# Luminescence Materials for Dye-Sensitized Solar Cells: Advances and Directions
## 2 Fundamental Principles
### Equivalent Circuit Model of DSSCs  
The equivalent circuit of the DSSC consists of the current source, diode, capacitances, series resistance (\(R_{s}\)) and the shunt resistance (\(R_{sh}\)). \"The current source creates the photo-generated current density (\(J_{ph}\)) parallel to the diode, which is proportional to the sunlight irradiation. The diode represents the interface between the dye-coated semiconductor (the TiO\({}_{2}\)) and the electrolyte. It accounts for the non-linear behaviour at this interface and is typically represented by a diode equation. The series resistance accounts for the resistance encountered by the flow of electrons within the device's components, including the TiO\({}_{2}\) layer, conducting substrates and contacts. The shunt resistance represents any unintended paths (e.g., leakage currents) that allow the current to bypass the photovoltaic cell, reducing overall efficiency. The (\(R_{surf}\)) is the surface resistance. The (\(C_{pt}\)) and (\(R_{pt}\)) are the impedance through carrier transport on the surface of the counter electrode. The (\(C_{Elc}\)) and (\(R_{Elc}\)) are the impedance to carrier transport through the ions in the electrolyte with regard to the dye-electrolyte interface. The equivalent circuit model of the DSSC is shown in Figure 2. The capacitance element can be neglected since the capacitance at the dye-electrolyte interface tends to be relatively small compared to other factors affecting the performance of the device. [PERSON]'s current law is used and expressed in Equation (1). \[J\ =\ J_{ph}-J_{d}-J_{sh} \tag{1}\]  
The current density flowing through the diode is governed by  
\[J_{d}\ =\ J_{0}\bigg{[}\exp\bigg{(}\frac{q(V+JR_{s})}{nkT}\bigg{)}-1\bigg{]} \tag{2}\]  
Equation (3) represents the current flowing through the shunt resistance. The \(R_{surf}\), \(R_{Elc}\) and \(R_{pt}\) are resolved as \(R_{s}\ =\ R_{Pt}+R_{Elc}+R_{surf}\). \[J_{sh}\ =\ \frac{V+JR_{s}}{R_{sh}} \tag{3}\]  
The output current density (\(J\)) in the circuit can be expressed as  
\[J\ =\ J_{ph}-J_{0}\ \bigg{[}exp\bigg{(}\frac{q(V+JR_{s})}{nkT}\bigg{)}-1 \bigg{]}-\frac{V+JR_{s}}{R_{sh}} \tag{4}\]  
The short-circuit current density (\(J_{sc}\)) in a dye-sensitized solar cell (DSSC) represents the maximum current flowing through the cell when the voltage across it is zero (short-circuited). This current is solely due to the photo-generated carriers in the cell and is not influenced by the external load resistance (external circuit is removed). The expression for the \(J_{sc}\) in a DSSC can be derived from the diode equation itself under the condition that the voltage (\(V\)) across the cell is zero. Hence, the photo-generated current density becomes equal to the \(J_{sc}\). \[J\ =\ J_{sc}-J_{0}\ \bigg{[}exp\bigg{(}\frac{qV}{nkT}\bigg{)}-1\bigg{]} \tag{5}\]  
The open-circuit voltage (\(V_{oc}\)) of a dye-sensitized solar cell (DSSC) is the voltage across the terminals of the cell when no external load is connected, i.e., when the \(J\) flowing through the cell is zero. In the equivalent circuit model of a DSSC, the open-circuit condition occurs when the \(J\) is zero, meaning that the diode equation simplifies to  
\[V_{oc}\ =\ \frac{nkT}{q}\bigg{[}\ln\bigg{(}\frac{J_{sc}}{J_{0}}\bigg{)}+1 \bigg{]} \tag{6}\]  
The fill factor (FF) quantifies how closely the solar cell's (\(J\)-\(V\)) curve approaches the rectangular shape of an ideal diode's \(J\)-\(V\) curve. A higher fill factor indicates a more efficient conversion of light into electrical power and a better utilization of the cell's active area. It isdefined as the ratio of the maximum power output \((P_{max})\) of the solar cell to the product of the \((V_{oc})\) and \((J_{sc})\). \[FF\ =\ \frac{P_{max}}{J_{sc}\ V_{oc}} \tag{7}\]  
The efficiency (\(\eta\)) of the DSSC is an expression that measures how effectively the DSSC converts incident sunlight into usable electrical power and is commonly used to evaluate the performance of DSSCs.