Spontaneous emergence of straintronics effects and striped stacking domains in untwisted three-layer epitaxial graphene

Significance

The self-organized emergence of ABA and ABC stacking domains in a three-layer epitaxial graphene system grown on SiC is observed using conductive AFM. These domains self-assemble without the need of expert mechanical twisting and alignment, as usually obtained in exfoliated graphene. The size and geometry of the observed stacking domains depend on the interplay between strain and shape of three-layer regions, at times producing stripes of several tens of nanometers in width, extending for microns. These findings indicate the possibility of controlling the desired shape and periodicity through pregrowth patterning of SiC. Isolated, stripe-shaped ABA/ABC domains pave the way for different potential applications of graphene in electronic devices based on the unconventional quantum Hall effect, superconductivity, or charge density waves.

Abstract

Emergent electronic phenomena, from superconductivity to ferroelectricity, magnetism, and correlated many-body band gaps, have been observed in domains created by stacking and twisting atomic layers of Van der Waals materials. In graphene, emergent properties have been observed in ABC stacking domains obtained by exfoliation followed by expert mechanical twisting and alignment with the desired orientation, a process very challenging and nonscalable. Here, conductive atomic force microscopy shows in untwisted epitaxial graphene grown on SiC the surprising presence of striped domains with dissimilar conductance, a contrast that demonstrates the presence of ABA and ABC domains since it matches exactly the conductivity difference observed in ABA/ABC domains in twisted exfoliated graphene and calculated by density functional theory. The size and geometry of the stacking domains depend on the interplay between strain, solitons crossing, and shape of the three-layer regions. Interestingly, we demonstrate the growth of three-layer regions in which the ABA/ABC stacking domains self-organize in stable stripes of a few tens of nanometers. The growth-controlled production of isolated and stripe-shaped ABA/ABC domains open the path to fabricate quantum devices on these domains. These findings on self-assembly formation of ABA/ABC epitaxial graphene stripes on SiC without the need of time-consuming and nonscalable graphene exfoliation, alignment, and twisting provide different potential applications of graphene in electronic devices.

Two-dimensional (2D) twisted superlattices represent a unique platform to induce electronic correlation into systems with weak interactions. For example, emergent many-body electron phenomena have been observed by stacking one monolayer of graphene on another at the magic angle (1), by twisting double-bilayer graphene (2, 3), or by twisting and aligning ABC trilayer graphene with hexagonal boron nitride (4–6). Recent research on different types of twisted superlattices has demonstrated the emergence of superconductivity, ferroelectricity, magnetism, and a correlated many-body band gap (7–9). These twisted superlattices with emergent properties are based on exfoliated graphene layers, or other types of exfoliated 2D materials, which are deposited on a substrate and expertly mechanically twisted and aligned with the desired orientation. Unfortunately, technological applications and device fabrication based on manually twisting exfoliated layers are challenging; furthermore, twisting of exfoliated graphene layers has only produced Bernal-stacked (ABA) and rhombohedral-stacked (ABC) domains patterns with a triangular geometry (10, 11). Previous works (12–14) have shown that in epitaxial graphene, the peculiar growth of graphene on a SiC substrate leads to striped patterns of alternating AB/AC stacking domains. The formation of AB and BA domains in epitaxial graphene has been described by the two-dimensional Frenkel–Kontorova model combining the interlayer interaction and the elastic forces within the layer (15). Different studies (12–16) have shown that strain and boundaries energy minimization leads to the formation of striped patterns that are energetically more favorable than triangular stacking domain patterns.

Here, we show that the dislocations previously observed in two-layer epitaxial graphene (12–16) cause in three-layer epitaxial graphene a change in the crystal structure from Bernal stacking to rhombohedral stacking (ABA ↔ ABC), resulting in real stacking faults in between the ABA and ABC regions. This is a straintronics-based scalable approach to produce in epitaxial graphene ABA and ABC stacking domains with different geometry, from triangles to stripes, by directing the growth of graphene on SiC(0001) without the need of graphene mechanical exfoliation and twisting, a process extremely challenging and time-consuming. Conductive AFM (c-AFM) shows the surprising presence in three-layer epitaxial graphene of striped domains with dissimilar conductance, matching the contrast so far observed only in ABA and ABC domains of twisted exfoliated graphene (17). These conductance domains, never observed before in epitaxial graphene to the best of our knowledge, mostly present themselves as spatial stripes with width varying between 30 and 70 nm. Using c-AFM, we investigate the electronic properties of epitaxial graphene in regions composed of two layers (monolayer graphene plus buffer layer or two quasi-free standing graphene layers without buffer layer) and three layers (bilayer graphene plus buffer layer), see Fig. 1. We show that two-layer regions do not reveal any electronic pattern in c-AFM experiments, while three-layer regions exhibit surprisingly regular conductance stripes of a few tens of nanometers, indicating alternating domains of higher and lower conductance. The observed stripes, which do not appear in any AFM topographical image, follow the shape of the three-layer regions and align along the longer side of these regions. The conductance of the high-conductive domains is between 1.2 and 2 times larger than that one of the low-conductive domains, the same ratio found by c-AFM and DFT calculations in exfoliated twisted graphene for ABA and ABC stacking domains (17). Furthermore, these conductance striped patterns are independent of the AFM tip scanning angle and are not present in quasi-free standing bilayer graphene (two-layer graphene on SiC without a buffer layer). The difference in conductance between the alternating stripes changes weakly with the applied voltage and remains unaltered by repeated applications of load and shear. This scalable growth method is promising for controlling the presence and shape of ABA/ABC domains by directing the growth of graphene on SiC without the need for graphene exfoliation and twisting. Growing isolated regions of 2L/Bfl/SiC epitaxial graphene is a simple and robust method to create large stripes (up to micrometer-scale long) of rhombohedral graphene, alternating with Bernal stripes. So far twisting of exfoliated graphene has only produced triangular ABA/ABC patterns, which are not easily amenable to fabrication of electronic devices. The here shown stripes, on the other hand, are perfectly shaped to fabricate FETs or other devices where electrodes can be directly placed at the extremes of the stripes, and current flows along the stripes.

Fig. 1.

Spontaneous emergence of striped stacking domains in untwisted three-layer epitaxial graphene. (A) Schematic setup of conductive AFM experiments performed on an epitaxial graphene film on SiC. (B) Atomic structure of epitaxial graphene films on SiC(0001). (C and D) Schematic diagrams showing stacking order domains in 1L graphene plus buffer layer (two-layer film) (C), and 2L graphene plus buffer layer (three-layer film) (D) on SiC(0001). The dotted horizontal lines between AB (ABA) and AC (ABC) stacking domains represent strain soliton networks. (E) c-AFM image (1 × 1 µm²) of an epitaxial graphene film grown in Argon taken at 3.75 mV bias voltage and 25 nN normal force. The color ranges from 10 nA (black) to 55 nA (light green). In this conductance image are visible two-layer regions with no stripes marked as 1L/Bfl/SiC-S2 and 1L/Bfl/SiC-S3, corresponding to different SiC terraces, and a three-layer region, 2L/Bfl/SiC(0001), exhibiting stripes in conductance. The stripes inside the three-layer region correspond to ABA stacking domains (dark green), and ABC stacking domains (black). (F) cross-sectional profile corresponding to the red line in (E), showing a periodicity of 45 nm.

Results

Epitaxial graphene films are grown by thermal sublimation of Si from a SiC substrate (18–22). Initially, a buffer graphene-like layer is formed, which is partially covalently bonded to the SiC substrate (23–26); subsequentially, a first graphene layer is formed by the release of the buffer layer into a fully free-standing graphene layer, while a new buffer layer forms between SiC and graphene. While the growing temperature is still high enough, the graphene growth continues, and a second graphene layer starts to form by releasing the buffer layer and forming a new one. Here, we investigate by conductive-AFM (Fig. 1A) epitaxial graphene films grown on SiC(0001) presenting two-layer regions, i.e., regions composed of one layer graphene plus the carbon interfacial buffer layer, and three-layer regions, i.e., regions composed of bilayer graphene plus the carbon interfacial buffer layer. We name these regions as 1L/Bfl/SiC(0001) and 2L/Bfl/SiC(0001), respectively (Fig. 1B). The epitaxial graphene films are grown either in Argon or in high-vacuum environment using the thermal sublimation method (18–22). By tuning the growth parameters, i.e., temperature, heating time, and gas pressure, it is possible to control the size of the three-layer regions. The prepared epitaxial graphene samples are named based on the environmental gas used during the growth process. Samples Ar-EG1, Ar-EG2, and Ar-EG3 are grown in Argon, while samples HV-EG1 and HV-EG2 are grown in high vacuum (Methods).

During the epitaxial graphene growth, consisting of thermal induced Silicon sublimation, release of the buffer layer, and growth of a new buffer layer at the interface between graphene and SiC, stacking domains develop to release the strain created by the lattice mismatch between graphene and SiC and by their different thermal expansion rates (13, 14). These strain-induced stacking faults have been previously observed in two-layer epitaxial graphene films, composed of monolayer graphene plus a buffer layer grown on SiC(0001) (13, 27). All strain is channeled into stacking faults which form in the transition region between AB and BA stacking domains and give rise to strain solitons (12) (Fig. 1C). Stacking faults in two-layer epitaxial graphene have been studied by scanning tunneling microscopy (STM) (28, 29), thermoelectric imaging (30), transmission electron microscopy (TEM) (12, 16, 31–33), and low-energy electron microscopy (LEEM) (13, 14, 28), but no studies have been conducted on their local conductivity or on the local conductivity and stacking order of three-layer epitaxial graphene. Furthermore, the presence of AB/BA domains in two-layer epitaxial graphene films has never been detected by AFM, as expected since AB and BA domains do not present differences in morphology or electronic properties. Once a new graphene layer is formed (trilayer graphene, namely 2L/Bfl/SiC), these dislocations likely cause a change in the crystal structure from Bernal stacking to rhombohedral stacking (ABA ↔ ABC), resulting in real stacking faults in between the ABA and ABC regions (Fig. 1B). Indeed, a previous investigation using high-resolution transmission electron microscopy of the stacking sequence of several layers of graphene formed on Si shows that graphene layers may exhibit an ABC-type stacking (32). Using the Slonczewski–Weiss–McClure model based on the tight-binding method, the authors suggest that a γ₅ like interatomic interaction, which corresponds to the formation of a linear trimer of ABA type stacking, is spontaneously weakened by the interaction between graphene and SiC. This can lead to the destabilization of the ABA stacking and to the formation of the ABC stacking.

Fig. 1E shows a typical c-AFM image of an epitaxial graphene sample (Ar-EG1). The image exhibits three different regions. Based on the surface topography (34, 35), frictional properties (24, 36), and surface potential (37, 38), we identify the areas with stripes in the cAFM signal as three-layer regions, i.e., 2L/Bfl/SiC(0001) (SI Appendix, Figs. S1–S3). Imaging of topography, surface potential, friction, and conductance helps to distinguish between two-layer regions [1L/Bfl/SiC(0001)] and three-layer regions [2L/Bfl/SiC(0001)] and different SiC terraces. As highlighted in the work of Momeni Pakdehi (39) and Sinterhauf (40), 1L/Bfl/SiC areas show roughly the same contact potential signal (SI Appendix, Fig. S1 C and D) even for different S2 and S3 terraces, with a difference smaller than 10 mV. On the other hand, the difference in contact potential between 2L/Bfl/SiC and 1L/Bfl/SiC is about 200 mV. Therefore, KPFM (the contact potential imaging method) allows clear distinction between the 2L/Bfl/SiC and the 1L/Bfl/SiC areas (SI Appendix, Fig. S5). The same clear distinction is present in the friction and conductive AFM images, showing lower friction (and lower conductance) in the 2L/Bfl/SiC compared to 1L/Bfl/SiC (SI Appendix, Figs. S1 and S2 and Fig. 2). The two two-layer regions correspond to two different 6H silicon carbide terraces S2 and S3 (39, 40) and do not show any presence of stacking domains in conductance and topography, in agreement with previous studies on epitaxial graphene. On the other hand, when imaging the three-layer region [2L/Bfl/SiC(0001)] by c-AFM, surprisingly we observe a unique clear spatial modulation of the electronic current, with characteristic conductance stripes of about 45 nm in width, see Fig. 1F. Previous c-AFM experiments and density functional theory (DFT) calculations have shown that ABA and ABC stacking domains in exfoliated twisted three-layer graphene present different electrical conductivity (10, 17). The ratio between the high and low conductance observed in the different domains of three-layer epitaxial graphene in Fig. 1E and reported in Fig. 1F is around 1.7, a value similar to the one measured by c-AFM in the ABA/ABC domains in exfoliated twisted three-layer graphene (10, 11, 17). Therefore, we conclude that the strain-induced AB/BA stacking domains discussed above and previously observed in two-layer regions of epitaxial graphene (13, 16, 27, 28) evolve into ABA and ABC domains when an extra layer is grown at the SiC interface (see cartoon in Fig. 1 C and D). Since the growth of epitaxial graphene always starts from the bottom, due to the sublimation of Silicon on the SiC surface, in the case of three-layer regions, ABA and ABC stacking domains visible by c-AFM likely emerge from an atomic reconstruction in the three carbon layers regions, i.e., 2L graphene plus buffer layer (Fig. 1E) (13). In Fig. 1E, a triangular shape is visible at the center of the three-layer region, while the rest of the area exhibits stripes parallel to the longest sides of the three-layer region. The geometrical patterns of the observed conductance domains follow the strain-induced reconstruction of the ABA/ABC domains. The formation of AB and BA domains in case of 1L/Bfl/SiC(0001) has been described by the two-dimensional Frenkel–Kontorova model combining the interlayer interaction and the elastic forces within the layer (15). This model shows that the reconstruction is driven by the minimization of strain energy at the SiC/buffer layer/graphene layer interface (13–15). Since triangular patterns require the crossing of domain boundaries (solitons), and crossing boundaries/solitons require extra energy compared to parallel noncrossing boundaries/solitons (13–15), depending on the strain in the three-layer region, stripes can be more energetically favorable than triangles. Indeed, adaptive geometric phase analysis calculations have recently shown that in certain situations, it is energetically favorable to form striped stacking domain boundaries instead of triangular moiré domain patterns by elongating triangular domains along one direction to avoid the crossing of the solitons (12–16). The same mechanism is behind the formation of striped patterns in 2L/Bfl/SiC(0001), where the strain located between buffer layer and the lower graphene layer (14) produces stacking domains of different shapes. c-AFM images of three-layer regions with triangular and striped patterns are reported in SI Appendix, Fig. S4, showing that stripes are favorable when the isolated three-layer regions have an elongated geometry. In Fig. 1E, we also remark that the quasivertical conductance stripes are separated by the quasihorizontal stripes by a bright narrow line, which corresponds to a dislocation line in the graphene structure (14).

Fig. 2.

Conductance, topography, friction, and surface potential. (A) Large area (4 × 4 µm²) c-AFM image of local conductance of an epitaxial graphene film grown in Ar, taken at 5 mV while applying a normal force of 0 nN, (color range 120 to 220 pA). (B) c-AFM conductance zoomed-in image of an area of the same sample in (A) (color range 550 to 950 pA). (C–E) Topography (color range 0.0 to 0.5 nm), friction force (color range 6 to 10 nN), and KPFM surface potential (color range is −0.35 to −0.17 V), respectively, of the area in (B). A normal load of 0 nN and a bias of −10 mV are applied in (B–D) and images are (1.6 × 1.6 µm²) in (B–E).

Fig. 2A displays a c-AFM image of local conductance on a 4 × 4 µm² area of an epitaxial graphene sample grown in Ar, encompassing many three-layer regions of different sizes and shapes. All the three-layer regions in the conductance image exhibit visible stripes and patterns (more images can be found in SI Appendix, Fig. S4). In Fig. 2 B–E, we perform several AFM measurements to compare conductance (Fig. 2B), topography (Fig. 2C), friction force (Fig. 2D), and surface potential (Fig. 2E) of specific areas that include three-layer and two-layer regions. First, we notice that the two-layer regions have a distinct topography (34, 35), friction force (24, 36), and surface potential (37, 38) compared to the three-layer regions, as commonly observed previously. Furthermore, no conductance patterns/stripes are found in the two-layer regions, in agreement with previous reports on epitaxial graphene (25, 41, 42). Second, interestingly, the stripes which can be observed in c-AFM in the three-layer regions are not detectable in either topography, friction, or surface potential [Kelvin probe force microscopy (KPFM)]. While on twisted trilayer exfoliated graphene on SiO₂, Li et al. (43) reported a work function difference 10 to 20 meV between ABA and ABC domains, here, no contrast is found in the surface potential images of the three-layer regions (Fig. 2E). The lateral resolution of KPFM (44) is 60 nm when using a tip radius of 25 nm, as in these experiments. This resolution is too low to detect the stripes because the typical size of the stacking domains is about 40 nm, as observed in the c-AFM measurements (Fig. 2B). This limited KPFM lateral resolution and possibly the signal-to-noise ratio prevent observing stripes in the surface potential signal.

To gather a better understanding of the conductance patterns observed in three-layer regions, we perform c-AFM measurements at different bias voltage, V, normal force, and scanning angle at room temperature and in ambient conditions. Fig. 3A shows a local conductance image of a generic area of an epitaxial graphene sample grown in Argon, where we highlight the different regions that are investigated at different bias voltages and normal loads. We also note the presence of two-layer regions (1L/BfL) corresponding to two different 6H silicon carbide terraces S2 and S3, as previously reported (39, 40), their respective current versus bias characteristics at zero load are plotted in SI Appendix, Fig. S6. Although I/ΔV depends on the distribution and shape of the various bilayer/trilayer graphene regions from the AFM tip to the drain electrode, we use the Ohm’s law, to determine the average resistance of the different regions in Fig. 3A as follows, 14.0 MΩ, 15.4 MΩ, 15.3 MΩ, and 20.4 MΩ for two-layer S2 regions, two-layer S3 regions, three-layer ABA-regions, and three-layer ABC-regions, respectively. The difference in electric current between the ABA and ABC domains for the areas shown in Fig. 3A measured at zero load by c-AFM as a function of the bias voltage is reported in Fig. 3B, showing that the difference in conductance varies linearly with the bias. We notice that while the current path is undetermined, the current is flowing through the 1L/BfL film which is covering the majority of the sample, therefore in average, we do not observe large differences when measuring the same type of graphene (i.e., number of layers, etc.) in different areas and with different geometry. For example, see SI Appendix, Fig. S6 where we compare two distinct areas and geometries. Fig. 3C reports on the relative change in current between the ABA and ABC domains of Fig. 3A, indicating that the relative change also linearly depends on the bias. A relative change value of 18% is found for −100 mV, and a value close to 30% is found for 100 mV. Fig. 3D shows the load dependence of the difference in current for the ABA and ABC domains, measured at zero bias voltage. In SI Appendix, Fig. S7, we also report the current as a function of the load for each domain type, showing a nonlinear increase of current with increasing load, due to the expected nonlinear increase in contact area between the tip and the surface at increasing loads. Accordingly, Fig. 3E shows that the relative change of conductance between the domains is not constant over the range of applied loads, it is about 30% for zero load and increases up to 50% at 60 nN. Fig. 3F shows the relative change between the current measured on the stacking domains ABA and ABC for different loads and biases on several samples prepared in different environments, see Methods section for sample details. The local conductance images of several regions on the different samples are depicted in SI Appendix, Fig. S4, showing the different sizes and shapes of 2L/Bfl/SiC(0001) regions. Overall, the relative change is about 50% within the errors, in very good agreement with previous c-AFM data on twisted trilayer graphene and DFT calculations (17).

Fig. 3.

Voltage and load dependency of the current in the striped regions. (A) c-AFM image acquired at 0 nN and while applying 100 mV on an epitaxial graphene film grown in Ar (color range 3.5 to 9 nA). (B) Plot of the current difference between ABA and ABC domains as a function of applied bias. (C) Percentage change in current between ABA areas and ABC areas. Values in (B and C) are calculated from the local conductance images of the areas shown in a, obtained from c-AFM experiments at different bias voltages between −100 mV and 100 mV at 0 nN. (D) Current difference between the ABA and ABC stacked areas as a function of the applied load. (E) Relative percentage change of current between ABA areas and ABC areas. Values in (D and E) are obtained by increasing the normal load from 0 nN to 60 nN at a constant bias voltage of 0 mV. (F) Relative change of current between ABA and ABC areas obtained from c-AFM experiments performed on different epitaxial graphene samples grown in Ar (Ar-EG1, Ar-EG2, Ar-EG3), and in high vacuum (HV-EG1, and HV-EG2), the used bias voltage and normal load are indicated in the figure.

To demonstrate the robustness of the observed striped domain, we perform c-AFM experiments after shearing the surface with an AFM. Previous studies showed that shear can induce a change in the soliton network and therefore in the stacking domains, so we repeat the same experiments as in reference (11, 17); however, we do not observe any change in the conductance of the stripes and patterns. We also conduct c-AFM measurements on the same area at different scanning angles (0, 30, 60, and 90°) to determine the effect of the scanning direction on stacking arrangement (Fig. 4 A–D). Again, the striped domains are very robust, do not depend on scan angle/direction, and are not disturbed by local shear. Differently from triangular Moiré patterns of ABC/ABA domains on exfoliated graphene layers (11, 17), these observations demonstrate high stability of the conductance patterns against any external force or shearing, which will enable robust fabrication of nanodevices on the desired domains.

Fig. 4.

Angle dependency in epitaxial graphene and quasi–free standing epitaxial graphene. (A–D) c-AFM images (1.15 × 1.15 µm²) of epitaxial graphene samples grown in Ar (Ar-EG2) obtained for different c-AFM tip scanning angles, namely 0° (A), 30° (B), 60° (C), and 90° (D), at 7.8 nN and 0 mV (color range 0.0 to 1.5 nA), showing no differences. (E) Schematics of two-layers quasi-freestanding epitaxial graphene on SiC(0001) after hydrogen intercalation and release of the buffer layer. (F) c-AFM image (1 × 1 µm²) of a quasi–free standing epitaxial graphene sample, showing one-layer regions (1L/H-SiC) and two-layer regions (2L/H-SiC), as labeled in red and black, respectively (color range 0.3 to 1.0 nA). No stripe patterns are observed on any of the quasi–free standing graphene areas.

Finally, we perform c-AFM measurements on hydrogen intercalated epitaxial graphene films also referred to as quasi-freestanding epitaxial graphene (QFS-EG) (45–47) (Fig. 4E and Methods). In these films, the covalent bonds between the SiC surface and the carbon buffer layer are broken and substituted with Si–H bonds upon hydrogen intercalation (Fig. 4E). Therefore, the buffer layer is fully transformed into a graphene layer (Methods). Fig. 4F shows the local conductance image of QFS-EG presenting one and two-layer graphene regions on hydrogenated SiC, and no conductance patterns are observed in neither regions, indicating that different stacking orders in three-layer graphene are the origin of the striped patterns.

Conclusions

In conclusion, we demonstrate a straintronics-based scalable approach, which could be generalized to other 2D materials, to control the periodicity and shape of ordered and robust ABA/ABC domains in epitaxial graphene by directing the growth of graphene on SiC without the need of graphene mechanical exfoliation and twisting, which is a process extremely challenging and time-consuming.

The presence of ABA and ABC stacking domains in three-layer epitaxial graphene systems on SiC is demonstrated by conductive AFM, which shows a modulation in the conductance of these domains typically observed in twisted exfoliated graphene and predicted by DFT calculations. This conductance modulation, never observed before in epitaxial graphene to the best of our knowledge, is characterized by spatial stripes with width varying between 30 and 70 nm and it is not observed in quasi–free standing two-layer epitaxial graphene or in one-layer epitaxial graphene on the buffer layer. Furthermore, no stripe or triangle domains are observed in topography and friction AFM. The size of the stripes and the overall geometry of the stacking domains depend on the shape of the three-layer regions. Large areas present mixtures of triangles and stripes, while elongated regions present regular stripes along the long axis of the region, indicating the possibility to lithographically pattern the SiC substrate to achieve the desired shape/periodicity. Isolated, stripe-shaped ABA/ABC domains open the path to fabricate quantum devices on these domains to study the unconventional quantum Hall effect, superconductivity, or charge density waves in epitaxial graphene. Moreover, the possible presence of topological edge states in the ABC domains of epitaxial graphene could find applications in Floquet engineering, a concept to manipulate quantum systems (8). So far, twisting of exfoliated graphene layers has only produced triangular ABA/ABC patterns, which are not easily amenable to device fabrication. These findings on scalable self-assembly formation of ABA/ABC epitaxial graphene stripes on SiC provide different potential applications of graphene in electronic devices and suggest the possibility to lithographically pattern the SiC substrate to achieve the desired shape/periodicity of ABA/ABC domains for high-throughput fabrication of devices on these domains.

Methods

Growth of Epitaxial Graphene Films on SiC.

Epitaxial graphene films are grown on the Si-face of on-axis 6H SiC from different suppliers (II-VI Inc., Pam-Xiamen) by thermal Si sublimation under different growing environments (18–22). The first carbon layer forms on Si-face of SiC is an interface layer, named the buffer layer (Bfl). When the growing temperature is kept high, the thermal decomposition of SiC continues and a new buffer layer is formed, while the previously formed buffer layer is released into the first graphene layer. This process of a new buffer formation and release of the previous buffer layer continues until the temperature is reduced. It allows us to control the number of layers by controlling the growing parameters. We then refer to two-layer or three-layer epitaxial graphene when one or two layers of graphene sit on the buffer layer, respectively.

Two samples namely Ar-EG1 and Ar-EG-2 are grown on semi-insulating 6H-SiC in an argon environment with Argon flowing at 30 SLPH at 1,650 °C for 5 min. The sample Ar-EG3 is prepared on semi-insulating 6H-SiC in a static argon atmosphere at 1,650 °C for 5 min. Another sample, HV-EG1 (semi-insulating 6H-SiC), and HV-EG2 (conductive n-type 6H-SiC) are grown on 6H-SiC in a high vacuum (5 × 10⁻⁶ mbar) environment. Each of these samples has a large area covered with a mixture of two-layer epitaxial graphene (1L/Bfl/SiC) and three-layer epitaxial graphene (2L/Bfl/SiC). Further, the two different terraces of 6H-SiC, S2 and S3, lead to different graphene–substrate interactions. Hence, two distinct areas of two-layer epitaxial graphene are formed on the samples, labeled as 1L/BfLSiC-S2 and 1L/BfLSiC-S3. More information on the growth of epitaxial graphene samples can be found elsewhere (18–22). Quasi–free standing epitaxial graphene sample (QFS-EG) is obtained by hydrogen annealing of grown epitaxial graphene samples, detailed method is mentioned elsewhere (45–47). QFS-EG sample has a mixture of one-layer (1L/H-SiC) and two-layer (2L/H-SiC) graphene areas freely standing on the SiC substrate.

After the graphene growth, each sample is studied using Raman spectroscopy to identify the quality and number of layers of the prepared epitaxial graphene films. We use the micro-Raman confocal microscope WITec alpha300 RSA with a 100× magnification objective and numerical aperture NA = 0.9. The excitation laser wavelength is 532 nm, and the laser power is 30 mW. The integration time varies between 4 s and 5 s with five accumulations. The characteristic Raman spectrum consisting of D band (≈1,350 cm⁻¹), G peak (≈1,580 cm⁻¹), and 2D peak (≈2,700 cm⁻¹) (48) is shown in SI Appendix, Fig. S9. The full width at half maximum (FWHM) of the 2D peak can be used to determine the number of graphene layers (49). We plot the FWHM maps in SI Appendix, Fig. S9 B and C and corresponding histogram in SI Appendix, Fig. S9D, which demonstrates that the samples are a mixture of 1L/Bfl/SiC(0001) (about 80%) and 2L/Bfl/SiC(0001) (about 20%). Furthermore, before conductive AFM measurements, the investigated sample’s areas are also characterized by measuring surface topography, frictional properties, and surface potential using AFM (SI Appendix, Figs. S1 and S2). Regions with different numbers of graphene layers can be distinguished through changes in friction and surface potential (24, 36, 37). In particular, areas with a lower friction can be attributed to 2L/Bfl/SiC(0001) regions while areas with a higher friction can be attributed to 1L/Bfl/SiC(0001) (24, 36), and the surface potential difference between 2L/Bfl/SiC(0001) and 1L/Bfl/SiC(0001) is around 150 meV (37, 38) as expected from literature. Furthermore, analyzing height steps in surface topography gives us information about surface termination and the number of graphene layers. A step height of 0.75 nm represents a step/boundary between n + 1 and n epitaxial graphene layers because three silicon carbide layers must be decomposed to form one graphene layer (34). The lattice constant of SiC is 0.25 nm, which produces a 0.75 nm step if three SiC layers are decomposed, and this step is exactly the step height between 1L/Bfl/SiC(0001) and 2L/Bfl/SiC(0001). This study uses only the 6H polytype to prepare epitaxial graphene. SiC in 6H polytype has six possible surface terraces and three equivalent pairs. After the graphene growth, two surface terraces remain due to the different decomposition rates of surface terraces (35) with a height difference of 0.25 nm and 0.50 nm (35).

Conductive AFM Measurements.

Before performing c-AFM experiments, each investigated sample is glued to the metallic plate using the double scotch tape in the configuration that C-face of SiC is lying on the scotch tape and Si-face is facing up. Silver paste is used to create an electrical contact between the top graphene layer and the underneath metallic plate. First, we image a larger area of the surface by AFM and we ensure that the surface is very clean. If required, we clean the surface by performing a series of scans at decreasing scan sizes. The conductive AFM measurements are performed on a Brucker Multimode 8 AFM using a platinum-iridium coated antimony doped silicon AFM probe (Bruker SCM-PIT-V2 with a spring constant of about 3.0 N/m, Bruker CONTV-PT with a spring constant of about 0.1 N/m). Measurements are performed on different areas of different samples at various normal forces, scan velocities, and voltage bias. All measurements are carried out in ambient conditions.

KPFM Measurements.

The KPFM measurements are performed on a Brucker Multimode 8 AFM using a platinum-iridium-coated antimony doped silicon AFM probe (SCM-PIT-V2, Bruker with a resonance frequency of about 75 kHz and spring constant 3.0 N/m). Surface contact potential map is collected in frequency-modulation KPFM mode with a scan rate of 0.25 Hz. All measurements are performed in ambient conditions.

Data Analysis.

The current values are obtained by processing the raw conductive-AFM images in Gwyddion 2.61 software. The average current with a SD of 1L/Bfl/SiC(0001) areas is analyzed using Gwyddion tools. First, the corresponding areas are masked and then the statistics tool is used to get an average value and SD. To obtain current of 2L/Bfl/SiC(0001) areas, current cross-section profiles are taken with a thickness of 1.6 nm and horizontal direction at various areas. Then, a set of 35 curves for each scan is analyzed to obtain the average value with corresponding SD of a particular stacking domain and sample. The histograms of 35 curves for Fig. 3F are shown in SI Appendix, Fig. S8.

Supplementary Material

Appendix 01 (PDF)

Data, Materials, and Software Availability

The data supporting this study's findings are available from the Figshare repository at https://doi.org/10.6084/m9.figshare.27168915 (50). This repository contains the data presented in all figures, including those in SI Appendix. All other data are included in the manuscript and/or SI Appendix.