# On the Use of PEDOT as a Catalytic Counter Electrode Material in Dye-Sensitized Solar Cells
## 2 Dye-Sensitized Solar Cells: An Overview
where \(F\) is the electric field possibly present within the semiconductor and \(u_{n}\) is the electron mobility, related to the diffusion coefficient \(D_{n}\) by  
\[\mathbf{D_{n}}=\frac{\mathbf{k}\mathbf{T}}{\mathbf{e}}\mathbf{u_{n}} \tag{6}\]  
In the case of mesoporous semiconductors composed of a network of sintered nanocrystals, there is a significant population of localized states (L) in the band gap, which are generally regarded as non-conductive, as opposed to conductive delocalized conduction band (CB) states. Charge transport thus occurs by trapping and detrapping of the carriers from and to conductive states, and, if charge trapping and detrapping are sufficiently fast processes, transport can be described in terms of quasi-equilibrium charge densities in both localized and conductive states [29]. In this latter case, the electron diffusion coefficient \(D_{n}\) can be expressed according to 7 [30]. Figure 2.0  
where \(n_{L}\) and \(n_{CB}\) indicate the electron density in localized and conductive states, respectively, and \(D_{0}\) is the electron diffusion coefficient in the conductive states. With mesoporous TiO2, charge transport is among the slowest processes occurring in Dye-sensitized solar cells, with a time constant of the order of 1 ms [31]. Nevertheless, with suitable redox couples, such as the often-used \(\mathrm{I^{-}}/\mathrm{I_{3}}^{-}\) couple, regeneration of the dye occurs on a time scale ca. 3 orders of magnitude shorter, preventing to a large extent electron recombination with the oxidized dye. The major charge recombination loss is thus related to the bielectronic reduction of \(\mathrm{I_{3}}^{-}\), a slow process (on the tens/hundreds ms time scale) at the photoanode, due to the poor electrocatalytic properties of both TiO2 and FTO. This may result in nearly unit charge collection efficiency by sensitized TiO2 thin films having a typical thickness \(\leq\) 10 \(\mathrm{\SIUnitSymbolMicro m}\). As will be detailed in the following sections, \(\mathrm{I_{3}}^{-}/\mathrm{I^{-}}\), the most common redox mediator initially, has been replaced by cobalt and copper redox shuttles which, in some cases, allowed record power conversion to be reached but, being faster monoelectronic couples, also required tuning of the titania film thickness and appropriate surface insulation with respect to electron recapture by the oxidized form of these new redox mediators [32]. From a phenomenological point of view, Dye-sensitized solar cells have been shown to follow the diode equation according to Equation (8). Figure 2.1  
where \(J_{L}\) is the limiting current density depending on the absorbed photon flux, \(Vj=V+IR\) is the potential drop across the cell, related to the applied bias \(V\) in the presence of the potential drop \(IR\), where \(R\) can be regarded as the total series resistance of the cell and \(m\), is the ideality factor of the diode characterized by the equilibrium dark current density \(J_{0}\). \(m\), \(Jo\), and R are dependent on the specific chemical nature of the system and summarize the quality of the cell components and interfaces with respect to charge recombination and electron mediator regeneration kinetics [33]. A small dark current (low losses by charge recombination) and a small series resistance (which translates into a small overpotential loss for electrolyte regeneration) generally improve the PCE of the solar cell, given by  
Figure 2.2  
where \(V_{oc}\) is the open circuit photovoltage (V), \(J_{L}\) is the short circuit photocurrent density (A m\({}^{-2}\)), \(FF\) is the cell fill factor, and \(\mathrm{P_{s}}\) is the total optical power density at the cell surface (W m\({}^{-2}\)) [1].