Few-layer graphene exhibits exceptional properties that are of interest for fundamental research and technological applications. Nanostructured graphene with self-aligned domain boundaries and ripples is one of very promising materials because the boundaries can reflect electrons in a wide range of energies and host spin-polarized electronic states. In this chapter, we discuss the ultra-high vacuum synthesis of few-layer graphene on the technologically relevant semiconducting β-SiC/Si(001) wafers. Recent experimental results demonstrate the possibility of controlling the preferential domain boundary direction and the number of graphene layers in the few-layer graphene synthesized on the β-SiC/Si(001) substrates. Both these goals can be achieved utilizing vicinal silicon wafers with small miscuts from the (001) plane. This development may lead to fabricating new tunable electronic nanostructures made from graphene on β-SiC, opening up opportunities for new applications.
- silicon carbide
Extensive studies of mono- and few-layer graphene films, conducted during the last two decades, have revealed unique electronic properties of these low-dimensional materials [1, 2, 3, 4, 5, 6, 7], which make them very promising for developing new nanoscale carbon-based electronic technologies [8, 9, 10, 11, 12, 13]. Its unique transport properties make graphene a very attractive alternative to silicon in the traditional electronic technologies. However, for successful applications, it is necessary to develop methods of synthesizing low-cost, high-quality graphene films on insulating or semiconducting substrates of sufficiently large size.
Many methods of fabricating ultrathin graphene films have been reported. For example, graphene can be prepared using mechanical or chemical exfoliation from bulk graphite crystals [1, 3, 4, 14]. The mechanically exfoliated graphene layers demonstrate exceptional properties of two-dimensional electron gas, such as extremely high mobility of the charge carriers [15, 16]. However, the exfoliated graphene layers are hardly suitable for technological purposes. The procedures using unzipping of carbon nanotubes, reduction of graphite oxide, chemical vapor deposition, and high-temperature thermal graphitization of single-crystalline substrates were developed to fabricate large-area graphene films [1, 17, 18, 19, 20, 21, 22]. To eliminate possible problems associated with the graphene film transfer from one substrate to another, various methods have been developed for direct growing graphene on the technologically relevant non-conducting substrates [23, 24, 25, 26, 27, 28, 29, 30].
The hexagonal silicon carbide (α-SiC) wafers are considered the most promising semiconducting substrates for technological synthesis of high-quality graphene films [31, 32, 33, 34, 35, 36, 37]. Ultrathin graphene films are usually fabricated on α-SiC using silicon atom sublimation and graphitization of the carbon-enriched surface layers at temperatures above 1000°C . Epitaxial graphene layers synthesized on α-SiC in ultra-high vacuum (UHV) and argon atmosphere demonstrate 2D electronic properties [38, 39, 40, 41], which are nearly equivalent to the properties of ultrathin graphene films mechanically exfoliated from bulk graphite crystals. The angle resolved photoelectron spectroscopy (ARPES) studies of the 11-layer graphene on 6H-SiC(000-1) revealed sharp linear dispersions at the K-points typical of monolayer graphene .
However, the high price and small size of the single-crystalline α-SiC wafers are not compatible with commercial applications. In order to reduce the price of SiC wafers, epitaxial growth of cubic silicon carbide (β-SiC) thin films on silicon wafers was proposed in the 1980s . Using this method, β-SiC thin films with thickness of several microns could be grown on standard silicon wafers with diameters above 30 cm [44, 45, 46, 47] that is highly appealing for direct integration into existing electronic technologies. Fabrication of ultrathin graphene films on β-SiC surfaces, using high-temperature annealing in UHV, was reported for the first time in 2009, when Miyamoto et al. succeeded in synthesizing few-layer graphene on the β-SiC/Si(011) wafers . Then, a number of works demonstrating the feasibility of graphene synthesis on β-SiC/Si wafers of different orientations have been published [48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103]. Mostly, these studies have been conducted on β-SiC(111) thin films [51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81] and single-crystalline SiC(111) wafers [62, 63, 64]. However, some studies have been carried out on β-SiC(001) [50, 61, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 101, 102] and even on polycrystalline β-SiC substrates . Since Si(001) is widely used in electronic devices, few-layer graphene films synthesized on the β-SiC/Si(001) wafers can be fully compatible with the existing lithographic processing technologies.
This chapter is focused on the controllable UHV synthesis of few-layer graphene on the β-SiC thin films grown on the technologically relevant Si(001) wafers. Along with detailed atomic and electronic structure studies we present the recent results which uncover the mechanism of layer-by-layer graphene growth on β-SiC/Si(001) and pave the way to synthesize uniform few-layer graphene nanoribbons with desirable number of layers and self-aligned nanodomain boundaries on the low-cost silicon wafers.
2. Atomic and electronic structure of few-layer graphene synthesized on β-SiC/Si(001)
Few-layer graphene synthesis on the β-SiC/Si(001) wafers was demonstrated for the first time in the near-edge X-ray absorption fine structure (NEXAFS), core-level photoelectron spectroscopy (PES), ARPES, and local scanning tunneling microscopy (STM) experiments . Later, the few-layer graphene formation on the β-SiC/Si(001) substrates during high-temperature annealing in UHV was proved by independent Raman spectroscopy experiments . These works showed quasi-free-standing character of the synthesized graphene overlayers. Raman spectroscopy data also revealed the presence of a large number of defects in the few-layer graphene grown on the β-SiC/Si(001) wafers with the average distance between them on the order of 10 nm . However, the origin of these defects could be uncovered only in comprehensive studies using a set of complementary high-resolution micro-spectroscopic techniques, namely, low energy electron microscopy (LEEM), micro low energy electron diffraction (μ-LEED), core-level PES, ARPES, and atomic-resolution STM [85, 87].
Figure 1 shows typical large-area STM images taken from a β-SiC(001) surface before and after trilayer graphene synthesis in UHV [85, 87]. The image of the β-SiC(001)-c(2 × 2) structure (Figure 1(a)) reveals extra carbon atoms (bright protrusions) on the surface and monatomic steps. The root mean square (RMS) roughness analysis of the STM images demonstrates substantial enhancement of the surface roughness after the trilayer graphene synthesis. For comparison, the histograms calculated from the STM images of the same size (100 × 100 nm2) before and after trilayer graphene synthesis are shown on Figure 1(d), (i), and (j). Note that RMS of micrometer-scale β-SiC(001)-c(2 × 2) STM images typically varied between 1.0 and 1.5 Å, while the RMS values calculated from the images of trilayer graphene were in the range of 3.0–5.0 Å. The increase of the surface roughness after graphene synthesis is related to the atomic-scale rippling typical for free-standing graphene [104, 105]. STM investigations conducted in different surface areas of several samples  confirmed the continuity of the few-layer graphene films covering the β-SiC/Si(001) wafers. As an example, Figure 1(b) and (c) shows STM images measured at bias voltages corresponding to the bandgap of β-SiC. STM imaging was stable even in the vicinity of multiatomic steps (Figure 1(b)) and anti-phase domain (APD) boundaries (Figure 1(c)), separating the areas where the β-SiC crystal lattice is rotated by 90°.
STM studies [85, 87] showed that the top graphene layer consists of nanodomains connected to one another through domain boundaries (Figure 1(g) and (h)). The nanodomain boundaries (NBs) are preferentially aligned with the two orthogonal <110> directions of the SiC crystal lattice, as indicated in Figure 1(g) and (h). The domains are elongated in the  and directions on the right and left side of the APD boundary, respectively (Figure 1(c)). The length and width of the nanodomains on the SiC(001) substrate were in the range of 20–200 nm and 5–30 nm, respectively. These values correlate well with the average distance between defects derived from the Raman spectroscopy studies .
The continuity and uniform thickness of the graphene overlayer synthesized on the β-SiC/Si(001) wafers were confirmed in the LEEM experiments (Figure 2). The bright-field (BF) LEEM image measured at small electron energy shows uniform contrast throughout the all probed micrometer-sized surface area, including the regions containing defects (steps and APD boundaries). The number of graphene layers can be determined from the number of oscillations in the reflectivity I-V curves measured in a small energy window [106, 107]. In the reflectivity spectra shown on Figure 2(h), one can see three reproducible minima, which correspond to the uniform trilayer graphene coverage. The graphene film thickness is homogeneous over the surface and I-V curves are almost identical in the surface areas appearing dark and white in the dark-field (DF) LEEM images, as Figure 2(h) illustrates.
The μ-LEED patterns taken from micrometer-sized surface areas (Figure 2(d)) typically revealed 12 sharp double-split spots and 12 substantially less intense singular spots, corresponding to the nanostructured graphene, and singular spots from the SiC(001) substrate. The μ-LEED patterns measured from different APDs (Figure 2(e) and (f)) demonstrate 12 non-equidistant spots and six less intense singular graphene spots. The diffraction patterns measured from the APDs are rotated relative to one another by 90°. These LEEM and μ-LEED data demonstrate that each micrometer-sized APD contains graphene nanodomain families with three preferential lattice orientations, giving six preferential lattice orientations on larger (millimeter-scale) surface areas. For the trilayer graphene, four of these six lattice orientations are prevailing in the top layer. The core-level C 1s spectra measured from this sample (Figure 2(g)) demonstrate only two components with binding energies (BE) corresponding to silicon carbide (lower BE) and graphene (higher BE) in accordance with other core-level PES studies , proving the weak interaction of the few-layer graphene with β-SiC(001).
Atomically resolved STM studies presented in Figure 3 disclose the origin of 12 double-split spots in the LEED patterns (Figure 2(d)). STM images in Figure 3(a) and (b) demonstrate nanodomains elongated in the  and directions, respectively. The 2D fast Fourier transform (FFT) of the STM images consists of two systems of spots, which are related to two graphene lattices rotated by 27°. Inset in Figure 3(b) shows one of the FFT patterns. According to the μ-LEED data (Figure 2(e) and (f)), the graphene domain lattices are preferentially rotated by ±13.5° from the  and crystallographic directions of the substrate, which almost coincide with the preferential directions of the nanodomain boundaries. These two families of 27°-rotated domains are rotated by 90° relative to one another and produce two systems of 12 non-equidistant spots in the FFT and μ-LEED patterns (e.g. see Figure 2(e) and (f)). The sum of two 90°-rotated patterns with 12 non-equidistant spots produce the LEED pattern of graphene/β-SiC/Si(001) with 12 double-split spots, as the models shown in Figure 3(c–e) illustrate. These two orthogonal 27°-rotated domain families are usually resolved as horizontal and vertical nanoribbons in STM experiments (Figure 1(g) and (h)). The DF LEEM images taken from different reflexes in either of the double-split spots show a reversed contrast and confirm that the 27°-rotated domain families typically cover micrometer-sized surface regions in different APDs (Figure 2(b) and (c)).
Atomic-resolution STM images of the trilayer graphene on β-SiC(001) measured inside the nanodomains usually revealed either hexagonal (Figure 4(a)) or honeycomb (Figure 4(d)) patterns distorted by atomic-scale rippling . The line profile shown in Figure 4(c) reveals random vertical corrugations related to the atomic-scale rippling and regular oscillations with a period of ~ 2.5 Å corresponding to the graphene honeycomb lattice. Typical dimensions of the ripples are about several nanometers laterally and 1 Å vertically (Figure 4(b)), coinciding with values predicted by the theory for free-standing monolayer graphene . The random picometer-scale distortions of the sp2-hybridized carbon bond lengths in graphene/β-SiC/Si(001) are illustrated using smaller area STM images presented in Figure 4(d–f).
The uniformity of the atomic and electronic structure of the trilayer graphene/β-SiC/Si(001) on a millimeter-scale was confirmed by ARPES . As an example, the photoemission studies of the π band are shown in Figures 5 and 6. Since ARPES technique probes millimeter-scale sample areas, the effective surface Brillouin zone of graphene on β-SiC(001) comprises Brillouin zones of all rotated lattices (Figure 5(a)). The identical sharp linear dispersions typical of quasi-free-standing graphene are observed for all rotated domain variants (Figure 5(b) and (c)), with the Dirac points located at the Fermi level. The ARPES dispersion measured from the trilayer graphene/β-SiC/Si(001) sample along the – -direction of the surface Brillouin zone (Figure 6(b)) reveals the π band reaching the Fermi level. Figure 6(b) also displays a dispersion of the π band that backfolds at ~2.5 eV BE and originates from the M-point of the rotated graphene domain. In order to determine the position of the Dirac point, the dispersions were measured in a detection geometry perpendicular to the – -direction (short black line in Figure 6(a)) where the interference effects are suppressed and both sides of the Dirac cone are observed . The ARPES data shown in Figure 6(c) reveal sharp linear dispersions and tiny additional bands between the two split Dirac cones. According to the theoretical calculations presented in Ref. , the observed ARPES dispersions may correspond to a quasi-free-standing Bernal-stacked ABA-trilayer graphene formed on β-SiC(001).
The experimental data presented in this section were obtained during high-resolution studies of the trilayer graphene grown on a low-index β-SiC/Si(001) wafer using high-temperature annealing in UHV. They demonstrate the fabrication of uniform nanostructured graphene with two preferential NB directions on millimeter-sized samples. Such nanoribbon systems supported on the Si(001) wafers are very promising because the presence of the self-aligned boundaries can provide a sizeable energy gap in graphene . However, for technological applications it is highly desirable to control the thickness of the graphene overlayer and reduce the number of the preferential NB orientations from two to one. Note that thickness of the few-layer graphene synthesized on β-SiC/Si(001) wafers by different groups, utilizing very similar UHV thermal treatment procedures, varied from one to several monolayers [50, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 101].
3. Layer-by-layer graphene growth on β-SiC/Si(001)
For detailed understanding the mechanisms of the surface transformation and layer-by-layer graphene growth on β-SiC/Si(001) in UHV at high temperatures a series of experimental studies with in-situ control of the surface atomic and electronic structure during heating have been conducted [102, 109]. Figure 7 summarizes the β-SiC(001) surface transformations during annealing in UHV, monitored using in-situ core-level PES (Figure 7(a–g)) and ex-situ LEED and STM (Figure 7(h–l)).
The first steps toward successful graphene synthesis on β-SiC/Si(001) relate to the removal of the protective silicon oxide layer and the fabrication of a contaminant-free SiC(001)1 × 1 surface structure. This reconstruction can be fabricated after outgassing the sample holder and flash-heating the β-SiC/Si(001) wafers at 1000–1100°C. Then, the fabrication of a graphene overlayer includes the deposition of several monolayers (MLs) of silicon atoms onto the clean, carbon-rich SiC(001)1 × 1 surface and annealing at gradually increasing temperatures. Depending on the quality of the β-SiC thin film grown on the Si(001) wafer, the deposition and annealing cycles can be repeated until sharp 1 × 1 LEED pattern is observed.
Figure 7(a–g) shows the results of the PES experiments with real-time control during the direct-current sample heating with silicon deposited onto SiC(001)1 × 1 surface structure . During the measurements, a current was applied to heat the sample up to 1350°C (Figure 7(a)). The C 1s core-level spectra were taken in a snapshot mode during the sample heating with an acquisition time of 1s/spectrum, using a photon energy of 750 eV. Six core-level spectra taken at different stages of the surface graphitization are shown in Figure 7(b–g). Two main C 1s peak components can be distinguished in the spectra, which change their relative intensity with increasing temperature. Note that the absolute (but not the relative) binding energies of the individual components in this experiment could be modified by the voltage applied across the β-SiC/Si(001) wafer.
At lower temperatures (Figure 7(b)), a strong peak corresponding to the bulk carbon atoms dominates in the PES spectra. At temperatures above 1200°C (Figure 7(d–f)), an additional component (shifted to higher BE) starts to grow, while the relative intensity of the bulk component decreases. The change of the C 1s core-level shape corresponds to the carbonization of the top surface layers at high temperatures. At temperatures close to the silicon melting point (1350°C), the carbon-carbon bonds undergo a transition to sp2 hybridization corresponding to graphene lattice formation (Figure 7(g)). Ex-situ LEED measurements proved the existence of a graphene overlayer on the β-SiC/Si(001) wafer used for the PES experiments presented in Figure 7(b–g).
Figure 7(h–l) shows step-by-step LEED and STM studies of the β-SiC(001) surface atomic structure after heating in UHV at various temperatures. They prove consecutive fabrication of different β-SiC(001) surface reconstructions in accordance with Refs. [110, 111]. The LEED and STM data in Figure 7(h–l) were obtained after consecutive heating of the same β-SiC/Si(001) sample in UHV to 1000, 1150, 1200, 1250, and 1350°C, and cooling to room temperature. After annealing at temperatures of 700–1000°C a uniform, Si-rich SiC(001)3 × 2-reconstructed surface with large (001)-oriented terraces is fabricated (Figure 7(h)). Increasing the annealing temperature from 1000 to 1250°C leads to consecutive fabrication of the silicon-terminated 5 × 2 (Figure 7(i)), c(4 × 2) (Figure 7(j)), 2 × 1, and carbon-terminated c(2 × 2) reconstructions (Figure 7(k)). According to the LEED and STM studies, the most uniform graphene overlayers on β-SiC(001) can be obtained after flash heating (10–20 s) of the c(2 × 2) reconstruction at 1350°C with post-annealing at 600–700°C, which is similar to the method used for the synthesis of graphene on α-SiC [39, 112, 113]. The LEED pattern shown in Figure 7(l) reveals sharp substrate spots and 12 double-split graphene spots related to the formation of the few-layer graphene nanodomain network similar to the one presented in Figures 1 and 3.
The exact number of the graphene layers synthesized on β-SiC(001) during UHV heating could strongly depend on the vacuum conditions, annealing temperature and duration . To uncover the mechanism of the layer-by-layer graphene growth on the β-SiC/Si(001) substrates and find the way to control the number of synthesized graphene layers and preferential nanodomain boundary direction, in-situ high-resolution core-level and angle-resolved photoelectron spectroscopy, LEEM and μ-LEED studies have been carried out .
Figure 8 shows μ-LEED, LEEM I-V, ARPES and micro X-ray photoelectron spectroscopy (μ-XPS) data obtained from the same sample region in-situ during the high-temperature surface graphitization in UHV. The μ-LEED pattern and C 1s core level spectra taken in bulk- and surface-sensitive regimes from the β-SiC(001)-c(2 × 2) reconstruction prepared prior to graphene synthesis are shown in Figure 8(a). Then, the temperature of the β-SiC/Si(001) wafer was increased and graphene spots were observed in the μ-LEED patterns. The first graphene monolayer (Figure 8(b)) was formed after 10 short flashes at temperatures in the range from 1250 to 1300°C and pressures not exceeding 5 × 10−9 mbar. For the fabrication of 2 and 3 ML graphene (Figure 8(c) and (d)), 50 and 100 flash heating cycles, respectively, were applied at 1300°C. The number of the synthesized graphene layers was defined from the number of minima in the low energy part of the electron reflectivity I-V curves presented in Figure 8 (top). The graphs in Figure 8 (bottom) depict the evolution of the C 1s spectra acquired in normal emission from a circular sample area (d = 2 μm) at 325, 330, 400, and 450 eV photon energies for a SiC(001)-c(2 × 2) reconstruction (a), mono- (b), bi- (c), and trilayer graphene (d). The selected photon energies correspond to different surface sensitivities of the XPS measurements with the highest sensitivity achieved at 325 and 330 eV. The C 1s spectra were decomposed into individual components corresponding to different carbon atom chemical bonds . The results of the C 1s spectra decomposition are presented in Figure 8 together with the experimental data (black circles) where the red line is the graphene peak (Gr), the blue line is the bulk SiC peak, the brown line is the surface β-SiC(001)-c(2 × 2) component, the green dashed line is the background and the cyan line is the envelope. One can note that each spectrum displays only two main components. The Gr peak is shifted by ∼1.65 eV toward higher BE relative to the bulk SiC peak located at 282.9 eV. The intensity of the bulk SiC component decreases both with decreasing photon energy and increasing number of graphene layers. No other components except Gr and SiC were detected in the C 1s spectra, confirming the absence of strong chemical interactions between the graphene overlayer and β-SiC, which would provide additional components with higher BE . The intensities of the individual components in the photoemission spectra shown in Figure 8 can be used as a reference to distinguish between mono-, bi-, and trilayer graphene on the β-SiC/Si(001) wafers using XPS technique only. Measuring the XPS spectra in the normal emission geometry with 330, 400, and 450 eV photon energies, using the fast dynamic-XPS stations with real-time control of the core level spectra shape , one can stop the synthesis procedure when a desirable number of graphene layers (1, 2, or 3 ML) is synthesized.
The in-situ ARPES and μ-LEED measurements (Figure 8) uncover the origin of the 12 singular spots located between 12 double spots in the LEED pattern taken from the trilayer graphene synthesized on β-SiC(001) (Figure 2(d)) and explain the mechanism of the layer-by-layer graphene growth. The singular spots in Figure 2(d) are aligned with the SiC substrate spots in contrast with the ±13.5° rotated diffraction patterns corresponding to the rotated graphene nanodomain lattices shown in Figure 3. The middle row of images in Figure 8 shows the ARPES intensity constant-energy maps taken at E = EF – 0.5 eV and E = EF – 1.5 eV as a function of graphene coverage. The ARPES maps prove the conical shape of the Fermi surface for all preferential graphene nanodomain lattice orientations (two non-rotated lattices and four lattices rotated by ±13.5° relative to the two orthogonal <110> directions) at three graphene coverages studied. Notably, both μ-LEED and ARPES maps measured for the 1 ML graphene/SiC(001) system reveal almost the same intensities of the features corresponding to the non-rotated and ± 13.5° rotated domain lattices. The intensity of the diffraction spots and ARPES features corresponding to the non-rotated lattices is systematically suppressed when graphene coverage increases from 1 ML (Figure 8(b)) to 2 ML (Figure 8(c)), and then to 3 ML (Figure 8(d)). The non-rotated graphene lattice orientations are prevailing only at the beginning of the β-SiC(001) surface graphitization. In contrast, when graphene coverage reaches several monolayers, most of the β-SiC(001) surface is covered by nanodomains with four preferential graphene lattice orientations, rotated ±13.5° relative to the two orthogonal <110> directions (Figure 2(d)).
Figure 9 shows (a) LEEM and (b–e) ARPES data obtained from the 1 ML graphene/β-SiC(001) sample. Figure 9(b) and (c) shows the constant energy ARPES intensity maps measured from different APDs marked as B and C on panel (a). Figure 9(d) and (e) shows the dispersions obtained by a cut through the experimental data as indicated by the dashed lines in panels (b) and (c), respectively. Eighteen identical linear dispersions are clearly resolved, proving that domains with all six preferential lattice orientations at 1 ML graphene coverage exhibit the same electronic structure typical of free-standing monolayer graphene.
The prevalence of the μ-LEED and ARPES features associated with the non-rotated lattices at sub-monolayer coverages is a key to understand the mechanism of the graphene growth on the β-SiC/Si(001) wafers. Figure 10(a–c) illustrates how the non-rotated graphene domain lattice can match the SiC(001)-c(2 × 2) reconstruction. If the lattice parameters of the c(2 × 2) square unit cell (red square) are doubled, it matches well to a slightly distorted square (green lines) connecting carbon atoms of the graphene lattice, which can be laterally translated to cover the entire c(2 × 2) surface by the graphene overlayer (Figure 10(a) and (c)). The mismatch of these two quadrilaterals is below 2%, which is likely sufficient to initiate the growth of the non-rotated graphene monolayer on SiC(001)-c(2 × 2). Such a small mismatch cannot be found for other possible surface structures. Therefore, the SiC(001)-c(2 × 2) reconstruction is a necessary step for successful high-temperature graphene synthesis on β-SiC(001). This is very similar to results of the STM studies performed on β-SiC(111) , where the transition from a typical (√3 × √3)R30° to an intermediate (3/2 × √3)R30° structure matching the graphene (2 × 2) unit cell was observed before the formation of the honeycomb (1 × 1) overlayer.
The model in Figure 10 suggests that carbon dimers of the c(2 × 2) reconstruction (indicated by dotted black oval in Figure 10(a)) may be considered the smallest building blocks of the non-rotated graphene lattice, since the distance between carbon atoms in the dimers (1.31 Å) is reasonably close to that of the graphene honeycomb lattice (1.46 Å). In order for graphene growth to begin, extra carbon atoms must be present on the c(2 × 2) surface to provide the substantially higher density of carbon atoms in the graphene lattice. Additional carbon atoms are actually observed during the STM studies as random bright protrusions (Figure 1) or linear <110>-directed atomic chains decorating the SiC(001)-c(2 × 2) reconstruction (Figure 10(e)). These adatoms form chemical bonds with the dimers of the c(2 × 2) reconstruction at high temperatures and initiate the preferential growth of graphene nanodomains with lattices non-rotated relative to the SiC <110> directions. These domains cannot grow to micrometer-scale due to the presence of linear defects on the SiC(001)-c(2 × 2) surface (Figure 10(e)) and the mismatch between the c(2 × 2) and graphene lattices producing strain in the overlayer. However, the reasonably small mismatch of the c(2 × 2) and the graphene lattice (Figure 10(a)) leads to the prevalence of the two non-rotated lattice variants in the graphene/SiC(001) system until the first monolayer is complete. The next layers presumably grow on top of the first monolayer starting from the linear defects on the surface (either steps or < 110>-directed linear atomic chains), which is supported by the very fast suppression of the non-rotated domain features in the μ-LEED and ARPES maps with increasing graphene coverage (Figure 8). The second and third graphene layers can start to grow from the linear defects line-by-line  which define the positions and orientations of the nanodomain boundaries in the few-layer graphene/β-SiC(001) (Figure 10(f)). In this case, it is energetically favorable for graphene lattices in neighboring nanodomains to be rotated by 27° relative to one another, as the model in Figure 10(d) (bottom part) illustrates. The comparison of the atomic resolution STM images of the SiC(001)-c(2 × 2) and trilayer graphene/SiC(001) clearly shows the coincidence of the carbon atomic chain directions in the former structure (Figure 10(e)) and nanodomain boundary directions in the latter (Figure 10(f)). This result suggests that controlling the density and orientation of defects on β-SiC/Si(001) (e.g., steps on vicinal substrates) could allow the average size of the graphene domains and their orientation to be tuned. This can open a way for synthesis of self-aligned graphene nanoribbons supported by the technologically relevant β-SiC substrate.
4. Fabrication of self-aligned graphene nanoribbons using β-SiC thin films grown on vicinal Si(001) wafers
Synthesis of the uniform self-aligned trilayer graphene nanoribbon structure using β-SiC thin films grown on the vicinal Si(001) wafers with a miscut of 2° was reported in Ref. . STM studies revealed that nanodomains on the vicinal sample are preferentially elongated in one direction (coinciding with the step direction of the bare SiC(001) substrate). This is illustrated in Figure 11(a) and (b). Remarkably, the direction of the nanodomain boundaries in the trilayer graphene was the same in different APDs of the 2°-off β-SiC/Si(001) sample . Figure 11(c) shows an atomically resolved STM image containing three nanodomains and three boundaries (NB). Detailed analysis of the STM images measured from various graphene/SiC/Si(001) samples showed that NBs are frequently rotated by 3.5° relative to the  crystallographic direction as depicted in Figure 11(e). Since the graphene lattices in neighboring nanodomains are rotated by ±13.5° from the same  direction, they are asymmetrically rotated relative to the NBs. The lattices in neighboring domains are rotated by 10° counterclockwise (GrL)) and 17° clockwise (GrR) relative to the NB (Figure 11(c)). As Figure 11(e) illustrates, this asymmetry leads to the formation of a periodic structure along the boundaries, with a period of 1.37 nm. The periodic structure consists of distorted heptagons and pentagons, which is consistent with the atomically resolved STM image measured at the NB (Figure 11(d)). ARPES measurements, conducted on the same sample, showed sharp linear dispersions in the K-points for all preferential graphene lattice orientations (Figure 11(f) and (g)).
Recent theoretical studies  have demonstrated that graphene domain boundaries with a periodic atomic structure can reflect electrons over a large range of energies. This would provide a possibility to control the charge carriers in graphene without the need to introduce an energy bandgap. Figure 12(a) shows a schematic of a graphene nanogap device utilized for investigations of the transport properties of graphene synthesized on the β-SiC/2°-off Si(001) wafer . The voltage was applied perpendicular to the nanodomain boundaries to investigate the local transport properties of the self-aligned nanoribbon system with asymmetrically rotated graphene domain lattices (Figure 11). According to the theory , a charge transport gap of could be induced by a non-symmetric rotation of graphene lattices in neighboring domains, where ħ is the reduced Planck’s constant, νF is the Fermi velocity, and d is the periodicity along the NB. As indicated in Figure 11(d) and (e), the asymmetric rotation of the graphene lattices in the nanostructured trilayer graphene synthesized on β-SiC/2°-off Si(001) leads to a 1.37 nm periodicity along the NB. The formation of this periodic structure could be responsible for a transport gap of about 1.0 eV, which was observed in the low-temperature transport measurements (Figure 12). The transport gap is observed at temperatures below 100 K (Figure 12(b) and (c)). According to the dI/dV spectra shown in Figure 12(d), the transport gap is ~1.3 eV at 50 and 10 K and substantially smaller (~0.4 eV) at 100 K. The conductivity of the trilayer graphene/β-SiC(001) nanogap device is only 0.01 μS at small voltages and 100 μS at larger voltages when the electric current start to flow. This gives a high on-off current ratio of 104.
This successful demonstration of the transport gap opening in the nanostructured trilayer graphene (Figure 12) became possible because the NBs were uniformly aligned with the step direction of the vicinal β-SiC(001) substrate (Figure 11), i.e., perpendicular to the current direction in the electric measurements. Note that although the NBs with asymmetrical rotation of the graphene lattices were most frequently observed, boundaries with other atomic structures were also resolved in detailed atomic resolution STM studies of several few-layer graphene/β-SiC/Si(001) samples [85, 87, 93, 101, 102]. Despite the differences in the atomic structure, STM images generally revealed extreme distortions of the overlayer near the NBs (e.g., Figures 1(g) and 12). The graphene overlayer in these areas was usually bent upward and downward, forming semi-tubes with typical diameters of several nanometers. According to the STM data, the radii of curvature of the ripples in the few-layer graphene on β-SiC/Si(001) wafers were typically in the range of 2–5 nm . As revealed the theoretical calculations and recent experimental studies , the ripples formed at the NBs could also be responsible for the opening transport gap in graphene/β-SiC/Si(001). The self-aligned nanodomain boundaries with ripples can also be utilized to add the spin degree of freedom to graphene , since spin-orbit coupling can be induced by the curvature of the ripples .
We have summarized the results of high-resolution studies of the atomic and electronic structure of few-layer graphene synthesized in UHV on β-SiC thin films epitaxially grown on the technologically relevant Si(001) wafers. LEEM, μ-LEED, ARPES, and STM studies revealed that graphene overlayer on the β-SiC/Si(001) substrates consists of nanodomains with six preferential lattice orientations and two preferential nanodomain boundary directions. The number of the boundary directions can be reduced to one using vicinal wafers with small miscuts from the Si(001) plane. Thus, self-aligned graphene nanoribbon system supported by a wide-gap semiconductor substrate could be fabricated using 2°-off Si(001) wafer. In-situ studies of the few-layer graphene synthesis on the β-SiC/Si(001) wafers performed in UHV using micro-spectroscopic methods demonstrate that thickness of the graphene overlayer can be controlled in the course of the high-temperature synthesis and the procedure can be stopped when a desirable number of graphene layers (e.g., 1, 2, or 3 ML) is synthesized.
This work was carried out within the state task of ISSP RAS and supported by the Russian Foundation for Basic Research (Grant nos. 17-02-01139, 17-02-01291) and Erasmus plus mobility grant (2016-1-IE02-KA107-000479). We thank our colleagues S.V. Babenkov, H.-C. Wu, S.N. Molotkov, D. Marchenko, A. Varykhalov, A.A. Zakharov, B.E. Murphy, A. Locatelli, T.O. Menteş, S.L. Molodtsov, D.V. Potorochin, J. Buck, O. Seeck, M. Hoesch, and J. Viefhaus for fruitful discussions and help in the preparation of this manuscript.
Conflict of interest
The authors declare that there is no conflict of interest.