The steadystate currentvoltage curve and dynamic response of a dyesensitized solar cell (DSSC) is mathematically modeled based on electrical equivalent circuit. The effect of temperature and illumination on the steadystate and dynamic parameters of dyesensitized solar cells is studied. It is found that the dynamic resistance of DSSC decreases from 619.21
In recent years, dyesensitized solar cells (DSSCs) have attracted much attention as a potential lowcost alternative to single or polycrystalline pn junctionbased silicon solar cells. Various oxidebased materials such as NiO_{2}, Fe_{2}O_{3}, ZnO, SnO_{2}, and TiO_{2} have been studied for photoelectrochemical [
Usually the dye molecules have low absorption coefficient. The low absorption coefficient of a dye monolayer is compensated by the mesoporous structure of the TiO_{2} film, which leads to a strong increase in the number of TiO_{2}/dye/electrolyte interfaces through which photons pass, thus increasing the absorption probability. This phenomenon uses the increased surface area due to associated porosity of the TiO_{2} layer. In fact, studies on the DSSC electrode morphology showed that the light absorption coefficient
An operating DSSC is principally governed by the relative kinetic rates of several charge transfer steps. The charge transfer taking place from excited dye to TiO_{2} nanoparticle, from electrolyte to the dye, and from TiO_{2} to the load terminals plays very critical role in the performance of DSSC. Thus, it is very important to understand all the electronic processes taking place at the TiO_{2} nanoparticles level, as well as the dynamics of charge separation and charge transport at the metal/oxide interface. The schematic band diagram of dyesensitized solar cell is shown in Figure
Band diagram and electron transport in dyesensitized solar cell.
The redox electrolyte is responsible for the dye regeneration, becoming oxidized by electron injection to the TiO_{2} conduction band. Moreover, the electrolyte conducts the positive charges (holes) to the counter electrode, where the redoxcouple itself is regenerated. As the opencircuit voltage of the system corresponds to the difference between the redox potential of the electrolyte and the TiO_{2} Fermi level, the redox potential must be as positive as possible in order to assure high opencircuit voltages. Moreover, to overcome the problem related to slow chargetransfer reaction at the counterelectrode, a platinumbased catalyst must be employed. On the other hand, the overvoltage at the semiconductor/dye interface should be high since the dark current caused by electron back transfer to the electrolyte decreases the number of electrons available for photocurrent.
Under a steadystate condition of illuminated DSSC, the electron injection from excited dye molecules, transport in the mesoporous semiconductor (TiO_{2}) thin film, and recombination with electrolyte at the TiO_{2}/electrolyte interface can be described by the following electron diffusion differential equation [
The photocurrent (
Due to the nonlinear
The components of resistance offered by DSSC.
In order to estimate components of resistance offered by DSSC, a new and simple method is proposed here based on the equivalent circuit of DSSC shown in Figure
The equivalent circuit of DSSC.
A standard DSSC consists of three interfaces formed by FTO/TiO_{2}, TiO_{2}/dye/electrolyte, and electrolyte/PtFTO represented by an equivalent circuit shown in Figure
The terminal equation for current and voltage of the DSSC based on twodiode model (
For first boundary condition,
For the opencircuit condition and shortcircuit conditions DSSC, the following two expressions are given using the slope of one
Currentvoltage (
Simulated
The input data used for simulation purposes are compiled in Table
Values of model parameters used in simulated













16.9  0.4 × 10^{−16}  1.4 × 10^{−10}  10  3000  4.2  21.7  0.8  9.8  19  4.2  12.6 
It is evident from Figure
The curves at 0.65 sun and 0.1 sun were subsequently calculated using the same parameter as used at 1 sun, by only changing the light intensity in the simulation (i.e., the recombination constant and the quantum injection yield are taken to be independent of light intensity). It can be seen that shortcircuit current, maximum power point and opencircuit voltage are in general agreement with the experimental results.
Electrochemical impedance spectroscopy is a technique extensively used for characterizing the electrical behavior of systems in which overall performance is determined by a number of strongly coupled processes, each taking place at a different rate. The most common and standard procedure in impedance measurements consists of applying a small sinusoidal voltage perturbation and monitoring the resulting current response of the system at the corresponding frequency. The singlefrequency voltage perturbation is usually done at opencircuit conditions with magnitude
In the Nyquist plots, the respective electrochemical steps with different time constants are represented by the semicircles as shown in Figure
The EIS of simulated DSSC matches well the reported data [
The lowfrequency semiarc in the Nyquist plot represents the electrolyteplatinum interface and may be expressed as a chargetransfer resistance and a doublelayer capacitance [
The proposed model in Section
The values of the dynamic resistance at MPP are computed using the values of
Effect of illumination on steadystate and dynamic parameters of DSSC at 298.14 K.
Illumination (W/m^{2}) 





Efficiency, 

200  3.4  804.7  2.0  38.28  619.21  10.00 
400  6.8  829.5  4.3  18.52  306.55  10.75 
600  10.1  843.7  6.6  12.4  148.94  11.00 
800  13.5  853.6  8.8  9.66  90.34  11.00 
The calculated values of dynamic resistance of the DSSC show strong dependence on solar radiation. The decrease in the dynamic resistance with increase in solar radiation is attributed to the decreased
Effect of illumination on the
The effect of the cell temperature (
Effect of temperature on steadystate and dynamic parameters of DSSC at 800 W/m^{2}.
Temperature (K) 





Efficiency, 



298  13.5  853.6  8.8  9.66  90.34  11.00  3.22 × 10^{−7}  1.04 × 10^{−13} 
303  13.5  827.4  8.5  10.05  96.77  10.62  5.84 × 10^{−7}  3.41 × 10^{−13} 
308  13.6  801.2  8.1  10.45  102.95  10.12  1.04 × 10^{−6}  1.08 × 10^{−12} 
313  13.6  774.9  7.8  10.88  108.64  9.75  1.82 × 10^{−6}  3.31 × 10^{−12} 
The effect of cell temperature on the
Influence of saturation current
As the device temperature increases, negligible increase in shortcircuit current is observed; however, the opencircuit voltage rapidly decreases due to the exponential dependence of the reverse saturation current on the cell temperature as given by (
The effect of increase in the transfer recombination (which is related to recombination diode,
It is noteworthy to mention that the saturation current (
A mathematical model that simulates the steadystate currentvoltage curve and the dynamic response of a dyesensitized solar cell (DSSC) based on equivalent circuit of DSSC is proposed. The interfacial charge transfer and recombination losses at the oxide/dye/electrolyte interface are found to be the most influential factor on the overall conversion efficiency and included in the mathematical model. All parameters in the model can be related to quantities accessible experimentally. The model predicts the dynamic currentvoltage behavior of DSSC under varying illumination levels and temperatures. The implications of the model are discussed in terms of efficiencies potentially attainable in dyesensitized solar cells having diffusional mechanism of charge transport.
The authors would like to acknowledge the scientific discussions held with Professor Indrajit Mukhopadhyay of School of Solar Energy, Pandit Deendayal Petroleum University, Gandhinagar.