(Invited) Effect of Junction Resistance on the Percolation Conductivity of Metal Nanowire Networks for Transparent Conductors
Authors: Mishra Shreshtha , Xue Ying , Fata Nicholas , DeStefano Kevin , Hicks Jeremy , Ural Ant 
Published: February 2020

Random networks of one-dimensional (1D) nanoelements, such as carbon nanotubes, graphene nanoribbons, and metal nanowires, have attracted significant research interest recently for next-generation transparent conductors. As a result, these networks can be used in many device applications, such as touch screens, flat panel displays, solar cells, light-emitting diodes (LEDs), and wearable flexible electronics. Among these nanomaterials, metal nanowire networks, such as silver and copper, exhibit high optical transmittance, low sheet resistance, mechanical flexibility, and solution-based fast deposition. These unique properties make metal nanowire networks promising candidates to replace indium tin oxide (ITO), which suffers from brittleness, scarcity, high cost, and slow deposition.
At high optical transmittance values required for transparent conductors, the conductivity of metal nanowire networks is governed by percolation transport, which deals with the formation of long-range connectivity in random networks. As a result, Monte Carlo simulations need to be employed to theoretically calculate, predict, and optimize the conductivity of metal nanowire networks [1,2].
Two types of resistance contributions determine the overall conductivity of the nanowire network. The first is the nanowire-nanowire junction resistance and the second is the resistance of the nanowire itself. In most Monte Carlo simulations, it is assumed that the nanowire-nanowire junction resistance is much larger than the nanowire resistance, resulting in a junction resistance-dominated network [2-4]. Although this is the case for carbon nanotube networks, recent experiments have shown that, for metal nanowire networks, the junction resistance can be significantly lowered by post-deposition treatments, such as thermal annealing, plasmonic welding, joule heating, and mechanical pressing. In such cases, the nanowire resistance becomes comparable to the junction resistance and it can no longer be ignored. When the junction resistance becomes much lower than the nanowire resistance, the network becomes nanowire resistance-dominated, which is the lowest resistance limit for a given set of nanowire and device parameters. Despite the significant role the junction resistance plays in determining the percolation conductivity of metal nanowire networks, a systematic study of the effect of nanowire-nanowire junction resistance on the network conductivity as a function of other nanowire and device parameters is currently lacking.
In this work, we perform systematic Monte Carlo simulations to study the effect of the nanowire-nanowire junction resistance on the conductivity and percolation critical exponents of metal nanowire networks. We define a parameter called the resistance ratio, which is the ratio of the nanowire-nanowire junction resistance to the nanowire resistance per unit length. We perform Monte Carlo simulations of the nanowire network conductivity by varying the resistance ratio over a span of six orders of magnitude, ranging all the way from a junction resistance-dominated to a nanowire resistance-dominated network.
First, we study the effect of the resistance ratio on the nanowire network conductivity at different values of the other nanowire and device parameters, such as nanowire density, nanowire length, device length, device width, nanowire alignment, and nanowire curviness. Next, we study the effect of the resistance ratio on the percolation critical exponents. Approaching the percolation threshold, conductivity exhibits a power law dependence on nanowire and device parameters, which is characterized by percolation critical exponents. We first extract the critical nanowire density, nanowire length, device width, and alignment angle at the percolation threshold by calculating the percolation probability as a function of each variable. Then, we extract the critical exponents as a function of the resistance ratio for nanowire density, nanowire length, device width, nanowire alignment, and nanowire curviness. We find that the resistance ratio plays a crucial role in determining both the conductivity and the percolation critical exponents of metal nanowire networks.
This study illustrates how the junction resistance affects the macroscopic conductivity of transparent, conductive metal nanowire networks. It also shows that Monte Carlo simulations are an essential predictive tool for providing insights into percolation transport and optimizing the electronic properties of these networks. These results are not limited to metal nanowire networks, but can be extended to any two-dimensional (2D) or quasi-2D network, film, or nanocomposite consisting of 1D nanoelements.
References:
[1] J. Hicks, A. Behnam, and A. Ural, Phys. Rev. E 79, 012102 (2009).
[2] J. Hicks, J. Li, C. Ying, and A. Ural, J. Appl. Phys. 123, 204309 (2018).
[3] M. Jagota and N. Tansu, Sci. Rep. 5, 10219 (2015).
[4] R. M. Mutiso, M. C. Sherrott, A. R. Rathmell, B. J. Wiley, and K. I. Winey, ACS Nano 7, 7654 (2013).

Figure 1