**2. Main properties of metallic nanowire networks**

The main physical properties of metallic nanowire networks are optical properties (transparency and haziness), electrical resistance and mechanical properties (or more precisely the electromechanical properties mainly in bending or stretching modes). These properties depend on several parameters, including MNW dimensions (diameter and length), junction resistance and network density. We will briefly describe this dependence below. **Figure 1** shows single MNW and MNW network observed by electron microscopy at different scales.

MNW dimensions can influence the properties of MNW networks. MNW diameter, *DNW*, can be first compared with the mean free path of electrons, , in

**135**

*Metallic Nanowire Percolating Network: From Main Properties to Applications*

the bulk metal: if *DNW* is comparable or even smaller than , then surface scattering is increased (for bulk Ag is close to 50 nm). This was derived and observed experimentally by Bid et al. at the individual MNW level [29] and shown to be in good agreement with experiments on AgNW networks by Lagrange et al. [30]. Too small MNW diameter leads to large electrical resistance and to instability at lower temperature [30], while too large MNW diameter increases shadowing effects and then reduces the optical transparency; therefore a trade-off should be found. Also one should keep in mind that large *DNW* values lead to larger haziness. The influence of MNW length was, for instance, studied by Bergin et al. [31] or by Marus et al. [32]: generally speaking increasing MNW length results in an improvement of their optoelectronic performance. It is also worth noticing that the MNW length distribution can also play a role, as shown by Langley et al. [33], who showed that the critical density of MNW associated to the percolation threshold decreases when

*Electronic microscopy observation of silver nanowires and the associated network. (a) Transmission electron microscopy image of AgNW; (b, c) scanning electron microscopy images of random AgNW network fabricated* 

The junctions between MNW play also a key role. Recently Ponzoni showed that the relative contribution to electrical conductivity between nanowires and junctions could be very close [34], in good agreement with Bellew et al. who reported junction resistance measurements of individual silver nanowire junctions [35]. Bellew et al. were able to demonstrate, based on experimental data and modelling, that the junction contribution to the network's overall resistance could be reduced even beyond that of the nanowires themselves. It was shown experimentally by several methods that junctions' resistance could be reduced: for instance, Langley et al. showed that a thermal annealing can drastically reduce network resistance thanks to a local sintering of the junctions [36]; and Garnett et al. used light-induced plasmonic nano-welding to *optimize* junction resistance of MNW networks thanks to an efficient *localized* heating compatible with low-

The network density is a key parameter and influences both the optical transmittance and the electrical resistance. Instead of considering the network density (expressed as the number of MNW per unit area), one often prefers to consider the

tance is observed to decrease linearly with amd as shown by Bergin et al. [31] or by Lagrange et al. [30]. This can be simply explained by shadowing effects [30]. Conversely electrical resistance drastically decreases when amd is increased; therefore an inherent trade-off between high transparency (observed for low amd values) and low resistance (large amd values) has to be considered. **Figure 2a** illustrates the influence of amd value on the electrical resistance. Experiments performed on AgNW

). Optical transmit-

thermal-budget substrates such as polymeric substrates [37].

areal mass density, amd, expressed in mass per unit area (mg/m2

*DOI: http://dx.doi.org/10.5772/intechopen.89281*

*by spray on glass substrates observed at two different magnifications.*

**Figure 1.**

the MNW distribution is increased.

*Metallic Nanowire Percolating Network: From Main Properties to Applications DOI: http://dx.doi.org/10.5772/intechopen.89281*

**Figure 1.**

*Smart Nanosystems for Biomedicine, Optoelectronics and Catalysis*

The main TEs investigated in the last decades have been transparent conductive oxides (TCO) [1–4] with the most well-known and used one in the industrial area being indium tin oxide (ITO). And aluminium-doped zinc oxide (AZO) [2] and fluorine-doped tin oxide (FTO) [5] have been also the subject of many studies. While TCO can exhibit good or even very good physical properties, the recent industrial needs have prompted a search of new materials to replace TCO for several applications [6]. Indeed indium, for instance, can be scarce, its deposition often requires vacuum, and TCO by nature are brittle and therefore not compatible with flexible applications. Materials such as carbon nanotubes [7], graphene [8], conducting polymers [9, 10], metallic grids [11] and metallic nanowire networks [12, 13] have been mainly studied for this purpose, and some of them exhibit already promising properties for several applications. In particular, several studies have lately demonstrated that metallic nanowire (MNW) percolating networks can exhibit high electrical conductivity, high optical transparency and high flexibility [12, 14, 15]. The main investigated are silver nanowire (AgNW) and copper nanowire (CuNW). The very high aspect ratio of the nanowires (i.e. length divided

by the diameter) allows these networks to achieve very good performances, similar to ITO, however by using much less raw material [12]. Such quantity are often expressed in terms of the so-called areal mass density (*amd*), defined as the required mass of metal (for MNW networks) or indium (for ITO thin layers) per

similar price per unit mass for both In and Ag, replacing ITO by AgNW networks appears to be a cost-effective alternative. Moreover MNW-based TEs exhibit two additional assets: they can be fabricated via solution-based methods, and they present outstanding flexibility (and even good stretchability). These two assets constitute clearly key points for an efficient industrial integration. Another advantage of MNW networks is their high optical transparency in the near-infrared spectrum, especially when compared with TCO: this is of importance for transparent solar cell applications. For those reasons, printed AgNW network-based electrodes have shown a potential as transparent and flexible electrodes in many displays such as solar cells [16–19], OLEDs [20], displays [21], supercapacitors [22], transparent heaters [23–25], radio-frequency antennas [26], antibacterial

In this contribution, we focus on TEs made of AgNWs or CuNWs and will first briefly discuss the role of the nanowire dimensions (both length and diameter) and network density on the physical properties. The network stability will be discussed followed by methods to enhance it, which appears to be a crucial issue for an efficient integration of this technology. Finally, we will briefly discuss the integration

The main physical properties of metallic nanowire networks are optical properties (transparency and haziness), electrical resistance and mechanical properties (or more precisely the electromechanical properties mainly in bending or stretching modes). These properties depend on several parameters, including MNW dimensions (diameter and length), junction resistance and network density. We will briefly describe this dependence below. **Figure 1** shows single MNW and MNW

MNW dimensions can influence the properties of MNW networks. MNW diameter, *DNW*, can be first compared with the mean free path of electrons, , in

of MNW network-based transparent electrodes for energy applications.

**2. Main properties of metallic nanowire networks**

network observed by electron microscopy at different scales.

for AgNW or CuNW

for ITO thin layers [12]. With rather

square metre. Their ranges are between 40 and 200 mg.m<sup>−</sup><sup>2</sup>

networks and roughly 750–1050 mg.m<sup>−</sup><sup>2</sup>

films [27] or smart windows [28].

**134**

*Electronic microscopy observation of silver nanowires and the associated network. (a) Transmission electron microscopy image of AgNW; (b, c) scanning electron microscopy images of random AgNW network fabricated by spray on glass substrates observed at two different magnifications.*

the bulk metal: if *DNW* is comparable or even smaller than , then surface scattering is increased (for bulk Ag is close to 50 nm). This was derived and observed experimentally by Bid et al. at the individual MNW level [29] and shown to be in good agreement with experiments on AgNW networks by Lagrange et al. [30]. Too small MNW diameter leads to large electrical resistance and to instability at lower temperature [30], while too large MNW diameter increases shadowing effects and then reduces the optical transparency; therefore a trade-off should be found. Also one should keep in mind that large *DNW* values lead to larger haziness. The influence of MNW length was, for instance, studied by Bergin et al. [31] or by Marus et al. [32]: generally speaking increasing MNW length results in an improvement of their optoelectronic performance. It is also worth noticing that the MNW length distribution can also play a role, as shown by Langley et al. [33], who showed that the critical density of MNW associated to the percolation threshold decreases when the MNW distribution is increased.

The junctions between MNW play also a key role. Recently Ponzoni showed that the relative contribution to electrical conductivity between nanowires and junctions could be very close [34], in good agreement with Bellew et al. who reported junction resistance measurements of individual silver nanowire junctions [35]. Bellew et al. were able to demonstrate, based on experimental data and modelling, that the junction contribution to the network's overall resistance could be reduced even beyond that of the nanowires themselves. It was shown experimentally by several methods that junctions' resistance could be reduced: for instance, Langley et al. showed that a thermal annealing can drastically reduce network resistance thanks to a local sintering of the junctions [36]; and Garnett et al. used light-induced plasmonic nano-welding to *optimize* junction resistance of MNW networks thanks to an efficient *localized* heating compatible with lowthermal-budget substrates such as polymeric substrates [37].

The network density is a key parameter and influences both the optical transmittance and the electrical resistance. Instead of considering the network density (expressed as the number of MNW per unit area), one often prefers to consider the areal mass density, amd, expressed in mass per unit area (mg/m2 ). Optical transmittance is observed to decrease linearly with amd as shown by Bergin et al. [31] or by Lagrange et al. [30]. This can be simply explained by shadowing effects [30]. Conversely electrical resistance drastically decreases when amd is increased; therefore an inherent trade-off between high transparency (observed for low amd values) and low resistance (large amd values) has to be considered. **Figure 2a** illustrates the influence of amd value on the electrical resistance. Experiments performed on AgNW

#### **Figure 2.**

*Effect of the network density, expressed here as the areal mass density (amd), on the electrical properties of percolating AgNW networks: (a) Minimum electrical resistance measured experimentally during thermal ramp versus the network areal mass density [36]; (b) illustration of the three regimes associated with different values of amd. Below a critical value, amdc, no finite electrical resistance can be measured. Just above very large resistance values are measured, while they decrease as a power law for larger amd values; the onset corresponds to the stick percolation. Another transition, less known and studied, exists between the percolative regime and the bulk regime; for the latter the electrical resistivity does not depend anymore on the network density [24].*

networks associated to different networks amd values show the existence of a critical value of amd, amdc, below which no finite resistance can be measured (see **Figure 2b**). This limit is associated to the stick percolation, and Monte Carlo simulations show that the amdc value is given by amdc = 5.64 < MMNW>/L2 where <MMNW > is the average mass of the MNW and L is the MNW length [33, 38]. Above amdc the measured electrical resistance is decreasing rapidly following a power law, as shown by **Figure 2a**: there is a rather good agreement observed between experimental data (symbols) and percolation theory (line) [30]. Some differences between real-world networks and Monte Carlo simulations were investigated lately by Langley et al. [33]. The real-world imperfections of a network concern the MNW length distribution, the non-isotropic MNW orientation and the MNW curvature: the influence of these three parameters on the onset network percolation was studied by Langley et al. [33]. For much larger amd value, another transition does exist between the percolative regime and the so-called bulk regime [24]; while this transition is much less known or investigated than stick percolation, such a transition occurs close to amd values that are considered in most applications.

Another way of looking at the influence of amd value on electrical properties of MNW networks is proposed in **Figure 3** where the electrical conductance is plotted versus relative amd. Below the critical amd value, amdc, the experimental resistance is infinite. Just above Sannicolo et al. demonstrated that a discontinuous activation of efficient percolating pathways takes place [39]: experimentally, for sparse networks abrupt drops of electrical resistance are observed. Such an original phenomenon was called 'geometrically quantized percolation' and was observed by lock-in thermography which evidenced the existence of individual hotter pathways

**137**

**Figure 3.**

or under electrical stress.

*Metallic Nanowire Percolating Network: From Main Properties to Applications*

through the network [39]. For larger amd values, one observes the percolative regime for which the electrical resistance is proportional to (amd-amdc)-γ where γ = 4/3, as shown by Lagrange et al. [30]. The previous expression has been used to fit the data of **Figure 3,** and a good agreement is observed for a large range of amd values, while percolation theory should be only valid for amd values slightly above amdc. For very large values of amd, the electrical resistivity does not depend upon

*Electrical conductance of AgNW network versus the relative areal mass density of the network; this shows the different electrical regimes (see Figure 2 and the text for more details). The red symbols correspond to* 

The stability of metallic nanowire networks appears as a crucial issue, specifically when such TEs undergo thermal and electrical stress [29, 30]. This concerns nearly all applications, and the stability is related to electrical and thermal stability but also long-term ageing and chemical degradation. Such instability can stem from different physical mechanisms such as diffusion of metallic atoms, electromigration processes during electrical stress or oxidation of silver or copper if networks are in contact with either humid atmosphere and/or in high temperature conditions and/

One of the first investigations of the instability of AgNW networks was reported by Khaligh and Goldthorpe [40]: they showed that when AgNW-based TEs undergo similar electrical currents than those encountered in organic solar cells, the TEs

amd value, and a metallic bulk behaviour should be then observed.

*experimental data, while the blue dash line corresponds to the percolation theory.*

**3. Stability of silver nanowire networks**

*DOI: http://dx.doi.org/10.5772/intechopen.89281*

*Metallic Nanowire Percolating Network: From Main Properties to Applications DOI: http://dx.doi.org/10.5772/intechopen.89281*

#### **Figure 3.**

*Smart Nanosystems for Biomedicine, Optoelectronics and Catalysis*

networks associated to different networks amd values show the existence of a critical value of amd, amdc, below which no finite resistance can be measured (see **Figure 2b**). This limit is associated to the stick percolation, and Monte Carlo simulations show that the amdc value is given by amdc = 5.64 < MMNW>/L2 where <MMNW > is the average mass of the MNW and L is the MNW length [33, 38]. Above amdc the measured electrical resistance is decreasing rapidly following a power law, as shown by **Figure 2a**: there is a rather good agreement observed between experimental data (symbols) and percolation theory (line) [30]. Some differences between real-world networks and Monte Carlo simulations were investigated lately by Langley et al. [33]. The real-world imperfections of a network concern the MNW length distribution, the non-isotropic MNW orientation and the MNW curvature: the influence of these three parameters on the onset network percolation was studied by Langley et al. [33]. For much larger amd value, another transition does exist between the percolative regime and the so-called bulk regime [24]; while this transition is much less known or investigated than stick percolation, such a transition occurs close to amd values that are considered in most

*Effect of the network density, expressed here as the areal mass density (amd), on the electrical properties of percolating AgNW networks: (a) Minimum electrical resistance measured experimentally during thermal ramp versus the network areal mass density [36]; (b) illustration of the three regimes associated with different values of amd. Below a critical value, amdc, no finite electrical resistance can be measured. Just above very large resistance values are measured, while they decrease as a power law for larger amd values; the onset corresponds to the stick percolation. Another transition, less known and studied, exists between the percolative regime and the bulk regime; for the latter the electrical resistivity does not depend anymore on the network* 

Another way of looking at the influence of amd value on electrical properties of MNW networks is proposed in **Figure 3** where the electrical conductance is plotted versus relative amd. Below the critical amd value, amdc, the experimental resistance is infinite. Just above Sannicolo et al. demonstrated that a discontinuous activation of efficient percolating pathways takes place [39]: experimentally, for sparse networks abrupt drops of electrical resistance are observed. Such an original phenomenon was called 'geometrically quantized percolation' and was observed by lock-in thermography which evidenced the existence of individual hotter pathways

**136**

applications.

**Figure 2.**

*density [24].*

*Electrical conductance of AgNW network versus the relative areal mass density of the network; this shows the different electrical regimes (see Figure 2 and the text for more details). The red symbols correspond to experimental data, while the blue dash line corresponds to the percolation theory.*

through the network [39]. For larger amd values, one observes the percolative regime for which the electrical resistance is proportional to (amd-amdc)-γ where γ = 4/3, as shown by Lagrange et al. [30]. The previous expression has been used to fit the data of **Figure 3,** and a good agreement is observed for a large range of amd values, while percolation theory should be only valid for amd values slightly above amdc. For very large values of amd, the electrical resistivity does not depend upon amd value, and a metallic bulk behaviour should be then observed.
