  The integration of two-dimensional $MoS_{2}$ with $GaN$ recently attracted
significant interest for future electronic/optoelectronic applications.
However, the reported studies have been mainly carried out using
heteroepitaxial $GaN$ templates on sapphire substrates, whereas the growth of
$MoS_{2}$ on low-dislocation-density bulk GaN can be strategic for the
realization of truly vertical devices. In this paper, we report the growth of
ultrathin $MoS_{2}$ films, mostly composed by single-layers ($1L$), onto
homoepitaxial $n-GaN$ on $n^{+}$ bulk substrates by sulfurization of a
pre-deposited $MoO_{x}$ film. Highly uniform and conformal coverage of the
$GaN$ surface was demonstrated by atomic force microscopy, while very low
tensile strain (0.05%) and a significant $p^{+}$-type doping ($4.5 \times
10^{12} cm^{-2}$) of $1L-MoS_{2}$ was evaluated by Raman mapping. Atomic
resolution structural and compositional analyses by aberration-corrected
electron microscopy revealed a nearly-ideal van der Waals interface between
$MoS_{2}$ and the $Ga$-terminated $GaN$ crystal, where only the topmost $Ga$
atoms are affected by oxidation. Furthermore, the relevant lattice parameters
of the $MoS_{2}/GaN$ heterojunction, such as the van der Waals gap, were
measured with high precision. Finally, the vertical current injection across
this 2D/3D heterojunction has been investigated by nanoscale current-voltage
analyses performed by conductive atomic force microscopy, showing a rectifying
behavior with an average turn-on voltage $V_{on}=1.7 V$ under forward bias,
consistent with the expected band alignment at the interface between $p^{+}$
doped $1L-MoS_{2}$ and $n-GaN$.
