Electronic structure of graphene and doping effect on ${\text{SiO}}_2$

First-principles calculations show that the electronic structure of graphene on ${\text{SiO}}_2$ strongly depends on the surface polarity and interface geometry. Surface dangling bonds mediate the coupling to graphene and can induce hole or electron doping via charge transfer even in the absence of extrinsic impurities in substrate. In an interface geometry where graphene is weakly bonded to an O-polar surface, graphene is $p$ doped, whereas $n$ doping takes place on a Si-polar surface with active dangling bonds. We suggest that electron and hole doping domains observed on ${\text{SiO}}_2$ are related to different surface polarities.

Figure 1

(Color online) Top view of a single graphene layer on (a) Si-terminated and (b) O-terminated ${\text{SiO}}_2$ surfaces. The blue (dark), yellow (white), and green (gray) balls denote the Si, O, and C atoms, respectively. The red lines represent the $2\times 2$ graphene unit cell.

Figure 2

Band structures of (a) single and (b) bilayer graphene on the Si-terminated ${\text{SiO}}_2$ surface are compared with those of the stable interface geometries of (c) single and (d) bilayer graphene on the O-terminated surface. The shaded regions represent the projected bands of bulk ${\text{SiO}}_2$, and the Fermi levels are set to zero.

Figure 3

Energy-band spectrum of (a) single and (b) bilayer graphene in the metastable interface geometry on the O-terminated surface, with the Fermi levels set to zero.

Figure 4

(Color online) Isosurfaces (white clouds) of the charge densities of two states just near the Dirac point for a single layer of graphene (a) on the inactive Si-terminated surface and (b) in the metastable interface geometry on the O-terminated surface. The blue and red lines (black) represent the hexagonal and triangular patterns of the charge distribution, respectively. The green balls in the clouds denote the C atoms, whereas blue (dark) and yellow (white) balls denote the Si and O atoms, respectively.

Figure 5

(Color online) (a) Atomic structure of single graphene and (b) energy-band spectrum of bilayer graphene on the partially hydrogenated Si-polar surface, with the Fermi level set to zero. The blue (dark), yellow (white), and green (gray) balls denote the Si, O, and C atoms, respectively, whereas the H atoms are indicated by arrows. The red lines represent the $2\times 2$ graphene unit cell.