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Tailoring the Energy Gap of Hybrid Hexagonal Boron Nitride Sheets Embedded with Carbon Domains of Different Shapes and Sizes

We present in this work the size-dependent and shape-dependent properties of carbon domains in hybrid h-BN/C sheets with the goal of tailoring their energy gaps. We have considered triangular, hexagonal, circular, and rectangular carbon domains embedded in h-BN sheets and optimized the structure of these h-BN/C sheets using the recently developed semi-empirical method, referred as SCED-LCAO. Calculated energy gaps of hybrid h-BN/C sheets exhibit interesting size- and shape-dependent properties. The energy gap of h-BN/C sheets embedded with rectangular domains shows a semi-metal behavior, while the size-dependence of the energy gap of hexagonal carbon domains exhibit a power-law decrease, and that of the energy gap of h-BN/C sheets with circular carbon domains show an oscillatory behavior. It is evident from the density of states calculations that the reduction in the energy gap of hybrid h-BN/C sheets compared to pristine h-BN sheets mainly arises from carbon domains. The bond distortions due to competing bond lengths (C-C, C-B, C-N, B-N, etc.) at the domain boundary also introduce states in the gap and this is particularly evident in sheets with smaller carbon domains.