Facile Fabrication of Ultra-Stretchable Metallic Nanocluster Films for

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Facile Fabrication of Ultra-Stretchable Metallic Nano-cluster Films for Wearable Electronics Vijay Venugopalan, Robin Lamboll, Darshana Joshi, and Kavassery Sureswaran Narayan ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b06834 • Publication Date (Web): 13 Jul 2017 Downloaded from http://pubs.acs.org on July 14, 2017

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ACS Applied Materials & Interfaces

Facile Fabrication of Ultra-Stretchable Metallic Nano-cluster Films for Wearable Electronics Vijay Venugopalan*1, 2, Robin Lamboll 3, Darshana Joshi 3, K.S.Narayan 1

1: Molecular Electronics Laboratory, Chemistry and Physics of Materials Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore-560064, India.

2: Department of Physics, Politecnico Di Milano, Piazza Leonardo Da Vinci, Milano, Italy 20133

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Email : [email protected] 3. Cavendish Laboratory, University of Cambridge, 19 JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdon

Keywords: Stretchable conductors; gold nano-clusters; flash deposition; wearable electronics; stretchable heaters


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ABSTRACT: With recent progress in flexible electronics, developing facile one-step techniques for fabricating stretchable conductors and interconnects remain essential. It is also desirable for these processes to have small number of processing steps, incorporate micro-patterning and be capable of being effortlessly implemented for manufacturing of wearable logic circuits. A low vacuum flash evaporation of Au nano-clusters is proposed as a facile method to fabricate highly stretchable conductors capable of fulfilling all such requirements. High metal-elastomer adhesion on textured substrates ensures low surface resistances (100% strain ~ 25 Ω-sq-1) where thin film Au accommodate strain like a ‘bellow’. Stretchability for conductors deposited on non pre-stretched textured substrates up to 150% and smooth PDMS substrates up to 200% are shown. The system is modelled on a microscopic system calculating 2-D current continuity equations. Devising low cost techniques for fabricating stretchable conductors remains essential and in that direction stretchable circuits, heating elements have been demonstrated.



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1. Introduction: The emergence of stretchable electronics has considerably expanded the scope of large area electronics by providing the capability to inundate sensors, actuators and other electronic components on movable and deformable surfaces which was previously unreachable by conventional electronics. This has led to innovative solutions in flexible lighting1, display2, smart electronic skins3-6, futuristic robots 6-8, energy devices9, 10, bio-interfaced prosthetic devices11-13 for neuro-stimulation and other such applications. To achieve an useful range of stretchability, metallic films14-16, CNT’s5, 17, graphene18; conducting polymers19; composites20, 21; metal nano-structures2225

have been employed. Translating these solutions into manufacturing of highly conducting and

stretchable components however needs further addressing. Composites of a variety of metallic nano-structures and nano-wires with elastomers have proven to be an effective method to obtain very high stretchability for conductors5,

17, 20, 21

. Another approach widely employed involves

depositing a variety of conductors on pre-stretched elastomers, which upon relaxation may give rise to self-similar serpentine or wavy structures wherein very little strain is experienced by the conductors upon deformation25-27. However all of these techniques often involve multiple step chemical processes and require added steps of wet-lithography for fabricating interconnects and logic circuits22, 25 which provide hindrances for large throughput fabrication. Alternatively, a significant focus of research has been on the direct metallisation of elastomers for stretchability due to its simplistic nature for fabrication14-16,

24, 28-30

. While metallic films

withstand maximum strains of only 2~5%, metallised elastomers can withstand much higher level ( > 50 %) of strain16. Strides were made into the metallisation of elastomers for stretchable electronics using e-beam deposition14 and sputtering 16. The resultant conductors are susceptible to delamination of the metallic films from the elastomer, limiting the maximum strain they can be 4 ACS Paragon Plus Environment

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stretched up to. To overcome these limitations alternate solutions included incorporating adhesion layers16, deposition on pre-stretched substrates and using out-of-plane geometries26 amongst others, which enhance the performance significantly. However limitations in terms of maximum strain, strain direction, as well as scalability and ease of integration into industrial fabrication processes are yet to be solved by a single method. A step forward for achieving higher performances was realized through metal implantation, which provides much better adhesion, makes it possible to stretch the conductors to higher strains and also enables cyclic loading at higher peak strains15, 24. These processes, however involve high vacuum conditions (10-5 mbar), requiring lengthy processing time-frames and intensive fabrication setups making it challenging to integrate them into production lines or a micro-fabrication process. Here we improvise to achieve similar figures of merit (small changes is sheet resistivity with strain, higher peak strain for cyclic strain), but with considerably simpler fabrication procedures and in the process making this approach scalable and readily available. In this report, we demonstrate that a flash deposition of gold (typically ~ 3-4 seconds) in a typical coil-based resistive thermal evaporator, produce highly stretchable metallised elastomers at low vacuum (0.5×10-2 mbar) conditions. The Coil Flash Thermal Evaporation (CFTE) method is known to produce Au nano-clusters with low ionisation and kinetic energies, which minimizes carbonization of elastomers during deposition31,

32

. A large fraction of clusters are charged,

enhancing the film growth to form robust metallic films31. The metallic films obtained are capable of withstanding 150% strain on textured substrates and up to 200% strain on PDMS. We deposit these nano-clusters on a porous and textured surface and achieve enhanced intercalation and a higher metal-substrate adhesion. Au films on the textured substrates have higher figures of merit than smooth PDMS substrates and show small drift in resistivity with strain. They remain robust after straining cyclically at 50% peak strain and show a small increase in resistance at 70% peak 5 ACS Paragon Plus Environment


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strain which is better than standard e-beam and sputtered samples14, 16, 29. Further, they also better ion-implanted samples in terms of initial conductivity and maximum cyclic strain15,

24

. It is

important to note that we obtain these performances without the requirement of adhesion layers unlike in the case of e-beam deposition as observed by Lacour et.al14, 26, 33. Moreover the simplicity of this one-step approach makes it cost-effective (~0.1 US$/Sample for 1cm2 stretchable heating element) and readily available for large scale throughput fabrication of patterned stretchable electrodes and interconnects. We find that the Au films stretch and relax like a 2-D ‘bellow’ resulting in high stretchability and robustness to cyclic strains. We utilize a 2-D microscopic model to map the stretched conducting films. Finally we demonstrate the utility of these metallized structures on textured substrates for twistable/stretchable LED circuits and stretchable heating elements.

2. Experimental Methods: CFTE-Deposition Setup: The setup for deposition is a standard deposition chamber (Hind High Vacuum-Lab Coater) with thermal resistance sources used for evaporation of metals. For the CFTE a tightly clamped coil of length: 16 mm, pitch: 2 mm and width: 7.5 mm is utilized. Plated Au of 70 mg is used for evaporation. The current is initially slowly increased to let the plated Au melt and completely wet the coil. Thereafter a flash deposition is carried out where large current is passed for 3-4 seconds where the CFTE deposition takes place. For all depositions the coilelastomer distance was carefully maintained at a distance of 60mm. For measuring the corresponding film thicknesses, the deposition of Au is also made on glass substrates placed along with the elastomers. The thickness are then measured using a standard DekTak Profilometer. In order to measure the size of the nanoclusters, lower quantities of Au needs to be evaporated so that 6 ACS Paragon Plus Environment

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the size of the clusters can be measured before the process of film formation begins. For this purpose 5-10 mg of Au was evaporated. This was evaporated directly onto a Cu coated TEM grid which was placed in the sample chamber at the same distance of 60mm. Sample Preparation: Sylgard 184 Silicone Elastomer was mixed with its curing agent, 7.5% by weight to make PDMS elastomers. The mixture was then drop-casted and heated at 60 ºC overnight to obtain films ~300 micrometers thick. The nitrile fabrics were directly used as obtained from KC500 powder free exam gloves, with a thickness of ~ 200 micrometers. The metal films on the substrate for resistivity measurements are 1-3 mm in width and a few centimeters in length. The distance between the contacts for measurements were always kept at 10-15 mm for break tests and 5 mm for the cycles test. For the R⊥ measurements where the changes in conductivity are measured perpendicular to the strain, the width of the metallic films are increased to 6-10 mm keeping the length same. The distance between the measuring contacts are at least 4-5 mm in the R⊥ measurements. Measurements and Contacts: An eutectic alloy (49% Bi, 21% In, 18% Pb and 12% Sn) with a low M.P. of 58 ºC is used as conformable contacts for surface resistivity measurements. The contacts are liquefied during stretching and are allowed to cool and solidify, in conformity with the sample topography for accurate measurements (~0.5cm2 or lower contact area). Sheet resistances are measured by 4-probe and 2-probe methods using a HP34401 Multimeter. However most measurements are performed in the 2-probe configuration since no differences are observed between 4-probe and 2-probe measurements. A homebuilt uni-axial stretcher with a precision to stretch up to 1 µm (accuracy of 1500 K (< 3700K, M.P. of Tungsten) at low vacuum at current of 25 A for a short duration (< 5 seconds) through the coil. The


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Figure 1 – (a) Schematics showing the formation of low energy Au nano-clusters incident on stretchable elastomers. (b) TEM image of the deposited nano-clusters during the early stages of cluster coalescence. The green arrows show some of the deposited nano-clusters having a grainy morphology on a background of coalesced clusters. Scale bar-20nm (c) The size distribution of the metal nano-clusters is shown along with a Normal fit (average cluster size ~3.7nm). (d) Shows the setup with eutectic liquid alloy contacts used for measurements. The discontinuity regions and the method to map them is shown. (e) Shows the change in resistance R(x) along the sample length for 25% and 70% strained samples emphasizing the discontinuity effect. Axes: (25% Bottom-Left & 70%- Top-Right) flash 9 ACS Paragon Plus Environment


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deposition creates nano-clusters of metal particles that strike the non-stretched elastomers placed at a distance of 60 mm from the coil (Figure 1(a)). A large fraction of the created nano-clusters are positively charged and grow through electrostatic interactions in the gas phase31 until they impinge on the elastomer. Upon rapid deposition, the clusters follow a standard growth mechanism to form highly conductive films (3×10-5 Ω-cm)34. Figure 1(b) shows a TEM image of the nano-clusters during the early stages of film formation.

The clusters are predominantly ~ 2-5 nm in dimensions

with a few clusters 6-8 nm in size. The average size of the clusters is 3.7nm as calculated from the normal distribution in Figure 1(c). The clusters seen as small dark spots in the TEM (indicated by the arrows) are set against a background of already deposited and coalesced clusters which have formed larger (15-30 nm) grains. Experimental conditions were varied from standard deposition to observe pristine clusters before film formation (See Experimental). The sizes of the clusters are a function of the coil-elastomer distance due to the electrostatic interactions of the clusters in the gas phase31. Shorter distances can possibly deliver smaller nanoclusters with higher energies. However in our experiments we observe carbonization of the elastomers from the flash deposition at shorter coil-elastomer distances. In our earlier work19 we have observed that the choice of substrates is critical for the fabrication of deformable and stretchable conductors. PDMS and textured nitrile rubber are used as smooth and porous surfaces for this purpose. PDMS is chosen as an archetypical substrate. We envision that a more textured elastomer (Figure S1) would greatly enhance the interaction between the substrate and the impinging Au-nanoclusters, thereby greatly improving the adhesion of resultant metallic films. Various adhesion tests show that the adhesion of Au in the CFTE method is superior compared to the standard physical vapour deposition (PVD) of Cr-Au films on PDMS [Table 1]. Under water/ethanol sonication and a scotch tape test standard PVD on PDMS fabricated Au films show a complete or sizeable loss in conductivity, whereas the CFTE films on PDMS are much less 10 ACS Paragon Plus Environment

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Sample Treatment PDMS Cr-Au PVD

Textured Rubber Au PVD

PDMS Au CFTE

Textured Rubber Au CFTE

Water Sonication 10 minutes

98 Ω/□

78 Ω/□

82 Ω/□

4.8 Ω/□

Alcohol Sonication 10 minutes

∞

570 Ω/□

47.18 Ω/□

17.8 Ω/□

Scotch Tape Pressed

∞

kΩ/□ - ∞

4200–Mega Ω/□

9.58 Ω/□

Table 1- Shows the effect of sonication in water and alcohol for ten minutes and a scotch tape test on different electrodes (relaxed). Cr (10nm) - Au (100nm) films are the least robust while adhesion of CFTE Au on textured rubber is the strongest. The increase in sheet resistivity upon a scotch tape test for the CFTE method on textured rubber is due to the partial tearing of the substrate upon the removal of the tape. The sheet resistance for the pristine films are ~ 4-8 Ω/⃞ for each case.

affected. Further CFTE films on textured surfaces perform better and remain impregnable against a scotch-tape test and sonication for 10 minutes in H2O and ethanol. The rubber’s textured surface with corrugations and depressions results in a higher nanocluster-substrate interaction. This in turn enhances the metal-elastomer adhesion and assists the formation of a more robust composite compared to a smooth PDMS surface. The possibility of implantation of CFTE clusters into the substrates remains to be ascertained but in any case it is expected to be lower than ion implanted conductors, due to the lower energies of the impingent nano-clusters here31, 32, 34. We note here that 11 ACS Paragon Plus Environment


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the adhesion of metallic films on elastomers is a critical parameter to achieve high deformability and stretchability19. We now proceed with testing the stretchability of the CFTE conductors using a home built uniaxial stretcher. We observe that the nature of electronic probe contacts and their position are critical in determining the changing resistivity of the conductor with strain (Figure 1(d)). In our earlier work with straining polymeric conductors19 we demonstrated that providing non-invasive contacts to the stretchable conductor is decisive for recording the true change in resistivity with strain. We make similar observations here. For instance, metallic films on textured nitrile rubbers maintain high-conductivity up to 150% strain when the electronic contacts for measurements are placed on the strained section of the sample. However, if the measuring contacts are placed at the unstrained and clamped section of the sample conductivity is maintained only up to 72-75% strain (Figure 1(e)). To investigate the discrepancy, we measure the variation of resistance R(x) with x, the distance taken from the stationary probe-contact placed on one of the clamps (Figure 1(d)). The other probe-contact for measurement is then displaced along the conductor starting from the clamped unstrained section towards the strained portion of the conductor Figure (1d) (See methods). Figure 1(e) shows R(x) for two different samples (strained up to 25% and 70% strain); measured from one end of the sample along the length. A large discontinuity in resistivity at the interface between the clamped and stretched sections of the conductor is observed. This discontinuity extends up to a few percent of the way into the strained section of the sample, while the magnitude of the discontinuity itself increases with increasing strain. At 70% strain, the resistance of the discontinuous region is several orders of magnitude higher than that of the stretched sample resistance. Larger cracks and voids in the metallic film are clearly visible at the interface in scanning electron microscopy (SEM) images (Supplementary Figure S2). We attribute the origin of this discontinuity to a small degree of non-planarity in straining and also the boundary 12 ACS Paragon Plus Environment

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conditions present between the strained and unstrained sections of the metal. This observation provides a useful solution for improving the design of stretchable circuits wherein individual rigid devices are connected to stretchable inter-connects away from the stretched-rigid interface thereby circumventing the problem of boundaries. Changes in sheet resistivity shown thereafter are of the strained sections unless specified. We utilize a low-melting alloy as contacts35, 36 and place them within the strained portion of the conductor to measure the true values of sheet resistance. Surface resistance as a function of strain is shown in Figure 2(a, b). Sheet resistivity is measured on metal strips 1-3 mm in width while the measuring alloy contacts are placed away from the clamped edges (distance between measuring contacts ~ 10-15 mm). Metal-substrate adhesion is critical for achieving higher stretchability by providing strain delocalization. Hence, the performance of CFTE-conductors fabricated on textured rubber is significantly better than those fabricated on smooth PDMS (Figure 2a). Conductors on textured rubbers exhibit a small shift in sheet resistance (Rs) up to 100% strain (~ 25 Ω-sq-1) and maintain conductivity up to a strain of 150%. This shift in resistance up to 100% strain is very small in comparison to conductors made by implanted Au clusters15, 24. The different metal-substrate adhesion translates into the varying figures of merit for the stretchable conductors on two substrates viz. PDMS and textured rubber28. CFTE-Au films on PDMS exhibit finite conductivity until the substrates break. A break test for one such film experiment is shown in Figure (2b) where we see finite conductivity up to a strain of 200%. This is one of the largest strains that have been achieved for metallic thin-films coated on non pre-strained substrates15, 16, 26. The differences in metallic adhesion between the two substrates are evident with some delamination being observed from the edges of the Au cracks on stretched PDMS samples (Figure S3), which is absent on textured substrates even at much higher strains. Figure 2(c) shows surface resistance as a function of strain in the direction perpendicular to stretching for both PDMS and 13 ACS Paragon Plus Environment


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textured substrates. The anisotropy in sheet resistance (R‖/R⊥) increases up to a maximum of 5, at 100% strain on textured substrates and 75% strain on PDMS, beyond which a rapid increase is recorded. This differs from the polymeric conductors where the anisotropy plateaus at intermediate strain regimes19. The highly adhesive performing conductors on textured substrates are tested for robustness under cyclic loading. It must be noted that the alloy probe-contacts are placed at the clamped sections of the sample for cyclic testing since heating the contacts multiple times during cyclic loading cause irreversible damage to the stretchable conductor. Hence, the experimentally recorded resistance includes the discontinuity effect and is thereby much higher than the true resistance of the strained conductor, also confirmed by our model. The effect of cyclic loading could not be tested for strains greater than 70% due to the discontinuity in resistance at the interface as discussed earlier. In Figure 2(d) we show that the conductors maintain their original conductivity after cyclic stretching at 25% and 50% peak strains. Cycling at a much higher peak strain of 70% results in a marginal increase of ~ 25% in sheet resistivity. The resistance profile of individual cycles is shown in Figure S4. To probe the high performance we first map the microstructure evolution of the stretched CFTEAu conductors. At the onset we observe that the difference in adhesion translates into a significant variation in the micro-structure of stretched CFTE-Au films on PDMS and textured rubber. Much larger cracks (lengths ~ 20-60 µm and widths ~ 7-10 µm at 50% strain) are present in CFTE-Au films on PDMS in comparison to the cracks on textured rubber (10-30 µm in length and 2-6 µm in width at 50% strain). However, the cracks observed here on PDMS are considerably smaller and the metal is much less delaminated than e-beam deposited Au on PDMS29; confirming better adhesion in the CFTE method of fabricating stretchable conductors. It is worth noting that in the case of textured substrates, a few large cracks randomly evolve (length ~ 80-120 µm and width ~ 20-25 µm at 150% strains) which causes electrical failure of the samples at a maximum of ~ l50% 14 ACS Paragon Plus Environment

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Figure 2 – (a) Break test showing the effects of the ‘Edge’ in measurements. Differences between conductors on PDMS and textured rubber are shown. Values predicted by the model as described in Section 4 are also plotted. (b) Break test for stretchable electrodes on PDMS, up to substrate break, where conductivity is maintained up to 200% strain (c) R⊥ as a function of strain is plotted for both substrates. (d) The change in sample sheet resistance with cyclic loading at 25%, 50% and 70% peak strains is shown.

strain itself. This can be reconciled by the fact that some cracks grow more favourably due to an uneven textured morphology of the substrate. However a dominant single crack of a critical length running across the width of the film is never present. 15 ACS Paragon Plus Environment


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A binary construct of the microstructure is shown in Figure 3(a) for strained CFTE-Au films on textured rubber. Figure 3(b) is the voltage distribution across the microstructure for strains corresponding to the strains at Figure 3(a). The voltage distributions are calculated from the model which will be described in section 4. Cracks in the range of 10-30 µm in length and 2-4 µm in width develop at 50% strain, which grow 15-40 µm long, 4-8 µm wide at 100% strain and 20-60µm long, 10-16 µm wide at 150% strain. Interestingly, the contribution of each crack in the elongation of the conductor is at least one order of magnitude more than the Au film thickness, as each crack widens in micrometers with stretching37. Straining the conductors also resulted into the nucleation of cracks along with their widening. From the mapping of cracks (Figure S5), it is seen that continuous straining leads to a gradual increase of crack density in the film with saturation reached at ~ 100% strain. Further straining results in the formation of much wider cracks presumably caused by the coalescence of smaller cracks. It must be kept in mind that the substrates under study are highly compliant (2-5 MPa) and do not constrict strain localisation. Hence high adhesion in our case suppresses strain localisation acting on rigid metallic films28, and this in conjunction with widening of each crack makes it possible to stretch the CFTE-Au films to very high strains. To understand the basis of the stability of our conductors under cyclic stretching at high strains, we perform similar SEM imaging of cycled samples. The crack distribution changes within the sample with cyclic straining, as seen in Figure 3(c-f). It is observed that the crack density increases upon cyclical straining due to the nucleation of a large number of cracks having small widths (Figure 3c and 3f). Delamination from the edges of the micro-cracks upon cyclic stretching as in the case of e-beam deposited metals29, 33 is not observed here. The constraint for delamination arising from good adhesion coupled with an increasing fatigue of the metal due to cyclic loading creates multiple nucleation sites for defects within the micro-structure. The newly formed defects grow into cracks giving rise to the observed increase in crack density with cyclic straining. Cyclic straining and 16 ACS Paragon Plus Environment

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Figure 3 – (a) A binary image displaying the evolving metal microstructure with strain on textured rubber. Arrows indicate the increasing dimensions of the cracks with strain. (b) Voltage distribution maps when 1 V is applied across conductors stretched at 50%, 100% and 150% strain are shown. These maps are generated from SEM images using the model described in section 4. (c, e) SEM images of conductors after 1 and 101 cycles at 50% peak strain which shows the formation of larger number of cracks having small widths after cyclic strain.



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All SEM images are of the samples maintained in a strained condition. (d, f) Schematic view of the ‘2-D bellow’ type mechanism of opening and closing of the cracks under cyclic strain for conductors after 1 and 101 cycles respectively. relaxing makes the structure open-and-close in a planar ‘bellow’ like fashion. Figure 3(d,f) shows an artistic impression of the bellow mechanism. In this mechanism, for the same applied strain a larger number of cracks would entail each bellow to open-and-close lesser. This leads to an efficient and a more even redistribution of local strain on the CFTE-Au film near the crack edges. This local strain relaxation28 ensures a small degree of debonding and necking near the crack edges of the CFTE-Au films thereby providing a robust mechanism to stretch the films cyclically to higher peak strains. Hence an increased crack density with cyclic strain due to good adhesion of CFTE-Au films efficiently redistributes localized strain and ensures an unexpectedly small change in resistivity with strain. This mechanism is different to a standard e-beam deposited Cr-Au films where the metallic film deforms out of plane under cyclic strains due to debonding and delamination of the film33. It must also be noted that e-beam deposited films are cyclically stretched only at a maximum strain of 20%23,33,38, smaller than what is applied here.

4. Modelling: A lack of debonding, delamination and an out of plane movement of the conductor allows us to model our system as a 2-D conductor to quantitatively obtain sheet resistivity values. This isn’t be feasible where out of plane deformation occurs like in the case of e-beam deposited metals at strains greater than 20% 33. Our model predicts the microscopic origin of resistance38 in a cracked surface. We refer to the SEM images of the conductor in relaxed and various stretched states. A 2-D gridbased current conservation continuity equation is then applied to it with each pixel being a grid point. Using the geometric mean resistance between grid points, Ohm’s law between nearest 18 ACS Paragon Plus Environment

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neighbours may be expressed as𝐼𝑖𝑗 = (𝑉𝑗 − 𝑉𝑖 ) ∗ √𝜎𝑖 𝜎𝑗 , where 𝜎𝑖 is the conductivity of the ith element and the current flows from jth element to the ith element. 𝜎𝑖 are normalised to 1 for a conductive patch and 0 for a crack (the exposed substrate beneath). In this case, taking the square root of the conductivity is unnecessary. Image analysis of SEM images (425 × 614 µm) determines which pixels are cracks and which are conductive, giving us an experimental distribution of conductivity. Current conservation (at a grid point with Au) then gives us ∑𝑗 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑖 𝐼 = 𝜎𝑖 ∑𝑗 𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡 𝑡𝑜 𝑖 (𝑉 − 𝑉𝑖 )𝜎𝑗 = 0 𝑖𝑗 𝑗

(1)

Factoring out 𝜎𝑖 , we obtain the same equations as used in38, however here it is derived from assumptions where 𝐼𝑖𝑗 = −𝐼𝑗𝑖 always holds, as is required physically. The value of V on the insulating pixels is undefined but irrelevant. We then have to add boundary conditions of 𝑉 = 0 on the left side and 𝑉 = 1 (normalised) on the right side. These equations are assembled into a large sparse matrix of the form AV = B. The matrix A represents the identity matrix on rows corresponding to the boundary conditions and encodes equation (1) otherwise. V is the column matrix of all the pixel potentials (𝑉𝑖𝑗 ). B is a column matrix of zeros, except on rows corresponding to boundary conditions on the right hand side, where it is one. The resistance of the system is then proportional to the inverse of the current flowing from any column into the next. The absolute resistance can then be established using the unstretched, crackless system. A readily available code (https://github.com/Rlamboll/CrackedSurfaceResistance) for the model is available where more details of the formulism can be found. Using this, the voltage distribution across the stretched conductor for a given applied voltage is calculated and shown in Figure 3(b) for the textured rubber. As discussed earlier, it can be clearly observed that larger cracks are detrimental towards a uniform voltage drop across the conductor. The values obtained from this model are plotted in Figure (2a) for the textured rubber. These values match very well to the experimental values measured directly 19 ACS Paragon Plus Environment


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on the strained conductor up to 100% strain. However at 150% strain the model deviates from the measured value due to the evolution of a few large cracks in the film that cannot be effectively captured through SEM. The model was also applied to the 50% stretched PDMS case (Figure 2b). It is useful to apply this model to sample that have undergone cyclical stretching Figure 3(c,e). For cyclic loading end contacts are used and the measured values are affected by the boundary effect. Applying the model the discontinuity effects are removed. We find that after 101 cycles with 50% strain the sheet resistance value is only 39.5 Ω-sq-1 from the model, compared with the measured 85 Ω-sq-1 in (Figure 2d). Similar analysis on sample strained at 25% for 250 cycles yielded a sheet resistance value of only 20.1 Ω-sq-1, lower than 30 Ω-sq-1 that was measured through end contacts.

5. Applications: For applications we explore the flexible-stretchable CFTE-Au films on textured substrates due to the higher adhesion of Au films and their superior performances in comparison to smooth PDMS substrates. The robustness and practical applicability are tested by driving a 4V LED through the stretchable CFTE-Au electrodes. Twisting the conductors did not change the driving voltage of the LED. Figure 4(a) shows that when the conductors are twisted even up to 1800o there is very little drop in the current (~ 10%) flowing through the LED. Stretching the conductors however, results in a gradual decrease in the current delivered to the LED, with voltage maintained at a constant value. Figure 4(b) shows the decrease in intensity of the LED when the electrodes are strained, with the inset showing some intensity present when the conductor is stretched up to a ~ 100% strain. Rubber substrates are widely used in textile industries as well as for protective clothing. We integrated our CFTE-Au films onto protective gloves as an ‘electronic second skin’ that can be readily applied to joints of arms and curved surface for robotic applications3, 5. The integration can be easily achieved by simple procedures of attaching or sticking the electrodes onto the textile. 20 ACS Paragon Plus Environment

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Figure 4 – (a) Images showing the small change in the LED intensity while twisting the CFTE-Au films from 00 up to 18000 (b) Change in resistance of the CFTE-conductor and the corresponding change in Intensity of an LED as a function of strain on the conductor. Insets shows intensity of the LED’s (c) LEDs incorporated on gloves using CFTE-Au films as stretchable connecting wirings for applications in textile electronics. The electrodes successfully withstand multiple bi-axial strains at the two finger joints (A, B) and knuckles (C). Yellow lines are guide to the eye, with the strained 21 ACS Paragon Plus Environment


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conductor on the back of the hand (d) Predicted joule heating 2-D maps are shown for a stretched conductors (50% strain) and an unstrained conductor (inset) as calculated from SEM images. Hotspots across the sample is predicted. Applied volt =1V (e) Maximum current-carrying capacity as a function of input power for conductors with strains of 0%, 30% and 40% is plotted. Corresponding increase in the efficiency of joule heating with strain is seen in the plot of temperature against input power for the heating element.

In this example two LED’s are incorporated on to the tip of the gloves and connected to the stretchable conductors that are stitched to the gloves. Figure 4(c) shows the incorporated LED’s on gloves. Fisting of the palm creates multiple strains on the inter-connect electrodes. Minimum strains of ~ 30%, 10% and 5% are expressed at (A), (B) and (C) sections of the electrodes (Figure 4(c)) with a varying bi-axial component. The LED’s on the cloth work seamlessly with no obvious deterioration in performance, concomitantly allowing a complete freedom for fist movements. The LED’s on the protective gloves also performed very well in underwater and 70% ethanol conditions (Supplementary video). The LEDs can be readily replaced by any electronic device such as a sensor, camera, DEA etc. which opens up many possibilities for niche applications such as sensing human motions. As a further development, we apply these conductors as flexible and stretchable heating elements to fabricate stretchable heaters. The motive behind such an application lies in the evolved microstructure upon straining (Figure 3(b)). The geometry of the microstructure is expected to create a funneling effect on the current, so the current is channelled in the strips between the cracks. Hence, the increased localized current at local spots of the conductor due to this ‘funneling effect’ should locally increase the I2R values (joule heating) and should increase the overall efficiency of the heating of the substrate. This funneling effect creating local hot-spots 22 ACS Paragon Plus Environment

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in the film is also when stretched conductors are modelled (Figure 4(d)). Figure 4(d) shows the square of the current (I)2 flowing through the conductors proportional to the joule heating. The inset shows the squared current level for an unstrained conductor. The generation of hot spots in a stretched conductor is clearly seen. We then fabricate macroscopic stretchable heating elements over larger areas (100 mm2).We reach a maximum temperature of 120ºC at 0% strain and 101ºC at 40% strain (Figure 4(e)). Further increase in input power carbonizes the substrates due to heat. Our devices get more power efficient (Figure 4(e) top) with strain despite the decreasing current carrying capacity (Fig. 4e bottom) and increasing resistance of the heating element with strain. This is attributed to the high performing small shift in resistance we observe with strain for the CFTEAu films. This allows the funneling effect to dominate over the above effects and improve the joule heating efficiency with strain. The heating element achieves 101ºC at an I/P power of 1.28 Watts at 40% strain compared to 2 Watts I/P power required at 0% strain; a 36% increase in efficiency. To fully appreciate the applicability and importance of this process, it is worth noting that in our experimental setup, a batch of (~ 60) such heating elements (each ~ 1cm2 area) can be fabricated in a timeframe under ten minutes, at a total materials cost of less than 8 Indian Rupees (~0.1 US$)/sample and more importantly a lower additional cost for the process of deposition. The stability of the heating elements is itself not tested since it also depends more on the thermal stability of the substrates rather than the electrode properties, and which can be improved by the right choice of substrates.

6. Conclusions: In conclusion, we have fabricated highly deformable and stretchable conductors utilizing a CFTE of metal nano-clusters that form robust thin metallic layers and maintain conductivity up to 200% on PDMS and 150% on textured rubber. High metal-elastomer 23 ACS Paragon Plus Environment


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adhesion is obtained with textured substrates. The CFTE-Au films on textured substrates are highly robust and perform significantly better than e-beam, sputtered and implanted electrodes and exhibit only a small increase in resistance with strain (25 Ω-sq-1 at 100% strain). The films stretch and relax in a bellow type open-and-close mechanism which allow for a robust performance with cyclic straining. The CFTE-Au films are then modelled with a grid based microscopic system by applying 2-D current continuity equations. The CFTE is a one-step low vacuum process (0.5 × 10-2 millibar), not requiring intensive fabrication setups and large processing durations associated with other vapour deposition based processes. The facile nature of this process opens up possibilities for easy incorporation of these electrodes for various functionalities involving deformable electronics like textile electronics, bio-interfacing of devices, lab-on-chip devices, robotics and stretchable metallic interconnects. Low cost and high throughput should make it possible to easily facilitate the integration of this process into numerous industrial production lines and clean room fabrication setups for ubiquitous electronics. Supplementary Information: Textured elastomer morphology, SEM of the conductor with the Edge Effect, Strained PDMS conductor and Resistance Profile for individual strain cycles during cyclic stretching, mapping of cracks is available.

Acknowledgements: V.V. and R.L. acknowledge Prof.Neil Greenham at University of Cambridge for useful discussion. KSN acknowledges Department of Science and Technology, Government of India for partially funding the project. 24 ACS Paragon Plus Environment

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Facile Fabrication of Ultra-Stretchable Metallic Nanocluster Films for

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