Effect of Voids on the Percolation Conductivity of Carbon Nanotube Networks
Authors: Alzahrani Sara , Gorle Devendra Kumar , Qiu Andrew , Ural Ant 
Published: August 2024

Two-dimensional (2D) networks consisting of one-dimensional (1D) wires, such as carbon nanotubes, metal nanowires, and graphene nanoribbons, are promising candidates for next-generation flexible transparent conducting electrodes in devices such as organic light-emitting diodes (OLEDs), solar cells, touch screens, smart windows, transparent heaters, and liquid crystal displays. Nanotube networks also have broad application potential in flexible electronics, such as thin film transistors, wearables, electronic skin, and internet of things (IoT) sensors.
The electrical conductivity of carbon nanotube networks is governed by percolation, which deals with the formation of long-range connectivity in random networks. As a result, Monte Carlo simulations need to be employed in order to compute the electrical properties of these networks [1,2]. Understanding the impact of voids, which could be present due to lack of control in the deposition process or introduced intentionally, on the percolation conductivity of carbon nanotube networks is critical for applications such as transparent conductive electrodes, thin film transistors, sensing, and hardware security.
In this work, we generate two-dimensional square carbon nanotube networks with square voids located at the center of the nanotube network. We define the relative void size as the ratio of the length of the side of the void to the length of the side of the nanotube network. We first study the impact of voids on networks consisting of randomly oriented and straight nanotubes. We compute the percolation probability in these networks as a function of nanotube density for different relative void sizes ranging from 0 (no void) to 0.8. Assuming a Gaussian percolation probability density function (PDF), we find that both the mean and standard deviation of the PDF increase with increasing relative void size. We then compute the relative conductivity change as a function of nanotube density for different relative void sizes and find that it increases approximately linearly with relative void size.
According to percolation theory, the conductivity of a nanotube network has a power-law dependence on nanotube density. Next, we extract the local power-law critical exponent as a function of nanotube density for different relative void sizes. We find that the critical exponent approaches 2 at high density for all relative void sizes, in agreement with previous observations for junction-resistance dominated networks without voids [1,3].
Furthermore, we generate curvy carbon nanotubes using third order Bezier curves characterized by the curviness angle and aligned nanotubes using an orientation characterized by the alignment angle [1,2]. Using the same procedure as randomly oriented and straight nanotubes, we then investigate the impact of voids on the electronic properties of networks consisting of curvy and aligned nanotubes, including percolation probability, mean and standard deviation of the PDF, relative conductivity change, and nanotube density critical exponent.
Our results demonstrate the impact voids have on the percolation conductivity of two-dimensional networks consisting of one-dimensional wires such as carbon nanotubes. These results also show that Monte Carlo simulations are an essential predictive tool for providing insights into the electronic properties of nanotube and nanowire networks, which are promising candidates for a wide range of applications such as flexible transparent conductors, thin film transistors, and resistive switching memory.
References:
[1] N. Fata, S. Mishra, Y. Xue, Y. Wang, J. Hicks, and A. Ural, Journal of Applied Physics 128, 124301 (2020).
[2] J. Hicks, J. Li, C. Ying, and A. Ural, Journal of Applied Physics 123, 204309 (2018).
[3] M. Zezelj and I. Stankovic, Physical Review B 86, 134202 (2012).