**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. [93]. 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 [93]. **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 [110] crystallographic direction as depicted in **Figure 11(e)**. Since the graphene lattices in neighboring nanodomains are rotated by ±13.5° from the same [110] 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

#### **Figure 11.**

*(a) STM image of the vicinal SiC(001)-3 × 2 surface. The step direction is close to the [110] direction of the SiC crystal lattice. (b) Large-area STM image of graphene nanoribbons synthesized on the vicinal SiC(001). (c) and (d) Atomically resolved STM images of the graphene surface. The domain lattices are rotated 17° clockwise (GrR) and 10° anticlockwise (GrL) relative to the NB. The NB is itself rotated 3.5° anticlockwise from the [110] direction. (e) Schematic model of the NB for the asymmetrically rotated nanodomains in panels (c) and (d). For the angles shown a periodic structure of distorted pentagons and heptagons is formed. (f) Effective surface Brillouin zone corresponding to four rotated graphene domain variants. (g) Dispersion of the π-band in the graphene along the KA-KB direction indicated in panel (f) [93].*

**147**

**Figure 12.**

*Controllable Synthesis of Few-Layer Graphene on β-SiC(001)*

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 [115] 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 [93]. 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 [115], a charge transport gap of *<sup>E</sup> <sup>g</sup>* <sup>=</sup> ℏν *<sup>F</sup>* <sup>2</sup>*<sup>π</sup>* \_\_\_ <sup>3</sup>*<sup>d</sup>* <sup>≈</sup> 1.38 \_\_\_\_\_\_ *<sup>d</sup>*(nm) (eV) 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

*(a) Schematic drawing of the nanogap device fabricated on the trilayer graphene/β-SiC/2°-off Si(001) sample. (b) I-V curves measured at 150, 200, 250 and 300 K. (c) I-V curves measured at 10, 50, and 100 K. (b) and (c) are measured with the current directed across the self-aligned NBs. (d) Corresponding dI/dV curves for* 

*temperatures below 150 K. Reproduced from Ref. [93] with permission of ACS.*

*DOI: http://dx.doi.org/10.5772/intechopen.86162*

*Silicon Materials*

start to grow from the linear defects line-by-line [114] 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** 

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. [93]. 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 [93]. **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 [110] crystallographic direction as depicted in **Figure 11(e)**. Since the graphene lattices in neighboring nanodomains are rotated by ±13.5° from the same [110] 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

*(a) STM image of the vicinal SiC(001)-3 × 2 surface. The step direction is close to the [110] direction of the SiC crystal lattice. (b) Large-area STM image of graphene nanoribbons synthesized on the vicinal SiC(001). (c) and (d) Atomically resolved STM images of the graphene surface. The domain lattices are rotated 17° clockwise (GrR) and 10° anticlockwise (GrL) relative to the NB. The NB is itself rotated 3.5° anticlockwise from the [110] direction. (e) Schematic model of the NB for the asymmetrically rotated nanodomains in panels (c) and (d). For the angles shown a periodic structure of distorted pentagons and heptagons is formed. (f) Effective surface Brillouin zone corresponding to four rotated graphene domain variants. (g) Dispersion of the π-band in the* 

*graphene along the KA-KB direction indicated in panel (f) [93].*

**films grown on vicinal Si(001) wafers**

**146**

**Figure 11.**

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 [115] 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 [93]. 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 [115], a charge transport gap of *<sup>E</sup> <sup>g</sup>* <sup>=</sup> ℏν *<sup>F</sup>* <sup>2</sup>*<sup>π</sup>* \_\_\_ <sup>3</sup>*<sup>d</sup>* <sup>≈</sup> 1.38 \_\_\_\_\_\_ *<sup>d</sup>*(nm) (eV) 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

#### **Figure 12.**

*(a) Schematic drawing of the nanogap device fabricated on the trilayer graphene/β-SiC/2°-off Si(001) sample. (b) I-V curves measured at 150, 200, 250 and 300 K. (c) I-V curves measured at 10, 50, and 100 K. (b) and (c) are measured with the current directed across the self-aligned NBs. (d) Corresponding dI/dV curves for temperatures below 150 K. Reproduced from Ref. [93] with permission of ACS.*

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 [101]. As revealed the theoretical calculations and recent experimental studies [101], 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 [101], since spin-orbit coupling can be induced by the curvature of the ripples [116].
