Scripta Materialia 161 (2019) 70–73

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Effect of varying the density of Ag nanowire networks on their reliabilityduring bending fatigue

Minkyu Park a, Wonsik Kim a, Byungil Hwang c,⁎, Seung Min Han a,b,⁎a Department of Material Science and Engineering, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yousung-gu, Daejeon 34141, Republic of Koreab Graduate School of EEWS, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yousung-gu, Daejeon 34141, Republic of Koreac School of Integrative Engineering, Chung-Ang University, Seoul 06974, Republic of Korea

⁎ Corresponding authors.E-mail addresses: bihwang@cau.ac.kr (B. Hwang), smh

https://doi.org/10.1016/j.scriptamat.2018.10.0171359-6462/© 2018 Acta Materialia Inc. Published by Elsev

a b s t r a c t

a r t i c l e i n f o

Article history:Received 5 July 2018Received in revised form 12 October 2018Accepted 12 October 2018Available online 22 October 2018

The effect of varying the density of Ag nanowire networks on their reliabilitywas explored during cyclic bending.The reliability of the Ag nanowire networkwas degraded as the density of nanowires decreased, which is in con-trast to E-beam evaporated dense Cu thin films that showed enhanced reliability for thinner films. The cause forsuch a reverse trend is explained by a percolationmechanism considering that the failure in the Ag nanowire net-work occurs locally at the junctions that are randomly distributed as opposed to fatigue-induced channel crackformation in a Cu thin film.

© 2018 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords:Cyclic bendingReliabilitySilver nanowireNetwork structureWearable device

With increasing demand in flexible devices, it is critical to ensure re-liability of all components under cyclic loading. Traditional electrodematerials made from metal thin films has limited flexibility that limitsits use in flexible devices. In order to overcome the shortcomings of con-ventional electrodes to be applied in flexible devices, several solutionshave been reported. Among those, silver nanowire (AgNW) networksare promising candidates due to their excellent electrical performancewhile also being mechanically robust under cyclic bending [1,2]. Flexi-bility and stretchability of conventional metal thin film electrodes canbe achieved bymodifying their structure into serpentine, wavy, orwrin-kled patterns. However, such modifications require lithography or pat-terning techniques which induce high cost and inconveniences [3–7].Use of spray-, drop- or dip-coated AgNW in the form of a network hasalso demonstrated tomaintain its electrical conductivity at large strainsthat can thus replace the conventional electrodes for flexible electrodesat a significantly lower processing cost [8–11]. AgNWnetworks showedexcellentmechanical reliability in comparison tometal thin films due totwo factors: 1) network geometry that can endure larger strain withoutinducing large deformations on the individual nanowires and 2) highstrength of the metal nanowires as each wire does not accumulate dis-locations duringdeformation [12–14] thusmaking it an excellent choicefor flexible electrodes.

Although extensive studies to improve the electrical and mechanicalperformance of AgNWnetworks are undergoing, analysis of the reliability

an01@kaist.ac.kr (S.M. Han).

ier Ltd. All rights reserved.

with the focus onfinding themechanism for resistance increase under cy-clic bending is still needed. In this work, we report that failure in AgNWnetworks occur at junctions (hence point-type local failure) while fatiguefailure in metal thin films results in channel cracks, and this difference infailure mode can result in a density or thickness dependence of the reli-ability. Bending fatigue behavior of AgNW networks of different networkdensities was therefore analyzed and compared to that of Cu thin filmelectrodes. Although all comparisons are made to Cu thin films, analysiswith respect to Ag thin films can be found in Fig. S1.

AgNW network films as well as Cu blanket thin films were all sub-jected to cyclic bending at 2% tensile strain up to 200,000 cycles whilemonitoring the resistance in-situ, where the increase in fractional resis-tance is given by ΔR/R0 = (R − R0)/ R0. Experimental details can befound in the Supplementary material. As shown in Fig. 1, AgNW net-works exhibit a rapid increase in ΔR/R0 in the initial stages, but therate of increase decreases with increasing bending cycles resulting intotal ΔR/R0 of ~2 at 200,000 cycles. On the other hand, a 300 nm thickCu thin film shows a much faster increase in ΔR/R0 that results in ΔR/R0 N 100 after 200,000 cycles. Superior ability of AgNW network inmaintaining its conductance compared to that of metal thin films is inagreement with previous reports due to its network geometry andhigh strength of the nanowires [8–10,12–16].

Fracture morphology of Cu metal thin films and AgNW networksafter cycling are shown in Fig. 1c. Almost all cracks in the Cu film arealigned perpendicular to the bending direction and protrusions at thetop surface can be observed. It is well known that fatigue causes disloca-tion pile-ups at the film/substrate interface, which then can result in

Cycles (n) Cycles (n)

Fig. 1. Comparison of normalized fractional resistance change for different thicknesses of (a) Cu thin films and varied densities of (b) silver nanowire networks. (c) SEM images of Cu thinfilms and silver nanowire networks after 200,000 cycles of bending with 2% tensile bending stress. Cracks generated in Cu thin films are perpendicular to the bending direction, however,failure occur at junctions between nanowires in silver nanowire networks.

71M. Park et al. / Scripta Materialia 161 (2019) 70–73

protrusions and crack formation, leading to an increase in ΔR/R0

[17–20]. On the other hand, failure generated in a AgNW networkmostly occur at junctions between two individual nanowires as shownin Fig. 1c. It is expected that the induced stresses are concentrated ator near the junctions to cause localized failure. Thus, metal thin filmshave line cracks that run perpendicular to the bending direction,whereas non-directional point-type disconnections occur in theAgNW networks at junctions. We show below that this difference infailure mode results in opposite trend in thickness dependent reliabilityof AgNW networks and Cu thin film electrodes.

The effect of varying the thickness of the electrode was explored bypreparing Cu thin films with thicknesses of 100, 200 and 300 nm andAgNW networks with different densities, which essentially representdifferent thickness of AgNW stacks. Because cross-sectional surfaceand thickness of AgNW networks cannot be determined directly, sheetresistance is used for presenting the densities of the AgNW networks.AgNWswith different sheet resistance of 3.32 to 61.2Ω/sq, and thus dif-ferent wire densities were chosen for comparison. The ΔR/R0 of the100 nmthick Cu thinfilm after 200,000 cycleswas 9.7, butΔR/R0 greatlyincreased to 102.6 for the 300nm thick Cu film as shown in Fig. 1a. Thus,thinner Cu thin films show better reliability with smaller ΔR/R0, whichis consistent with other literature on bending fatigue studies of metalthin films [21]. As themetal film gets thinner, heavier constraint on dis-locationmotion make them stronger, and thus protrusions that form asa result of dislocation pile-up and subsequent crack formation are re-duced. For the case of AgNWnetworks with different thicknesses, how-ever, an opposite trend was observed where an increase in the densityand hence the thickness resulted in smaller ΔR/R0 as shown in Fig. 1b.ΔR/R0 for a high density AgNW network (R0 = 3.32 Ω/sq) was 0.38,whereas a relatively low density AgNW network (R0 = 61.2 Ω/sq)showed ΔR/R0 of 1.54 at the end of 200,000 bending cycles. This inter-esting behavior of enhanced reliability in denser AgNW network indi-cates that its bending fatigue mechanisms differ from those of metalthin films.

Themechanism for the increase in resistance of metal thin films dueto fatigue failure is largely determined by how cracks are initiated andpropagated. In conventional metal thin films, small cracks form andpropagate in the direction perpendicular to the applied bending strainto relax the applied bending strain and finally form line cracks. Hinder-ing the crack propagation can be an effective strategy in enhancing thereliability, and Kim at el. has nicely shown that an array of nanoholes in-troduced to Cu thin films can blunt the crack propagation and therebyenhance the overall reliability [22]. One can then think about the ex-treme case of having large holeswith thinwalls, whichwould be similarto a network of nanowires, and crack propagation is expected to bemore confined. Thus, cracks that are formed at the junctions of thenanowire network will be localized to that junction and propagationof the cracks in thedirection perpendicular to the applied bending strainwould be difficult. Thus, this point-type failure in a network is expectedto have the reversed trendof reduced reliability for thinner or less densenetworks as the total number of junctions decreases.

The enhanced reliability in high density AgNWnetworks can also beexplained by considering an electrical percolation behavior of the net-work. For simplicity, nanowire arrays of different densities are modeledas grids of different size, and all failures are limited to occur only at junc-tions with probability of each junction failure being equal. The AgNWnetwork is thus represented as a film consisting of n x n unit squareswhose unit length corresponds to the distance between neighboringjunctions. In this calculation, we assumed that the squares connectedin series along the resistancemeasurement direction (x), and in parallelalong the transverse direction (y) (Fig. 2a and Fig. S3). Eachfilled squarehas resistance of 2 Ω, and each vacant squire has 10,000 Ω. For a n x nsystem, completely filled squares result in a total resistance of n*R foreach serial line that are in turn connected in parallel to result in a totalresistance of n/nR = R of 2 Ω as shown in Fig. S3. For the case of acompletely filled square array, changing n will not result in a variationof the total resistance. However, for a finite fraction of vacancies, thetotal resistance will depend on the size of the n x n array or the density

Fig. 2. (a) High and low density of AgNWnetworks modeled as a simple grid with 1/8 ratio of junction failures. Red squares denote junction failures in the silver nanowire network. Blueand white unit squares represent conducting segment and vacancies in a further simplified grid structure. (b) Calculated resistance change of simplified silver nanowire networks as afunction of vacancy fraction. The parameter n represents the number of unit squares in a line; thus, higher n value can be considered as higher density of the silver nanowire network.Schematic illustrations for representing the importance of the same fraction of junction failures in (c) a low density silver nanowire network and (d-f) for high density silver nanowirenetworks.

72 M. Park et al. / Scripta Materialia 161 (2019) 70–73

of the network. For a fixed fraction of vacancies (vacant area / total areaof n × n array), the calculation of the resistance for the casewith smallern or less dense network yields much higher values than for larger n ordenser network (Fig. 2b). This therefore implies that the same numberof junction failures increases the resistance of a low density AgNW net-work more significantly than that of a high density AgNW network.

This percolation behavior can be explained qualitatively as follows.Four examples of partially damaged AgNW networks with same ratioof failed junctions are shown in Fig. 2(c–f). For lower density AgNWnet-work (Fig. 2c), fewer junctions are present so that a single junction fail-ure can act as a critical bottleneck for current flow and thus can causesignificant resistance increase because there are less alternative electri-cal pathways left. However, for higher density AgNWnetwork (Fig. 2d),there are still many undamaged electrical pathways left even for thesame fraction of damaged junctions. As a result, it can be said that thedenser AgNWnetwork can exhibit higher electrical reliability under cy-clic bending even when the same ratio of junction failures is present.This behavior does not apply to Cu films because cracks are propagatedwithin the complete cross-section of the films for all film thicknesses, incontrast to the point–type local failure found in AgNW networks.

In addition, numerical calculations are correlated with the experi-mental observations to further support the percolation behavior thatis responsible for the density dependent reliability of the AgNW net-works. In order to work with a system that closely resembles the actualAgNWnetwork density, the average number of junctionswas estimatedfrom SEM images of AgNW networks with high and low densities. Highand low density AgNWnetwork specimens used in this study has initial

20 22 24 26 28 30

0.0

0.1

0.2

0.3

0.4

0.5

R-R

0/R

0

Vacancy fraction (%)

Rs =3.32 ohm , n = 18344

(a)

Fig. 3. Relationship between the fractional resistance increase and vacancy fraction in the

sheet resistances of 3.32 Ω/sq and 61.2 Ω/sq, respectively, that corre-sponds to n values of 18,344 and 4255, respectively. For each system,the expected vacancy fraction is calculated for varying fractional resis-tance change as shown in Fig. 3. The fraction of vacancies that corre-sponds to a given fractional resistance change is then extrapolatedfrom the plots in Fig. 3. After 200,000 bending cycles, the high densityAgNW network with R0 = 3.32 Ω/sq shows a ΔR/R0 of 0.38 which cor-responds to a fractional vacancy fraction of 27.7% while the low densityAgNW network with R0 = 61.2 Ω/sq showed a ΔR/R0 of 1.53 corre-sponding to a fractional vacancy fraction of 60.8%. Thus, the total num-bers of vacancies in the low and high density AgNW networks after200,000 cycles are calculated as 11.0 × 106, and 93.2 × 106, respectively.Although the total number of vacancies was smaller in the low densityAgNW network compared to that of high density AgNW network, theincrease in fractional resistance in the low density AgNW network ishigher than for the high density AgNW network due to the relativelylarge fraction of vacancies in the low density AgNW network, which isconsistent with the percolation behavior.

In order to further confirm that the electrical percolation behavior isresponsible for the difference in reliability of high and low densityAgNW networks, AgNW networks with the same density and thus thesame sheet resistance but with different sample dimensions (0.2, 0.5,1, 4 mm width) were tested and compared in Fig. 4a. It is shown thatAgNW networks with narrower widths show more rapid increases inresistance during cyclic bending, however, patterned Cu thin filmswith varying line width (Fig. 4b) show no clear trend with only mar-ginal differences. These results again support the mechanism outlined

54 56 58 60 62 64 66

0.0

0.4

0.8

1.2

1.6

2.0

R-R

0/R

0

Vacancy fraction (%)

Rs =61.2 ohm , n = 4255

(b)

AgNW networks with different sheet resistance of (a) 3.32 Ω/sq, and (b) 61.2Ω/sq.

Cycles (n) Cycles (n) Cycles (n)

VerticalLateral

Fig. 4. Resistance change of (a) same density and resistance (40 Ω/sq) of silver nanowire networks with different widths and (b) 100 nm thick Cu thin films with different widths.(c) Different response of Cu thin films and silver nanowire networks in terms of directional resistance variations after cyclic bending. Resistances were measured at the ends of thelength of electrodes, where the directions of resistance measurement and bending were perpendicular for the lateral pattern (left) and parallel for the vertical pattern (right).

73M. Park et al. / Scripta Materialia 161 (2019) 70–73

above since larger width sample has more electrical pathway than nar-row strips, and more conduction pathways results in enhanced reliabil-ity of the network due to the percolation behavior.

Another critical difference betweenAgNWnetworks and continuousCu thin films is that fatigue damage in AgNW networks would result inan isotropic resistance increase whereas in Cu thin films it yields ahighly anisotropic resistance change as shown in Fig. 4c. Point-type fail-ures in AgNW network mostly occur with random distribution andhence no directionality in resistance is expected. However, line cracksin Cu films will form perpendicular to the applied bending strain direc-tion to relax the tensile stresses and hence a strong anisotropy in resis-tance change is expected. For the case of Cu thin films, ΔR/R0 measuredin the direction parallel to the bending direction is 8.7 times higher thanΔR/R0measured in the direction perpendicular to the bending direction.Such difference in directionality of resistance change between AgNWnetworks and Cu films should thus be considered in designing elec-trodes for flexible devices with a given bending direction and currentpath.

In summary, it is revealed that the degree of degradation of the elec-trical resistance in AgNWnetworks can be suppressed by increasing thedensity of AgNW, which also show an opposite trend compared to Cuthin film electrodes which show more fatigue damage with increasingfilm thickness. This opposite behavior can be explained by assumingthat point-type failures distributed randomly are found in a nanowirenetwork while line cracks that propagate perpendicular to the strainingdirection are generated in Cu thin films. Numerical calculations of a gridwith vacancies that model point failures in a network revealed that forthe same areal fraction of vacancies, high density AgNW networks re-tain more alternative electrical pathways in comparison to low densityAgNW networks. Furthermore, this electrical percolation behavior ofthe AgNWnetwork is shown to be responsible for a sample size depen-dencewhere narrower strips aremore prone to rapid increase inΔR/R0.The outcomes of this study on the effect of varying the density or thick-ness of AgNWnetworks is expected to be useful in designingmore reli-able electrodes for flexible devices.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

S.M.H.would like to acknowledge the financial support from theNa-tional Research Foundation of Korea (NRF) grant funded by the Korea

government (MSIP) (No. NRF-2016R1A2B3011473), the R&D Conver-gence Program of the MSIP (Ministry of Science, ICT and Future Plan-ning) and National Research Foundation of Korea (NRF) grant fundedby the Korea government (No. NRF-2014R1A4A1003712). B. H. wouldlike to acknowledge the financial support from the National ResearchFoundation of Korea (NRF), which is funded by the MSIP (No. NRF-2018R1C1B5043900).

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.scriptamat.2018.10.017.

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