# The Effect of Local Doping of the Polymer-Polymer Interface Using Cu\({}_{2}\)O Particles
## 3 Results and Discussion
Thus, by equating these currents with each other, it is possible to estimate the concentration of its own charge carriers:  
\[n_{0}=\frac{\varepsilon\varepsilon_{0}U_{n}}{eL^{2}}, \tag{7}\]  
It is also possible to estimate the effective mobility of the charge carriers:  
\[\mu_{eff}=\frac{jL^{3}}{\varepsilon\varepsilon_{0}U_{n}^{2}} \tag{8}\]  
The parameters of charge carriers calculated according to (7) and (8) are as follows: for the PDPh-PDPh interface, the concentration of charge carriers is \(n_{0}\approx\) 1.7 \(\times\) 10\({}^{17}\) m\({}^{-3}\) and the mobility of the charge carriers is \(n_{\text{eff}}\approx\) 1.2 \(\times\) 10\({}^{-2}\) cm\({}^{2}\)/V\(\cdot\)s for the PDPh-Cu\({}_{2}\)O-PDPh interface \(n_{0}\approx\) 2.5 \(\times\) 10\({}^{17}\) m\({}^{-3}\) and \(\mu_{eff}\approx\) 2.5 \(\times\) 10\({}^{-1}\) cm\({}^{2}\)/V\(\cdot\)s, respectively. The presented evaluation results showed that the introduction of an island Cu\({}_{2}\)O film along the polymer-polymer interface practically does not affect the concentration of charge carriers. At the same time, the island film strongly affects the mobility of charge carriers, increasing it by almost an order of magnitude along the interface. The potential barrier height at the metal-polymer boundary was estimated based on the Richardson-Dashman equation [35] using the formula:  
\[e\varphi_{\text{B}}=kT\ln\left(\frac{SA^{**}T^{2}}{I_{S}}\right) \tag{9}\]  
where \(T\) is the temperature, \(k\) is the Boltzmann constant, \(e\) is the electron charge, \(S\) is the contact area, \(A^{**}\) is the Richardson constant and \(I_{S}\) is the saturation current. The saturation current is located from the intersection of the linear approximation of the VAC in semi-logarithmic coordinates (ln(\(I\)) \(-\)\(U\)) with axis \(U\) = 0 V. Thus, in order to estimate the value of \(I_{S}\), the voltage characteristics shown in Figure 4a were converted in semi-logarithmic coordinates. The corresponding dependencies are shown in Figure 4.  
As a result, the following values of the height of the potential barrier were obtained: for the PDPh-PDPh interface--\(\varphi_{\text{B}}\approx\) 0.45 eV; for the PDPh-Cu\({}_{2}\)O-PDPh interface--\(\varphi_{\text{B}}\approx\) 0.34 eV. One can confidently state the change in the transport of charge carriers along the polymer-polymer interface when an island Cu\({}_{2}\)O film is placed on it. Apparently, this may be an important confirmation that it is the interface that is the transport layer for charge carriers. Increasing the mobility of charge carriers to values comparable to the parameters of charge carriers in Cu\({}_{2}\)O (2.34 \(\times\) 10\({}^{-1}\) cm\({}^{2}\)/V\(\cdot\)s [22]) also confirms this conclusion. Noteworthy is the significant decrease in the height of the potential barrier at the contact of the metal electrode with the quasi-two-dimensional polymer-polymer region. Such a decrease in the potential barrier can be explained on the basis of the 3D/2D contact model considered in [36]. According to this model, the injection of charge carriers into a two-dimensional one occurs by sequentially passing through a potential barrier located under the electrode and a barrier formed at the edge of the metal electrode. There are several assumptions in this model. First of all, it is assumed that a three-dimensional metal electrode is formed directly on a two-dimensional region. At the same time, there is no strong surface interaction between the metal electrode and the two-dimensional region due to the overlap of orbitals between metal atoms and molecules below the underlying layer. In the case of metal and polymer surface contact, relatively weak adhesion occurs very often. This may indicate the implementation of the contract at the expense of Van der Waals forces. It can lead to a limitation of the injection current due to a potential barrier of a certain height. In our case \(\varphi_{\text{B}}\approx 0.45\) eV.