# EBIC Imaging of Conductive Paths Formed in Graphene Oxide as a Result of Resistive Switching
## 3 Results and Discussion
However, in order to contribute to the observed EBIC image at a zero bias, the e-h pairs generated by an electron beam in Si substrate should be separated by a potential barrier at the Si/GO interface. As the experimentally determined sign of the current collected at the bright spots indicates a flow of holes, e-h pairs must be separated by an electric field directed to the structure surface to contribute to the collected current. This implies that the potential barrier should be formed near the GO/Si interface. Formation of this potential barrier can be due to either the existence of a negative charge inside the GO film or the difference in the work function values for n-type Si and graphene oxide. As shown in [21], the presence of a negative charge within the virgin GO film can be ruled out by the capacitance-voltage measurements, revealing the presence of a positive charge that drives n-Si in accumulation. On the other hand, the work function values for GO can vary from 3.7 eV to 5.1 eV [45] and may be larger than that for n-Si (\(\sim\)4.5 eV). Therefore, if the GO properties are locally changed during the process of resistive switching, then a barrier separating generated carriers and collecting holes can be formed owing to the changed GO work function. Although the origin of the hole collecting barrier is not known, we can conclude that this barrier is formed at the interface of the n-Si substrate and the conductive channels are formed within the GO film. This conclusion further confirms the existing link between the bright spots in EBIC mode and the conductive paths in the GO film. The induced current in Si depends on the number of generated excess carriers, which, for the fixed beam current, is proportional to both \(E_{b}\) and the collection probability of the excess carriers. The diffusion length in Si is usually larger than 30-100 \(\upmu\)m; therefore, the collection probability should be close to 1 even for \(E_{b}\) = 30 keV. However, the collection probability in the studied structures is notably smaller than 1 and decreases with an increasing \(E_{b}\). As will be discussed below, this can be considered as an indication of the contact size of the nanometer range. A decrease in the induced current observed after transition from a high to a low resistance state can be determined by considering a conductive path as a contributor to  
Figure 5: Deposited energy dependence on depth per one primary electron calculated for \(E_{b}\) of 10 keV (blue) and 20 keV (wine). The inset shows the deposited energy depth dependencies at a small depth. series resistance for the hole collecting barrier. If the resistance of the conductive path is \(R_{path}\), its effect on the measured current \(l_{c}\) can be described as  
\[l_{c}=I_{ind}-I_{0}[\exp(\frac{el_{c}R_{path}}{nkT})-1] \tag{1}\]  
where \(I_{0}\) is a reverse saturation current flowing through the measured structure, \(k\) is Boltzmann constant, \(T\) is temperature, \(n\) is the ideality factor, and \(I_{ind}\) is the current induced by an e-beam inside a semiconductor in the short-circuit condition. It is easy to see from Equation (1) that, under the same excitation conditions, \(I_{c}\) increases with decreasing \(R_{path}\), thus allowing to monitor local resistance changes. As an example, the neighboring conductive paths with different brightness are shown in Figure 6. As the SE image in Figure 6b does not reveal any surface defects, which could lead to the contrast difference, a variation in conductive path resistance and/or, as shown below, its radius could be reasons for the different brightness (Figure 6a). The very bright spot shown in Figure 4 is most likely associated with an agglomeration of parallel nano-size conductive paths with a very low combined resistance. Additionally, the bright spots can be revealed only if \(R_{path}\) is rather low, i.e., only if a conducting channel connects the rectifying contact with the top Al electrode.