  The self-assembly of heteroepitaxial GaN nanowires using either molecular
beam epitaxy (MBE) or metal-organic vapor phase epitaxy (MOVPE) mostly results
in wafer-scale ensembles with ultrahigh ($>10$ $\mu$m$^{-2}$) or ultralow ($<1$
$\mu$m$^{-2}$) densities, respectively. A simple means to tune the density of
well-developed nanowire ensembles between these two extremes is generally
lacking. Here, we examine the self-assembly of SiN$_x$ patches on TiN(111)
substrates which are eventually acting as seeds for the growth of GaN
nanowires. We first found that if prepared by reactive sputtering, the TiN
surface is characterized by \{100\} facets for which the GaN incubation time is
extremely long. Fast GaN nucleation is only obtained after deposition of a
sub-monolayer of SiN$_x$ atoms prior to the GaN growth. By varying the amount
of pre-deposited SiN$_x$, the GaN nanowire density could be tuned by three
orders of magnitude with excellent uniformity over the entire wafer, bridging
the density regimes conventionally attainable by direct self-assembly with MBE
or MOVPE. The analysis of the nanowire morphology agrees with a nucleation of
the GaN nanowires on nanometric SiN$_x$ patches. The photoluminescence analysis
of single freestanding GaN nanowires reveals a band edge luminescence dominated
by excitonic transitions that are broad and blue shifted compared to bulk GaN,
an effect that is related to the small nanowire diameter and to the presence of
a thick native oxide. The approach developed here can be principally used for
tuning the density of most III-V semiconductors nucleus grown on inert surfaces
like 2D materials.
