Optical absorbance and band-gap engineering of (BN)1-x(C2)x two-dimensional alloys: Phase separation and composition fluctuation effects

The ${(\mathrm{BN})}_{1\ensuremath{-}x}{({\mathrm{C}}_{2})}_{x}$ alloys are promising materials for band-gap engineering in two-dimensional electronics. In this work, we provide a complete scenario of statistical possibilities for the distribution of atoms and its influence on electronic and optical properties. Using first-principles calculations combined with the generalized quasichemical approximation to account for disorder effects, we study the properties of these two-dimensional alloys as a function of their average composition. Our results show that atomic arrangements with C-C and B-N bonds are energetically favored over the ones with B-B and N-N bonds, explaining the known tendency to phase separation, verified by a $T\ensuremath{-}x$ phase diagram. We calculate the energy gap as a function of the composition considering both composition fluctuation and phase separation effects. Experimental data are discussed in this context. Finally, we obtain absorption spectra reproducing a two-peak pattern for intermediate carbon concentrations found experimentally and identified with phase-segregated instead of homogeneous alloys.