## How to mesure solar cells

Henrik Friis DamThue Trofod Larsen-Olsen infinityPV solar simulator - ISOSun infinityPV multiwavelength LED characterizer - ISOSunMLC

To measure a solar cell, some theory of how the solar cell works and responds to a load is needed. First the basic of how the solar cell works from an electric component perspective, valid for both polymer solar cells and inorganic solar cells, is shown in Figure 1.

Figure 1: The equivalent circuit diagram for a solar cell.

The individual parts of the equivalent circuit diagram consists of a current source arising from the absorbed light generating electrons and holes, a diode from the directional properties of the solar cell stack and a series resistor $R_S$, for the resistance in the open diode state and a shunt resistance $R_{SH}$, for the resistance in the closed diode state. The total current through the circuit can therefore be described as $$I = I_{L} - I_{D} - I_{SH}$$ where $I$ is the output current of the solar cell, $I_L$ is the photo-generated current, $I_D$ is the diode current and $I_{SH}$ is the shunt current. Expanding the equation with the substitution of the diode current with the equation of current in a diode and the shunt current with the resistive loss terms results in $$I = I_{L} - I_{0} \left\{\exp\left[\frac{q(V + I R_{S})}{nkT}\right] - 1\right\} - \frac{V + I R_{S}}{R_{SH}}.$$ The equation is a function of the internal parameters and the voltage drop between the two contact points. Therefore the most used method of testing solar cells is to perform an IV curve measurement.

### IV-curves

Measuring solar cell performance by performing an IV sweep, is done by scanning an applied voltage across the solar cell and measure the current response of the solar cell. A solar simulator (e.g. infinityPV ISOSun) is typically used for precise measurements. What is acquired is a current voltage curve, where the current of the solar cell is plotted against the applied voltage.

Figure 2: Example IV curve for a solar cell with an illustration of the square summing up the maximum power spanned by the $V_{Pmax}$ and $I_{Pmax}$ crosses and the open circuit voltage and short circuit current points.

• Open Circuit Voltage ($V_{OC}$)

The open circuit voltage of the solar cell is the maximum voltage that the solar cell will supply; that is the voltage without any load applied.

• Short Circuit Current ($I_{SC}$)

The short circuit current of a solar cell is the maximum current of the solar under conditions of a zero resistance load; a free flow or zero volt potential drop across the cell.

• Fill factor ($FF$)

The issue with the two states, $I_{SC}$c and $V_{OC}$, is that the most interesting aspect of a solar cell is not the flow with no potential drop, nor the potential drop with no flow, but the product of these two; the power. When either the potential drop or the current flow is zero, the power being the product of the two will be zero. Therefore, a more interesting aspect is the maximum power and how large the maximum power is in respect to the product of the Voc and Isc. This term is what is referred to as the fill factor. The ratio between the maximum power (represented by the square in figure 2) and the full square spanned by the Voc and Isc values. $$FF=\frac{I_{Pmax} V_{Pmax} } {I_{SC} V_{OC} }$$

• Power conversion efficiency ($PCE$)

The primary parameter extracted from the IV curve is the power conversion efficiency (PCE), which describes the general efficiency of the solar cell; that is the ratio of generated electricity to incoming light energy. The formula for the PCE is $$PCE= \frac{I_{SC} V_{OC} FF}{P_{light} }$$

### How to extract the maximum power of the solar cell

To find the fill factor and the maximum power of the solar cell, the power in each point of the IV curve can be found by the power being the product of the voltage and current, $$P=V I$$ Plotting the power as a function of the voltage results in the green curve (triangular datamarkers), where the maximum power point (MPP) is the peak point of the power curve with the corresponding points on the voltage and current axes, $V_{Pmax}$ and $I_{Pmax}$, being the corresponding voltage and current values.

Figure 3: IV curve and the power curve of the solar cell, with indicated maximum power point (MPP). Notice that J is the current density.

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