Tuning the Schottky barrier heights at MoS$_{2}$$\mid$metal contacts: a first-principles study

The nature of the Schottky barrier at metal contacts with the two-dimensional semiconductor MoS$_{2}$ is controversial. Using first-principles DFT calculations we show that the Schottky barrier height (SBH) for high work function ($>$ 4.7 eV) metals typically obeys the Schottky-Mott limit, provided that a potential step that arises at the metal-MoS$_{2}$ interface is taken into account. It suggests that selecting a metal with an appropriate work function may reduce the SBH to zero. However, we find that for low work function metals the Fermi level is pinned below the conduction band edge of MoS$_{2}$ , leading to SBHs of 0.1-0.3 eV. We attribute the pinning to the metal-MoS$_{2}$ interaction at the interface perturbing the electronic structure of MoS$_{2}$ , and causing a broadening of the MoS2 conduction band edge. Inserting a monolayer of boron nitride (BN) between the metal surface and the MoS$_{2}$ layer disrupts this interaction. In addition the BN layer effectively decreases the metal work function, thereby enabling a line-up of the Fermi level with the MoS$_{2}$ conduction band with a vanishing SBH.