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Fill Factor of Solar Cells

Fill factor (FF) is an important measurement that you can use to evaluate the efficiency of solar cells. To calculate fill factor, you need to divide the maximum possible power output of a cell by its actual power output. This will give you a measurement that you can use to assess the performance of your solar cell. Solar cells with a higher fill factor have a higher efficiency and are therefore more desirable. 

How to Calculate Fill Factor?

You can find the fill factor of a solar cell using an IV curve. Fill factor can be defined using the equation:



Where Pmax is the maximum power output, JSC is the short circuit current density and VOC is the open circuit voltage. Fill factor is often referred to as a representation of the squareness of the IV curve. One way to picture Pmax, is as the maximum rectangular area that can fit inside the J-V curve of your solar cell. If JSC x VOC defines another rectangle, then FF represents how close these two rectangles are to one another. Hence, it represents the "squareness" of the graph.

fill factor is the measurement of squareness of JV curve
FF : The squareness of the JV curve

To find a value for Pmax, you need to identify the co-ordinates on the J-V curve that correspond to the maximum power output. This is the point where the product of V x J is highest, and you can find this value computationally. Once Pmax is calculated, you can substitute this value into the fill factor equation above, along with JSC and VOC, and solve for FF. Alternatively, you can plot Power (=V x J) against holding voltage (V) to get a power curve. The peak of this graph will give you the VMPP, and you can use the J-V curve to find the associated JMPP at this point.

power curve and J-V curve to find FF
Power curves can be used with J-V curves to determine Pmax, and therefore FF.

Shunt and Series Resistance

Fill factor is determined by the series resistance (Rₛ) and shunt resistance (Rₛₕ) of a cell. Series resistance refers to the resistance of the cell’s internal components, while shunt resistance is resistance due to the external connections. These two resistances act in opposition, and the fill factor is a measure of how balanced they are within a device. 

Series resistance refers to any resistance that occurs between device layers, at the external contacts, or through other components of the device. Increased series resistance will reduce the current flow through your solar cell, reducing the device's efficiency. To reduce series resistance, solar cells must be designed with low material resistance and improved contact design.

The term shunt resistance refers to power losses due to the recombination of electrons and holes via alternate pathways. In other words, any recombination through a route that is not through the solar cell material, such as through a defect in your device. An increased level of shunting reduces the current through the cell, and in extreme cases, low shunt resistance will cause the device to short circuit. For this reason, you should aim to increase the shunt resistance of your solar cell. Low shunt resistance is an indicator of a manufacturing defect rather than a material property.

Optimizing Fill Factor for your Devices

In order to maximise fill factor, you need to reduce series resistance and increase shunt resistance. This can be done by optimizing the design of the solar cell, for example, by changing:

  • The size and shape of the cell
  • The thickness of the device layers
  • The choices of active layers or transport layers
  • The solar cell doping profile and the doping concentration

More specifically, there are lots of actions that you can take to improve the fill factor of your device. You can use surface treatments such as texturing, roughening, and doping. This will maximise shunt resistance by increasing the number of current pathways through the active layer. Surface treatments can also reduce a cell’s series resistance by increasing the number of points of contact between the cell and the contacts. Additionally, you can also choose charge carrier layers such as ETLs and HTLs. This is based on their ability to block the passage of minority carriers and help reduce the number of current-carrying paths. Thus, increasing the shunt resistance. You can also increase the FF by ensuring that there is a good connection between your device and its external contacts. This connection can be improved by applying conductive paint at the contact points to improve charge transfer.

Organic photovoltaics (OPVs) and perovskite solar cells (PSCs) are two of the most promising technologies in the field of solar energy production. For OPVs, you can optimize the fill factor by optimizing the morphology of acceptor and donor materials within the active layer. Reducing the thickness of the active layer can also maximise the fill factor. For PSCs, improving the crystallinity of the perovskite material and reducing the number of defects can help increase the fill factor.

In addition to optimizing the cell design, it is also important to use good-quality materials in the production of solar cells. High-grade materials that are free of defects can reduce series, increase shunt resistance, and improve FF. Finally, it is also important to ensure that the temperature of the cell is kept as low as possible during operation. High temperatures can cause thermal losses and reduce the fill factor.

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Contributing Authors

Reviewed and edited by

Dr. Mary O'Kane

Application Scientist

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