Thickness dependence of work function, ionization energy, and electron affinity of Mo and W dichalcogenides from DFT and GW calculations

Transition-metal dichalcogenides (TMDs) are promising for two-dimensional (2D) semiconducting devices and novel phenomena. For 2D applications, their work function, ionization energy, and electron affinity are required as a function of thickness, but research on this is yet to cover the full family of compounds. Here, we present the work function, ionization energy, and electron affinity of few-layer and bulk $M{X}_{2}$ ($M=\text{Mo},$ W and $X=\text{S}$, Se, Te) in 2H phase obtained accurately by the density functional theory and GW calculations. For each compound, we consider one-, two-, three-, four-layer, and bulk geometry. In GW calculations, accurate results are obtained by nonuniform $q$ sampling for two-dimensional geometry. From band energies including the GW self-energy correction, we estimate the work function, band gap, ionization energy, and electron affinity as functions of the number of layers. We compare our results with available theoretical and experimental reports, and we discuss types of band alignments in in-plane and out-of-plane junctions of these few-layer and bulk TMDs.