  Three-dimensional interconnected nanowire networks have recently attracted
notable attention for the fabrication of new devices for energy
harvesting/storage, sensing, catalysis, magnetic and spintronic applications
and for the design of new hardware neuromorphic computing architectures.
However, the complex branching of these nanowire networks makes it challenging
to investigate these 3D nanostructured systems theoretically. Here, we present
a theoretical description and simulations of the geometric properties of these
3D interconnected nanowire networks with selected characteristics. Our analysis
reveals that the nanowire segment length between two crossing zones follows an
exponential distribution. This suggests that shorter nanowire segments have a
more pronounced influence on the nanowire network properties compared to their
longer counterparts. Moreover, our observations reveal a homogeneous
distribution in the smallest distance between the cores of two crossing
nanowires. The results are highly reproducible and unaffected by changes in the
nanowire network characteristics. The density of crossing zones and
interconnected nanowire segments are found to vary as the square of the
nanowire density multiplied by their diameter, further multiplied by a factor
dependent on the packing factor. Finally, densities of interconnected segments
up to 10$^{13}$ cm$^{-2}$ can be achieved for 22-$\mu$m-thick nanowire networks
with high packing factors. This has important implications for neuromorphic
computing applications, suggesting that the realization of 10$^{14}$
interconnections, which corresponds to the approximate number of synaptic
connections in the human brain, is achievable with a nanowire network of about
10 cm$^{2}$.
