Effective medium theory for the conductivity of disordered metallic nanowire networks

O’Callaghan, Colin; Rocha, C. G.; Manning, Hugh G.; Boland, John J.; Ferreira, M. S.

doi:10.1039/c6cp05187a

Cited by 59 publications

(62 citation statements)

References 28 publications

(64 reference statements)

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“…4 do not vary significantly when d exceeds 3. A similar dependence of fluctuations of the equivalent resistance versus distance has been observed in the aforementioned modeling of 2D nanowire networks' topology [37]. In both cases, the random distribution of the resistance between connected nodes is the source of fluctuations.…”

Section: Random Distribution Of the Resistor Valuessupporting

confidence: 74%

“…The effective medium corresponds therefore to an efficient averaging of R(i,j ) and makes the theory useful to approximate a random resistor network by its equivalent ideal resistor network. The same effective-medium approach has also been applied to study the conductive properties of nanowire networks in two dimensions [37]. Here cross-connections between randomly dispersed nanorods form an irregular conducting net to which Eq.…”

Section: Random Distribution Of the Resistor Valuesmentioning

confidence: 99%

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Modeling the electrical properties of three-dimensional printed meshes with the theory of resistor lattices

2018

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The electrical properties of conducting meshes are investigated numerically by solving the related Kirchhoff equations with the Lanczos algorithm. The method is directly inspired by the recursion technique widely used to study the electronic and vibrational spectra of solids. The method is demonstrated to be very efficient and fast when applied to resistor networks. It is used to calculate equivalent resistances between arbitrary pairs of nodes in simple resistive lattices. When the resistance fluctuates statistically from bond to bond, the method makes it possible to evaluate the fluctuations of the electrical properties of the network. It is also employed to assign an effective bulk resistivity to a discrete conducting three-dimensional mesh.

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Section: Random Distribution Of the Resistor Valuessupporting

confidence: 74%

Section: Random Distribution Of the Resistor Valuesmentioning

confidence: 99%

Modeling the electrical properties of three-dimensional printed meshes with the theory of resistor lattices

2018

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“…We also use the MNR method to describe the percolating network of nanowires, including both linear and contact resistances (ρ and R c ) as in Ref. 1,5,19 , and adding the electrode/nanowire contact resistance in the model, for the first time. A closed form expression for the effective resistance, as a function of these physical parameters, is estimated numerically, by means of Monte-Carlo simulations and fitting of the obtained data points.…”

Section: Stick Conductancementioning

confidence: 99%

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

Benda

Lebental

Cancès

2019

Journal of Applied Physics

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We study by means of Monte-Carlo numerical simulations the resistance of two-dimensional random percolating networks of stick, widthless nanowires. We use the multi-nodal representation (MNR) 1 to model a nanowire network as a graph. We derive numerically from this model the expression of the total resistance as a function of all meaningful parameters, geometrical and physical, over a wide range of variation for each. We justify our choice of non-dimensional variables applying Buckingham π−theorem. The effective resistance of 2D random percolating networks of nanowires is found to write as R eq (ρ, Rc, Rm,w) = A N, L l * ρl * + B N, L l * Rc + C N, L l * Rm,w where N , L l * are the geometrical parameters (number of wires, aspect ratio of electrode separation over wire length) and ρ, Rc, Rm,w are the physical parameters (nanowire linear resistance per unit length, nanowire/nanowire contact resistance, metallic electrode/nanowire contact resistance). The dependence of the resistance on the geometry of the network, one the one hand, and on the physical parameters (values of the resistances), on the other hand, is thus clearly separated thanks to this expression, much simpler than the previously reported analytical expressions. I. INTRODUCTIONThe study of random percolating networks of conducting nanowires has become in the last years a hot topic of investigation. Numerous applications are possible thanks to the outstanding electrical and optical performances of such thin films, combined to their low cost and ease of fabrication. Applications are as diverse as thin film transistors based on carbon nanotubes networks (CNNs) 2,3 , CNNs-based field-effect transistors 4 , transparent conductive (high transmittance, low resistance) thin-film electrodes based on silver nanowires 1,5 or carbon nanotubes (CNTs) 6 -useful for instance in the context of solar cells, the conducting nanowire network acting as a charge carrier collector 7 -and sensors 4 . The conductivity, as well as the sheet transmittance of such thin film nanowire networks has been extensively studied experimentally and theoretically 6,8,9 . These systems are well approximated by random 2D networks, and we study in this paper the dependence of their effective resistance on all structural and physical parameters. We focus on the functional dependence of the resistance on physical parameters, motivated by sensor applications of nanowire networks. In this context, physical parameters, such as nanowire linear resistance, or nanowire/nanowire contact resistance, can vary, due to environment changes. The geometry and structure of the network is thus not sufficient to understand properly the resistance variations.Many parameters impact the total effective resistance of nanowire random networks. Structural parameters such as the density (or coverage), the aspect ratio of electrode separation to wire length, and the alignment of the wires (i.e. the statistical distribution of their angles with respect to a fixed direction) are, among others, known to play on the trans...

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“…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).…”

Section: Introductionmentioning

confidence: 99%

Transparent electrodes with nanorings: A computational point of view

Azani¹,

Hassanpour²,

Tarasevich

et al. 2019

Journal of Applied Physics

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Four samples of transparent conductive films with different numbers of silver nanorings per unit area were produced. The sheet resistance, transparency, and haze were measured for each sample. Using Monte Carlo simulation, we studied the electrical conductivity of random resistor networks produced by the random deposition of the conducting rings onto the substrate. Both systems of equal-sized rings, and systems with rings of different sizes were simulated. Our simulations demonstrated the linear dependence of the electrical conductivity on the number of rings per unit area. Size dispersity decreased the percolation threshold, but without having any other significant effect on the behavior of the electrical conductance. Analytical estimations obtained for dense systems of equal-sized conductive rings were consistent with the simulations.

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Effective medium theory for the conductivity of disordered metallic nanowire networks

Cited by 59 publications

References 28 publications

Modeling the electrical properties of three-dimensional printed meshes with the theory of resistor lattices

Modeling the electrical properties of three-dimensional printed meshes with the theory of resistor lattices

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

Transparent electrodes with nanorings: A computational point of view

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