Electrical Mapping of Silver Nanowire Networks: a Versatile Tool for

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Electrical Mapping of Silver Nanowire Networks: a Versatile Tool for Imaging Network Homogeneity and Degradation Dynamics during Failure Thomas Sannicolo, Nicolas Charvin, Lionel Flandin, Silas Kraus, Theodora D. Papanastasiou, Caroline Celle, Jean-Pierre Simonato, David Munoz Rojas, Carmen Jiménez, and Daniel Bellet ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b01242 • Publication Date (Web): 03 May 2018 Downloaded from http://pubs.acs.org on May 5, 2018

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Electrical Mapping of Silver Nanowire Networks: a Versatile Tool for Imaging Network Homogeneity and Degradation Dynamics during Failure Thomas Sannicoloa,b, Nicolas Charvinc, Lionel Flandinc,*, Silas Krausa, Theodora D. Papanastasioua, Caroline Celleb, Jean-Pierre Simonatob,*, David Muñoz-Rojasa, Carmen Jiméneza, Daniel Belleta,* a

Univ. Grenoble Alpes, CNRS, Grenoble INP, LMGP, 38000 Grenoble, France

b

Univ. Grenoble Alpes, CEA, LITEN, 38000 Grenoble, France

c

Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, Grenoble INP, LEPMI, 38000

Grenoble, France KEYWORDS. Transparent electrodes, metallic nanowire, percolation, stability, crack, hotspot

ABSTRACT. Electrical stability and homogeneity of silver nanowire (AgNW) networks are critical assets for increasing their robustness and reliability when integrated as transparent electrodes in devices. Our ability to distinguish defects, inhomogeneities, or inactive areas at the scale of the entire network is therefore a critical issue. We propose one-probe electrical mapping (1P-mapping) as a specific simple tool to study the electrical distribution in these discrete structures. 1P-mapping has allowed to show that the tortuosity of the voltage equipotential lines of AgNW networks under bias decreases with increasing network density, leading to a better

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electrical homogeneity. The impact of the network fabrication technique on the electrical homogeneity of the resulting electrode has also been investigated. Then, by combining 1Pmapping with electrical resistance measurements and IR thermography, we propose a comprehensive analysis of the evolution of the electrical distribution in AgNW networks when subjected to increasing voltage stresses. We show that AgNW networks experience three distinctive stages: optimization, degradation, and breakdown. We also demonstrate that the failure dynamics of AgNW networks at high voltages occurs through a highly correlated and spatially localized mechanism. In particular the in situ formation of cracks could be clearly visualized. It consists of two steps: creation of crack followed by propagation nearly parallel to the equipotential lines. Finally, we show that current can dynamically redistribute during failure, by following partially damaged secondary pathways through the crack.

Emerging indium-free transparent electrodes have attracted intense attention in many technological fields, including optoelectronic devices (solar cells, LEDs, touch screens), transparent film heaters (TFHs), and electromagnetic devices. 1–5 In particular, silver nanowire (AgNW) networks successfully combine high flexibility, high optical transparency, and high electrical conductivity.6–9 But unlike metal oxide-based thin films like indium tin oxide (ITO) or fluorine doped tin oxide (FTO), AgNW-based electrodes consist of non-homogeneous material. They are made of interconnected AgNWs, playing the role of conductive medium, and allowing electrical current to flow. Hence, electrical current may not flow identically in all network locations, leading to possible local hotspots, inactive areas, or early failure mechanisms. 10,11 Depending on the target applications, the level of electrical homogeneity might be as critical as the overall conduction level. Electrical homogeneity is indeed likely to have a substantial


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influence on device performance, after integration of the AgNW-based electrode. For instance, network areas where the NW density severely deviates from the average value might constitute hotspots responsible for early degradation of TFHs made of AgNWs.10–12 When integrated in a solar cell, such inhomogeneities might also reduce device efficiency through a slight increase in series resistance and therefore a lower form factor in the J-V curve. Thus, in order to maximize performance, electrical stability, and reliability of devices incorporating AgNW-based electrodes, one needs to get reliable quantitative information about the parameters and the mechanisms influencing the electrical distribution in AgNW networks. At the microscale, current mapping of AgNW networks using either conductive mode atomic force microscopy13 or passive voltage contrast imaging in scanning electron microscopy (SEM) 14 has been already performed, leading to the local identification of nanowires physically connected or isolated from the percolating cluster. However, these methods do not provide information on the actual pathways that the current follows along the network. Kumar et al. have recently developed both numerical and analytical approaches to estimate the fraction of NWs efficiently taking part in current distribution. 15 These authors suggested that a significant fraction of the NWs within the active cluster do not participate efficiently in the electrical conduction. This induces the presence of hotspots close to the percolation threshold that disappear progressively at higher network density. Also recently, thermoreflectance imaging has been successfully used to detect the presence of hotspots and study the local degradation mechanisms in either pristine AgNW networks,16 hybrid graphene-AgNW networks,17 or polymer assisted-templated Ag networks.18 All these studies provided interesting information regarding current distribution in AgNW networks at the microscale. However, in depth experimental analysis of electrical distribution in


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such networks at the macroscale is still missing. In our previous contribution, we investigated the case of low density AgNW networks (close to the percolation threshold, nc ).12 By using Lock-in (LiT) thermography, we demonstrated the occurrence of a discrete activation process of efficient percolating pathways through the network when either thermal or current annealing is performed. Nevertheless, the vast majority of successful integrations of AgNWs in devices have so far concerned network densities n ranging from 5 nc to 10 nc.19 It is then mandatory for industrial purpose to tackle the electrical distribution issue by also investigating these networks. In the present work, we thus focus our analysis of the electrical distribution on “standard” dense AgNW networks. We have developed a one-probe electrical mapping (1P-mapping) set-up for imaging the electrical homogeneity of AgNW networks at the macroscale. In this study we show that compared with other existing mapping techniques, 1P-mapping is a simple method which can extract precious information about the electrical homogeneity of AgNW networks at the macroscale (several cm²), in a relatively short time (several minutes), and without restriction regarding the environment. At first, we show that the deposition technique used to fabricate AgNW networks, such as spin-coating or spray-coating, can drastically influence the electrical map of the resulting electrode. We then show that the homogeneity of the electrical field increases with increasing network density, as indicated by straighter voltage equipotential lines. Conversely, low network densities result in larger tortuosity of the equipotential lines, and disordered structures. We continue by proposing a deep analysis of the evolution of the AgNW networks electrical distribution under various voltage stresses. The latter analysis was conducted via a threefold approach combining electrical resistance measurements, 1P-mapping, and infrared (IR) thermography. More specifically, we show that AgNW networks follow three


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distinctive stages – optimization, degradation, and breakdown – when subjected to an increasing voltage. Much attention is dedicated to the failure dynamics at high voltage. We show that electrical breakdown take the form of a global or statistical phenomenon, even being able to visualize in situ the formation of a crack. Thus after appearing, cracks propagate in a controlled manner parallel to the bias electrodes. We finally show that electrical current undergoes redistribution during failure, following more resistive and partially damaged secondary pathways across the cracks.

Results and discussion Electrical mapping of AgNW networks The 1P-mapping method was first validated by measuring the impact of both AgNW deposition protocol and network density on the electrical homogeneity of the AgNW networks. AgNWs were synthesized using the polyol process and according to a previously published procedure.20 The average diameter and length of the nanowires were 79 ± 10 nm and 7 ± 3 μm, respectively. The nanowires were dispersed in methanol and deposited either by spray-coating or spin-coating on 25 mm × 25 mm glass substrates (Corning® EAGLE XG, 1.2 mm thick). Further experimental details about the nanowire synthesis and deposition process can be found in the materials and methods section. A schematic representation of the 1P-mapping set-up is provided in Figure 1a (pictures are shown in Figure S1 in the Supporting Information). The samples were placed on a 1 mm-thick metallic chuck. Silver paste-based contacts were manually deposited at each end of the


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specimen. The left contact electrode was connected to the ground, while a non-zero electrical potential was applied to right electrode (typically 1 V in this study, i.e. 20 times lower than the critical voltage to initiate electrical instabilities. Further details about the set-up are reported in the Materials and Methods section).

Figure 1. (a) Schematic representation of the one-probe electrical measurement (1P-mapping) set-up developed for macroscale electrical mapping of AgNW networks. The left silver paste electrode is connected to ground (deep blue), while 1.0 V is applied to the right silver paste electrode (deep red). The entire mapping procedure is motorized and computer controlled by a LabVIEW code. (b-c) 1P-maps corresponding to AgNW networks deposited by spray-coating (b) and spin-coating (c). The spray-coated sample (b) exhibits parallel equipotential lines due to the random orientation of the nanowires during the deposition process. On the contrary, the spincoated sample (c) exhibits non parallel equipotential lines (radial distribution) resulting from the preferential orientation of the nanowires during the deposition process.

The probe is first placed at the surface near the origin {X =0, Y = 0} (see Figure 1a). The probe is then slowly moved downwards along the z-axis, until contact with the network is achieved. The first measurement of the local electrical potential can be performed. In the sequence, the voltage bias is not applied continuously but only after the probe contacted the surface to prevent charging effect. Then the voltage is turned off, the probe raised up and moved along the


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X direction (step of 1 mm). The second measurement is obtained the same way, and so on. In the present case, the distance between two successive measurements was adjusted to 1 mm, which was considered as reasonable considering the size of the samples. However this distance could be decreased down to a lower value. Given that the maximum spatial precision of the loading machine is 0.1 mm, we believe that 0.25 mm is a reasonable minimum for the distance between two successive measurements. The resolution of the 1P-mapping technique is also influenced by the dimension of the probe tip used during the experiment. While the present resolution was enough considering the size of the samples, it could be easily improved by using miniature probes packed into a dense array connected to a channel multiplexer. The trajectory followed by the probe is also depicted in Figure 1a. In these conditions, the duration required for scanning a 25×25 mm² sample is about 15 min. The entire procedure is motorized and computer controlled by a LabVIEW code.

Impact of the NW deposition technique on electrical homogeneity Figure 1b and 1c show 1P-maps of AgNW networks deposited by spray-coating (b) or spincoating (c), with similar macroscopic electrical resistance (55 Ω and 16 Ω, respectively). The spray-coated sample exhibits linear, smooth and vertically aligned equipotential lines. This corresponds to a homogenous distribution in electrical voltages and currents. This is attributed to both the random orientation of the nanowires during the deposition process as well as the low resistance value of the network (note that the influence of the network density is further investigated in next section). On the contrary, the 1P-map associated to the spin-coated network exhibits non parallel equipotential lines. The non-isotropic and centripetal orientation of the


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equipotential lines originates from the spin-coating procedure, which involves a preferential orientation of the AgNWs along the centrifugal force during the deposition process. Another example of 1P-map associated to a spin-coated AgNW network of higher resistance (R = 3 kΩ) is provided in Figure S2. Such a preferential orientation of the nanowires when using deposition methods like spincoating,21 horizontal deep-coating,22 capillarity printing,23 Meyer rod coating,24,25 or grazing incidence spraying,26 was already demonstrated at the nanoscale using nanocharacterization imaging techniques. In cases where the target applications require a high level of electrical homogeneity, such deposition methods should therefore be considered with caution. On the contrary, deposition of AgNWs by spray-coating yielded much more randomly oriented AgNW networks.9,21 For the sake of comparison, SEM images of AgNWs deposited either by spin or spray-coating showing the corresponding local NW orientations are provided in Figure S3. In this work, 1P-mapping technique has allowed to demonstrate that the electrical homogeneity of AgNW networks at the macroscale is drastically influenced by the deposition technique used to make the networks. More generally, such 1P-mapping might be very convenient to assess either the preferential or random orientation of any thin film made of interconnected conductive nanostructures (carbon nanotubes, graphene flakes, metallic nanowires of any sorts, hybrids, etc.) as well as for characterizing their electrical homogeneity at the macroscale. In the next sections of the present contribution, all the AgNW specimens were fabricated by spray coating.

Impact of the network density on electrical homogeneity


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The effect of the network density n on electrical homogeneity was also investigated with several samples with varying density. By increasing the number of scans performed by the spray nozzle, the network density could be varied in a controlled manner. The local morphology of the fabricated samples was firstly explored with SEM. Figure 2A1-A3 reports the SEM images of three selected samples. The network density is clearly different from one sample to another. This control over the network density is confirmed with the measurements of the electrical conduction after deposition. The resistance after deposition was indeed reduced from 68 kΩ (A1), to 329 Ω (A2), and even 26 Ω (A3). A careful calculation of the areal mass density (amd) was also performed. The total NW length per unit area was first determined by analyzing SEM images associated to each AgNW network. This was performed with the “Ridge Detection” plugin using ImageJ software.27 The corresponding value of amd can then be simply extracted as follows:

𝑎𝑚𝑑 = 𝑛 ∗ 𝑚𝑁𝑊 = (

𝐿𝑒𝑞 ) ∗ 𝑚𝑁𝑊 𝐿𝑁𝑊 ∗ 𝑆𝑡𝑜𝑡

(1)

with n the number of NWs per unit area (i.e. the network density), mNW the average mass of an individual AgNW, Leq the total length of NWs in the SEM image, LNW the average NW length, and Stot the surface of the SEM image. More details regarding the ImageJ-based protocol developed to calculate the amd of any AgNW network are provided in the Supporting Information, §3. In the present case, amd values of 50 ± 4 mg m-2 (A1), 63 ± 7 mg m-2 (A2), and 86 ± 7 mg m-2 (A3), were obtained.


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Figure 2. (A1-A3) SEM images of AgNW networks with increasing density. Their measured electrical resistances were 68 kΩ (A1), 329 Ω (A2), and 26 Ω (A3), respectively. (B1-B3) 1Pmaps associated with the samples depicted in (A1-A3). The left silver paste electrode is connected to ground (deep blue), while 1.0 V is applied to the right silver paste electrode (deep red). Black areas in (B1) indicate artefact measurements associated to voltage measurements below 0 V: these disconnected areas are only possible close to the percolation threshold and disappear for denser networks.

Electrical mapping of the three samples was performed thereafter. The results are depicted in Figure 2B1-B3. X and Y axis correspond to the real X and Y sides of the samples (in mm), while the color scale represents the electrical potential values recorded when probing the network with the 1P-mapping set-up (deep blue indicates 0 V, while deep red indicates 1 V). Black areas are disconnected from the rest of the network. With this set of data, it is possible to reconstruct equipotential lines across the network. Figure 2B1-B3 exemplifies that dense networks correspond to straight equipotential lines placed in a smooth and organized fashion. In contrast, a


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sparse network (B1) leads to very tortuous equipotential lines. These electrical maps demonstrate that the network density not solely influences the overall conduction level of the network (resistance value), but also the local electrical distribution. The denser the network, the lower the fluctuations of the electrical potential. Dense networks afford higher electrical homogeneity. The level of electrical homogeneity may be tentatively quantified with the numerical value of the average tortuosity of the equipotential lines. The network tortuosity was here extracted from the spatial coordinates of 9 specific equipotential contours (V = 0.1, 0.2, … 0.9 V). The individual tortuosity of each line was defined as the ratio between the total length of the line L, and the distance between the two extremities of the line L0 (for high network densities with vertical straight lines, L0 is very close to the height of the substrate). The overall electrical tortuosity was then defined for a given sample as the mean value of the 9 numbers, being equal to 1.323 (B1), 1.063 (B2), and 1.001 (B3), for the three selected samples, respectively. These tortuosity values appropriately match with the visual information in Figure B1-B3. On the quantitative standpoint, the network with the lowest density is more than 30 % more tortuous than the two other specimens. This shows that this approach is very sensitive to characterize electrical differences.

Electrical stability and failure dynamics of AgNW networks at high voltage To ensure that AgNW networks can be efficiently integrated into functional devices, it is also mandatory to evaluate their electrical stability when subjected to large electrical bias. An electrical stress for a long duration could improve or degrade the conductive properties of the AgNW-based electrodes: the Joule heating effect on the network can indeed both favour the sintering of the junctions reducing the contact resistance (network optimization),12,28–30 and


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destabilize the morphology of the nanowires via spheroidization or electromigration (network degradation).11,31–33 In this study, the influence of electrical stress on the AgNW network integrity was investigated via a threefold approach combining electrical resistance measurements, 1P-mapping, and infrared (IR) thermography, revealing huge modifications of the electrically-active percolating clusters when the networks are close to voltage breakdown.

Voltage plateau experiments Time dependence measurements of the electrical resistance were performed using a Keithley source-meter-unit. A series of samples were investigated at various voltage plateaus. Interlaced with electrical resistance measurements, imaging of the electrical distribution between plateaus was carried out using the 1P-mapping set-up described hereinbefore. This procedure did not change the structure of the device under test. Figure 3 reports the corresponding results for an AgNW network associated with an initial resistance of 26 Ω. The sample was subjected to 10 min successive voltage plateaus at different levels: from 4 V up to electrical breakdown at 22 V (close-ups in the evolution of the electrical resistance during the plateau at 20 V and the 3 plateaus at 22 V are reported in Figure S5). Between each plateau, no bias was applied during few minutes so that the sample could cool down to ambient temperature. The evolution of the electrical resistance of the AgNW network during the successive voltage plateaus is reported in Figure 3A. When applying voltage, the elevation of the network temperature by Joule effect induces an increase in the network electrical resistance as a consequence of phonon-induced scattering.33–35 This increase in the electrical resistance with temperature can be modeled as follows:


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𝑅(𝑇0 + 𝛥𝑇) = 𝑅0 (𝑇0 )(1 + 𝛽𝑅 𝛥𝑇)

(2)

Where T0 is the room temperature, ΔT is the increase in temperature, and βR is the temperature coefficient of resistivity, which equals 3.8×10-3 K-1 for bulk silver.36 In the case of AgNW networks βR was measured to be around 2.2×10-3 K-1.37 According to Lagrange et al.,37 the difference between bulk silver and AgNW networks might arise from the presence of junctions between AgNWs which could behave differently, as well as defects such as grain boundaries or twins present in AgNWs. Thanks to several thermal loss mechanisms, thermal equilibrium is reached after a few seconds. According to Sorel et al.35 and Lagrange et al.,33 the energy balance of the system (substrate + AgNW networks), which combines the input power, the increase in temperature, and thermal losses, has the following analytical solution: T(t) ≈ 𝑇0 +

𝐼²𝑅 𝛼𝐴

[1 − exp (−

𝛼 𝑚𝐶/𝐴

𝑡)]

(3)

With t the time, T0 the room temperature, I²R the input power, C the heat capacity of the system, m the mass of the system, A the substrate area, and 𝛼 the heat transfer constant, which takes into account the parameters of heat losses by convection, radiation, and conduction. When the temperature has reached its steady-state value, the corresponding electrical resistance is also expected to remain constant (see Equation 2) until the voltage plateau has been completed. Any decrease or increase detected in the electrical resistance after reaching the theoretical steady-state should therefore be considered as the signature of either a non-reversible optimization or degradation process of the AgNW specimen.


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According to Figure 3A, for voltage plateaus up to 16 V, the steady-state resistance remains rather constant, which means that the network is not undergoing any optimization nor degradation mechanism. At least, no positive nor negative influence of the temperature can be detected during the 10 min plateau. From a morphological point of view, until 16 V, the elevation of the network temperature is not high enough neither to induce the sintering of the junctions nor to induce degradation of the nanowires by spheroidization or electromigration.

Figure 3. (A) Electrical resistance of an AgNW network deposited on a metallic support, measured while voltage plateaus of 10 min each are successively performed from 4 V, up to electrical breakdown at 22 V. The green dashed line indicates the evolution of network resistance after cooling at room temperature, i.e. when not influenced by Joule effect. (B) Zoom in the third 22 V plateau. (C) Intermediate 1P-maps of the sample between the voltage plateaus (left


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electrode is connected to ground while 1 V is applied to right electrode). The images show the electrical equipotential lines against the coordinates (X,Y) of the sample for the following step: (C1) reference, i.e. before any voltage plateau, (C2) after voltage plateau at 18 V, (C3) after voltage plateau at 22 V – 1st time, and (C4) after voltage plateau at 22 V – 3rd time. Note that 1Pmapping and voltage plateaus are not performed simultaneously but one after the other, and after having let the sample cool down to room temperature before any new electrical measurement. Also note that voltage plateaus can also always be manually stopped in case of an important and fast increase in the electrical resistance (at 22 V in the present case).

During the 18 V plateau, the steady-state resistance starts to slightly decrease, meaning that the sample is evolving towards a more optimized state. This can be interpreted as the Joule effectinduced sintering of the NW junctions. 12,33 As a consequence, the overall resistance of the network at room temperature (i.e. after cooling down the sample between two successive plateaus) is reduced too. This is well depicted by the shape of the green dashed line in Figure 3A, which fits the starting-point values of the electrical resistance in the early stage of each voltage plateau. Between 4 V and 16 V, the green dashed line is straight, meaning that the network is in a stable state, whereas from 16 V, the line starts falling down, meaning that the network is getting more electrically efficient. At 20 V, the resistance is not decreasing anymore, which means that the optimization process has been completed (see Figure 3A and Figure S5A). On the contrary, at 22 V the electrical resistance starts increasing slowly during 2 min (increase of around 1 Ω min -1, see Figure S5B). This can be viewed as the electrical signature of the early stages of a degradation process: the Joule effect-induced elevation of the network temperature starts getting so high that PlateauRayleigh instabilities are likely to appear, inducing the spheroidization of several junctions. Since the increase in resistance becomes much faster at the end of the 22 V voltage plateau (see Figure S5B), the plateau was stopped before completion so that intermediate 1P-mapping could


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be performed to assess the electrical distribution. The 22 V plateau was then repeated twice with early interruption in both cases to extract the electrical distribution. It resulted in an accelerated increase of the electrical resistance at each step (see Figure S5C-D). This sets the voltage limit or “breakdown” of this sample to 22 V. The degradation of the network is also noticeable by looking at the increasing trend of the green dashed line from the end of the 20 V voltage plateau. For the sake of reproducibility, the influence of increasing voltage plateaus on the AgNW network integrity was tested several times using the same protocol, and led to the same observations. Another example of voltage plateau experiment is provided in the Supporting Information (see Figure S6). The breakdown process takes place at 22 V. This value seems high as compared to that reported in the literature. For AgNW networks exhibiting similar initial resistance, voltage at breakdown were for instance reported to be around 8 V by Lagrange et al.33 However, in the latter case the AgNW networks were thermally insulated, to avoid conduction loss in the mechanical support. In the present study, the samples were placed on a metallic support, acting as a very efficient heat-sink, and thus reducing the temperature elevations. As a consequence, the electrical limitations of the sample were pushed to higher voltage. Generally speaking, the variability of the electrical and thermal performance and limitations associated to an AgNW network according to its close environment (substrate, support, pressure, etc.) should cautiously be taken into consideration when designing AgNW-based devices. Combining electrical resistance measurement with 1P-mapping is very helpful for analyzing and visualizing the mechanisms involved in the electrical breakdown of the samples. Figure 3C1 reports the “reference” 1P-map associated to the AgNW network in its initial state, i.e. before starting stressing the sample. The electrical distribution is quite homogeneous all over the


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sample. For samples exhibiting such a low electrical resistance (26 Ω in the present case), the voltage equipotential lines are indeed expected to be very straight (see Figure 2B3). The electrical map captured after the voltage plateau at 18 V, i.e. after the optimization step, was very similar to the reference map (see Figure 3C2). During the voltage plateau at 22 V, after detecting the fast increase in electrical resistance (at t ≈ 2 min, see Figure S5B), the voltage was immediately stopped in order to track the electrical distribution via 1P-mapping. It yielded the detection of a sharp discontinuity in the electrical potential and the creation of a so-called “electrical potential crack”, that was only partial at this stage of the experiment (see Figure 3C3). The same type of electrical mapping was performed after the third voltage plateau at 22 V. The latter was stopped in a very short time (t ≈ 5 s) due to the very fast increase in the network electrical resistance (R max = 136 Ω). The corresponding 1Pmapping exhibited a complete “electrical potential crack” along the entire height of the sample, in the extension of the previous partial crack (see Figure 3C4). The Joule effect induced elevation of the network temperature was so high in some locations that it yielded a correlated destruction of the network via the propagation of a crack perpendicular to the direction of the current flow. To our knowledge, this is the first visual evidence of the degradation dynamics of an AgNW network through a crack formation. Apart from the crack, the network mostly exhibits the same electrical potential as the corresponding electrode – 0 V (left part), 1 V (right part). This implies that the morphology of the nanowires has not been altered by electrical breakdown, apart from the vicinity of the crack. If some local degradation of the nanowires had occurred randomly, the measurement of the electrical potential would indeed have also varied in the corresponding areas.


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The consequences at the local scale of such a vertical crack through the network were inspected with a SEM (see Figure 4). The network areas located away from the crack look exactly the same as that of a pristine material (A1). This is in agreement with the constant electrical behavior observed in Figure 3C4. On the contrary, the microstructure of the area within the crack is clearly altered, the macroscopic variations in electrical behavior being caused by a large degradation of the AgNWs. One can easily identify at first glance the coexistence of totally (Figure 4A2) and partially spheroidized AgNWs (Figure 4B1). Other intermediate configurations are also distinguished in the crack. Figures 4B2 and 4B3 show for instance the presence of extremely thin metallic filaments joining adjacent fragments of what were originally continuous AgNWs. They present uneven surfaces, not achievable from synthesis. Such intermediate structures and local destructions might originate from the short duration of the electrical breakdown process. The very local degradation process evidenced with the electrical mapping induces a rapid change in the distribution of the local resistance and thereby the electrical current. The latter tends to redistribute into less resistive locations. Therefore, some of the spheroidization cannot be completed and several nanowires “freeze” in a very unstable morphology. This results in a singular structure, thermodynamically unfavorable, described as a partial spheroidization of AgNWs. Although this partial spheroidization phenomenon may seem odd, it is reproducible and certainly has a physical explanation. We propose that it first arises from spatial statistical fluctuations of the AgNW dimensions, network density, and current. Although the electrical distribution appears homogeneous at the centimeter scale when using the 1P-mapping technique, it seems reasonable to assume that local fluctuations occur in this discrete and random structure. From a kinetic point of view, the nanowires that belong to more critical locations are likely to spheroidize first. This


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phenomenon will lead to the local loss of part of the network through a percolation breakage mechanism. Because the macroscopic voltage is held constant during the experiment, the current flow (which is now smaller due to the increase in network resistance) has to be redistributed after the first hotspot had reached breakdown value and corresponding wires have evolved into spheres. The first neighbors of the degraded area will be the most affected, as a consequence of the constriction of current flow into them. Hence, the corresponding NWs are likely to reach the current-induced temperature limit as well. They get spheroidized too, and modify the current distribution of their neighbors, and so on. The strong positive feedback in this mechanism leads to the controlled creation and propagation of a crack along the equipotential lines, perpendicular to the direction of current flow. This mechanism is responsible for the propagation and total breakdown of the network. A schematic representation of the proposed mechanisms involved in the propagation of the crack is provided in Figure 5B.


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Figure 4. (A1-A2) SEM images of the sample (same one as in Figure 3) after electrical breakdown: far from the crack (A1), the AgNWs do not appear deteriorated, while close to the crack (A2), the AgNWs appear fully or partially spheroidized. (B1-B3) Additional SEM images captured along the area of the vertical crack. They show a combination of fully spheroidized nanowires (B1) – red circles, together with “partially” spheroidized nanowires (B2-B3) as well as the presence of small Ag filaments (yellow circles) much smaller than AgNWs themselves.

As already mentioned, Figure 3C4 suggests that the sample has totally “broken down”. The crack seems indeed almost completed. However, the final resistance measured seems surprisingly low with Rfinal = 136 Ω. This means that an electrical current is still able to flow throughout the network. It can be noticed that nearly all the current flow lines (perpendicular to the voltage equipotential lines) converge on the bottom part of the crack, meaning the huge majority of electrical power is distributed in the bottom part of the crack. More generally, there might exist other safe NW bridges across the crack where current can still flow. The latter are not detectable with 1P-mapping, probably because of the limitation in spatial resolution (1 mm).


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Voltage ramp experiments Complementary to voltage plateau experiments, the electrical behavior of AgNW networks when subjected to voltage ramp was also investigated. In that case, the electrical analyses were combined with in situ IR imaging of the sample under bias, using a FLIR A320G IR camera placed above the sample. IR imaging is classically used for assessing the spatial homogeneity of AgNW network-based transparent film heaters and has been often employed in literature.4,38–40 In the present section, we demonstrate that IR thermography can also be very helpful to describe the failure dynamics at rather high voltage. Figure 5A0 reports the evolution of the electrical resistance of a standard AgNW network (R initial = 72 Ω) when subjected to a voltage ramp of 0.5 V min-1 (the set-up for applying voltage was exactly the same as in the experiment associated with 1P-mapping). At the beginning, between “step 1” and “step 2” (see the corresponding pink squares in A0), a slow increase in resistance can be detected due to enhanced electron-phonon interaction as the input power increases (see Equation 2), followed by a sharp decrease in resistance close to step 2 (t ≈ 28 min, V = 15 V). As already mentioned, the latter decrease in resistance originates from the electrical sintering at higher voltage which results in a more intimate contact between adjacent NW (optimization of the junction resistance). On the contrary, from step 2 the resistance starts increasing again. This can be interpreted as the early stage of a degradation process. The switch at step 2 between the optimization and degradation phases is much clearer in linear scale, as depicted in Figure S7a which shows a zoom in the low resistance data presented in Figure 5A0. At higher voltage, from step 2 to step 4 (t = 45 min, V = 22 Ω), the resistance keeps increasing slowly, meaning that the


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degradation process is on-going (see also Figure S7b for a zoom). From step 4, the resistance starts diverging, leading to the electrical breakdown of the sample. A full movie of thermal emission during the entire voltage ramp was recorded with the IR camera. The entire movie along with the associated temperature color scale is available in the Supporting Information (M001). Figure 5A1-A5 only reports the thermal emission maps of the sample corresponding to “step i” (i=1-5), depicted in Figure 5A0. Similarly to the 1P-maps associated to AgNW networks of high electrical conductance (R ≈ 10-100 Ω), the recorded thermal maps at low voltage were found to be homogeneous (Figure 5A1). The integrity of the network thermal homogeneity was preserved until the end of the optimization phase (Figure 5A2), which is also in accordance with the integrity of 1P-maps until optimization, as depicted in Figure 3C1-C2. During the degradation phase, i.e. between step 2 and step 4, the heat distribution tends to narrow to a vertical central part of the network parallel to the contact electrodes (Figure 5A3). At step 4, the accelerated increase in resistance matches with the appearance of a “thermal” crack that is clearly detectable at the bottom in Figure 5A4. The crack started to propagate from the bottom border of the sample. Around 2 min after the starting point of breakdown, the crack was almost completed as shown in Figure 5A5. The propagation mechanism of the crack is related to the displacement of the local current stress peak, which keeps being constricted to the top extremity of the deteriorated area, leading to a runaway-like destruction phenomenon. A schematic representation of the mechanisms involved in the crack propagation is provided in Figure 5B. As observed in the many samples tested, it seems that the cracks often start and propagate from both the top (see Figure S8a) and bottom edges with the same probability due to the symmetry of the


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samples and the setup. Although some cracks started propagating from the central area of the sample (see Figure S8b), they seem more likely to originate from the edges of the samples. The breakdown phase lasted slightly more than 2 min while the preceding degradation phase lasted around 15 min. Here again, no hotspots were detected in the areas located outside the crack, in accordance with the 1P-map depicted in Figure 3C4, where no damage could be detected elsewhere than close to the crack. The narrowing of the thermal distribution during the degradation phase (A3) suggests that even before the final breakdown phase, most of the local deterioration of the nanowires take place in the central part of the sample. Moreover, the shape of thermal distribution during degradation presages the future shape of the crack after breakdown. For instance, the most narrowed area during the degradation (bottom of the network) corresponds to the starting point of the later crack. As a consequence, the creation of the crack might take place in two distinct and successive steps involving a slow “degradation” phase (≈ 15 min) at first, and a fast “breakdown” (≈ 2 min) at last. However, it can be noticed that some hotspots keep flickering inside the crack even during the final breakdown phase (see Figure 5A5 and movie M001). Therefore, some damaged areas might still be able to intermittently drive current. Such phenomenon is further explored in the last part of the present article.


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Figure 5. (A0) Evolution of the electrical resistance of an AgNW network when subjected to a voltage ramp of 0.5 V min-1. (A1-A5) Corresponding thermal maps captured in situ with an IR camera at specific times during the experiment depicted in A0: (A1), (A2), (A3), (A4), and (A5) correspond to pink squares in A0. The corresponding temperature color scale is provided with the associated movie (M001) in the Supporting Information (it ranges from 24 °C to 146 °C). (B) Schematic representation of the mechanisms involved in the crack propagation at failure (runaway-like propagation).

“Life” in the crack The detection of flickering areas in the crack depicted in Figure 5A5 combined with the relatively low value of the electrical resistance after breakdown measured for the sample depicted in Figure 3 imply that these samples are still electrically “alive” even after breakdown. This suggests that the vertical crack detected is not fully completed. There might exist AgNW bridges allowing electrical current to flow out. In order to get more information about the mechanisms taking place after this so-called “preliminary breakdown”, the sample depicted in Figure 3 – for which breakdown had occurred at 22 V – was subjected to additional post mortem


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voltage plateaus at 3 V, 8 V and finally 9 V. Here again, live visualization of the temperature distribution during the voltage plateaus was recorded thanks to the IR camera placed above the sample. The set-up for applying voltage was exactly the same as in previous experiments. At the end of the preliminary experiment depicted in Figure 3, the network resistance was 136 Ω (see Figure 3B). Figure 6 reports the evolution of the network electrical resistance measured during the additional voltage plateaus at 3 V (A0), 8 V (B0), and 9 V (B0). Several IR images captured during the plateaus and showing the thermal distribution at distinctive times are also provided in Figure 6A1-A5 (3 V), Figure 6B1-B2 (8 V), and Figure 6B3-B4 (9 V). Note that the corresponding IR full movies along with their associated temperature color scales are available in the Supporting Information under the names “M002”, “M003”, and “M004”, respectively. First of all, at 3 V, according to the IR images, most of the electrical current is flowing through the bottom part of the crack (A2-A5). This is coherent with the shape of the equipotential lines depicted in Figure 3C4, which converge toward the same area. Besides, since the applied voltage is not as high as before (3 V instead of 22 V), the measured electrical resistance of the sample is found generally stable (A0). It is not diverging anymore, meaning that the sample is not being damaged anymore. On the contrary, some significant and intermittent drops in resistance can be observed in the curve, for example at t = 12 s, t = 24 s, t = 29 s, and t = 45 s (A0). When trying to correlate these drops with the IR images, some small but clear hotspots can be detected (see arrows in A3 and A5). Such secondary hotspots may last either a very short time (A3) or several seconds (A5). The time sequences when these hotspots are visible in the IR camera fit exactly with the duration of the resistance drops depicted in A0.


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In order to bring a quantitative evidence for the correlation between this hotspot flickering effect and the drops in resistance measured in A0, the maximum temperature (in Kelvin) collected in the restricted areas of the hotspot detected at t = 12 s (S1) and the area of the hotspot detected at t = 45 s (S2) was plotted against time (see the dark S1 and light S2 red curves in Figure 6A0): the drop in resistance at t = 12 s fits exactly with a strong intensity peak in the S1 curve. Similarly, the drops in resistance detected between t = 45 s and t = 49 s fit perfectly with the higher intensity plateau detected in S2 during the same time-slot. To a lesser extent, this intensity plateau is also detected in S1. This is due to the fact that S1 and S2 hotspot areas are very close to each other, which induces interference in the collected intensity signals.


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Figure 6. (A0-B0) Evolution of the electrical resistance of the same AgNW network as in Figure 3, during additional voltage plateaus at 3 V (A0), 8 V (B0), and 9 V (B0), performed after preliminary electrical breakdown occurred (note that there are two different X axis in B0). (A1A5) IR images captured with the camera during voltage plateau at 3 V: (A1) just before voltage application, (A2) just after voltage was turned on, (A3) at t = 12 s, (A4) at t = 40 s, (A5) at t = 46 s. (B1-B2) same as (A1-A5) but with voltage application of 8 V and at different times. (B3-B4) same as (A1-A5) but with voltage application of 9 V and at different times. The corresponding temperature color scales are provided with the associated movies (M002, M003, and M004) in the Supporting Information.

The observation of flickering effects associated to secondary hotspots in the crack can be interpreted as follows: after preliminary breakdown, the crack area does contain wires that are


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not entirely spheroidized. The area at the bottom part in the IR images appears safe and therefore contributes as the preferential pathway to the current flow. In the present case at 3 V, the preferential safe bridge (at the bottom) does not turn off when secondary bridges get highlighted. Besides, once the secondary bridges turn off, the electrical resistance increases back to its initial value (A0). This implies that no deterioration of the preferential bridge has occurred yet. However, during the 8 V plateau, the electrical resistance increased very slightly (from 120 Ω to 162 Ω) until t = 12 s, and then increased dramatically (up to 1430 Ω) in a very short time (B0). The experiment was temporarily stopped at this stage. On the IR images, it can be seen that the preferential bridge at the bottom is getting hotter and hotter during the plateau at 8 V (B1-B2). The Joule-induced deterioration in this area might be responsible for the high increase in resistance at the end. It also has to be noted that at 8 V, several secondary bridges can be detected even in the early stage of voltage application (B1). Such bridges “woke up” at higher voltage (8 V) whereas they were inactive at lower voltage. At least, there were not detectable by the present IR set-up. Surprisingly at 9 V, the resistance starts decreasing back (from 714 Ω down to 334 Ω). In the corresponding IR images (B3-B4), the main hot spot at the bottom is not detectable anymore. Once again, some damage might have occurred in this preferential area, as revealed by the high increase of resistance detected at the end of the voltage plateau at 8 V (B0). On the contrary, in this case electrical current seems to be much more fairly distributed in many secondary bridges along the crack. As long as some more bridges “wake up”, more and more conductive paths are available for current, leading to a much more even current distribution, and therefore, to a decrease in electrical resistance.


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Such an unexpected failure behavior provides valuable information about how the electrical current is able to dynamically redistribute over AgNW networks during failure. The secondary hotspots detected first in A3 and A5 and later in B3 consist of NW cluster-based bridges, not preferentially used as conducting pathway by electrical current at the beginning, but likely to be chosen as secondary pathways once other preferential pathways are not available anymore. The reasons why such bridges are not continuously active, as well as the statistics and probability of activation, remain not yet fully understood and would require further experiments. Moreover, it still has to be determined whether these flickering effects (see M004) and secondary activation processes are intimately related only to the failure dynamics of AgNW networks at high voltage, or consist of a general AgNW electrical behavior taking place at any time in the network, but with enhanced detectability at failure.

Conclusions. In this work, we have reported an efficient electrical mapping technique for imaging current distribution in AgNW networks. 1P-mapping was found very relevant for extracting the voltage equipotential lines in networks under various bias. The tortuosity of the voltage equipotential lines associated to AgNW networks of increasing density could be estimated: the higher the network density, the lower the tortuosity, leading to a higher electrical homogeneity. It was also demonstrated that the NW deposition techniques used for fabricating AgNW networks can drastically influence the electrical distributions in the resulting electrodes. When combined with electrical resistance measurements, 1P-mapping was also found very helpful for highlighting electrically-induced instability mechanisms in “standard” AgNW networks (i.e. associated with an initial resistance of 10-100 Ω). When subjected to increasing


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voltage plateaus or voltage ramps, the electrical behavior of AgNW networks undergoes distinct phases comprising “optimization” (Joule effect-induced sintering of the junctions) at first, then “degradation” (Joule effect-induced morphological instabilities of some AgNWs), and finally “breakdown”. It was demonstrated experimentally that the latter breakdown stage involves the formation and propagation of a crack parallel to the contact electrodes. As a consequence, the failure dynamics in AgNW networks at high voltage does not rely on a “global” destruction of the network, as it is the case for thermal annealing at high temperature.41 On the contrary, the constriction of current flow to the extremities of an initial defect causes further defects in the adjacent locations of the initial defect, thus causing the propagation of a crack parallel to the bias electrodes. On the other hand, far from the crack, the NWs remain unchanged. Moreover, due to the fast propagation of the crack, some of the NW areas near the crack may not be fully destructed during breakdown (partial spheroidization), and therefore may act as secondary conductive bridges available for current flow. In future works, issues about electrical distribution and stability should also be considered after final encapsulation of AgNW networks, for instance, after deposition of an additional protecting thin layer. Beyond the study of thin films made of interconnected conductive entities, we believe that the imaging techniques and analysis presented here are suitable for characterizing efficiently the homogeneity and current distribution in any thin conductive film.

Materials and methods


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Silver nanowire synthesis. AgNWs were synthesized according to a previously published procedure.20 A 160 mL ethylene glycol (EG) solution of NaCl (10 mg) and PVP (3.54 g, Mw = 40 000 g mol−1) was vigorously stirred at 120 °C and then cooled down to room temperature. This solution was injected slowly using a syringe pump into 80 mL of a magnetically stirred EG solution of AgNO3 (1.36 g) at 120 °C. The injection rate was set to inject the entire solution in 8 min. At the end of the addition, the reaction mixture was further heated at 160 °C, refluxed for 80 min and cooled down to room temperature in ambient air. To remove the nanoparticles synthesized with the nanowires, a 48 h decantation procedure was used as detailed elsewhere.20 Finally, the AgNWs were dispersed in methanol. Electrode fabrication. The fabrication of electrodes was performed on Eagle XG™ glass substrates of alkaline earth boro-aluminosilicate type glass. Deposition was carried out by spincoating or spray-coating. In the case of spray-coating, the air-brush spraying was performed using a vertically mounted commercial airbrush (ExactaCoat Benchtop Ultrasonic Spraying System, from Sono-Tek Corp.). In a typical spray-coating experiment, the substrate was placed on a hot plate at 90 °C. The entire process was performed in air as previously described. Electrical mapping set-up. Electrical mapping of AgNW networks at the macroscale was performed using a one-probe (1P) electrical measurement set-up. A schematic representation of the set-up is provided in Figure 1a. The samples were placed on a 1 mm-thick metallic chuck. Silver paste-based contacts were manually deposited at two opposite sides of the specimen. In each case, left contact electrode was connected to ground, while electrical potential was applied to right electrode (typically 1 V in this study, i.e. 20 times lower than the critical voltage to initiate electrical instabilities). Voltage was applied by the mean of a Keithley 2602 sourcemeasure-unit (SMU). Note that voltage is not applied continuously, but only after the probe


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contacted the surface to prevent charging effect. In each single measurement, the duration of electrical supply is about 100 ms, which corresponds to a total time of electrical supply of 62.5 s for a 25  25 mm² sample (much lower than the 15 min of the entire mapping procedure). Under these circumstances, the 1P-mapping characterization is safe and does not alter the sample. The mapping probe was purchased from Harwin (ATE Spring Probe - P25-0423) and was springloaded to avoid mechanical deterioration of the samples. The spring force at “full travel” (i.e. when the probe is in deepest contact with the network), is 1.47 ± 0.29 N, which corresponds to an equivalent mass of 150 ± 30 g. The diameter of the spherical probe tip used in this study is 1.8 mm. The probe is moved by a customized computer numerical control (CNC) mill, driven by a LabVIEW software which: (i) sends G-code instructions to the system, and (ii) controls the SMU acquisition. Pictures of the electrical mapping set-up are provided in Figure S1. In total, 35 specimens have been investigated in this work, which we therefore consider as representative.

ASSOCIATED CONTENT Supporting Information (text) §1: Pictures of the electrical mapping set-up (Figure S1) §2: Spin coating versus spray-coating: deposition set-up and nanowire orientation (Figure S2-S3) §3: Calculation of the AgNW network areal mass density (Figure S4) §4: Evolution of the electrical behavior of AgNW network under electrical stress (Figure S5-S8) Supporting Information (video) “M001”: Movie showing the IR emission during the voltage ramp depicted in Figure 5


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“M002”: Movie showing the IR emission during the voltage plateau at 3 V depicted in Figure 6 “M003”: Movie showing the IR emission during the voltage plateau at 8 V depicted in Figure 6 “M004”: Movie showing the IR emission during the voltage plateau at 9 V depicted in Figure 6 The authors declare no competing financial interest.

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] *E-mail: [email protected] *E-mail: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

ACKNOWLEDGMENT The authors gratefully acknowledge financial support from the Univ. Savoie Mont Blanc with the AAP 2015 (CRACN project) to develop the 1P experimental facilities. This project was also supported by the French National Research Agency in the framework of the “Investissements d’avenir” program (ANR-15-IDEX-02) through the project Eco-SESA. This work was also performed within the framework of the Centre of Excellence of Multifunctional Architectured


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Materials "CEMAM" n° AN-10-LABX-44-01. David Muñoz-Rojas acknowledges funding through the Marie Curie Actions (FP7/2007-2013, Grant Agreement No. 631111).

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Electrical Mapping of Silver Nanowire Networks: a Versatile Tool for

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