Carbon-rich boron carbon nitride monolayers (BNC _x ): tuning graphene with localized borazine units

We present that embedding a hexagonal borazine motif (B₃N₃) into graphene enables systematic graphene engineering for mechanically robust and direct-gap two-dimensional materials. Using first-principles calculations, we investigate carbon-rich boron carbon nitride monolayers containing localized borazine units, BNC _x (x = 4, 6, 12), motivated by recent bottom-up synthesis with molecular precursors. All three monolayers are dynamically stable and metastable relative to phase-separated graphene and h-BN. Their Raman spectra are sensitive to the bond composition, functioning as the structural fingerprint. The localized borazine unit does not compromise mechanical robustness of the graphene honeycomb structure while lifting the Dirac-point degeneracy and opening direct band gaps of 2.13, 1.43, and 0.92 eV for BNC₄, BNC₆, and BNC₁₂, respectively. Deformation potential theory predicts room-temperature hole and electron mobilities reaching 8.72 × 10⁴ and 5.83 × 10⁴ cm² V^-1 s^-1, respectively. These trends toward the graphene limit highlight the potential of BNC _x layers with the localized units for systematic graphene engineering. In particular, BNC₄ and BNC₆ lie between semimetallic graphene and insulating h-BN, exhibiting stronger visible-light absorption than graphene.