## 3 Results and Discussion
\[I=C\bigg{[}\frac{A-BV}{e^{\{\frac{A-B\text{-}V}{I}\}}-1}-\frac{A+BV}{e^{\{\frac{A +B\text{-}V}{I}\}}-1}\bigg{]} \tag{3}\]  
where \(A\) is proportional to the activation energy of the process \(E_{a}\) through the Boltzmann constant \(k_{B}\):  
\[A=\frac{E_{a}}{k_{B}} \tag{4}\]  
\(B\) depends on both temperature and material, and \(C\) has an exponential dependence on the tunneling distance \(S\):  
\[C\propto exp^{\ (-S)} \tag{5}\]  
The curve fitting the data according to Equation (3) is also reported in Figure 3 as the red line. As can be seen, Equation (3) agrees very well with the data. Repeated measurements furnish an activation energy \(E_{a}\) of about 70 meV. Thermally excited carriers can pass through the barrier by quantum-mechanical tunneling. When the temperature increases, the number of thermally excited carriers increases and thus current increases. This is shown in Figure 4 where the current measured for an applied voltage of 10 V is measured while the temperature is changed stepwise from 26 \({}^{\circ}\)C to 85 \({}^{\circ}\)C. It can be seen that the current also increases stepwise. The thermal characterization of the CNP film was then performed measuring the I-V curves in the temperature range of 300 to 400 K with a step of 10 K. Heating cycles were repeated over various days. The film showed a good repeatability of the response to the heating cycle, recovery and stability over time. That can be seen by the reproducibility of the curve shown in Figure S6 in the supplementary material, taken at ambient temperature and at 50  
The resistance significantly decreases when the temperature increases from 300 K to 400 K; however, the rate of such a decrease is almost linear with T up to 320 K, and it reaches a plateau above 340 K. The change in the resistance of the film also showed good reproducibility over days, within a few percent. The decrease in the electrical resistance with increasing temperature indicates that the conduction of the CNP film is thermally activated. This is consistent with the presence of an energy barrier that the electron needs to overcome while moving from one grain to another. From the fitting of the curves with Equation (3) (see Table S1 in Supplementary Materials) results that \(E_{a}\) slightly increases with T, indicating that the conduction process cannot be described by a Arrhenius behavior. This is also shown by the nonlinear trend in the plot in Figure 6, in which the \(ln(R/R_{0})\) versus \(1/(k_{b}\,^{*}\)T) is reported, where R\({}_{0}\) is the resistance of the film at ambient temperature and \(k_{b}\) the Boltzmann constant. The C parameter obtained from the fit increases with T. This indicates that the tunneling distance reduces with the increase of T, which can be justified by the thermal expansion of the film grains. Figure 4: Current measured for an applied voltage of 10 V when the temperature is raised stepwise from the ambient temperature to 85 \({}^{\circ}\)C.  
\[\delta=\frac{N_{p}v_{th}}{(1-\varphi)}\frac{\pi}{6}D_{p}{}^{3}t_{dep} \tag{1}\]0 **(a)** I-V curves measured for applied voltage ranging from \(-\)10 V to 10 V at ambient temperature and T increasing from 300 to 393 K with a step of 10 K. **(b)** Electrical resistance, \(\Delta V/\Delta I\), measured in the temperature interval of 300 K–400 K and the temperature dependence of the derivative of resistance with respect to the temperature. The change of resistivity with respect to temperature can be exploited for temperature sensing. In analogy with negative coefficient thermistors, the temperature coefficient of resistance (TCR) can be defined by the following Equation:  
\[\delta=\frac{N_{p}v_{th}}{(1-\varphi)}\frac{\pi}{6}D_{p}{}^{3}t_{dep} \tag{1}\]1  
The measured TCRs are shown in \[\delta=\frac{N_{p}v_{th}}{(1-\varphi)}\frac{\pi}{6}D_{p}{}^{3}t_{dep} \tag{1}\]2 The values range from \(-100\times 10^{-4}\) K\({}^{-1}\) to \(-170\times 10^{-4}\) K\({}^{-1}\), which are comparable to that of Polysilicon (from \(-250\times 10^{-4}\) K\({}^{-1}\) to \(-10\times 10^{-4}\) K\({}^{-1}\)) [46].