Fractal dendrite-based electrically conductive composites for laser-scribed flexible circuits

Fractal metallic dendrites have been drawing more attentions recently, yet they have rarely been explored in electronic printing or packaging applications because of the great challenges in large-scale synthesis and limited understanding in such applications. Here we demonstrate a controllable synthesis of fractal Ag micro-dendrites at the hundred-gram scale. When used as the fillers for isotropically electrically conductive composites (ECCs), the unique three-dimensional fractal geometrical configuration and low-temperature sintering characteristic render the Ag micro dendrites with an ultra-low electrical percolation threshold of 0.97 vol% (8 wt%). The ultra-low percolation threshold and self-limited fusing ability may address some critical challenges in current interconnect technology for microelectronics. For example, only half of the laser-scribe energy is needed to pattern fine circuit lines printed using the present ECCs, showing great potential for wiring ultrathin circuits for high performance flexible electronics.

Note: the bulk density of carbon nanotube is about 1.3 g cm -3 , 35 while the bulk density of silver is 10.49 g cm -3 .
Supplementary Table 6. Parameters of f c , k and n of various materials in equation (4).  The exchange-correlation potentials were treated by the generalized gradient approximation with Perdew-Burke-Ernzerhof functional. 4 The energy cutoff for the plane-wave basis set was 500 eV. The Brillion zone was sampled 7 × 7 × 1 grid meshes for the 2 × 2 slab, 5 × 5 × 1 grid meshes for the 3 × 3 slab, and 3 × 3 × 1 grid meshes for the 4 × 4 slab by using Γ-centered scheme during the calculation.
The Hellmann-Feynman force acting on each atom was converged to below 0.01 eV Å -1 for geometrical optimization.
To check the reliability of the above methods, several tests were performed. The optimized geometry of the isolated NH 2 OH molecule is shown in Supplementary Fig. 6a. The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) are shown in Supplementary Fig. 6b and c, respectively. The distribution of frontier molecular orbital of NH 2 OH shows that a covalent bond will form between the N atom and Ag atom for the NH 2 OH adsorption on the surface of silver, a common trend of many open-shell atoms and small molecules adsorption on the metal surface. 6,7,8,9,10 For the lattice constant of bulk silver, the calculated value is 4.15 Å, which is in agreement with the experimental value 4.0855 Å with an error of 1.54%. The calculated cohesive energy of silver is 2.49 eV, which is consistent with Stachiotti's result (2.52 eV). 9 We also investigated the structural properties of the clean Ag (111), Ag (110) and Ag (100) surfaces and the results are listed in Supplementary Table 2. The ratio of change of the interlayer distance is defined as: where, d ij is the interval between layer i and j. d 0 is the interlayer spacing in the bulk. The negative number here means contraction of the interlayer distance as compared to the bulk structure, and vice versa. The spacing between the first and second layer decreases for all the three surfaces, but that between the second and third layer increases for (110) and (100) surfaces. It is found that the largest relaxation is on (110) surface, because it is the most loosely packed one among all three surfaces. 5 Moreover, surface energy (γ) can be calculated by: where E slab is the total energy of the slab, bulk E Ag is the energy per atom in the bulk of silver, N is the total number of Ag atoms contained in the slab, unrel E slab is the energy of the un-relaxed slab, and A is the surface area. Since the upper part of the slab is allowed to relax while the rest is fixed to the bulk positions, the factors 0.5 are introduced in the above equation. 11 The calculated surface energies of Ag (111), Ag (110) and Ag (100) are also listed in Supplementary Table 2, which are consistent with other theoretical and experimental results. Moreover, the (111) surface is more stable than the other two surfaces in agreement with previous experimental and theoretical results. 6,[13][14][15][16][17][18] Adsorptive behavior of NH 2 OH molecule. The adsorption energy of NH 2 OH molecule (E ad ) on silver can be defined as:  In our experiment, hydroxylamine plays a key role in the reactions as both the reductant and surface coupling agent.
When we reduce the concentration of hydroxylamine, the nucleation process of silver crystal decreases and the seed crystals tend to grow into more basic structures (such as FD I). By contrast, when we increase the concentration of hydroxylamine to a large extent, more complicated structures (such FD VI) are obtained. Further analysis is under exploration.

Characterization of FDs as the SERS Substrates.
FDs have abundant nano-tip structures, some of which may act as "hot spots" for the surface enhanced Raman scattering (SERS) enhencement. Supplementary Fig. 11 displays the SERS spectra of Rhodamine 6G (R6G) on the surface-modified silver samples (FD III, FD VI, and Ag flake). From this spectra, we can observe that the Raman spectra of the 10 -6 M R6G adsorpted silver samples were dominated by the relatively strong peaks at 1648, 1566, 1508, 1361, 1280, 1197, 1077, 936, 767, 622 and 421 cm -1 , which agreed well with the previous report. 19 The intensity of the peaks of FD III and FD VI were much higher than that of the Ag flake. Thus, FDs might have potential application in SERS enhancement.
BET analysis of FDs. In order to better investigate the characteristic of specific surface area (SSA) of the FDs, we analyzed the samples by Brunauer-Emmett-Teller (BET). Supplementary Fig. 12 shows the nitrogen adsorption isotherm of the as-prepared FDs; the featured hysteresis of the isotherm between desorption and adsorption branches indicates the presence of mesopores. 18 The SSA of FD III and FD VI were 4.6128 m 2 g -1 and 6.3122 m 2 g -1 , respectively. By contrast, the SSA of Ag flake was too small to be measured (not shown here). The results can well confirm that these micro-sized FDs have a relatively large specific surface area than the commercial Ag flakes. k +n (f -f ) ( Then we can determine and from the y-intercept and slope of the fitted curve respectively. As for FD I, the best-fit curve was obtained by taking f c = 0.0273 (corresponding to the Ag weight content of 20 wt%) as it is where the ECC shows the most abrupt change. Using this method, we found that k = 1.

Structural models and Computational methods of 3-D Monte Carlo percolation simulation. A 3-D Monte Carlo
simulation using the classical Hoshen-Kopelmen algorithm was employed to study the percolation probability of the ECC samples. 36 In order to ensure our models more close to the real situation, we constructed the models according to the SEM observations. FD I, FD III, and FD VI were modeled and scattered into the simulation domain randomly for  Table 7) are carefully chosen so as to statistically approximate to the real particles. Surface effects, such as iodine treatment effect and other contact resistances, 24 are ignored in the simulation to simplify the computation, which lead to minor underestimation of the percolation probability.
The particle models used in the simulation are constructed in a L 3 space, where L is the typical size of the concerned particles. When considering from the smallest dendritic features (about 20 nm) to the largest macroscopic composite thickness (being set to about 100 m), a high resolution simulation (Fig. 5d) is necessary to cover all the huge range of length scales in the particle system. In this modeled simulation, typical results are obtained from a 11L × 5L × 5L to 20L × 10L × 10L (depends on particle type) periodic domain with the total number of nodes reaching one billion, and the results attain a sufficiently high resolution to resolve the nano-scale features while maintaining the macroscopic statistical properties of the particle system. The domain size is chosen thru a domain size test, by observing the stability of statistic at each mass fraction points at increasing domain size. It is observed that the percolation statistic converges when domain size reached the range 10L-20L. This is consistent with some classical numerical studies on percolation. 37 In general, more complex shape requires larger domain and more systems for each mass fraction point to stabilize the percolation statistic. The total number of system simulated for a single particle shape is about 4000 to 12000 systems. Each single system has about 0.1 to 1.0 billion nodes. For each shape, we compute a number of systems (100 to 400) at each mass fraction point to provide stable statistics, and only limited statistical fluctuation is observed in the percolation probability curves. If the curves are not sufficiently smooth with respect to the percolation threshold range obtained, we increase the number of system calculated until a stable statistic is obtained at each mass fraction point.
Computational results of percolation. The overall silver mass content of each dendrite crystal in the L 3 unit is set to about 6.7 ~ 15.4 wt% (taking the filler density as the one for bulk silver, i.e. 10.49 g cm -3 ). When the above models are used for the Monte Carlo simulation, the percolation state curves are drawn versus silver mass fractions (Fig. 4c). The resulting curves show that all FDs, regardless of the secondary features, critically percolate at around 12.8 ~ 18.5 wt%, while those of the spherical model (64.6 wt%) and planar flake model (47.5 ~ 66.0 wt%) require much more silver content to percolate through the domain. As for the simulated results, the percolation probability of the spherical model appeared to be close to the theoretical criticality value (i.e. the Scher-Zallen invariance). 38 For that of the Ag flake model, the issue of rotational freedom of Ag flakes was considered. When Ag flakes are allowed to orient randomly along the radial axis, the percolation threshold decreased (47.5 wt%) accordingly; when the Ag flakes are not allowed to rotate in that manner, the percolation threshold increased (66.0 wt%), which is consistent with previous report. 39 As shown in Fig.   4c, the pink zone marks the region between the two extremities, and the other examined flake cases with medium rotational freedom fell well between the two extreme values.
The interrelationships among different particles showed remarkable agreement with those relations observed in experiments (Fig. 4a), showing the same trend and order of percolation preference. This agreement between computational and experimental results provides evidence for the validity of our modeling on percolation.

Evaluation of device applications of FD based ECCs.
Currently, most of the packaging methods for the touch panel sensor module for smartphones and tablet PCs include G + F (glass front cover plus film module), G + G (glass front cover plus glass module), OGS (one glass solution), On-Cell (on color filter) and In-Cell (in TFT-LCD module) etc.
Among them, thin film based modules have become the mainstream (about 48% and 94% of the global market shares for smartphone and tablet PC in 2014, respectively). 40 In order to realize finer border and better film transparency, polymer films e.g. PET are often used as the common substrate for the film module (as shown in Fig. 5b). In order to evaluate the feasibility of the FD based ECC samples in touch panel applications, we adopted a benchmark commercial silver paste (FP FTL-630LE, Korea, polyester resin based) as the control sample and systematically evaluated the wiring performance of the FD based ECC samples for such application.
In order to better compare the samples, we adopted polyester resin for the FD based ECCs, which showed equal electrical conductivity to the epoxy based FD-ECC. FD III-ECC (50 wt% of silver) was screen-printed on PET substrate (shown as Supplementary Fig. 25) with the same thickness as the commercial silver paste (FTL-630LE, FP, Korea, 75 wt% of silver). Both samples were cured at 150 °C for 20 min, and then were laser-scribed with different power (StrongLaser Co., laser wavelength: 1064 nm, straight line processing speed: 1000 mm s -1 , maximum laser power 20 W, a photographic image of the laser micro-processing system is shown in Supplementary Fig. 26). In order to ensure adequate wiring capability (20 μm width fine lines up to decimeter length scale), 30% of the laser power is required for the benchmark ECC; while for FD III-ECC, only 15% of the laser power is enough. Supplementary Fig. 28 and 29 showed the optical microscopic images of the laser-scribed ECCs (KH-7700 3-D video microscope). FD III-ECC sample had regular patterns with the laser power of 15%, which showed similar patterning resolution to that of the commercial one patterned with 30% (not shown here). The volume resistivity of the laser-scribed circuit line is summarized in Supplementary Fig. 27, suggesting that FD III-ECC possesses excellent conductivity, especially at low laser power levels.
The above results indicated that the FD-ECCs have excellent potential in the flexible display applications with low cost and high performance.  Fig. 32). The reliability test proved that the FDs based ECCs (with as low as 10 wt% filler loading) had sufficient reliability for practical applications.
Simulation of the electromagnetic enhancement effect on a single FD branch. When illuminated by the laser beam, there are mainly two parts of electromagnetic (EM) thermal contribution for heating up the FDs. One is from the increased illuminated surface area per particle which promotes the absorption of heat accumulated from the illuminated area; another part is from the enhanced resonation with EM waves due to the presence of the unique nano-size features.
Based on the finite element analysis (FEA) method, we studied the resonance situation of the EM waves on the FD nano-features. The Maxwell equations were solved by the HFSS packages from ANSYS and the Ag complex dielectric constant was obtained from Johnson et al. 41 Based on the experimental observations summarized in Supplementary Table   1, we built the typical fractal fishbone-like models which were morphologically similar to the primary branches of various FDs, and assumed the lengths of all models were 2200 nm. The accumulation of EM field near some of the nano-structures with appropriate size was observed and compared with that of the particles having less complex features, as shown in Supplementary Fig. 33 (a) ~ (h). Based on the simulation results, under a large range of EM frequencies (from 532 nm to 6000 nm), most parts of the FD have EM resonance; particularly, thermal effect is significantly enhanced in the nano-sized regions.

Supplementary Methods
Multi-channel micro-droplet reaction system. In order to effectively manipulate the morphology and size of the precipitates and to ensure reproducibility in mass preparation, we set up a multi-channel micro-droplet reaction system, which can conveniently control the molar ratio of the reagents and the reacting rate in a continuous preparation condition.
The digital photo of the platform is shown in Supplementary Fig. 1a. Typically, 2.0 L of AgNO 3 (0.06 M) and NH 2 OH (Alfa Aesar) (0.24 M) aqueous solutions were prepared in two beakers, respectively. The solutions were pumped at the same velocity and joined together at the end of two or more needles. After forming the single droplets, the mixed liquid dropped down and continued reacting in the conical flasks array. During the reaction, the conical flasks were shaken gently at room temperature on the orbital shaker. A large amount of precipitate was observed in the conical flasks within several minutes. It was then filtered and washed by de-ionized water for three times, and then dried in a vacuum desiccator at room temperature. The as-synthesized FDs with various morphologies were shown in Supplementary Fig. 2.
Preparation of FDs. The size distribution of various FDs prepared at various conditions is shown in Supplementary   Table 1. Within a broad processing window, formation of FDs with various kinds of geometric characteristic and size can be obtained. For instance, when we controlled the molar ratio of NH 2 OH to AgNO 3 to 1 : 1 and the pumping rate to 0.5-5 mL min -1 , only the urchin-like FDs with rod-like branches were obtained, named with FD I. When these two key parameters were increased to 4 : 1 and 2.5 mL min -1 , we obtained FD II with rod-like branches and nano-sized secondary rims grown on them. The detailed reaction conditions of these six types of FDs are shown in Fig. 1a and Supplementary Preparation of Au FDs. Besides preparing the Ag FDs, this multi-channel micro-droplet reaction system can be used to prepare Au FDs as well. For example, by controlling the molar ratio of NH 2 OH to HAuCl 6 in the range of 2 to 40 and the pH value in the range of 4.5 to 8.0, Au FDs can be obtained in a scalable way ( Supplementary Fig. 4). The as-prepared Au FDs were characterized by its primary structures sized 1 to 1.5 m and secondary structures sized 40 to 50 nm. The morphological difference between Au FDs and Ag FDs can be attributed to the different reaction kinetics.