## 3 Results and Discussion
### Photoelectrochemical Properties of TiO\({}_{2}\)/FTO and Au/TiO\({}_{2}\)/FTO Photoelectrodes
The obtained hodographs can be approximated by an equivalent electrical circuit [34] shown in Figure 6b, the approximation parameters are given in Table 2. The circuit consists of a series resistance \(\mathrm{R_{D}}\), which includes the resistances of conductive glass and electrolyte \(\mathrm{R_{w}}\), which is associated with the transfer of charge carriers from the photoelectrode surface to the electrolyte solution, and \(\mathrm{R_{K}}\), which is responsible for the processes that occur on the counter electrode and at the interface between the phases, the counter electrode/electrolyte. The capacitors \(\mathrm{C_{1}}\) and \(\mathrm{C_{2}}\) in the diagram denote electric double layers arising at the interface between the phases of the working electrode/electrolyte and the counter electrode/electrolyte, respectively. The \(\mathrm{R_{D}}\) parameter shows the resistance in the electrochemical circuit associated with the resistance of the solution itself, the connection of electrodes to an external circuit, etc. As a rule, this value is no more than 10 \(\Omega\) and depends only slightly on the nature of the photoelectrode. The \(\mathrm{R_{k}}\) parameter, which reflects the processes occurring on the counter electrode, sharply decreases when gold is deposited on titanium dioxide. In the case of the \(\mathrm{R_{W}}\) parameter, which reflects the processes occurring at the working electrode, it is difficult to establish certain patterns. In the general case, changes in resistance are associated with the features of the microstructure of the samples, the formation of an electric double layer, and the transfer of charges across the phase interface. Additionally, the lifetimes of charge carriers were calculated from the impedance data and are shown in Table 2. The lifetime of electrons for a sample containing gold is almost an order of magnitude higher than that for titanium dioxide. Note that an increase in the short-circuit current density also occurs 10 times. The deposition of gold on the surface of titanium dioxide leads to an improvement in the separation of electron-hole pairs, which is quantitatively reflected in the same changes in the electron lifetime and short circuit current density. According to modern concepts, plasmonic nanoparticles can affect the photoelectrochemical properties in three ways: plasmon-induced resonant energy transfer, scattering, and hot electron injection (direct or indirect mechanism) [35]. The most probable mechanisms are a combination of scattering and injection of hot carriers into the semiconductor \(\mathrm{TiO_{2}}\) layer. This assumption follows from Table 2, where it is shown that the addition of plasmonic gold nanoparticles leads to an increase in the concentration of charge carriers from 2.0 \(\times\) 10\({}^{17}\) to 2.5 \(\times\) 10\({}^{18}\) cm\({}^{-3}\). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Sample** & \(\mathrm{R_{K}}\)**, \(\Omega\)** & \(\mathrm{R_{W}}\)**, \(\Omega\)** & \(\mathrm{R_{D}}\)**, \(\Omega\)** & \(\mathrm{R^{2}}\)** & \(\mathrm{\tau_{r}}\)**ms** & \(\mathrm{V_{fb}}\)**, \(\mathrm{V}\)** & \(\mathrm{N_{r}}\)**m\({}^{-3}\)** \\ \hline \(\mathrm{TiO_{2}}\)/FTO & \(254\pm 1\) & \(0.83\pm 0.05\) & \(10.0\pm 0.2\) & \(0.999\) & \(0.12\) & \(-0.34\) & \(2.0\times 10^{17}\) \\ \hline Au/\(\mathrm{TiO_{2}}\)/FTO & \(1.0\pm 0.1\) & \(3.05\pm 0.03\) & \(4.8\pm 0.1\) & \(0.989\) & \(1\) & \(-0.43\) & \(2.5\times 10^{18}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Approximation of data obtained using impedance spectroscopy. Figure 6: Nyquist plots for \(\mathrm{TiO_{2}}\)/FTO and Au/\(\mathrm{TiO_{2}}\)/FTO (**a**); equivalent circuit used to simulate the frequency dependence of the impedance of an electrochemical cell (**b**).