Geometrical properties of three-dimensional crossed nanowire networks

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 is 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:msup><a:mn>10</a:mn><a:mn>13</a:mn></a:msup><a:mspace width="4pt"/><a:msup><a:mrow><a:mi>cm</a:mi></a:mrow><a:mrow><a:mo>−</a:mo><a:mn>2</a:mn></a:mrow></a:msup></a:mrow></a:math> can be achieved for 22-<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>µ</c:mi><c:mi mathvariant="normal">m</c:mi></c:mrow></c:math>-thick nanowire networks with high packing factors. This has important implications for neuromorphic computing applications, suggesting that the realization of <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:msup><e:mn>10</e:mn><e:mn>14</e:mn></e:msup></e:math> interconnections, which corresponds to the approximate number of synaptic connections in the human brain, is achievable with a nanowire network of about <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mn>10</f:mn><f:mspace width="0.28em"/><f:msup><f:mrow><f:mi>cm</f:mi></f:mrow><f:mn>2</f:mn></f:msup></f:mrow></f:math>.