We explain the nature of the electronic energy gap and optical absorption spectrum of carbon-boron-nitride (CBN) monolayers using density functional theory, GW and Bethe-Salpeter calculations. The band structure and the optical absorption are regulated by the C domain size rather than the composition (as customary for bulk semiconductor alloys). The C and BN quasiparticle states lie at separate energy for C and BN, with little mixing for energies near the band edge where states are chiefly C in character. The resulting optical absorption spectra show two distinct peaks whose energy and relative intensity vary with composition in agreement with the experiment. The monolayers present strongly bound excitons localized within the C domains, with binding energies of the order of 0.5-1.5 eV dependent on the C domain size. The optoelectronic properties result from the overall monolayer band structure, and cannot be understood as a superposition of the properties of bulklike C and BN domains.
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