remain present. Finally, after 11 min and 15 min of growth, no more pits are found, and graphene covers the whole surface. The most intriguing feature for the two last samples is the change in the XPS spectra, which now present a shoulder at high energy, revealing the presence of a buffer layer at the interface between graphene and SiC (S1 and S2 components⁹ in Supplementary Fig. S2c, d). Accordingly, Raman characterizations of the 4 and 15 min samples (Supplementary Fig. S3a) also evidence a transition from hydrogenated interface to buffer layer. The hydrogenation of the interface (instead of the presence of the buffer layer) is frequently observed when growing graphene using hydrogen-CVD, and transition from hydrogenated interface to buffer layer interface has already been observed when increasing temperature or reducing pressure²⁷. However, such transition has not been observed when varying growth time.

This change in the structure of the interface with the growth time suggests a dehydrogenation of the interface during graphene formation. However, the XPS spectra show that the transition is rather sharp: at 7 min

<figure><img src="image_5.png" /><figcaption>**Fig. 1** | AFM images after conventional cooling. The samples were obtained with growth times ranging from 1 min (a) to 15 min (f), and conventional cooling, i.e. under hydrogen and argon. The rough surface in (a) is that of SiC. The wrinkles in images (b) and (c) reveal the presence of graphene and suggest that its interface with</figcaption></figure>

SiC is hydrogenated. The smoother surfaces in (e) and (f) are those generally obtained after a complete graphene growth. Vertical scale (dark to bright contrast) is Δz = 3 nm for all AFM images.
of growth, there is no signature of a buffer layer, but for 11 min, its signature is perfectly visible. Such a rapid dehydrogenation, precisely between 7 min and 11 min of growth, seems unlikely to occur. We therefore explain this by a hydrogenation of the interface during cooling: for all the samples presented above, graphene was first formed on a buffer layer, but for some of the samples, buffer layer became graphene through hydrogenation of the interface during cooling under hydrogen and argon.

The mechanisms involved here should be similar to that previously reported for graphene grown by Si sublimation and then exposed to hydrogen at temperature between 700 and 1000 °C<sup>13,14,37</sup>; hydrogen saturates the dangling bonds of the SiC surface while the sp<sup>3</sup> carbon atoms of the buffer layer are transformed into sp<sup>2</sup>, hence transforming it into a graphene layer. These experiments used lower temperatures, and therefore required longer times, for example 20 min at 700 °C in the study by Forti et al.<sup>37</sup>. In our case, graphene is exposed to hydrogen for about 6 min of cooling in the 1550-700 °C temperature range (see temperature profile, Supplementary

<figure><img src="image_6.png" /><figcaption>**Fig. 2** | XPS C1s spectra after conventional cooling. The samples were obtained with different growth times and conventional cooling. Spectra are normalized and shifted with respect to the SiC peak. The spectra for 11 and 15 min of growth are those of graphene on a buffer layer, as evidenced by the high-energy shoulder due to interface peaks. In contrast, the absence of such a shoulder on the graphene peaks for 2, 4 and 7 min of growth indicates that the graphene/SiC interface is hydrogenated for these samples.</figcaption></figure>

Fig. S1). This leads to the hydrogenation of the interface only when the graphene coverage is incomplete and that free graphene edges facilitate hydrogenation, i.e. for short growth times (≤7 min). On the contrary, when continuous layers are formed (≥11 min), the interface is not hydrogenated after growth and the buffer layer survives to the cooling.

According to our hypothesis, we can trace the structure of our samples before cooling. For example, after 4 min of growth, the surface was probably covered by a buffer layer, itself covered by graphene platelets which, after hydrogenation during cooling, gave an almost complete covering of graphene with second-layer platelets. Beyond effects on the interface with SiC, hydrogen can also etch SiC<sup>38</sup> as soon as it is exposed to the gas phase. The presence of pits between the platelets can therefore be attributed to openings of the buffer layer by hydrogen etching, followed by localized SiC etching through these openings.

## Increasing hydrogen effects with post-growth annealing

We have observed above that for partial coverage, conventional cooling (i.e. with hydrogen in the gas phase) leads to the hydrogenation of the interface between the SiC and the buffer layer, the latter then becoming an additional layer of graphene. However, this effect has been only observed for partial coverage of graphene, whereas the buffer layer survives to the cooling when the graphene covers it completely. To see to what extent this type of sample can withstand hydrogen, we will now try to reinforce the effects of this gas after graphene growth.

To do this, after switching off the propane flow, the sample was maintained at the growth temperature for an additional minute before switching off the heating for cooling. Figure 3 shows the AFM images and XPS spectra of two samples obtained with 4 min and 15 min of growth. After 4 min of growth plus 1 min of annealing, no more graphitic peak can be found in the XPS spectrum, indicating that a large part of graphene has been etched by hydrogen. Accordingly, the AFM image shows rougher SiC terraces with irregular shapes, but occasionally decorated by small flat patches which may indicate regions of surviving buffer layer or partially intact graphene. When applying the same 1 min post-growth annealing to a longer growth (15 min), there is still graphene on the surface, but this time decorated by long wrinkles, suggesting hydrogenation of the interface. This is first confirmed by XPS with the disappearance of the interface peaks (Supplementary Fig. S2e) and the increase in intensity of the graphitic peak due to the formation of the second graphene layer. This is also confirmed by Raman characterization with the observation of a Raman signature compatible with a bilayer graphene without buffer layer (Supplementary Fig. S3b).

Thus, while the conventional cooling alone (with 6 min of exposure to hydrogen between 1550 °C and 700 °C) is insufficient to hydrogenate the interface when graphene covers the entire surface (as seen in previous

<figure><img src="image_7.png" /><figcaption>**Fig. 3** | AFM images and C1s XPS spectra of samples with 1 min of post-growth annealing. Post-growth annealing was conducted at the growth temperature with the same hydrogen and argon flow as for growth and conventional cooling. The sample with a growth time of 4 min exhibits a rough SiC surface in AFM (a), and concurrently, no graphene peak in the XPS spectra (c). On the other hand, the</figcaption></figure>

sample with a growth time of 15 min is covered with graphene on a hydrogenated interface, as attested by its smoother morphology with a wrinkle in AFM (b) and by the XPS spectrum without a shoulder on the graphene peak (c). Vertical scale is Δz = 5 nm for both AFM images, and the XPS spectra are normalized and shifted with respect to the SiC peak.
<figure><img src="image_8.png" /><figcaption>**Fig. 4** | AFM images and C1s XPS spectra of samples with argon cooling. Argon cooling is achieved by interrupting simultaneously heating, propane and hydrogen flows. The morphology is smooth, albeit discontinuous, on the sample with a growth time of 4 min (a), and perfectly smooth, except the SiC steps, on the sample with a</figcaption></figure>

growth time of 15 min (b). The XPS spectra (c) are that of graphene on a buffer layer, hence proving that argon cooling allows the suppression of hydrogen effects during this step. Vertical scale is $\Delta z = 5$ nm for both AFM images, and the XPS spectra are normalized and shifted with respect to the SiC peak.

<figure><img src="image_9.png" /><figcaption>**Fig. 5** | Structures of partial or complete layers after different cooling protocols. Hydrogen can have important effects on the graphene and on its interface with SiC during cooling, from the hydrogenation of the graphene/SiC interface to the etching</figcaption></figure>

of graphene or SiC. These effects are most pronounced when graphene coverage is partial or when the cooling is not performed rapidly after the growth. Conversely, these effects can be avoided with argon cooling.

section), adding 1 min of post-growth annealing at 1550 °C leads to its full hydrogenation. Behind this minute of annealing lies a hidden growth parameter: the cooling rate. Adding 1 min of post-growth annealing may have similar effects than reducing the cooling rate. Hence, in a reactor with slower cooling dynamics, the range of growth conditions under which graphene can form on a buffer layer would be greatly reduced, and graphene might even never survive cooling under hydrogen and argon.

## Suppression of hydrogen effects with argon cooling

While conventional cooling preserves the buffer layer when it is completely covered with graphene, this is not the case for samples with partial coverage due to the presence of hydrogen. To preserve as much as possible the structure of the samples at the end of the growth, it might therefore be preferable to cool them under argon alone, without any hydrogen likely to modify the interface and to etch graphene. We therefore grew samples similar to those presented in the first section (Figs. 1 and 2), i.e. with growth times ranging from 0 min to 15 min, except that hydrogen and propane flow were interrupted simultaneously at the end of the growth process, leaving only the argon flow in the reactor for the cooling. In this section, we will first consider AFM images and XPS spectra of the samples with 4 min and 15 min of growth (Fig. 4).

After 15 min of growth, cutting off the hydrogen at the very start of cooling does not change anything compared to conventional cooling: AFM

images do not present any new morphology features, and the XPS again shows the spectrum of graphene on a buffer layer. The AFM image of the 4 min growth shows a morphology characterized by platelets, as observed with conventional cooling (Fig. 1c), but without wrinkles in graphene or pits in SiC. Finally, the signature of the buffer layer can be clearly observed with XPS on both samples. Cooling in argon alone therefore seems to have frozen the graphene growth as it was at the end of the growth plateau. We will exploit this in the next section to observe the different stages of graphene formation.

To summarize, we have applied different cooling sequences to partial or complete layers of graphene on a buffer layer. The observations, summarized in Fig. 5, reveal how these different cooling sequences can modify or not our samples after growth. Conventional cooling, keeping the same hydrogen/argon mixture as for growth, does not appear to have any effect on the complete graphene layer, but can lead to hydrogenation of the buffer layer when graphene coverage is partial. By increasing the hydrogen exposure with a 1 min post-growth annealing, a complete graphene layer can also be hydrogenated, while the partial layers can be fully etched. Conversely, cooling under argon alone, which avoids any effect of hydrogen, is the most likely to preserve the structure of our samples with a buffer layer.

## Observation of the successive stages of graphene growth

Studying the cooling was therefore a prerequisite to study the formation of graphene using hydrogen CVD. Having done this, we can now study the
<figure><img src="image_10.png" /><figcaption>**Fig. 6** | AFM images of samples with argon cooling. The cooling under argon allows the observation of the different stages of the formation of graphene on SiC. **a, b** Morphology of the as-received substrate and after the 5 min ramp to the growth temperature. **c** After 1 min of growth, the surface is covered by the buffer layer (exhibiting a characteristic roughness), and graphene nucleates on it in the form of ribbons along the SiC steps or islands in the centre of SiC terraces. The height difference between graphene and uncovered buffer layer cannot be determined</figcaption></figure>

properly due to differences of AFM tip interaction. **d, e** Graphene ribbons and islands grow laterally and begin to coalesce. **f** The coalescence is almost complete, but very small domains of uncovered buffer layer can still be found. **g, h** The coalescence is complete: SiC is fully covered by graphene on a buffer layer. The differences in morphology between 11 and 15 min are due to variations in the local offcut of the SiC substrate.

complete series of samples with different growth times followed by argon cooling to observe the different stages of graphene formation. The AFM images of the entire growth series plus a flash annealing and the initial substrate are presented in Fig. 6 (including the 4 min and 15 min samples, already presented in the previous section).

Before any process, the substrate presents 0.25 nm-high SiC steps (Fig. 6a). After the flash annealing (growth time = 0 min, Fig. 6b), the surface appears smoother, and 0.75 nm-high SiC steps already appear: the temperature ramp up under hydrogen allows the reorganization of the SiC steps (see AFM profiles in Supplementary Fig. S6). Given the preponderance of the effects of hydrogen (during the ascent) over those of argon (during the descent), we can assume that the morphology of this sample is close to that of the SiC surface at the very beginning of growth.

The SiC steps are still visible after 1 min of growth (Fig. 6c), but they are now decorated with islands in the centres of the terraces and multiple ribbons at the edges of the steps. When increasing the contrast, we can see that these islands and ribbons are smoother than the rest of the terraces, suggesting that they correspond to areas of graphene. STM images taken at the edges of the steps also confirm that the ribbons are indeed graphene on a buffer-layer (Supplementary Fig. S8). The islands are too dispersed to be observed by STM, but given their flatness, we can assume (and this will be

verified later) that they are also graphene. Finally, the rough surface covering most of the terraces can be attributed to the buffer layer³⁹. Both XPS and Raman spectra (presented and discussed later) are consistent with our interpretation of the AFM and STM images, thus confirming that the 1 min sample is covered by a buffer layer with graphene islands and ribbons.

In our AFM setup, the height of the graphene islands or ribbons on SiC cannot be determined by tapping AFM: depending on the amplitude set-point, graphene islands can appear above or below the surrounding buffer layer (Supplementary Fig. S7). Similar discrepancies in height measurements between two different materials have already been reported using tapping AFM and attributed to various effects⁴⁰⁻⁴³. Consequently, we will discuss only the lateral sizes of the islands and ribbons in the following.

After 1 min of growth, the lateral dimensions of islands are up to 200 nm, while ribbons widths range from 50 nm to 250 nm (adding up the widths of the contiguous ribbons). With a further minute of growth (growth time = 2 min, Fig. 6d), the graphene ribbons and islands expand to reach sizes of between 200 nm and 400 nm. Apart from the islands and ribbons, we still find the rough surface of the buffer layer. After a total of 4 min of growth (Fig. 6e), most of the surface is covered with platelets (400 nm to 700 nm in lateral size) and ribbons of graphene. The rough surface of the buffer layer can still be seen between these graphene domains. At 7 min (Fig.
<figure><img src="image_11.png" /><figcaption>**Fig. 7 | Evolution of graphene coverage with growth time.** a C1s XPS spectra (normalized and shifted with respect to the SiC peak) of graphene samples obtained with different growth times and argon cooling. The graphene peak, and therefore the graphene coverage, is seen to increase up to 4 min of growth. From this growth time, all XPS spectra are almost superimposed up to 15 min, indicating that graphene</figcaption></figure>

coverage remains stable. b Average number of graphene layers estimated with Raman spectroscopy (integrated intensity of the G peak normalized to the one of a reference HOPG sample) on the same samples. In accordance with XPS, the average number of graphene layers determined with Raman spectroscopy evolves slowly from 0.94 at 7 min of growth to 1.02 after 15 min.

6f), the terraces are perfectly smooth and continuous, excepting the presence, at the step edges, of scarce small domains (with up to 100 nm lateral size) of buffer layer not covered with graphene: we are therefore at the very end of coalescence. This is consistent with the localized SiC etching at the step edges observed on the same sample with a conventional cooling (Fig. 1d). Finally, after 11 min of growth (Fig. 6g), there is no longer any uncovered buffer layer: coalescence is complete. When the growth time is further increased to 15 min (Fig. 6h), we only observe a change in the SiC step distribution which can be attributed to local variations of substrate residual offcut.

## Nucleation and diffusion

Our series of samples allows us to observe the different stages of the formation of graphene. Firstly, the SiC surface is reorganized by hydrogen etching during the 5 min temperature ramp. After the introduction of propane, the buffer layer forms very quickly, covering the entire surface in less than 1 min. The graphene then forms either ribbons along the SiC steps or islands in the centre of the terraces. Between 1 min and 4 min, the ribbons and islands can be seen to expand by lateral growth, with no new islands appearing: for all samples, there is approximately one island every 500 nm along a given terrace. The coalescence occurs mainly between 4 min, when few islands or ribbons begin to merge, and 7 min when a large part of the surface is covered by graphene. However, as specified above, the coalescence is fully achieved only after 11 min of growth.

We therefore observe a classic evolution with nucleation limited by diffusion: once the buffer layer has been created, the species diffuse onto it and nucleate either along a step if they find one, or on a terrace. The absence of islands near the steps can be explained by an adatom capture mechanism that prevents the nucleation of islands in this zone. On the contrary, islands can nucleate in the centre of terraces if another island is not too close, which finally results in a rather regular spacing of islands. After 1 min of growth, any carbon atom on the surface can feed the growth of an island or a ribbon by travelling a maximum of 400 nm, which gives an order of magnitude of the diffusion length. On the sample obtained with a 2 min growth, presenting a slightly different step spacing (attributed to local offcut variations), we observe the absence of islands on the narrower terraces (600 nm to 700 nm wide), but their presence in the centre of the wider terraces (900 nm to 1100 nm wide).

The nucleation of graphene and the formation of ribbons along the steps is not very surprising insofar as it has been widely observed and described$^{10,44-48}$. On the other hand, the observation of island nucleation at the centre of the terraces - a phenomenon that is quite commonly observed in other growth systems with an external source - seems to be unprecedented for graphene on SiC, and most of the graphene islands reported in the literature appear to be the result of growth non-uniformities more than that of homogeneous nucleation$^{39,49}$. The nucleation of self-organized graphene islands is therefore singular and constitutes a notable difference from the mechanisms of growth by annealing of SiC.

## Self-limitation of the growth

Overall, the AFM observations of our sample series show that the growth rate is not uniform: after nucleation during the first minute, the graphene grows rapidly to cover half the surface after 2 min, then almost the entire surface after 4 min. Once the surface is covered with graphene, extending the growth time does not allow a second layer to form. These observations are consistent with the evolution of the XPS spectra shown in Fig. 7a: the intensity of the graphene peak is clearly seen to increase up to 4 min of growth, after which there is no significant variation until 15 min. The average number of graphene layers can be quantified with Raman spectroscopy using the integrated intensity of the G peak normalized to the one of a reference HOPG sample$^{50-52}$ (the Raman spectra are presented as supplementary material in Supplementary Fig. S4a). As shown in Fig. 7b, the average number of graphene layer reaches 0.94 and 1 at 4 min and 7 min of growth, respectively, and remains at 1.02 after 15 min of growth. From the Raman maps (Supplementary Fig. S4b), we can also estimate that the proportion of multilayers remains below 1% up to 7 min of growth and increases to only 3% and 5% at 11 min and 15 min of growth respectively.

We can notice here the importance of the argon cooling to describe the evolution of graphene coverage with time: while conventional hydrogen cooling (Fig. 2) led to a non-uniform behaviour when increasing growth time, argon cooling (Fig. 7) allows the clear observation of the self-limitation of the growth.

We have also grown a series of samples where the growth time was set to 15 min and the propane flow varied from 5 sccm to 50 sccm (the sample grown with 10 sccm of propane is common to the growth time and propane flow series). Figure 8 shows the XPS spectra and some AFM images of this sample series. With 5 sccm of propane (Fig.
<figure><img src="image_12.png" /><figcaption>**Fig. 8** | Graphene growths with different propane flow. a C1s XPS spectra (normalized and shifted with respect to the SiC peak) of graphene samples obtained with propane flows ranging from 5 sccm to 50 sccm and cooling under argon. The graphene peak, and therefore the graphene coverage, remains stable up to 30 sccm. From 40 sccm, the increase in intensity of the graphene peak is due to the formation of graphitic clusters which can be seen with optical microscopy. b Average number of graphene layers estimated with Raman spectroscopy (integrated intensity of the G</figcaption></figure>

peak normalized to the one of a reference HOPG sample) on the same samples. Differently from XPS, Raman spectroscopy can be performed between the graphitic clusters. Consequently, the average number of graphene layers determined with Raman spectroscopy evolves slowly from 1.02 with 10 sccm to 1.16 with 50 sccm. c–e AFM images of selected samples. The morphology between graphitic clusters on samples grown with 20 sccm (d) and 50 sccm (e) remains quite smooth. Vertical scale is Δz = 5 nm for all AFM images.

8c), the AFM shows that the coverage is almost complete, and the XPS spectrum is superimposed on that of the monolayer obtained with 10 sccm. Between 10 sccm and 30 sccm, the XPS spectra are still almost superimposed, demonstrating the independence of graphene thickness with respect to propane flow in this range. At 20 sccm (Fig. 8d) and 30 sccm, the morphology is characterized by the presence of SiC depressions of depth 0.25 nm. Finally, from 40 sccm to 50 sccm (Fig. 8e), the intensity of the graphitic peak increases with propane flow. For these last samples, optical microscopy shows the formation of graphitic clusters of increasing density and size with increasing propane flow (Supplementary Fig. S9). However, between these clusters, a rather smooth morphology can still be found, similar to the one obtained at 20 sccm, and domains of bilayer graphene can still be distinguished in the AFM phase image. The increase in the XPS signal at 40 sccm and 50 sccm therefore seems to be mainly due to the formation of graphitic clusters. Raman spectroscopy performed between carbon clusters (Supplementary Fig. S5) confirms that graphene monolayer is still present on the surface, even for large propane

flow, although the average number of layers slightly increases from 1.02 to 1.16 when propane flow varies from 10 sccm to 50 sccm, as shown in Fig. 8b. Accordingly, the monolayer coverage decreases from 97% to 83%. So, the self-limitation to a monolayer highlighted in the previous section when the growth time is varied is also observed with propane flow.

## Discussion

In the previous part, we have shown that under specific conditions the growth of graphene on a buffer layer using CVD under hydrogen can be self-limited to a single layer, so that increasing growth time and propane flow does not allow the formation of a second layer. We have made similar observations in other growth conditions (hydrogen partial pressure and temperature) leading to the formation of a buffer layer, and more generally, CVD under hydrogen never allowed us to grow more than one monolayer of graphene on a buffer layer (disregarding the bilayer patches, never covering more than 15% of the surface). We suggested in ref. 36 that the growth of graphene was self-limited. Here, we clearly establish this self-limitation to
one monolayer by studying a large set of graphene samples cooled under argon.

Graphene on a buffer layer is usually grown by Si sublimation during SiC annealing. Contrarily to our method, SiC annealing allows the growth of more than one layer of graphene on a buffer layer, as shown in earlier works by Emtsev et al.⁹, but slow-down or even self-limitation of growth have also been reported. Ouerghi et al. observed a slowdown of growth in the case of ultra-high vacuum annealing of on-axis 6H-SiC, and attributed this to a limitation in the diffusion of silicon out of the substrate after the completion of the first graphene layer³⁹. Tanaka et al.⁵³ gave precise experimental figures for the case of 4°-off 6H-SiC annealed at 1600 °C in ultra-high vacuum: while 2.1 monolayers are formed during the first minute, the following 9 min only bring about 0.3 additional monolayers. Finally, in the case of on-axis 3C-SiC/Si annealed in ultrahigh vacuum, Zarotti et al. reported a layer number increasing with the square root of the time, also suggesting a slowdown related to layer completion effects⁵⁴. The effect of growth time is less well documented in the case of argon annealing, but various groups have shown that increasing the annealing time enables more than one monolayer to be deposited: for example, Virojanadara et al. obtained a sample with domains of 1–4 monolayers when annealing on-axis 6H-SiC(0001) under 1 bar of argon⁵⁵, while Wang et al. obtained domains of 2–4 monolayers on the same type of substrate but at 10 mbar⁵⁶.

Hence, the slowing or self-limitation of graphene growth by SiC annealing has mainly been explained by a kinetic argument: the greater the graphene coverage, the longer it takes for silicon to diffuse out of the SiC via graphene-free areas. However, in the case of propane-hydrogen CVD studied here, the presence of an external carbon source allows to rule out explanations based on out diffusion of silicon from SiC. On the other hand, possible thermodynamics effects have also been suggested by Nemec et al.⁵⁷ on the basis of first-principle calculations in the case of 3C-SiC surface under ultra-high vacuum: moving from silicon-rich to carbon-rich conditions, different surface equilibrium states appear, corresponding successively to reconstructions of the SiC, to the presence of the buffer layer, to a monolayer of graphene on the buffer layer, and then to an increasing number of layers up to graphite. Hence, the self-limitation of the growth could be explained by a purely thermodynamic argument. However, the self-limitation reported here may also be explained by the difficulty of nucleating graphene islands on the first graphene layer. Actually, difficulties to nucleate islands have also been encountered when attempting to grow III-nitrides on such graphene films³⁰.

From the comparison with SiC annealing, the self-limitation of the growth to one monolayer appears specific to the CVD growth under hydrogen. More precisely, this self-limitation is specific to growth conditions leading to the formation of a buffer layer: in a previous work, we showed that CVD also allows (still on the Si-face) the growth of multilayer graphene with azimuthal disorder on a fully hydrogenated interface²⁷ using lower growth temperature and higher hydrogen partial pressure. Under such growth conditions, increasing growth time or propane flow always leads to an increase of the few-layer graphene thickness²⁶,²⁷, and graphene samples with azimuthal disorder have generally an average thickness above 2 monolayers. The increase in disordered graphene thickness when increasing growth time and propane flow proves that, for such growth conditions, disordered graphene grows from carbon atoms carried by the propane flow. In conditions leading to the formation of a buffer layer, the different growth behaviour (i.e. the self-limitation when varying propane flow or growth time), together with the similar graphene structure than that obtained by SiC annealing, may suggest the same carbon feeding mechanisms as in the case of SiC annealing, or in other words, from carbon atoms of the substrate. Nevertheless, this possibility cannot be established with our experiments, and the origin of carbon atoms forming graphene on a buffer layer remains an open question.

To conclude, the growth of graphene on SiC under hydrogen CVD presents many differences with respect to the annealing of SiC under argon, such as the absence of “natural” carbon excess on the surface or the possible hydrogenation of the interface instead of the buffer layer expected on the Si-

face. This study allows us to evidence other specificities of this growth method, starting with effects of hydrogen during cooling down, possibly leading to the transformation of the buffer layer into graphene, or even to the total etching of the graphene layer.

In previous studies, the hydrogenation of the graphene/SiC interface encountered in certain growth conditions was explained by the hydrogenation of the SiC before and during graphene growth. It is actually the case at lower growth temperature or higher hydrogen partial pressure than considered here, and this leads to the formation of graphene with azimuthal disorder²⁶. Inversely, the formation of monocrystalline graphene on a hydrogenated interface²⁸, previously interpreted only on the basis of mechanisms occurring during growth step, could now be attributed to the growth of a buffer layer followed by its transformation into graphene during cooling down, but this point will be addressed in another study.

Hydrogen effects during cooling are emphasized with partial graphene coverage or when cooling rate is reduced, but can also, in contrast, be suppressed by switching hydrogen flux off during cooling, leaving only the argon flow. Such argon cooling, which allows growth to be frozen at different stages of graphene formation, constitutes a new way to understand the growth mechanisms occurring during CVD under hydrogen. Here, argon cooling allowed observations of the rapid formation of the buffer layer and the graphene nucleation in the form of ribbons at the step edges and islands in the centres of sufficiently wide terraces, the lateral growth of ribbons and islands, and finally their coalescence to form a single layer of graphene. After that, increasing growth time or propane flow does not allow the formation of another layer, proving that under such growth conditions, graphene growth is self-limited to a single layer.

This behaviour is different from that observed under other growth conditions²⁷, which reopens the question on the origin of the carbon atoms forming graphene. This question, as well as that on the origin of the self-limited growth, requires works which may be based on nucleation studies or growth simulations. Meanwhile, the self-limited growth of graphene using hydrogen CVD makes this method particularly attractive for graphene growth at the wafer scale.

## Methods

### Growth

Samples were grown in a resistively heated hot-wall CVD reactor originally designed for SiC epitaxy on 2-inches diameter⁵⁸. The substrates are 6H-SiC(0001) on-axis (~0.04°) from Xiamen Semiconductors cleaved into ~0.4 to 1 cm² pieces. The basic recipe for growing a continuous graphene monolayer is carried out entirely under a laminar flow of 6 slm of hydrogen and 6 slm of argon at a regulated pressure of 800 mbar. The total gas flow of 12 slm is high compared to that used for graphene growth by Si sublimation (0 to 1 slm in ref. 59), but similar to that used for SiC epitaxy or annealing in such CVD reactors (10–20 slm in ref. 60). After the 5 min ramp-up to the growth temperature of 1550 °C, graphene is grown by adding 10 standard cubic centimetres (sccm) of propane for 15 min. After the growth, the sample is cooled down to room temperature under hydrogen and argon (referred to as conventional cooling) at an initial cooling rate of 4 °C/s (a typical temperature profile is presented in Supplementary Fig. S1). Such recipes at 1550 °C under H₂ and argon have already been proven to grow monolayer graphene whose properties have been studied by angle-resolved photoemission spectroscopy in ref. 28, quantum Hall effect measurements in ref. 29, transmission electronic microscopy and STM in ref. 36. In addition, Supplementary Figs. S10–S12 present XPS and Raman spectroscopy at the sample scale demonstrating the uniformity of the monolayer graphene at different scales.

With respect to this basis recipe, we have varied the growth time, the propane flow and the post-growth steps, as indicated in Table 1. Concerning the post-growth steps, we have either added a 1 min post-growth annealing (i.e. the propane flow is stopped, but the temperature is maintained at 1550 °C for 1 min), or stopped the hydrogen flow at the beginning of the cooling down (referred to as argon cooling). For recipe with conventional or argon cooling, we have varied the growth time from 0 (flash annealing) to
<table><caption>**Table 1 | Summary of growth conditions**</caption><thead><tr><th rowspan="2">Series</th><th colspan="2">Growth step</th><th rowspan="2">Post growth annealing</th><th rowspan="2">Cooling</th></tr><tr><th>Propane flow</th><th>Growth time</th></tr></thead><tbody><tr><td>Conventional cooling</td><td>10 sccm</td><td>0–15 min</td><td>–</td><td>H<sub>2</sub> + Ar</td></tr><tr><td>Post-growth annealing</td><td>10 sccm</td><td>4 and 15 min</td><td>1 min</td><td>H<sub>2</sub> + Ar</td></tr><tr><td>Ar cooling (time)</td><td>10 sccm</td><td>0–15 min</td><td>–</td><td>Ar</td></tr><tr><td>Ar cooling (propane)</td><td>5–50 sccm</td><td>15 min</td><td>–</td><td>Ar</td></tr><tr><td>Other growth parameters</td><td colspan="2">1550 °C, 800 mbar, 50% H<sub>2</sub> + Ar</td><td></td><td>800 mbar</td></tr></tbody></table>

15 min. Finally, propane flow has been varied from 5 sccm to 50 sccm for the argon cooling only.

## Characterizations

All samples were studied using X-ray photoelectron spectroscopy (XPS) and atomic force microscopy (AFM). XPS has been conducted on a Thermo Scientific Kα-system equipped with Al Kα monochromated source (spot size about 0.1 mm²). To compare samples, C1s spectra are normalized and shifted with respect to the SiC peak. AFM images have been acquired with a Veeco dimension III setup in tapping-mode and processed using WSxM software⁶¹. Some samples were also studied by Raman spectroscopy using a home-made setup based on an Acton spectrometer fitted with a Pylon CCD detector and a 600 grooves/mm grating. The samples were excited with a 532 nm continuous wave laser through a ×100 objective (numerical aperture 0.9, spot full width at half maximum ~400 nm).

## Data availability

Data used for this study are available upon reasonable request from the corresponding author.

Received: 6 February 2025; Accepted: 2 April 2025;

Published online: 24 April 2025

## References

1. Van Bommel, A. J., Crombeen, J. E. & Van Tooren, A. LEED and Auger electron observation of the SiC(0001) surface. *Surf. Sci.* **48**, 463 (1975).

2. Badami, D. V. X-ray studies of graphite formed by decomposing silicon carbide. *Carbon* **3**, 53 (1965).

3. Forbeaux, I., Themlin, J.-M. & Debever, J.-M. Heteroepitaxial graphite on 6H-SiC(0001): Interface formation through conduction-band electronic structure. *Phys. Rev. B* **58**, 16396 (1998).

4. Charrier, A. et al. Solid-state decomposition of silicon carbide for growing ultra-thin heteroepitaxial graphite films. *J. Appl. Phys.* **92**, 2479 (2002).

5. Berger, C. et al. Ultrathin Epitaxial Graphite: 2D Electron Gas Properties and a Route toward Graphene-based Nanoelectronics. *J. Phys. Chem. B* **108**, 19912 (2004).

6. Dagher, R. et al. A comparative study of graphene growth on SiC by hydrogen-CVD or Si sublimation through thermodynamic simulations. *Cryst. Eng. Comm.* **20**, 3702 (2018).

7. Mishra, N., Boeckl, J., Motta, N. & Iacopi, F. Graphene growth on silicon carbide: A review. *Phys. Status Solidi A* **213**, 2277-2289 (2016).

8. Shtepliuk, I., Khranovskyy, V. & Yakimova, R. Combining graphene with silicon carbide: synthesis and properties - a review. *Semicond. Sci. Technol.* **31**, 113004 (2016).

9. Emtsev, K. V. & Speck, F. Seyller, Th., Ley, L., and Riley, J. D. Interaction, growth, and ordering of epitaxial graphene on SiC(0001) surfaces: A comparative photoelectron spectroscopy study. *Phys. Rev. B* **77**, 155303 (2008).

10. Emtsev, K. V. et al. Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide. *Nat. Mater.* **8**, 203 (2009).

11. Ohta, T. et al. Interlayer Interaction and Electronic Screening in Multilayer Graphene Investigated with Angle-Resolved Photoemission Spectroscopy. *Phys. Rev. Lett.* **98**, 206802 (2007).

12. Kopylov, S. et al. Charge transfer between epitaxial graphene and silicon carbide. *Appl. Phys. Lett.* **97**, 112109 (2010).

13. Riedl, C., Coletti, C., Iwasaki, T., Zakharov, A. A. & Starke, U. Quasi-Free-Standing Epitaxial Graphene on SiC Obtained by Hydrogen Intercalation. *Phys. Rev. Lett.* **103**, 246804 (2009).

14. Virojanadara, C., Zakharov, A. A., Yakimova, R. & Johansson, L. I. Buffer layer free large area bi-layer graphene on SiC(0001). *Surf. Sci.* **604**, L4 (2010).

15. Speck, F. et al. The quasi-free-standing nature of graphene on H-saturated SiC(0001). *Appl. Phys. Lett.* **99**, 122106 (2011).

16. Ristein, J., Mammadov, S. & Seyller, T. Origin of Doping in Quasi-Free-Standing Graphene on Silicon Carbide. *Phys. Rev. Lett.* **108**, 246104 (2012).

17. Hass, J. et al. Why Multilayer Graphene on 4H-SiC(000-1) Behaves Like a Single Sheet of Graphene. *Phys. Rev. Lett.* **100**, 125504 (2008).

18. Varchon, F., Mallet, P., Magaud, L. & Veuillen, J.-Y. Rotational disorder in few-layer graphene films on 6H-SiC(000-1): a scanning tunneling microscopy study. *Phys. Rev. B* **77**, 165415 (2008).

19. Luxmi, S., He, N. G., Feenstra, R. M., & Fisher, P. J. Comparison of graphene formation on C-face and Si-face SiC {0001} surfaces. *Phys. Rev. B* **82**, 235406 (2010).

20. Drabińska, A. et al. Growth kinetics of epitaxial graphene on SiC substrates. *Phys. Rev. B* **81**, 245410 (2010).

21. Moreau, E., Ferrer, F. J., Vignaud, D., Godey, S. & Wallart, X. Graphene growth by molecular beam epitaxy using a solid carbon source. *Phys. Status Solidi A* **207**, 300 (2009).

22. Al-Temimy, A., Riedl, C. & Starke, U. Low temperature growth of epitaxial graphene on SiC induced by carbon evaporation. *Appl. Phys. Lett.* **95**, 231907 (2009).

23. Hwang, J. et al. Epitaxial growth of graphitic carbon on C-face SiC and sapphire by chemical vapor deposition (CVD). *J. Cryst. Growth* **312**, 3219 (2010).

24. Strupinski, W. et al. Graphene Epitaxy by Chemical Vapor Deposition on SiC. *Nano Lett.* **11**, 1786 (2011).

25. Kruskopf, M. et al. Come back of epitaxial graphene for electronics: large-area growth of bilayer-free graphene on SiC. *2D Mater.* **3**, 041002 (2016).

26. Michon, A. et al. Direct growth of few-layer graphene on 6H-SiC and 3C-SiC/Si via propane chemical vapor deposition. *Appl. Phys. Lett.* **97**, 171909 (2010).

27. Michon, A. et al. Effects of pressure, temperature, and hydrogen during graphene growth on SiC(0001) using propane-hydrogen chemical vapor deposition. *J. Appl. Phys.* **113**, 203501 (2013).

28. Jabakhanji, B. et al. Tuning the transport properties of graphene films grown by CVD on SiC(0001): Effect of in situ hydrogenation and annealing. *Phys. Rev. B* **89**, 085422 (2014).

29. Ribeiro-Palau, R. et al. Quantum Hall resistance standard in graphene devices under relaxed experimental conditions. *Nat. Nanotechnol.* **10**, 965 (2015).
30. Journot, T. et al. Remote epitaxy using graphene enables growth of stress-free GaN. *Nanotechnology* **30**, 505603 (2019).

31. Dau, M. T. et al. The valley Nernst effect in WSe₂. *Nat. Com.* **10**, 5796 (2019).

32. Giannazzo, F., Panasci, S. E., Schilirò, E., Koos, A. & Pécz, B. Integration of graphene and MoS₂ on silicon carbide: Materials science challenges and novel devices. *Mater. Sci. Semiconductor Process.* **174**, 108220 (2024).

33. Yang, Z. et al. A new direct growth method of graphene on Si-face of 6H-SiC by synergy of the inner and external carbon sources. *Appl. Surf. Sci.* **436**, 511 (2018).

34. Liu, Q. et al. Chemical vapor deposition graphene of high mobility by gradient growth method on an 4H-SiC (0001) substrate. *Appl. Surf. Sci.* **454**, 68 (2018).

35. Liu, Z. et al. Induced growth of quasi-free-standing graphene on SiC substrates. *RSC Adv.* **9**, 32226 (2019).

36. Ben Jabra, Z. et al. Hydrogen-Mediated CVD Epitaxy of Graphene on SiC: Implications for Microelectronic Applications. *ACS Appl. Nano Mater.* **4**, 4462 (2021).

37. Forti, S. & Starke, U. Epitaxial graphene on SiC: from carrier density engineering to quasi-free standing graphene by atomic intercalation. *J. Phys. D: Appl. Phys.* **47**, 094013 (2014).

38. Masahara, K. et al. Pre-growth treatment of 4H-SiC substrates by hydrogen etching at low pressure. *Mater. Sci. Forum* **338-342**, 1041–1044 (2000).

39. Ouerghi, A., Ridene, M., Mathieu, C., Gogneau, N. & Belkhou, R. From nanographene to monolayer graphene on 6H-SiC(0001) substrate. *Appl. Phys. Lett.* **102**, 253108 (2013).

40. Verdaguer, A. et al. Water-mediated height artifacts in dynamic atomic force microscopy. *J. Phys. Chem. Chem. Phys.* **14**, 16080–16087 (2012).

41. Souza, J. C. et al. Wettability effect of graphene-based surfaces on silicon carbide and their influence on hydrophobicity of nanocrystalline cerium oxide films. *J. Colloid Interface Sci.* **441**, 71 (2015).

42. Nemes-Incze, P., Osváth, Z., Kamarás, K. & Biró, L. P. Anomalies in thickness measurements of graphene and few layer graphite crystals by tapping mode atomic force microscopy. *Carbon* **46**, 1435 (2008).

43. Arrighi, A., Ullberg, N., Derycke, V. & Grévin, B. A simple KPFM-based approach for electrostatic- free topographic measurements: the case of MoS₂ on SiO₂. *Nanotechnology* **34**, 215705 (2023).

44. Oliveira, M. H. Jr., Schumann, T., Ramsteiner, M., Lopes, J. M. J. & Riechert, H. Influence of the silicon carbide surface morphology on the epitaxial graphene formation. *Appl. Phys. Lett.* **99**, 111901 (2011).

45. Robinson, J. et al. Nucleation of Epitaxial Graphene on SiC(0001). *ACS Nano* **4**, 153 (2010).

46. Ohta, T., Bartelt, N. C., Nie, S., Thürmer, K. & Kellogg, G. L. Role of carbon surface diffusion on the growth of epitaxial graphene on SiC. *Phys. Rev. B* **81**, 121411(R) (2010).

47. Norimatsu, W. & Kusunoki, M. Formation process of graphene on SiC (0001). *Phys. E* **42**, 691 (2010).

48. Hassan, J. et al. Quasi-free-standing monolayer and bilayer graphene growth on homoepitaxial on-axis 4H-SiC(0001) layers. *Carbon* **82**, 12 (2015).

49. Nagase, M., Hibino, H., Kageshima, H. & Yamaguchi, H. Contact conductance measurement of locally suspended graphene on SiC. *Appl. Phys. Express* **3**, 045101 (2010).

50. Camara, N. et al. Anisotropic growth of long isolated graphene ribbons on the C face of graphite-capped 6H-SiC. *Phys. Rev. B* **80**, 125410 (2009).

51. Kumar, B. et al. Growth protocols and characterization of epitaxial graphene on SiC elaborated in a graphite enclosure. *Phys. E* **75**, 7 (2016).

52. Landois, P. et al. Growth of low doped monolayer graphene on SiC(0001) via sublimation at low argon pressure. *Phys. Chem. Chem. Phys.* **19**, 15833 (2017).

53. Tanaka, S., Morita, K. & Hibino, H. Anisotropic layer-by-layer growth of graphene on vicinal SiC(0001) surfaces. *Phys. Rev. B* **81**, 041406(R) (2010).

54. Zarotti, F. et al. Time evolution of graphene growth on SiC as a function of annealing temperature. *Carbon* **98**, 307 (2016).

55. Virojanadara, C. et al. Homogeneous large-area graphene layer growth on 6H-SiC(0001). *Phys. Rev. B* **78**, 245403 (2008).

56. Wang, T. Growth of epitaxial graphene on SiC (0001) by sublimation at low argon pressure. Thèse de l'Université Montpellier, https://theses.hal.science/tel-01946415v1/document (2018).

57. Nemec, L., Blum, V., Rinke, P. & Scheffler, M. Thermodynamic Equilibrium Conditions of Graphene Films on SiC. *Phys. Rev. Lett.* **111**, 065502 (2013).

58. Leycuras, A. Growth of CVD Thin Films and Thick LPE 3C-SiC in a Specially Designed Reactor. *Mater. Sci. Forum* **338**, 241 (2000).

59. Momeni Pakdehi, D. et al. Homogeneous Large-Area Quasi-Free-Standing Monolayer and Bilayer Graphene on SiC. *ACS Appl. Nano Mater.* **2**, 844–852 (2019).

60. Chassagne, T. et al. Investigation of 2 Inch SiC Layers Grown in a Resistively-Heated LP-CVD Reactor with Horizontal “Hot-Walls”. *Mater. Sci. Forum* **457-460**, 273–276 (2004).

61. Horcas, I. et al. WSXM: A software for scanning probe microscopy and a tool for nanotechnology. *Rev. Sci. Instrum.* **78**, 013705 (2007).

## Acknowledgements

The authors gratefully thank Jean-Roch Huntzinger (Laboratoire Charles Coulomb) and Benjamin Grévin (Institut Néel) for fruitful discussions and Frédéric Georgi (CEMEF-Mines Paristech) for XPS facilities. This work was supported by the Region Sud - Provence-Alpes-Côte d'Azur through the PlaGGe project, by the French National Research Agency (ANR) through the VanaSiC project (ANR-22-CE24-0022-01), and by a France 2030 government grant managed by the ANR in the framework of the PEPR Electronique through the ADICT project (ANR-22-PEEL-0011).

## Author contributions

C.M., A.E.A., M.P. (CRHEA) and A.M. grew the graphene sample, C.M., A.E.A., M.K., M.A. and M.P. (L2C) performed the characterizations, all the authors analysed and discussed the data, A.M. and C.M. wrote the manuscript with contributions from all co-authors, I.B., S.J., B.J., Y.C. and A.M. oversaw the project.

## Competing interests

The authors declare no competing interests.

## Additional information

**Supplementary information** The online version contains supplementary material available at https://doi.org/10.1038/s41699-025-00554-4.

**Correspondence** and requests for materials should be addressed to Adrien Michon.

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