Optical properties of a hexagonal C/BN framework with sp² and sp³ hybridized bonds

We investigated the optical properties and roles of sp²- and sp³-hybridized bonds of a hexagonal C/BN family using first-principles calculations. The calculated phonon dispersions confirm the dynamic stability of Hex-(BN)₆C₁₂ and Hex-C₁₂(BN)₆. The complex dielectric function evolves from the infrared to the ultraviolet region and has a significant anisotropy for different polarizations. The reflectivity and refractive index spectra show that the sp²-hybridized C atoms are more sensitive to the light from infrared to visible region than B-N pairs while the C atoms and B-N pairs have a similar sensitivity to high frequencies. The sharp peaks of the energy-loss spectrum are all concentrated in the 23-30 eV energy region, which can be used to identify these hexagonal structures. The calculated band structures show Hex-C₂₄ and Hex-(BN)₆C₁₂ are metals, but Hex-C₁₂(BN)₆ and Hex-(BN)₁₂ are semiconductors with indirect band gaps of 3.47 and 3.25 eV, respectively. The electronic states near the Fermi level primarily originate from sp²-hybridized atoms. In addition, sp²-hybridized bonds are the main elements affecting the optical and electronic structure of C/BN materials with sp²- and sp³-hybridizations. We expect that the results presented will help understand the optical properties of C/BN materials containing sp²- and sp³-hybridized C atoms and B-N pairs.