Two-dimensional (2D) materials with lower lattice thermal conductivities and high figures of merit are useful for applications in thermoelectric (TE) devices. In this work, the thermoelectric properties of monolayer Cu<sub>2</sub>S and Cu<sub>2</sub>Se are systematically studied through first-principles and Boltzmann transport theory. The dynamic stability of monolayer Cu<sub>2</sub>S and Cu<sub>2</sub>Se through elastic constants and phonon dispersions are verified. The results show that monolayer Cu<sub>2</sub>S and Cu<sub>2</sub>Se have small lattice constants, resulting in lower phonon vibration modes. Phonon transport calculations confirm that monolayer Cu<sub>2</sub>Se has lower lattice thermal conductivity (1.93W/mK) than Cu<sub>2</sub>S (3.25W/mK) at room temperature, which is due to its small Debye temperature and stronger anharmonicity. Moreover, the heavier atomic mass of Se atom effectively reduces the phonon frequency, resulting in an ultra narrow phonon band gap (0.08THz) and a lower lattice thermal conductivity for monolayer Cu<sub>2</sub>Se. The band degeneracy effect at the valence band maximum (VBM) of monolayer Cu<sub>2</sub>S and Cu<sub>2</sub>Se significantly increase their carrier effective mass, resulting in higher Seebeck coefficients and lower conductivities under p-type doping. The electric transport calculation at room temperature shows that the conductivity of monolayer Cu<sub>2</sub>S (Cu<sub>2</sub>Se) under n-type doping about 10<sup>11</sup>cm<sup>–2</sup> is 2.8×10<sup>4</sup> S/m (4.5×10<sup>4</sup> S/m), obviously superior to its conductivity about 2.6×10<sup>2</sup> S/m (1.6×10<sup>3</sup> S/m) under p-type doping. At the optimum doping concentration for monolayer Cu<sub>2</sub>S (Cu<sub>2</sub>Se), the n-type power factor is 16.5 mW/mK<sup>2</sup> (25.9 mW/mK<sup>2</sup>), which is far higher than p-type doping 1.1 mW/mK<sup>2</sup> (6.6 mW/mK<sup>2</sup>). Through the above results, the excellent figure of merit of monolayer Cu<sub>2</sub>S (Cu<sub>2</sub>Se) under optimal n-type doping at 700 K can approach to 1.85 (2.82), which is higher than 0.38 (1.7) under optimal p-type doping. The excellent thermoelectric properties of monolayer Cu<sub>2</sub>S (Cu<sub>2</sub>Se) are comparable to those of many promising thermoelectric materials reported recently. Especially, the figure of merit of monolayer Cu<sub>2</sub>Se is larger than that of the well-known high-efficient thermoelectric monolayer SnSe (2.32). Therefore, monolayer Cu<sub>2</sub>S and Cu<sub>2</sub>Se are potential thermoelectric materials with excellent performances and good application prospects. These results provide the theoretical basis for the follow-up experiments to explore the practical applications of 2D thermoelectric semiconductor materials and provide an in-depth insight into the effect of phonon thermal transport on improvement of TE transport properties.
