Altermatt Lecture:   The PV Principle

 
 

2.8:  The solar cell under illumination

Band diagram with illumination Band diagram with QFLs

In the dark, the energy supply comes from outside of the cell (via the applied voltage), and under illumination, the energy supply occurs inside the cell (via photogeneration of electron-hole pairs), see the figure above. This causes the current to reverse its direction under illumination. See the red arrows in the above figure.

What happens to the voltage under illumination? You learned on the role of a p-n junction page that the voltage difference between the two contacts is equal to the splitting of the quasi-Fermi energies. Hence, to find out what the voltage does under illumination, we need to have a look at how the photogeneration of electrons and holes acts on the quasi-Fermi energy.

The quasi-Fermi energies are the energy of the mobile electrons and holes, respectively, available to the external circuit.

Note that we look at a steady-state situation, where light is shining constantly on the solar cell and where the photogenerated carriers thermalise to the band edges continuously.

We saw on the voltage production page that thermalisation happens so fast that the carriers relax to the conduction band edge long before they reach the contacts. Hence, it is the thermalised carriers that determine the quasi-Fermi levels. For this reason, it does not matter to the voltage whether energetic electrons are brought in by an applied bias in the dark or by photogeneration under illumination.* This implies that the quasi-Femri levels, and with them the voltage, behave under illumination the same way as in the dark. Have a look at the figure below.

Combining this with the reversal of the current, it follows that the dark IV curve shifts down to negative currents under illumination, and keeps its shape. See the figure below.

Light IV curve

Figure: Current–voltage curve in the dark (blue) and under illumination (red).

* This is an assumption that may not be completely fulfilled and is called superposition-principle, meaning that the illuminated I-V curve is simply the shifted dark IV curve.

 

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