## 3 Results and Discussion  
The morphology of the CNP film was investigated by AFM. Figure 1a shows the acquired image of a continuous granular film with the grain size of the order of 200 nm. The AFM image reproduces the topological map of the deposited material on a sample area of 4 \(\times\) 4 \(\mu\)m\({}^{2}\). The maximum height of the film was 350 nm, so the volume of the  
Figure 1: (**a**) AFM image of the collected flame-formed CNPs deposited on the substrate. (**b**) Distribution of the heights measured in the AFM image. parallelepiped where all the particles are contained is 5.6 \(\upmu\)m\({}^{3}\). The integral of the height profile over the base area gives the volume occupied by the particles. The ratio between this integral and the volume of the parallelepiped is the volume fraction occupied by the carbon film; the complement to 1 is the void fraction. The distribution of the heights as obtained from the \"Roughness analysis\" tool in the AFM software is shown in Figure 1b. The void fraction of the film was \(\varphi\) = 0.56. As discussed in detail in [39], for a thermophoretically deposited film, the thickness, \(\delta\), is expressed by:  
\[\delta=\frac{N_{p}v_{th}}{(1-\varphi)}\frac{\pi}{6}D_{p}{}^{3}t_{dep} \tag{1}\]  
where \(N_{p}\) and \(D_{p}\) are the number and average diameter of the particles in flame, \(v_{th}\) is the thermophoretic velocity and \(\varphi\) is the void fraction of the film. In our deposition process, \(v_{th}\) =7 cm/s [39], \(N_{p}\) \(\sim\) 10\({}^{11}\) part/cm\({}^{3}\)\(D_{p}\) = 25 nm [40], and \(t_{dep}\) = 4 s, \(\varphi\) = 0.56 resulted in \(\delta\) \(\sim\) 500 nm. Figure 2 reports the Raman spectrum of the sample. It shows two main prominent peaks at the wavenumbers of 1350 and 1600 cm\({}^{-1}\) corresponding to the D and G bands of carbon materials [41, 42]. The intensity of the D band peak is dependent on the number of defects and boundaries in the graphitic areas, while the G band provides information about the sp\({}^{2}\) bonded carbon networks. The wideness of the bands indicates that the structure consists of very small crystallites. Based on the intensities of these bands, the average crystallite size of the graphitic component, \(L_{a}\), can be estimated using the following equation [41]:  
\[L_{a}^{2}\Big{(}\mathrm{nm}^{2}\Big{)}=5.4\times 10^{-2}\times E_{L}^{4}\Big{(} \mathrm{eV}^{4}\Big{)}\frac{I(\mathrm{D})}{I(\mathrm{G})} \tag{2}\]  
where \(E_{L}\) is the energy of the incident photon. From the spectrum in Figure 2, we obtain a \(I(\mathrm{D})/I(\mathrm{G})\) value of 0.9, which results, according to Equation (2), in \(L_{a}\) = 1.2 nm. This value of \(L_{a}\), roughly corresponds to the aromatic building blocks of particles formed in a similar flame that were imaged by AFM [24, 25]. The particle structure consisting of an aggregate of large aromatic molecules is also consistent with the presence of a fluorescence background in the spectrum in Figure 2.  
Further results of the size characterization of the pristine CNPs and the XPS and UPS analysis of the CNP film, performed in previous works, are shown in Figures S1-S5 in the Supplementary Materials. The I-V curve measured in the voltage range \(-\)10 V to 10 V is shown in Figure 3. The curve is symmetrical and non-linear, which is typical of granular systems [43]. Figure 2: Raman spectrum of flame-formed carbon nanoparticles. In these materials, the phenomenon of local electrical conduction can be described as the tunneling of electrons between two neighboring particles in a percolative network [44,45]. Based on these assumptions, [PERSON] and [PERSON] [43] derived the following theoretical equation that predicts the bulk I-V characteristic of a granular material in which the electrical conduction is governed by tunneling and percolation between grains.