Work functions of two-dimensional black phosphorus from first principles

We performed first-principles calculations to investigate the work function of two-dimensional black phosphorus (BP) as a function of the number of layers. First, we considered pristine BP layers using the density-functional theory (DFT) and GW approximation. The work function of pristine BP obtained from DFT tends to increase slightly as the number of BP layers decreases from four-layer to monolayer. In our GW calculation of pristine BP layers, the work function is increased, compared with DFT results. The increase of the work function depends very weakly on the number of layers. Second, we also investigated the effect of the metal substrate on the work function of BP layers. In this case, we performed DFT calculations. The presence of metal substrate increases the work function of BP and makes it depend more strongly on the number of layers than the pristine case.