Electronic properties of mixed-phase graphene/$h$-BN sheets using real-space pseudopotentials

A major challenge for applications of graphene is the creation of a tunable electronic band gap. Hexagonal boron nitride has a lattice very similar to that of graphene and a much larger band gap, but B-N and C do not alloy: B-C-N materials tend to phase separate into $h$-BN and C domains. Quantum confinement within the finite-sized C domains of a mixed B-C-N system can create a band gap, albeit within an inhomogeneous system. Here we investigate the properties of hybrid $h$-BN/C sheets with real-space pseudopotential density functional theory. We find that the electronic properties are determined not just by geometrical confinement, but also by the bonding character at the $h$-BN/C interface. B-C terminated carbon regions tend to have larger gaps than N-C terminated regions, suggesting that boron-carbon bonds are more stable. We examine two series of symmetric structures that represent different kinds of confinement: a graphene dot within a $h$-BN background and a $h$-BN antidot within a graphene background. The gaps in both cases vary inversely with the size of the graphenic region, as expected, and can be fit by simple empirical expressions.

Figure 1

In these gedanken structures, a pair of hexagonal dots with voids covering one set of potential interfaces has only one type of bond, either B-C or N-C, at the interface between the graphene and $h$-BN domains. Dangling bonds are terminated with hydrogen. Large green, medium gray, small dark blue, and small white spheres are boron, carbon, nitrogen, and hydrogen, respectively. Only the smallest case, with three interfacial bonds, is shown here—expanded systems with 6, 9, or 12 interfacial bonds per unit cell were also examined.

Figure 2

The local density of states of boron and nitrogen bound to carbon atoms for unit cells of the symmetry depicted in Fig. 1 with 3 or 12 B-C or N-C bonds. The boron-derived valence levels are generally at lower energies than their nitrogen counterparts.

Figure 3

The structures used to look into the influence of B and N on band gap size. Large green balls are boron, medium gray is carbon, and small dark blue is nitrogen. The original bands of graphene are shown as dashed lines. Boron doping opens a gap of 0.61 eV, while nitrogen opens a 0.39 eV gap.

Figure 4

A graphene dot in a $h$-BN background and a $h$-BN antidot in a graphene background. The large green, medium gray, and small dark blue spheres are boron, carbon, and nitrogen, respectively.

Figure 5

Variation in band gap with graphene dot and $h$-BN antidot diameter for the family of structures where the dot-dot (or antidot-antidot) separation $L$ is twice the dot (or antidot) diameter $D$, as depicted in Fig. 4. The diameter of the antidot also tracks the thickness of the multiply connected graphene region. The curves are fits to the empirical gap function given in the text.

Figure 6

An anisotropic graphene dot within a $h$-BN matrix, elongated to the point that it begins to resemble a graphene nanoribbon. Large green balls are boron, medium gray balls are carbon, and small blue balls are nitrogen.