Origins of bandgap bowing character in the common-anion transition-metal-dichalcogenide ternary alloyed monolayer: ab initio investigation

Abstract

Density functional theory is employed to investigate the origins of bandgap bowing character in transition-metal-dichalcogenide ternary alloyed monolayers (TMD-MLs). The available experimental photoluminescence (PL) data in literature have confirmed the existence of bowing character in the common-anion ternary alloys (e.g. Mo _1− _x W _x S _2 ) and its complete absence in the common-cation ternary alloys (e.g. MoS _2(1− _x _) Se _2 _x ). Our theoretical modeling of bandgap energy versus alloy composition, ${E}_{\text{g}}\left(x\right)$ , in these respective alloys have yielded trends and bowing parameters in excellent agreement with the available PL data (i.e. B = 0.26 eV and zero, respectively). Calculated band structures showed that the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) states in TMD-ML to be fully attributed to the metal atoms and to follow the symmetry of the irreducible representations A _1 ′ (singlet ${d}_{{z}^{2}}$ state) and E ′ (doublet of ${d}_{{x}^{2}-{y}^{2}}$ and d _xy states) of the point group D _3 _h , respectively. Consequently, in case of common-cation TMD-ML alloys, ${E}_{\text{g}}\left(x\right)$ is linear and the bowing is absent. Whereas, in case of common-anion TMD-ML alloys, ${E}_{\text{g}}\left(x\right)$ is quadratic and the bowing is present because of the existence of competition between the cations (i.e. metal atoms) in contributing to HOMO/LUMO states. Our theoretical findings are corroborated with the available experimental data and have direct impact in TMD-based photonic nano-device applications.