title: Effective medium theory for the conductivity of disordered metallic nanowire networks.
abstract: Motivated by numerous technological applications, there is current interest in the study of the conductive properties of networks made of randomly dispersed nanowires. The sheet resistance of such networks is normally calculated by numerically evaluating the conductance of a system of resistors but due to disorder and with so many variables to account for, calculations of this type are computationally demanding and may lack mathematical transparency. Here we establish the equivalence between the sheet resistance of disordered networks and that of a regular ordered network. Rather than through a fitting scheme, we provide a recipe to find the effective medium network that captures how the resistance of a nanowire network depends on several different parameters such as wire density, electrode size and electrode separation. Furthermore, the effective medium approach provides a simple way to distinguish the sheet resistance contribution of the junctions from that of the nanowires themselves. The contrast between these two contributions determines the potential to optimize the network performance for a particular application.
authors.affiliation: School of Physics, Trinity College Dublin, Dublin 2, Ireland and Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN), Trinity College Dublin, Dublin 2, Ireland and AMBER Research Centre, Trinity College Dublin, Dublin 2, Ireland. ocallaco@tcd.ie.
authors.forename: Colin
authors.initials: C
authors.lastname: O'Callaghan
authors.affiliation: School of Physics, Trinity College Dublin, Dublin 2, Ireland and Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN), Trinity College Dublin, Dublin 2, Ireland and AMBER Research Centre, Trinity College Dublin, Dublin 2, Ireland. ocallaco@tcd.ie.
authors.forename: Claudia
authors.initials: C
authors.lastname: Gomes da Rocha
authors.affiliation: Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN), Trinity College Dublin, Dublin 2, Ireland and AMBER Research Centre, Trinity College Dublin, Dublin 2, Ireland. ocallaco@tcd.ie and School of Chemistry, Trinity College Dublin, Dublin 2, Ireland.
authors.forename: Hugh G
authors.identifier: http://orcid.org/0000-0001-6803-7297
authors.initials: HG
authors.lastname: Manning
authors.affiliation: Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN), Trinity College Dublin, Dublin 2, Ireland and AMBER Research Centre, Trinity College Dublin, Dublin 2, Ireland. ocallaco@tcd.ie and School of Chemistry, Trinity College Dublin, Dublin 2, Ireland.
authors.forename: John J
authors.initials: JJ
authors.lastname: Boland
authors.affiliation: School of Physics, Trinity College Dublin, Dublin 2, Ireland and Centre for Research on Adaptive Nanostructures and Nanodevices (CRANN), Trinity College Dublin, Dublin 2, Ireland and AMBER Research Centre, Trinity College Dublin, Dublin 2, Ireland. ocallaco@tcd.ie.
authors.forename: Mauro S
authors.initials: MS
authors.lastname: Ferreira