Predictive Model for the Electrical Transport within Nanowire Networks

Abstract

Thin networks of high aspect ratio conductive nanowires can combine high electrical conductivity with excellent optical transparency, which has led to a widespread use of nanowires in transparent electrodes, transistors, sensors, and flexible and stretchable conductors. Although the material and application aspects of conductive nanowire films have been thoroughly explored, there is still no model which can relate fundamental physical quantities, like wire resistance, contact resistance and nanowire density, to the sheet resistance of the film. Here we derive an analytical model for the electrical conduction within nanowire networks based on an analysis of the parallel resistor network.The model captures the transport characteristics and fits a wide range of experimental data, allowing for the determination of physical parameters and performance limiting factors, in sharp contrast to the commonly employed percolation theory. The model

Effective resistance of random percolating networks of stick nanowires: Functional dependence on elementary physical parameters

“…Given the unveiled additive nature for the effective resistance of random percolating networks of nanowires, another possible application is to estimate the values of unit base (single nanowire, single contact) resistances ρ, R c and R m,w (as done recently by Forró and al. 9 ). Let us indeed consider at least three nanowire networks devices, made up of the same nanowires (whose local intrinsic properties, as linear or contact resistances, are thus the same) but of different densities and (or) aspect ratios.…”

“…Finally, Forró and al. 9 also recently derived an analytical expression of the sheet resistance of random 2D networks of nanowires, valid at rather high densities (well above the percolation threshold), as a function of both geometrical parameters (wire density, wire length and electrode separation) and physical parameters R c (contact resistance) and R w -wire resistance, equal in our notations to ρl * where l * is the length of a wire -as seen in Eq. (6) of Ref.…”

“…The values of A, B and C are derived from least-squares fitting of the simulated function (x, y) →R eq (x, y) to a functional form (x, y) → Ax + B + Cy. The chosen grid of points is {(xi, yj)} i,j where xi = l * 1µm (1 + i)0.01, yj = (1 + j)0.1 and (i, j) ∈ [[0, 99]] × [[0,9]]. A(N ) and B(N ) and C(N ) are the approximation errors on these three coefficients from the linear regression (square root of the diagonal terms of the estimated parameters covariance matrix).…”

Transparent electrodes with nanorings: A computational point of view

“…Numerous works have been devoted to the electrical and optical properties of transparent films with elongated fillers such as NTs, NWs, and nanorods. [3][4][5][6][7][8][9][10][11][12][13][14] However, the use of films containing conducting nanorings [15][16][17] looks extremely attractive since, in this case, there are no dead ends in the percolation cluster, i.e., the percolation cluster is identical to its geometrical backbone. In a two-dimensional continuum percolation, the number density is defined as where N is the number of objects randomly deposited onto a square substrate of size L×L with periodic boundary conditions (PBC).…”

Effect of tunneling on the electrical conductivity of nanowire-based films: Computer simulation within a core–shell model

“…24 By contrast, a nonlinear dependency of the electrical conductivity of NWNs on both the wire resistance and the contact resistance has also been proposed. 22 Figure 2 demonstrates the linear dependence of the electrical resistance of the NWNs on the electrical resistance of junctions when tunneling is excluded from the consideration by setting the cutoff distance r = 0.…”