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In search of an improved strategy to form low-resistance contacts to MoS₂ and related semiconducting transition metal dichalcogenides, we use ab initio density functional electronic structure calculations in order to determine the equilibrium geometry and electronic structure of MoO₃/MoS₂ and MoO₂/MoS₂ bilayers. Our results indicate that, besides a rigid band shift associated with charge transfer, the presence of molybdenum oxide modifies the electronic structure of MoS₂ very little. We find that the charge transfer in the bilayer provides a sufficient degree of hole doping to MoS₂, resulting in a highly transparent contact region.