Electrical conductivity of nanoring-based transparent conductive films: A mean-field approach

Abstract

We have studied the electrical conductivity of nanoring-based, transparent conductive films, these being promising elements for flexible electronic devices. Both the wire resistance and the junction resistance were taken into account. We have calculated the dependency of the electrical conductivity on the number density of the rings. We have proposed a mean-field approach to estimate the dependency of the electrical conductivity on the main parameters. Comparison of direct computations of the electrical conductivity and the estimates provided by the mean-field approach evidenced the applicability of this approach for those cases where the wire resistance dominates over the junction resistance and where both resistances are of the same order. For these two cases, both the direct computations and the mean-field approach evidenced a linear dependence of the electrical conductivity of the films on the number density of the conductive rings. By contrast, the dependence of the electrical conductivity on the number density of the conductive rings is quadratic when the junction resistance dominates over the wire resistance. In this case, the mean-field approach significantly overestimates the electrical conductivity since the main assumptions underlying this approach are no longer fulfilled.

Random 2D nanowire networks: Finite-size effect and the effect of busbar/nanowire contact resistance on their electrical conductivity

“…By contrast, in the case of nanoring-based 2D systems, the discrete consideration in the framework of the MFA, carried out in the present study, gave no improvement as compared to the continuous consideration. 7 In any case, although the MFA is supposed to be valid only for very dense systems, its estimates of the electrical conductivity are fairly reasonable even at very moderate values of the number density.…”

“…This formula coincides with that which was obtained within the framework of the continuous approximation. 7 Now, let us assume that the contacts are evenly distributed over the ring. Hence, the angle between any two nearest contacts is 4nr 2 −1 , while sin ϕ k ≈ 4nr 2 −1 and 1 − cos ϕ k ≈ (32n 2 r 4 ) −1 .…”

“…This review should be extended by some recently published works devoted to nanostick-and nanowirebased random 2D networks. [3][4][5][6][7][8][9] Ref. 2 proposed a closedform approximation of the functional dependence of the effective resistance (R 0 ) of 2D random networks of zerowidth stick nanowires on their physical parameters…”

“…9 In the case of nanoring-based films, when the junction resistance dominates over the wire resistance while the busbar/nanowire contact resistance and the junction resistance are of the same order of magnitude, the MFA significantly overestimates the electrical conductivity when compared to the computations. 7 Thus, the contribution of the busbar/wire resistance to the sheet resistance seems to be important.…”

“…Since details of the computer simulation have been described previously, [7][8][9]14 we present in Sec. II A only a brief sketch using the nanoring-based system as an example.…”