  Low-dimensional metal-semiconductor vertical heterostructures (VH) are
promising candidates in the search of electronic devices at the extreme limits
of miniaturization. Within this line of research, here we present a
theoretical/computational study of the NbS$_2$/WSe$_2$ metal-semiconductor
vertical hetero-junction using density functional theory (DFT) and conductance
simulations. We first construct atomistic models of the NbS$_2$/WSe$_2$ VH
considering all the five possible stacking orientations at the interface, and
we conduct DFT and quantum-mechanical (QM) scattering simulations to obtain
information on band structure and transmission coefficients. We then carry out
an analysis of the QM results in terms of electrostatic potential, fragment
decomposition, and band alignment. The behavior of transmission expected from
this analysis is in excellent agreement with, and thus fully rationalizes, the
DFT results, and the peculiar double-peak profile of transmission. Finally, we
use maximally localized Wannier functions, projected density of states (PDOS),
and a simple analytic formula to predict and explain quantitatively the
differences in transport in the case of epitaxial misorientation. Within the
class of Transition-Metal Dichalcogenide systems, the NbS$_2$/WSe$_2$ vertical
heterostructure exhibits a wide interval of finite transmission and a
double-peak profile, features that could be exploited in applications.
