Two-dimensional (2D) MoSi$_2$N$_4$ monolayer is an emerging class of air-stable 2D semiconductor possessing exceptional electrical and mechanical properties. Despite intensive recent research efforts devoted to uncover the material properties of MoSi$_2$N$_4$, the physics of electrical contacts to MoSi$_2$N$_4$ remains largely unexplored thus far. In this work, we study the van der Waals heterostructures composed of MoSi$_2$N$_4$ contacted by graphene and NbS$_2$ monolayers using first-principle density functional theory calculations. We show that the MoSi$_2$N$_4$/NbS$_2$ contact exhibits an ultralow Schottky barrier height (SBH), which is beneficial for nanoelectronics applications. For MoSi$_2$N$_4$/graphene contact, the SBH can be modulated via interlayer distance or via external electric fields, thus opening up an opportunity for reconfigurable and tunable nanoelectronic devices. Our findings provide insights on the physics of 2D electrical contact to MoSi$_2$N$_4$, and shall offer a critical first step towards the design of high-performance electrical contacts to MoSi$_2$N$_4$-based 2D nanodevices.
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