Effect of roughness on the conductivity of vacuum coated flexible paper electrodes

Flexible conducting materials are required for the design and fabrication of a host of applications involving flexible electronic items. A flexible substrate like paper or polymer is generally employed for deposition of metal by a variety of pro-cesses. Among many physical properties, the roughness of the substrate is considered an important parameter, although, its exact role on effective conductivity of the coating is not known. Nor any study has been carried out to understand how the three-dimensional porous structure of the substrate surface affects the microscopic packing of grains that constitute the metal coating. With the objec-tive of elucidating the effect of substrate roughness on the conductivity of paper electrodes, we have used six different commonly available papers for vacuum coating with copper. For a smooth substrate, the grains that constitute the coating appear spherical, however, turns ellipsoidal as the substrate roughness and heterogeneity is increased; ellipsoidal grains result in higher packing efficiency leading to higher conductivity. We have also presented a model to relate the packing efficiency to the asphericity, polydispersity, and skewness of size distribution of grains.

TA B L E 1 Different types of substrates used for coating: Their make, surface roughness, and surface energy (PVD) [20][21][22] and vacuum filtration. [23] Over the past decade paper-based conductors have been widely used in various technological applications such as circuits, [24] electrical shielding, [25] electromagnetic shielding, [26] chemical sensor, [27,28] and electrochemical sensor. [29] There are several paper substrates available, with wide variation in topographical and surface chemical heterogeneity. Despite, paper being increasingly used in making flexible electronic devices, it is not known which specific characteristics of the paper are important and what are their optimum values that are expected to result in an ideal flexible conductor. Even the surface of a specific kind of paper varies spatially and randomly in regard to its hierarchical roughness and surface energy, both of which are expected to affect the integrity of the conductive coating.
In this report, we have examined six different commercially available papers to show that for vacuum coated thermally evaporated copper coating, the electrical resistance decreases with increase in roughness of the substrate; surface having the largest root mean square roughness results in minimum resistance. In general, the roughness of the substrate is thought to increase the effective path length of electrons, thereby increasing the electrical resistance. However, results presented here show that resistance of the coating is a function of its micro-structure that varies with the topographical heterogeneity of the surface. The vapor of copper condenses on the substrate via nucleation of grains, the shape and size of which depend on the surface heterogeneity. On a rough surface, the grains tend to be elongated and ellipsoidal rather than being spherical for a smooth substrate; their packing efficiency too becomes different. For a substrate consisting of sharp topographical features, the integrity of the coating diminishes because of the effect of the large curvature at these locations, resulting in increase in the resistance. For a perfectly smooth substrate, the occurrence of spherical grains decreases the packing efficiency, thereby diminishing the integrity of the coating with the consequent increase in resistance. We have also developed a model relating statistical characteristics of the packing of grains to identify substrates, which are expected to result in minimum resistance.

MATERIALS AND METHODS
Papers of different types: Trace paper, Printing paper, Drawing sheet, Sparkly paper, Circular patterned were procured from the local market and were used as acquired without any treatment (

Surface roughness and surface energy of substrates
Five different commercially available paper and silicon wafer were used as substrates for coating by thermal evaporation of copper. Table 1 presents the surface roughness and surface energy values measured for these substrates. The surface roughness values were measured using contact mode profilometry with scan size 200 µm x 200 µm and 500 µm x 500 µm. The roughness values of these substrate were also measured using AFM at 500 nm x 500 nm, 5 µm x 5 µm and 10 µm x 10 µm length scales. The Printing and Drawing papers were porous, whereas the Trace paper was rough but non-porous. The Trace paper, Printing paper and Circular patterned paper substrates showed similar surface F I G U R E 1 A, Schematic diagram depicts the process of vapor deposition. B, The optical image represents a typical copper-coated trace paper. C, The plot shows the variation of average resistance and copper layer thickness with the length for a Trace paper as a substrate. D, The bar chart represents resistance per unit length (RPL) for coating on different substrates; the bars 1-6 correspond to Trace paper, Printing paper, Drawing sheet, Sparkly paper, Circular patterned paper and Silicon wafer respectively. Cu = 0.7 gm of copper is used inside the coil in each case. E, The plot shows the variation of RPL with surface energy, (E1) and root mean square roughness, Δ (E2, E3) of different substrates. The data corresponding to roughness estimated at two different lengthscales: Δ 200μm (E2) and Δ 5μm (E3) is presented. The error bars represent the standard deviation of data from 3-5 sets of experiments roughness values for 5 µm x 5 µm and 200 µm x 200 µm length scales but the surface roughness of patterned paper was different from the other two for the scan area 500 µm x 500 µm.
The surface energy values were measured using Owens and Wendt model [30] with water and pentadecane as the liquids with known values of dispersive and polar components of surface energy. Pentadecane was found to completely wet the surface of all papers as mentioned in the supplementary material. These liquids penetrated the surface of only the printing paper. The surface roughness values could affect the measurement of contact angle of these liquids; therefore, the surface energy values that we estimated was in essence an effective surface energy, which gives an idea of interaction of the substrate with the copper layer deposited on it. The bonding of the copper coating with the substrate is expected to be stronger for larger surface energy of the substrate. In Table 1, we present the detail characteristics of these different substrates.
Surface energy values were estimated using Owens and Wendt [30,31] model (figure S 13 ) and the surface roughness was measured using Contact mode profilometry with scan size 200µm x 200 µm. The error values in each case represent the standard deviation of data from five measurements.

3.2
Effect of substrate on the resistance of the coated paper Figure 1A shows the schematic of the experiment in which the substrate, a flat sheet of paper was placed above a tungsten coil inside the closed chamber of a vacuum coating unit. The desired quantity of copper (Cu) placed inside a tungsten coil was heated inside the chamber, maintained at 10 −5 bar pressure. The exposure time and current were maintained at 30 seconds and 60 amp, respectively. Cu evaporated inside the coil, diffused out of it and then condensed on a substrate positioned vertically above the coil. Figure 1B depicts the optical image of a typical Cu-coated Trace paper (A4 size). The thickness of the copper coating as a function of radialdistance (represented as ⬜ Figure S 3 (c)) from the center of the trace paper was measured by Contact Mode Profilometry (figure S 3 (c, d)) (Bruker Dektak XTL). At the center of the paper, vertically above the position of the coil, the thickness was maximum; it decreased radially away because of the increase in diffusion length of the vaporized metal from the coil (Figure 1C). Therefore, small samples of radius 4 cm were cut out from the central portion of the coated paper for conductivity measurement, where the spatial variation in conductivity was expected to be limited. The electrical resistance of the copper layer on different substrates was measured via two different methods: by using a multimeter ( Figure  S 1 (b)) and by obtaining the Electrochemical Impedance (Autolab PGSTAT302N) ( Figure S 1 (c)). The resistance of copper coated paper increased with increase in length of the coated paper ( ). However, the resistance did not decrease to zero, for → 0 ( Figure 1C, S 1 (b)). The finite value of →0 signified the presence of contact-resistance of the wire and imperfect contact with the multimeter tips. In order to diminish any inconsistency due to this inaccuracy in the measurement, the resistance per unit length (RPL): Δ ∕Δ was calculated by obtaining the slope of the vs. curve. In subsequent analysis Δ ∕Δ (Surface resistance, RPL) or * (surface Conductivity) was used as the measured parameter. For all substrates, the impedance of the copper coating (figure S 1 (c)) was found to be independent of the frequency with zero phase angle, implying that the coating was a pure resistor, and its resistance varies linearly with length. The bar chart in Figure 1D shows that the RPL values of the coatings on different substrates vary by over an order of magnitude. Furthermore, the RPL values followed the same trend for both measurement methods, but there was some disparity between them. Measurement of resistance using multimeter was a step process with the steps increasing by 1 cm length, whereas, for impedance spectroscopy, the measurement was done for a single strip of length 5 cm. In both these measurement methods, the values get affected by the contact resistance; however, since for multimeter, measurement of resistance is done using steps of smaller lengths, the RPL values calculated using this method were expected to be more accurate. Therefore, in subsequent analysis, the RPL values from multi-meter measurement were used. Figure 1E shows the variation of RPL with surface energy and surface roughness. RPL of the substrate increases with an increase in the surface energy ( Figure 1(E1)) of the substrate, albeit with some exceptions. The data presented in Figure 1(E1) shows that for most papers, the surface energy of the substrate lies between 28-32 mJ m -2 , except for printing paper (Xerox paper), for which the surface energy was 46 mJ m -2 . The printing paper with maximum surface energy among all the substrates showed a modest RPL of 0.2 ohms cm -1 . The roughness, Δ of these surfaces were measured at two different length scales: 200µm x 200µm (represented as Δ 200μm ) using Contact mode profilometry (Bruker Dektak XTL) (Figure 1(E2)) and at 5µm x 5µm (represented as Δ 5μm ) by using Atomic Force Microscopy (Bruker MultiMode 8) (Figure 1(E3)). RPL of the coated substrates was found to increase with increase in the surface roughness Δ 200μm of most substrates except that for silicon wafer (Figure 1(E2)). Despite being atomically smooth with Δ much smaller than that of the Trace paper, Silicon wafer showed ten times higher value of RPL than the Trace paper. Figure 1(E3) demonstrates that the RPL of the coated substrates decreased with an increase in surface roughness Δ 5μm .
Scanning Electron Microscopy (SEM) (SUPRA 40 VP and CARL ZEISS EVO 50) images of different coated and uncoated papers presented in Figure 2(A-H), show that the copper coating was not a uniform and continuous film but consisted of closely packed grains of different shapes and sizes Figure 2E-H. It is worth pointing out that in 2 µm x 2 µm SEM scan of the patterned paper ( Figure 2E), it appeared smooth or featureless as compared to other substrates as the roughness features of it had lengthscales larger than than the scan size. However, the SEM and AFM images of the patterned papers at larger length scales: 2 µm x 2 µm, 5 µm x 5 µm and 200 µm x 200 µm, as presented in figure S 2 (e and V) and S 2 (q), show that roughness features do appear as sharp corners. Figure 2E-H, S 2 shows that the nature of the packing varied with substrates; it was closely packed for the Trace paper, but consisted of cracks at sharp corners and wavy edges that decorated the topography of different other papers (Sparkle and Patterned paper, figure S 2 (p,q)). Importantly, the cracks were also found for coating on the atomically smooth surface of the silicon wafer ( Figure 2H, S 2 (r)). Whereas for the paper substrates, the cracks appeared due to large curvature, for the Silicon wafer, it appeared due to hetroepitaxy. [32] Presence of cracks within the coating expectedly resulted in large RPL values. The SEM images in Figure 2 also show that the constituent grains for both silicon wafer and patterned paper were spheroidal ( Figure 2G, H), whereas for the trace paper the grains were ellipsoidal (figure 2E). The shape and size of the grains deposited on the substrates depend on surface heterogeneities. For example, surface with low surface roughness leads to formation of homogeneous uniform microstructure with inhibited grain growth and for coarser surfaces pinning of the grains lead to asymmetric grain growth. [34][35] Since the packing efficiency is expected to increase from spheroidal to ellipsoidal grains, the packing of grains for Trace paper was less susceptible to crack formation than the silicon wafer and the patterned paper. Nevertheless, the grains for a particular substrate were not of uniform size and shape, and the distribution in size and asphericity of grains on different substrates too was different. To capture the difference in statistical features of coating on different substrates, the length of major and minor axes ( and respectively) of grains were obtained, and their size and asphericity or aspect ratio (irrespective of the orientation of grain)were estimated as = √ and = ∕ respectively. In order to encapsulate the grains to measure the size and asphericity the contrast of the image was increased as shown in Figure 2E. For each case, a large number of  grains were examined to obtain the distribution in size and asphericity. The 2D packing efficiency was obtained by analysing the SEM images ( Figure S 2 (g-l)) from which the fractional area covered by grains or the packing efficiency | exp was estimated by using MATLAB. The grayscale values for SEM images ( Figure S 2 (g-l)) varied from one location to the other. Therefore, in order to obtain the representative data, 4-5 portions or islands were selected randomly from the SEM images (figure S 8 ) which were then subjected to image analysis. For Trace paper, Printing paper, Drawing sheet, Sparkly paper, Circular patterned paper and Silicon wafer, the packing efficiency | exp were estimated as 0.96 ± 0.01, 0.91 ± 0.01, 0.88 ± 0.01, 0.83 ± 0.05, 0.86 ± 0.01and 0.95 ± 0.01respectively. The distribution of size and aspect ratio of grains for coatings on few different substrates are plotted in Figure 2I-P. The grain size distribution was fitted using Origin 2019. These figures suggest that for printing and trace paper, the grain size follows lognormal distribution with positive skewness, whereas for drawing paper, patterned paper and silicon wafer, the grain size follows Gaussian distribution with a high fraction of small size grains (< 50 nm) (Figure S 4 ). In these plots, we have also presented the polydispersity, and skewness, as extracted from these fits. and could be calculated using two different methods: (a) by calculating mean , and standard deviation , from the grain size data extracted by the above method and (b) by fitting the grain size data to known distribution curves to obtain (mean distribution size) and (distribution width parameter). The results presented in Table 2, S 2 , and S 3 show that the calculated values for both these methods were comparable. The SEM images were analyzed in small islands and the size data were extracted by considering 40-50 randomly selected grains in each of these of these islands. Therefore, in order to interpret systematically the size data, the exact nature of the distribution that the grain sizes followed was required to be examined. Consequently, the and values derived from the resultant fits were used for subsequent results.

Effect of quantity of copper used for coating on the resistance of the coated paper
To examine the effect of the quantity of copper used on the resistance of the copper coating, the Trace paper was used as the substrate while different quantity of copper Cu =0.05-90 g was placed inside the heating coil. For estimating the thickness of the Cu coating thus formed, an indirect method had to be adopted, as the roughness of the substrate did not allow its accurate measurement. A small piece of the silicon wafer was attached to the substrate at the vicinity of its center using an adhesive, and the thickness of copper deposited on it was measured by AFM scanning (Figure S 3 ). Variation of on trace paper was considered to be similar to that on the silicon wafer. The RPL for different coating decreased with increase in as presented in Figure 3A. Figure  copper grains continued to be ellipsoidal, but the average grain size decreased with increase in Cu . In addition to surface heterogeneity, the grain shape and sizes are expected to be dependent on the energy of interaction of copper with the substrate. Copper-copper interaction is expected to be stronger (with zero interfacial energy) than the copper-paper interaction (finite value of interfacial energy). As a result, for the copper grains depositing on bare paper, interaction energy around it expected to be more heterogeneous spatially than that deposited on a layer of copper. Such heterogeneity can affect the crystal growth in different other systems. [36] As a result, the grains grow preferentially in one direction thereby assuming aspherical shape. The surface heterogenity decreases with increase in Cu , leading to formation of more homogenized grains. [33,34] The plots in Figure 3F,G show the size ( Figure 3F, S 6 ) and asphericity distribution ( Figure 3G, S 7 ) of these grains, which were analyzed to obtain and . In Figure 3H, the conductance of these different coatings, estimated as = (RPL) −1 is plotted against | exp as obtained by analysis of SEM images of the corresponding coating. These results show that increases almost linearly with | exp . A quantitative relation was established between and characteristics of the packing, importantly between , and . For both Gaussian and Log-Normal distributions, the packing density is known to increase with and of the distribution. [37][38][39] For spherical grains, this dependence can be expressed as : [40] = + ( , ) = + 1 + 2

2
(1) in which is the packing fraction of spherical grains with random close packing without any and . In contrast to spherical grains, for ellipsoidal grains is expected to depend also on asphericity, of grains. For a given substrate, the asphericity of grains varies according to the distribution as presented in figure (2(m-p), 3(g)).
For mono-disperse ( = √ = .) ellipsoidal grains packing efficiency varies with asphericity ( = ∕ varying) as a bell curve [41,42] However, for polydisperse grains the asphericity dependence on packing efficiency is not available in literature. The dependence of asphericity on packing efficiency can be extrapolated from monodispersed grains dependency as a weighted function. Therefore, the dependence on asphericity can be taken, 2 Δ , which Δ correspond to the probability of finding grains of asphericity . Since, by definition of asphericity < 1, the effect of higher-order terms can be neglected. Considering all the above points, equation one can be simplified as, = + ( , ) × ( ) + × ( ) . It has been shown earlier [41,42] that randomly distributed ellipsoidal grains F I G U R E 4 (A) The plot shows that conductance = ( ) −1 of coating in various substrates scales linearly with packing fraction | 1 calculated using equation 1 (represented by symbol ○). We have plotted here also the data = ( ) −1 vs | exp (represented by symbol □) as obtained from experiments. (B) The plot shows that data of conductance and the packing efficiency | 1 obtained for different substrates vary linearly with substrate roughness Δ 5 . The error bars represent the standard deviation of data from three sets of experiments pack more densely with a mixture of both spherical and aspherical grains. [37] For monodisperse ellipsoidal grains, maximum packing efficiency, max occurs at the aspect ratio of grains, ∼ 0.66, whereas for oblate and prolate spheroids, max occurs at = 0.6 and 1.8, respectively. [42] For polydisperse ellipsoidal grains, max is achieved when a large fraction of grains are of = 0.66. [37] It is then logical to consider that the fraction of grains, with asphericity varying from 0.60 to 0.75, is expected to contribute to the packing efficiency most significantly. Therefore, = ( ) = 0 ∑ 0.75 =0.60 Δ was considered to be proportional to the fractions of grains with asphericity from 0.60 to 0.75. Noting that the conductance of the coating varies linearly with the packing efficiency of the grains, as shown in Figure 3H, the data of conductance from all different experiments were fitted to packing efficiency, calculated using, with 0 , 1 and 2 as the fitting parameters which account for the relative contribution of asphericity, and to the packing efficiency. Figure 4A shows that this plot yields the fitting parameters, 1 = 0.4, 2 = 0.25 and 0 = 0.05 with x-intercept as 0.82, which matches closely with the packing efficiency of random-close packing of spheres, that is, 0.8. In this figure, we also presented the data of as a function of packing efficiency obtained from experiments, | exp (symbol ◻).
Finally, we have presented in figure 4B, the conductance of different coatings and the packing efficiency, | eq 1 against the roughness, Δ 5 m of the substrates. Since both and | eq 1 increase nearly linearly with Δ 5 m , this data signifies that roughness of the substrate increases the packing efficiency of the grains, which results in increased conductance of the coating.

3.4
Effect of layered or multiple coating on the resistance of the coated paper SEM images presented in Figure 3 show that the change in Cu effects the shape and size of copper grains. The RPL of the copper-coated trace paper was found to increase with decrease in the weight of copper in the coil. While the results presented in Figure 3 correspond to a single batch or layer of coating, the effect of number of layers on shape and size of the grains and consequently on the RPL was investigated. To explore this aspect, trace paper substrates were coated with copper inside vacuum coating unit (as described in Figure 1A), was cooled for 30 minutes and was then coated again with another layer of copper. The process was repeated over several cycles while keeping the total weight of copper loaded in the coil constant, Cu = 0.8gm. The samples 1-8 were coated as described in table S 5 .The bar chart in Figure 5A shows the variation of RPL for trace paper coated 1-4 times.
SEM images of these samples were analyzed to extract the grain sizes (S 10 ). Figure 5C and 5C show the grain size distribution and asphericity distribution for samples (1)(2)(3)(4)(5)(6)(7)(8) obtained by analyzing SEM images. The mean grain size and the size of the distribution was found to increase with increase in number of coating, except in case of four layers  Figure 5B, S 11 ) for which, the size of distribution and mean grain size was found to decrease. The fraction of aspherical grains was found to decrease with decrease in Cu for first few layer of coating ( Figure 5C, S 12 ).
The parameters , and were calculated from the fits (figure S 11 , S 12 ). The obtained parameters were used to calculate the effective packing efficiency using Equation 2. The conductance of trace paper electrode was found to increase linearly with the calculated packing efficiency | 1 ( Figure 5D). The plot yields the fitting parameters, 1 = 0.4, 2 = 0.25 and 0 = 0.05 with x-intercept as 0.83, which was similar to x intercept observed in Figure 4A.The RPL of the coated paper decreased with the amount of copper loaded in the coil for the initial coating process ( Figure 5A (2-7)). Both double ( Figure 5A (2-4)) and triple layered ( Figure 5A (5-7)) coated papers show a similar trend. Similar to the | 1 , RPL of the papers too was dominated by the Cu of the initial layers. For example, RPL of the double-layered coated papers, was dominated by Cu of the first layer; similarly, for three-layered coating, it was dominated by Cu of the first two layers. It is possible that copper layers, deposited initially present a less heterogeneous substrate for the subsequent layers, thereby limiting both the asphericity and the size of the copper grains of these layers. Agrain in free space can have growth inany direction and the introduction of other grain in the same space restrict the growth, directionality and orientation of the second grain [41,[43][44][45] Similarly, for the coating of first few layers, limitations in orientation or condensation of grain may besmaller than for coating of subsequent layers. Hence the RPL of the coated paper is dominated by the initial coating process and the subsequent layering of the paper might not result in decrease of the RPL.

Effect of bending and creasing on the resistance of coated paper
We also examined the effect of cyclic bending ("U" shape) and creasing ("V" shape) of the copper-coated trace paper F I G U R E 6 (A) The figure shows the experimental setup for measuring the resistance of coated trace paper with bending. The images show the corresponding change in resistance and the radius of curvature for a 5 cm x 1 cm sample (Scale Bar: 0.5 cm). (B) The images depict the bending of the sample to "V" shape and the corresponding crack formed at repeated bending. (C) The plot shows that the change in resistance ∕ 0 variation for repeated bending cycles with the radius of curvature (represented by symbol □) and the change in resistance for "V" shape bending with the number of bending cycles (represented by symbol ○) as obtained from experiments. The error bars represent the standard deviation of data from five sets of experiments on the surface resistance. Figure 6A and 6B depict the images of the experiment. The coated paper was clipped between crocodile clippers of multimeter, and the resistance of coated paper was measured in response to variation of radius of curvature, ( Figure 6A). The change in resistance of the paper was negligible compared to the change in ( Figure 6C, Video V1), for example, resistance varied by 1.02 time for change in by an order of magnitude ( Figure 5F). The change in resistance of coated paper was observed only when the paper was creased to < 20mm. In a cyclic experiment, the coated trace paper was creased to a "V-shape" bent and was then increased (Figure 6B), repeatedly. The resistance of the uncreased trace paper was measured after every cycle. Multiple creasing of the trace paper to ∼ 0 mm (e.g., in V-shaped crease) resulted in rapid increase of the resistance to the point of crack formation in the coated layer ( Figure 6C). Bending of the coated paper results in a negligible change in resistance ( > 20mm), but when the paper was creased to a "V-shape" ( ∼ 0 mm) bent over multiple times, for example, N > 35 cycles, crack appeared in the coating, with the resistance reaching infinity.

CONCLUSION
The study presented here is different from that discussed earlier on the packing efficiency of isotropic cylindrical particles. [46] Whereas in the previous study authors compared packing of hard spheres with that of cylindrical rods that did not involve any directionality (aspect ratio increasing only in single direction) or even the cylindrical rods with aspect ratio less than 1, over here, we have compared the packing of ellipsoidal grains both prolate and oblate. In the previous study the packing of isotropic thin cylindrical rods was discussed, whereas we have discussed the packing efficiency of aspherical, polydisperse grains as a function of weighted summation of various aspect ratios. Furthermore, in contrast to several other studies on paper electrodes, that primarily focused on roughness in macro-scale, [20] we have for the first time, analyzed grain structure of vapor deposited copper coatings to show that micro-scale roughness of a substrate, for example, that of Trace paper and Printing paper leads to poly-dispersed ellipsoidal grains. Surface roughness at both scales affects the conductance of the coated layer. As the roughness at micro-scale increases, the grain becomes more aspherical and the packing efficiency. Such coating with large packing efficiency of grains yields large electrical conductance.
In the other limit of substrates with large macro-scale roughness, for example, ones consisting of sharp corners, increase in surface roughness at macro-scale influences the integrity of the packing with the presence of microcracks at sharp edges, that decreases the conductance. For surfaces having intermediate roughness, the model presented here, relating the packing efficiency of grains to the polydispersity and skewness of size and asphericity distribution is expected to be useful also for determining the conductance of different other metal coatings on similar substrates. The conductivity of coated surfaces varied linearly with calculated packing efficiency | 1 .
In the case of multiple coating on the substrate, the grain shape and size are controlled by the amount of copper used in the coil for the first layer of coating. The resistance of coated paper, in experiment with cyclic bending and relaxing, changes insignificantly for bending radius of curvature larger than 1 cm and changes drastically for smaller radii of curvature. These copper coated trace papers is expected to be useful for various applications, e.g. as functional electrodes is designing flexible capacitive pressure sensor.

Coating of material
A high vacuum coating unit (Hind High vacuum Co. (P) Ltd., Model: 12A4D) was used thermal evaporation and deposition of copper on the substrate. A flat sheet of paper was placed above a tungsten coil inside the closed chamber of a vacuum coating unit. The desired quantity of copper (Cu) placed inside a tungsten coil was heated inside the chamber maintained at 10 −5 bar pressure. The exposure time and current were maintained at 30 second and 60 amp, respectively. Cu evaporates inside the coil, diffuses out of it and then condenses on a substrate positioned vertically above the coil.

Measurement of electrical resistance
The electrical resistance of the copper layer on different substrates was measured via two different methods: by using a multimeter ( Figure S 1 (b)) and Electrochemical Impedance (Autolab PGSTAT302N) ( Figure S 1 (c)). The DC resistance of the coated paper was measured as a function of length using a digital multimeter. The impedance of coated paper was measured by applying a potential of 5mv with a frequency range of 1 mHz to 10,000 Hz using two electrode system Electrochemical Impedance Spectroscopy (EIS).

Surface topography
The topography of the substrates before and after coating with copper was examined by carrying out Scanning Electron Microscopy (SEM) (SUPRA 40 VP and CARL ZEISS EVO 50) of the surfaces ( Figure S 2 (a-r)). Surface topography of the sample was also assessed using AFM. The sample surface was scanned using Peak force scanning mode of Bruker Multimode 8 AFM (Scan Assyt Air Tip) ( Figure S 2 (I-VI)).

Measurement of thickness of copper coating
The thickness of the copper layer was measured using an Atomic Force Microscope (Bruker Multimode 8). Tapping mode of AFM was used to image the copper surface (figure S 3 (a, b)) (TAP 150 silicon-nitride tip). The radial thickness change in the coating for trace paper was measured by Contact Mode Profilometry (figure S 3 (c, d)) (Bruker Dektak XTL).

5.5.1
Image processing and grain size measurement Grain size measurements of copper grains from SEM images was done using Microsoft PowerPoint. Random grains were enclosed with ellipses, and both major and minor axis diameters were extracted (figure S 2 (g), S 5 (a-f)). The size of the grains was estimated as √ , where and are the lengths of the major and minor axis, respectively. The asphericity of the grains was measured as ∕ (less than or equal to 1). The fractional area coverage or the 2D packing efficiency was estimated using MATLAB ( figure  S 8 (a,b)). The Grain size distribution was fitted using Origin 2019 (figure S 4 , S 6 ).

5.5.2
Surface roughness Surface roughness of the substrates was measured using AFM (Bruker Multimode 8). The samples were scanned using Peak force mode (Scan Assyt tip, Silicon nitride tip k = 0.4N/m) (figure S 9 ). Surface roughness at scales 500 nm, 5 µm & 10 µm were obtained from AFM scans(figure S 9 (g)). Dektak contact mode profilometer was used to measure the surface roughness at 200 µm and 500 µm scale (figure S 9 (h-j)).

Surface energy
The static contact angle of DI(De-Ionised) water and Pentadecane was measured on the substrates. The surface energy of the paper was then calculated by applying the Owens and Wendt [30] model (figure S 13 ).

Interfacial adhesion
Scotch tape test was performed to test the bonding of the copper with the substrate. The tape was first brought in contact with the copper coating and then peeled off. As shown in figure S 16 even after repeated peeling of the scotch tape there was no visible amount of copper that came off the substrate.