## 3 Results  
The porous nature of the films can be clearly seen in the SEM image in Figure 1a. To confirm the incorporation of ZrO\({}_{2}\) nanoparticles in the host carbon matrix, XRD diffractograms of samples prepared at different pyrolysis temperatures were obtained, as shown in Figure 1b. The XRD patterns of the ZrO\({}_{2}\) nanoparticles show a series of well-defined peaks at 2\(\theta\) values of 30.1\({}^{\circ}\), 34.9\({}^{\circ}\), 50.3\({}^{\circ}\), and 60\({}^{\circ}\), which are attributed to the diffractions of the (111), (200), (220), and (311) crystalline planes of the cubic phase according to JCPDS card no. 01-089-9069. The crystallite size of ZrO\({}_{2}\) nanopowder calculated using [PERSON]'s  
Figure 1: (**a**) SEM photo of a pyrogallol-formaldehyde/ZrO\({}_{2}\) (PF/ZrO\({}_{2}\)) sample. (**b**) The evolution of the XRD diffractograms with the pyrolysis temperature. (**c**) Schematic diagram showing the sample mounted in a heat sink and the electrical connections. equation is estimated to be equal to 3 nm and increases from 3 to 6 nm when the pyrolysis temperature increases above 600 \({}^{\circ}\)C [17]. In our previous studies [15; 18], we demonstrated that the incorporation of nanoparticles in the host carbon matrix ameliorated the textural properties and the dielectric behavior of the composite material. We proposed that the nanoparticles played the role of a structuring agent that improved the arrangement of the conduction chains. The electrical behavior of the pyrogallol-formaldehyde/ZrO2 (PF/ZrO2) composite was investigated using I-V characterization. The devices were sandwich structures (Ag/PF(ZrO2)/ Ag) using silver paint contacts on both faces. The I-V curves show NDR behavior at high voltages. Figure 2a shows two I-V curves with NDR for two different voltage scan rates. During the forward voltage scan, the current follows a linear behavior that changes to an exponential rise at high voltages. When the voltage scan is reversed, the current continues to increase while the voltage decreases, resulting in an NDR region over a voltage range. The return path has a higher current than the forward path, leading to an anticlockwise hysteresis in the I-V loop. Figure 2: (**a**) Current–voltage characteristics recorded with two different voltage ramp speeds. (**b**) Comparison between I-V curves measured with a pulsed method and with a voltage ramp method. I-V curves like those shown in this study have been reported in carbon nanocomposites [18] and other materials such as chalcogenide semiconductors [19] and transition-metal oxides [20]. The voltage scan rate also plays a significant role in the magnitude of NDR, as the duration of applied voltage determines the amount of heat generated through Joule heating. When the device enters the NDR regime, it is necessary to stabilize the I-V curve to prevent thermal runaway, which can damage the device. This can be achieved by decreasing the applied voltage or using a thick device with an intrinsic series resistance that limits the thermal runaway. Thermally activated transport is generally accepted as the cause of negative differential resistance (NDR) in materials such as carbon nanocomposites, chalcogenide semiconductors, and transition metal oxides. This phenomenon occurs due to the low thermal conductivity of the matrix material, and the response time is limited by the heat capacity and generation rate of the device. It is generally agreed that amorphous carbon materials behave as semiconductor materials. Several mechanisms have been proposed to describe the charge transport depending on the temperature range, encompassing the range from an easy thermally activated process obeying the Arrhenius equation to more complex mathematical models, such as variable range hopping. A study by [PERSON] [21] provides a comprehensive review of the models used to interpret the electrical conductivity of amorphous carbon.