▎ 摘　　要

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.