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We present in this work the size-dependent and shape-dependent properties ofcarbon domains in hybrid h-BN/C sheets with the goal of tailoring their energygaps. We have considered triangular, hexagonal, circular, and rectangularcarbon domains embedded in h-BN sheets and optimized the structure of theseh-BN/C sheets using the recently developed semi-empirical method, referred asSCED-LCAO. Calculated energy gaps of hybrid h-BN/C sheets exhibit interestingsize- and shape-dependent properties. The energy gap of h-BN/C sheets embeddedwith rectangular domains shows a semi-metal behavior, while the size-dependenceof the energy gap of hexagonal carbon domains exhibit a power-law decrease, andthat of the energy gap of h-BN/C sheets with circular carbon domains show anoscillatory behavior. It is evident from the density of states calculationsthat the reduction in the energy gap of hybrid h-BN/C sheets compared topristine h-BN sheets mainly arises from carbon domains. The bond distortionsdue to competing bond lengths (C-C, C-B, C-N, B-N, etc.) at the domain boundaryalso introduce states in the gap and this is particularly evident in sheetswith smaller carbon domains.

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