# The Effect of Local Doping of the Polymer-Polymer Interface Using Cu\({}_{2}\)O Particles
## 3 Results and Discussion  
Figure 4 shows typical volt-ampere characteristics (VAC) of two types of experimental structures measured along the polymer-polymer interface. The difference between these VAC is that curve two corresponds to a sample with an insular copper oxide film along the interface, and that curve two corresponds to a sample without an insular copper oxide film. It is clearly seen that the introduction of an insular layer of Cu\({}_{2}\)O along the polymer-polymer interface leads to an increase in the current flowing through the sample (Figure 4a, red curve) compared to the sample in which there is no insular layer (Figure 4a, black curve). Both dependences have a nonlinear character, which is often observed when injecting charge carriers into organic semiconductors and dielectrics. Usually, such dependence can be approximated by a function of the form  
\[I\sim U^{n}, \tag{4}\]  
where \(I\) is the current and \(U\) is the voltage. The conversion of the VAC in logarithmic coordinates allows us to estimate some parameters of the injection model. Figure 4b shows the VAC in logarithmic coordinates. It is clearly seen that in different ranges of applied voltage, the functional dependence I = f(U) is different. Both dependences have a nonlinear character. This is often observed when charge carriers are injected into organic semiconductors and dielectrics. The insertion of an island layer of Cu\({}_{2}\)O along the polymer-polymer interface leads to an increase in the current through the sample (Figure 4a, red curve) compared to the sample with no island layer (Figure 4a, black curve). For the volt-ampere characteristics, two areas of dependence are well distinguished: Ohmic at low voltages and superlinear at high voltages. Estimates of the electronic characteristics of experimental structures were carried out within the framework of a theoretical model for space-charge-limited currents [34]. This model has previously been successfully used to study charge transfer in complex multi-layer structures containing metal-polymer interfaces or polymer-polymer boundaries [10]. According to this model, at low voltages, the current is caused by its own charge carriers and therefore the VAC has a linear Ohmic form:  
\[j=\frac{en_{0}\mu L_{n}}{L}, \tag{5}\]  
Figure 4: (a) Volt-ampere characteristics measured along the interface of polymer films, (b) in semi-logarithmic and (c) logarithmic coordinates. 1—PDPh–PDPh, 2—PDPh–Cu\({}_{2}\)O–PDPh. \(I_{s}\)1,2—are the saturation currents for doped and non-doped samples. where \(j\) is the current density, \(L\) is the distance between the electrodes, \(U_{n}\) is the voltage corresponding to the transition point on the VAC from the linear to the superlinear section, \(n_{0}\) is the concentration of proper charge carriers, \(\mu\) is the mobility of charge carriers and \(e\) is the elementary electric charge (electron charge). The current of charge carriers injected from the electrode has a power dependence on the applied voltage:  
\[j=\frac{\varepsilon\varepsilon_{0}\mu U_{n}^{2}}{L^{3}} \tag{6}\]  
where \(\varepsilon_{0}\) = 8.85 \(\times\) 10\({}^{-12}\) F\(\cdot\)m\({}^{-1}\) is the dielectric constant and \(\varepsilon\) = 3 is the dielectric permittivity of the polymer. The equality of the currents described using Formulas (5) and (6) corresponds to the transition from a linear section to a superlinear one on the VAC curve.