# Electronic and Transport Properties of Epitaxial Graphene on SiC and 3C-SiC/Si: A Review
## 2 Electronic Band Structure
### Bilayer Graphene  
Bilayer graphene (BLG) synthesized on SiC(0001) are generally reported to be AB (Bernal) stacked with a 30\({}^{\circ}\) rotation with respect to the substrate [11]. In BLG, the charge carriers tunnel quantum  
Figure 1: Band structure for a monolayer graphene (dotted line), a bilayer graphene with AB stacking (dashed line), and R30/R2\({}^{+}\) rotational fault pair (single line). Band structure at the \(\mathbf{\mathrm{K}}\)-point is given in the inset. Reprinted with permission from Reference [23]. Copyright (2008) by American Physical Society.  
Figure 2: Electronic structure of monolayer EG on 3C-SiC(111) by ARPES. Reprinted with permission from Reference [19]. Copyright (2010) by American Physical Society.  
mechanically between the two layers, which causes a band dispersion that is nearly parabolic [40] (Figure 1) with an effective mass (\(\mathbf{m^{*}}\)) of about 0.033 m\({}_{\text{e}}\) (electron mass) [41].  
\[\mathbf{E_{\text{k\pm}}}=\pm\mathbf{v_{\text{F}}}^{2}\mathbf{k}^{2}\mathbf{t}^{-1} \tag{4}\]  
\(\mathbf{E_{\text{k\pm}}}\) describes the two bands with energies \(\mathbf{E_{+}}\) and \(\mathbf{E_{-}}\) that lies at the \(\mathbf{K}\) point, \(\mathbf{t}\sim 3\) eV is the energy of electron transition between the nearest neighbors spaced by a = 0.142 nm (lattice constant).  
In this case, the \(\mathbf{v_{\text{F}}}\) depends on the Fermi momentum (\(\mathbf{p_{\text{F}}}\)) divided by \(\mathbf{m^{*}}\) as \(\mathbf{p_{\text{F}}}/\mathbf{m^{*}}\)[42]. For higher energies corresponding to doping above \(5\times 10^{12}\) cm\({}^{-2}\), the linear dependence is a good approximation [41]. [PERSON] et al. performed an early investigation of the band structure properties of BLG on SiC(0001) using ARPES, and found \(\mathbf{E_{\text{F}}}\) to be 400 meV [34]. [PERSON] et al. reports \(\mathbf{v_{\text{F}}}\) to be 0.7-0.8 \(\times 10^{6}\) ms\({}^{-1}\) for BLG, which is 20% to 30% smaller than that of MLG with an \(\mathbf{E_{\text{F}}}\) at \(\sim\)300 meV above the Dirac point [31]. However, recent measurements put \(\mathbf{v_{\text{F}}}\) of MLG closer to \(1.2\times 10^{6}\) ms\({}^{-1}\)[43] with an \(\mathbf{E_{\text{F}}}\) of \(\sim\)350 meV. Bernal stacked layers exhibit [PERSON]'s phase of 2\(\pi\)[40] as confirmed by the quantum Hall effect [44].  
Charge transport in BLG, thus, involves massive chiral and parabolic dispersion carriers [42] (see Figure 1 with a zero band gap). The effect of the buffer layer is not included in contrast to the massless chiral, linear-dispersion carrier system for MLG.  
The band structure of BLG is sensitive to the lattice symmetry [34]. When the graphene layers of a BLG are made asymmetric, a band gap forms between the low-energy bands at the former Dirac point [34; 40] (see Figure 3). This means the band gap can be varied by means of an external transverse electrical field to control the density of electrons. The gap can be varied from 0 to 0.3 eV by changing the doping level between the two layers or by an external gate control [34; 45]. Thus, the BLG transitions from a semi-metal to an insulator [34]. An externally controlled symmetry breaking also changes the electronic conductivity and forms a BLG switch [34]. For this reason, digital electronic applications have been envisioned [25].