## 3 Results and Discussion
Therefore, holes may accumulate in the oxide (while electrons are easily transported away by the bias) causing a gating effect that increases the \(n\)-type doping. This process is dominant for MoS\({}_{2}\), where there is a limited release of energy and negligible S displacement because of the atomic thickness. Our results are of interest to evaluate the radiation hardness of 2D materials to develop devices working in high radiation environments (such as space or nuclear plants). Finally, we also performed a complete field emission characterization of PdSe\({}_{2}\) and MoS\({}_{2}\) nanosheets, to profit from the sharp edges of 2D materials as well as from a work function that, in these materials, decreases with the decreasing number of layers [37] (4.3 eV in monolayer PdSe\({}_{2}\)[19] and about 4.4 in monolayer MoS\({}_{2}\)[38]). The high aspect ratio and the low work function are desirable parameters to extract electrons from a material by means of an external electric field (field emission). The main interest in field emission is in the vacuum electronics context, in electrically operated floating gate memory cells or displays in electron and X-ray sources [39; 40; 41; 42; 43]. The most widely accepted theoretical framework to describe the field emission (FE) phenomenon was created by [PERSON] and [PERSON]. They developed the so-called Fowler-Nordheim (FN) theory [44] based on a one-dimensional free electron model to calculate the tunneling probability through a triangular barrier. In this model, the FE current is written as:  
\[\mathrm{I}=\mathrm{S}\cdot\mathrm{A}\phi^{-1}\left(\beta\frac{\mathrm{V}}{ \mathrm{d}}\right)^{2}\exp\left[-\mathrm{B}\ \phi^{3/2}\left(\beta\frac{\mathrm{V}}{\mathrm{d}}\right)^{-1}\right] \tag{2}\]  
where S is the emitting surface, \(\phi\) is the work function of the emitter, \(\beta\) is the field enhancement factor, V/d is the applied electric field (V is the applied voltage, d is the separation distance between the emitter and the anode), A and B are dimensional constants. Field emission measurements, reported in Figure 5, were performed in the high-vacuum chamber of a scanning electron microscope equipped with piezo-driven metallic nanoprobes, for both PdSe\({}_{2}\) and MoS\({}_{2}\) nanosheets. In particular, we placed one probe on the metal electrode contacting the nanosheet (cathode emitter), while the second tip (anode) was positioned at a controlled (with nanometric precision) separation distance d from the emitter. The current-voltage, I-V, characteristics are then measured by performing a voltage sweep up to maximum 100 V (to avoid circuit failure) and recording the flowing current with a resolution better than 0.1 pA. The layout of the FE setup is shown in Figure 5a. The field emission I-V characteristic measured for a 4-nm-thick PdSe\({}_{2}\) sample is reported in Figure 5b. The experiment was performed by positioning the tip anode at d = 200 nm from the emitter surface. We could then evaluate the turn-on field E\({}_{\text{turn-on}}\), i.e., the field at which the current starts to raise exponentially, and we found that E\({}_{\text{turn-on}}\approx\)80 V/\(\mu\)m, considering that E\({}_{\text{turn-on}}\) = V/(k\({}_{\text{tip}}\cdot\)d), where k\({}_{\text{tip}}\) = 1.6 is a correction factor to take into account the tip-shaped anode [45]. In addition, the field enhancement factor \(\beta\) can be evaluated from the slope m of the linear Fowler-Nordheim plot, ln\(\left(\mathrm{IV}^{-2}\right)\) vs V\({}^{-1}\), shown in Figure 5d, considering that \(\beta\ =\ -\mathrm{B}\ k_{\text{tip}}\mathrm{d}\ \phi^{3/2}\)/m, and we found \(\beta\) = 44 for the cathode-anode distance of 200 nm. Similarly, FE characterization was performed on monolayer MoS\({}_{2}\) (Figure 5c) at a separation distance d = 200 nm. The linear FN plot reported in Figure 5e confirmed the FE nature of the measured current. We found that the turn-on field is about 100 V/\(\upmu\)m and \(\beta\) = 54.