Altermatt Lecture:   The PV Principle


2.3:  Voltage production

Current increases as the bandgap decreases, as shown in the Figure 1. So, why don't we use semiconductor materials that have a smaller band gap than silicon? The reason is that a solar cell must produce both a current and a voltage to deliver power. It is like water flowing over a mill wheel: the power transferred to the mill wheel is higher if there is more water flowing (a larger current), and if the water splashes onto the wheel from higher up (from a higher potential). A semiconductor with a smaller band gap than Si delivers more current but also a smaller voltage (potential), and therefore may produce less power. This tradeoff can be intuitively understood as follows.

Because the photons from the solar spectrum have an broad range of energy, the electrons are excited to a broad range of energy states in the conduction band (see Figure 2). These excited electrons "bump" into the Si atoms (undergo phonon interaction) and transfer part of their excess energy to the Si atoms. Very soon, most electrons settle in near the conduction band edge (see lower figure, middle panel).

This process is called thermalization. It happens so fast that the electrons relax to the conduction band edge long before they reach the contacts. A lot of energy is lost to heat in this way and, essentially, we can only extract the energy per electron that is similar to the band gap.

Jgen vs bandgap energy

Figure 1: Maximum photogeneration vs bandgap energy.

In other words, the potential (voltage) between the two contacts is maximally about* as high as the gap energy. Hence, a semiconductor material with a smaller band gap produces a smaller voltage.

Thermalization also happens in the valence band: when the electrons are excited to the conduction band, they leave holes behind in the valence band, also in a broad range of states. The holes are "filled up" by electrons from higher up in the valence band, until the holes settle in near the valence band edge.

The electrons do not stay at the conduction band edge for ever. They relax back to the valence band and "fill" the holes. This is called recombination. However, this process takes a long time (up to milliseconds), which is long enough so many excited electrons reach the metal contact and deliver power to the circuit.

Absorption, thermalisation and recombination

Figure 2: Absorption, thermalisation and recombination.

* More precisely, the voltage between the two contacts is equal to the difference between the two quasi-Fermi levels indicated by the dashed lines, as will be explained in the interview with Peter Würfel.


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