  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.
