Direct band gap opening in graphene by BN doping: Ab initio calculations

Ab-initio calculations on graphene doped with boron nitride (BN) nanoribbons and patches show opening of a band gap in all cases. The smallest width of graphene in these hybrid layers controls the band gap that varies slowly around ∼0.75 eV when the width of graphene region is in the range of 2 to 5 zigzag chains. Most interestingly the band gap is direct in all the cases we have studied and nearly the same for different doping if the smallest graphene width is the same. These results show the possibility of ultrathin hybrid semiconductor graphene with band gap similar to silicon and an additional attractive feature that it is direct.

Figure 1

(Color online) Brillouin zone (outer hexagon) of a primitive unit cell of graphene with reciprocal lattice vectors ${\mathbf{b}}_{\mathbf{1}}$ and ${\mathbf{b}}_{\mathbf{2}}$. Γ, K, K′, and M show the symmetry k-points in the Brillouin zone. The inner hexagon is the Brillouin zone of a graphene supercell with edges three times the edge length of a primitive graphene unit cell. The reciprocal lattice vectors ${\mathbf{b}}_{\mathbf{1}}$′ and ${\mathbf{b}}_{\mathbf{2}}$′ of the supercell are related to ${\mathbf{b}}_{\mathbf{1}}$ and ${\mathbf{b}}_{\mathbf{2}}$ with ${\mathbf{b}}_{\mathbf{1}}$′ = ${\mathbf{b}}_{\mathbf{1}}$/3 and ${\mathbf{b}}_{\mathbf{2}}$′ = ${\mathbf{b}}_{\mathbf{2}}$/3. Interestingly in this case and in all cases with the supercell sides being integer multiple of three (3m, m, an integer), the Γ-point and the K-point corresponding to the primitive graphene unit cell coincide. One can see that the K-point of the primitive unit cell can be reached from Γ-point with 2${\mathbf{b}}_{\mathbf{1}}^{\prime }$ + ${\mathbf{b}}_{\mathbf{2}}^{\prime }$ translation. ${\mathbf{e}}_{\mathbf{1}}^{\prime }$ and ${\mathbf{e}}_{\mathbf{2}}^{\prime }$ are the unit vectors along $x$ and $y$ directions.

Figure 2

(Color online) Atomic structures with different distributions of C, B, and N atoms in the supercell. (a) Pure graphene, (b) alternate zigzag chains of C and BN, (c) nanoribbons of graphene and $h$-BN each with three chains, (d) pure $h$-BN layer, (e) a BN hexagon in graphene supercell, (f) a $h$-BN patch with seven hexagons in graphene supercell, (g) a $h$-BN patch with a crossed graphene mesh, (h) graphene patch with seven hexagons in a $h$-BN layer, (i) a quantum dot of graphene in $h$-BN, (j) a BN nanoribbon along the diagonal of the supercell, (k) a graphene patch with crossed-BN mesh, (l) graphene with a BN-zigzag chains, (m) one zigzag chain of carbon and five chains of BN (C1BN5), (n) two zigzag chains of C and four chains of BN (C2BN4), and (o) four chains of carbon and two chains of BN (C4BN2). Large (blue), medium (grey), and small (yellow) balls represent N, C, and B atoms, respectively.

Figure 3

(Color online) (a) Energy band gap for different configurations of BN-doped hybrid graphene in the supercell, as given in Fig. 2. The points have been connected to aid the eye and show the trend. Full line, broken line, and dash-dot line correspond to BN-zigzag nanoribbons, BN patches in graphene, and graphene patches in $h$-BN. The dots (b) and (j) correspond to alternate BN and C chains in the unit cell, as shown in Fig. 2b, and an armchair BN nanoribbon in graphene as shown in Fig. 2j, respectively. The points (a), (c), (d), (l), (m), (n), and (o) on the full line correspond to BN-zigzag nanoribbons as shown in Fig. 2. Inset shows the corresponding cohesive energy per atom. (b) Energy band gap variation with the width of the smallest graphene region bounded by BN in different doping cases as shown in Fig. 2. Points on the curve [(a), (c), (d), (l), (m), (n), (o)] indicate BN-zigzag nanoribbons, whereas the remaining points (green) indicate other cases with similar band gaps as that of nanoribbons.

Figure 4

(Color online) Energy bands along symmetry directions of the Brillouin zone of the supercell corresponding to the atomic structures shown in Fig. 2. The dashed line shows the top of the valence band.

Figure 5

(Color online) The total and partial DOS corresponding to the atomic structures in Fig. 2 obtained by using Gaussian broadening of 0.05 eV. Light blue (light grey), pink (grey), and blue (darker grey) curves show C, B, and N contributions. Red (darkest grey) curves represent the total density of states. Vertical dashed dotted line is the top of the valence band.