N)*

Recently, two-dimensional (2D) group-III nitride semiconductors such as h-AlN, h-BN, h-GaN, and h-InN have attracted attention due to their exceptional electronic, optical and thermoelectric properties. It has also been demonstrated, theoretically and experimentally, that properties of 2D materials can be controlled by alloying. In this study we performed density functional theory (DFT) calculations to investigate 2D Al_1-xGa_xN, Ga_1-xIn_xN, and B_1-xAl_xN alloyed structures. We also calculated the thermoelectric properties of these structures using Boltzmann transport theory based on DFT and the optical properties using the GW method and the Bethe Salpeter equation (BSE). Fundamental band gaps were also calculated with quantum Monte Carlo (QMC) methods for benchmarking purposes. We find that by changing the alloying concentration, the band gap and exciton binding energies of each structure can be tuned accordingly, and for certain concentrations, a high thermoelectric performance is reported with strong dependence on the effective mass of the given alloyed monolayer. With the ability to control such properties by alloying 2D group-III nitrides, this work presents new novel possibilities to engineer the electronic, optical and thermoelectric properties of 2D materials.