Comparison of the properties of two-dimensional and three-dimensional percolating networks of nanoparticles

Percolating networks of nanoparticles (PNNs) exhibit a range of brain-like properties and are well modeled by continuum percolation with tunneling. All of the PNNs studied to date for their potential use in neuromorphic computing have been two-dimensional (2D), formed by depositing particles onto flat insulating substrates. Since the brain itself is three-dimensional (3D), it is natural to ask whether improvements in the brain-like characteristics of the networks and in their usefulness for neuromorphic computing could be achieved by building 3D percolating-tunneling systems. Using realistic simulations, we investigated whether the properties would be significantly different if PNNs were fabricated in 3D, such that the network is no longer able to be represented as a planar graph. We found that the properties of 3D PNNs, including degree distributions and small-world characteristics, are surprisingly similar to those of 2D PNNs. We outline a possible method for fabrication of a 3D PNN and discuss the practical difficulties of achieving a truly percolating network. A straightforward analysis of power dissipation shows that 3D PNNs are likely to be considerably more difficult to cool than 2D PNNs. These results suggest that moving to 3D neuromorphic systems may not bring an improvement in computational performance.