Quantum Dots and Nanoroads of Graphene Embedded in Hexagonal Boron Nitride

T materials have drawn tremendous attention in the recent past in terms of both interesting fundamental physics and possible applications in future generation devices. Graphene and hexagonal boron nitride (h-BN) are the two most promising candidates for this purpose. 3 Single layers of graphene and h-BN have been fabricated and found to be stable at room temperature. 8 The most significant difference between the two isostructured materials lies in their electrical conductivity. Whereas graphene is a semimetal and a very good conductor, BN is an insulator (band gap ∼ 6 eV), which limits their applications in electronic devices. This void can be bridged by combining graphene and BN to make semiconducting material with a stoichiometry of BxCyNz. 11 Other than the solid solution of B, C, and N, it is also necessary to explore the possibility of fabricating a graphene BN composite material, where the two phases coexist separately, but in the same plane. Such a novel composite is the focus of the present work. Free standing nanostructures, such as nanoribbons and quantum dots (QDs) of graphene, have been discussed extensively in the literature. The effect of electron confinement leads to size-dependent electronic properties in graphene nanostructures. Interestingly, properties of graphene nanostructures are also dependent on the edge shapes, namely, zigzag (ZZ) and armchair (AC). For example, the tight bindingmodel predicts ZZ and AC nanoribbons to be metallic and seimconducting, respectively. Density functional theory-based calculations further show that ZZ edges are spin-polarized and corresponding nanoribbons are also semiconducting in nature. 14 Similar properties have been reported for graphene nanoroads and QDs embedded in graphane. Fundamentally free-standing and graphane-embedded nanostructures of graphene are similar. Whereas electrons are confined by an infinite potential (due to vacuum) in the former, the latter creates a finite potential well (due to wide-band-gap graphane) for the semimetallic graphene phase. In terms of device integration and mechanical integrity, nanoroads or QDs of graphene in a graphane matrix appear to be more promising than artificially cut freestanding nanostructures. A recent experimental discovery shows that insulating h-BN can also be used to host the graphene QDs. Instead of forming a solid solution of B, N, and C, graphene and h-BN have been found to occur in separate domains inside the composite. Immiscibility of the two phases has also been predicted by firstprinciples calculations. In this paper, we show that such a novel material can be qualitatively different from a graphene graphane composite due to polarity of the h-BN matrix. It is well known that edge and interface shape determines the properties of free-standing and embedded graphene QDs. Thus, in this work, we consider dots of hexagonal shape, making ZZ and AC interfaces with the constituent atoms of the h-BN matrix. Two of the representative unit cells are illustrated in Figure 1. The interatomic distance between any atomic pair is 1.45 Å (equal to the bond length of BN) prior to the relaxation. Because graphene has a smaller equilibrium interatomic distance (1.42 Å), the QD after relaxation will be under tensile stress, which ensures overall planarity of the C BN composite structure. The formation energy per atom ε(n) of a graphene QD, consisting of n(=2 nC) carbon atoms, is defined as