## 3 Results and Discussion  
To investigate the effect of polymer viscosity on the thickness difference of the silver-nanowire-embedded flexible electrodes, we first used polymer SU8 to embed silver nanowires because its viscosity can be controlled while maintaining its physical properties such as the elastic modulus, strength, and hardness. Figure 2a-c shows the viscosity of SU8 as a function of the solid content and the thicknesses at the center and edge of the electrode as functions of the spin speed for different viscosities. As seen in Figure 2a, we controlled the viscosity of SU8 by tuning the solid content and successfully fabricated silver-nanowire-embedded flexible electrodes. We subsequently measured the film thickness at the center, finding higher values for increasing prepolymer solution viscosity. For example, when SU8 was coated at 500 rpm, the thicknesses were 27.5 \(\pm\) 6.2 \(\upmu\)m, 33.3 \(\pm\) 7.8 \(\upmu\)m, 45.8 \(\pm\) 10.0 \(\upmu\)m, and 75.0 \(\pm\) 23.9 \(\upmu\)m for viscosities of 52 cps, 165 cps, 451 cps, and 1500 cps, respectively. As the viscosity increases, the solution is increasingly difficult to spread during spin coating, and solid residuals remain on the substrate. Thus, thicker silver-nanowire-embedded transparent electrodes are obtained after delamination from the substrate. When we increased the spinning speed, the film thickness decreased, being 27.5 \(\pm\) 6.2 \(\upmu\)m, 16.7 \(\pm\) 7.8 \(\upmu\)m, 12.5 \(\pm\) 4.6 \(\upmu\)m, and 11.3 \(\pm\) 3.5 \(\upmu\)m at spinning speeds of 500 rpm, 1000 rpm, 2000 rpm, and 3000 rpm, respectively, for a SU8 viscosity of 52 cps. This was because the centrifugal force increases at higher spinning speed, and the polymer spreads easier. The trend of the thickness at the edge was similar, but reached slightly higher values. For example, though the flexible electrode prepared with the SU8 of viscosity 52 cps had a thickness of 27.5 \(\pm\) 6.2 \(\upmu\)m at the center, its edge thickness was 71.7 \(\pm\) 11.1 \(\upmu\)m. We speculate that the edge of a PMMA-coated substrate acts as a barrier, inducing prepolymer accumulation at the edge of the substrate during spin coating. We then calculated the thickness difference by subtracting the thickness at the center from that at the edge. Figure 3a shows the thickness difference as a function of the spin speed for different prepolymer solution viscosities. As can be seen, the thickness difference was high at low spin speed and low at high spin speed. For example, it was 44.2 \(\upmu\)m at 500 rpm and 12.1 \(\upmu\)m at 3000 rpm for a SU8  
Figure 2: **(a)** Viscosity of the SU8 prepolymer solution as a function of the solid content and (b,c) electrode thickness at the (b) center and (c) edge as a function of the spin-coating speed for different prepolymer solution viscosities. The inset in (a) is a photograph of a SU8-embedded silver-nanowire-embedded electrode. viscosity of 52 cps. This is because a lower spin speed induces thicker films; consequently, the absolute value and difference of the thickness are high at low spin speeds. For similar reasons, the absolute value and difference of the thickness are low at high spin speeds. Therefore, to accurately compare the thickness difference among the samples with different viscosities, a normalized value is needed. Figure 3b presents the thickness ratio, calculated by dividing the thickness of the center by that of the edge for all the silver-nanowire-embedded electrodes in SU8. Although the thickness ratio was slightly different for different spin speeds and viscosities, it ranged between 50% and 70%, with a mean of approximately 60%. This indicates the existence of a specific thickness ratio, independent of the spin speed and prepolymer solution viscosity. Next, we examined the effect of viscosity with the NOA series (NOA63, NOA65, NOA71, and NOA73) polymers, which are the most common materials used to embed silver nanowires for electrodes because, in contrast with SU8, they are very transparent.