# Electroless Copper Patterning on TiO\({}_{2}\)-Functionalized Mica for Flexible Electronics
## 3 Results and Discussion
### Thickening of Cu-ELD Layers by Copper Electroplating
The temperature response of RTDs is typically quantified by calculating the temperature coefficient of resistance (TCR). Figure 11b shows the functional dependence of DCR on temperature. The DCR value, obtained after stabilization at the end of each 5 min heating step, is plotted against the corresponding temperature, revealing a linear correlation and an overall 6% change in resistance for this particular RTD pattern. The resistance-temperature dependence could be defined as R(T) = R\({}^{0}\)\(\times\) (1 + TCR \(\times\) T), where R\({}^{30}\) is the initial resistance, measured at 30 \({}^{\circ}\)C; thus, the TCR can be derived from the slope of the plot R(T)/R\({}^{30}-1\) vs. T. In the example in Figure 11b, the change is expressed in percentage; however, TCR values are commonly reported in ppm/\({}^{\circ}\)C. Experiments were performed in triplicate for the three Cu-ELD cases discussed previously, fabricated with 1, 1.5, and 2 min electroless deposition durations, and two additional samples were included for validation, fabricated with 1.25 and 1.75 min durations. The electroplating-thickened Cu-ELD layers from Section 3.3 were excluded due to their low initial DCR (\(\sim\)0.7 \(\Omega\)), which resulted in RTD changes below the 0.01 \(\Omega\) resolution of the LCR meter. The general trends in the RTD properties of the Cu-ELD layers, as influenced by electroless deposition time, are shown in Figure 12, along a summary of all of the numerical data, which is presented in Table 2. The DCR at a fixed temperature decreased exponentially  
Figure 11: Representative data showing the performance of Cu-ELD patterns as resistance temperature detectors for a Cu-ELD serpentine pattern developed on a TiO\({}_{2}\)/Mica substrate during 2 min of electroless deposition: (**a**) raw data showing the correlation between temperature and direct current resistance; (**b**) processed data showing the functional dependence used to estimate the temperature coefficient of resistance (TCR). with the increasing Cu-ELD duration, from 670 \(\Omega\) to 50 \(\Omega\) for deposition times between 1 and 2 min (Figure 12a). This behavior, which aligns with the AFM-measured thickness range of 71-131 nm, is consistent with exponential resistance increases observed in the literature for even vacuum-deposited copper layers [44]. The absolute change in resistance from 30 \({}^{\circ}\)C to 65 \({}^{\circ}\)C (\(\Delta\)R) was roughly proportional to the initial resistance R\({}^{30}\), as shown in Figure 12b. This suggests that thinner Cu layers, which have higher intrinsic resistance, exhibit larger measurable changes in resistance, potentially making their readout easier in practical applications. However, this linear relationship does not perfectly correspond to the estimated TCR values, which increased from 995 to 1800 ppm \({}^{\circ}\)C\({}^{-1}\) with increasing Cu-ELD durations and layer thicknesses. Even the best-case TCR was about 50% lower than the literature value for metallic copper (3930 ppm \({}^{\circ}\)C\({}^{-1}\)) [45], likely due to the influence of the photodeposited Ag catalyst, which generally has a lower TCR than copper, especially in thinner Cu layers.