Monolayer semiconducting transition metal dichalcogenide alloys: Stability and band bowing

The stability and band bowing effects of two-dimensional transition metal dichalcogenide alloys MX_{2(1-x )}X′_2x (M Mo, W, and X, X′ S, Se, Te) are investigated by employing the cluster expansion method and the special quasi-random structure approach. It is shown that for (S, Se) alloys, there exist stable ordered alloy structures with concentration x equal to 1/3, 1/2, and 2/3, which can be explained by the small lattice mismatch between the constituents and a large additional charge exchange, while no ordered configuration exists for (Se, Te) and (S, Te) alloys at 0 K. The calculated phase diagrams indicate that complete miscibility in the alloys can be achieved at moderate temperatures. The bowing in lattice constant for the alloys is quite small, while the bowing in band gap, and more so in band edge positions, is much more significant. By decomposing the formation of alloy into multiple steps, it is found that the band bowing is the joint effect of volume deformation, chemical difference, and a low-dimensionality enhanced structure relaxation. The direct band gaps in these alloys continuously tunable from 1.8 eV to 1.0 eV, along with the moderate miscibility temperatures, make them good candidates for two-dimensional optoelectronics.