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We’ve already talked about a few physical loss mechanisms inside solar cells that designers are trying to overcome, such as charge recombination, and reflections from the front surface. There are other loss mechanisms present, and we’ll be discussing several of those, as well as how they’re usually represented in a circuit model, below.
Both of these resistances diminish the effectiveness of the solar cell, so they are called parasitic resistances. Because the effects that are represented by series and shunt resistors are almost always present in solar cells, a more accurate circuit model then includes them both, as shown below.
We’ve just done something quite powerful. We’ve taken some pretty complex physical effects, like charge recombination, and contact resistance, and accounted for them in a mathematical model. Provided we know the values of the series and shunt resistances, we could then use this model to make predictions about device behavior under various conditions. The capability to make predictions, as you might imagine, is huge for researchers, so having models such as this one is very valuable.
There are a few important effects that we still haven’t accounted for in our model, however.
In studying solar cells, researchers want to know, in-depth, exactly how much electricity is generated for a given amount of incident light. They assign values and parameters to represent the proportions at each step of the process. One of the ones we’ve talked about earlier is the overall efficiency number. While this is the best bottom-line, overall value, there are some practical measures that can be used to investigate particular aspects of a solar cell in order to tweak and refine designs. Optical responsivity is one of these.
Optical responsivity is defined as the ratio of the electrical current out compared to the optical power into a solar cell. It’s sometimes also called spectral responsivity. While this might sound similar to overall efficiency, optical responsivity is a function of wavelength. It varies depending on the energy of light shone upon the cell, whereas efficiency is usually given for the entire spectrum of the sun’s radiation (and compares power out rather than current out). A typical graph for optical responsivity of silicon is shown below.
while the charge q of an electron is 1.6×10-19 coulombs. Current is charge per second, while power is energy per second, so in a given second the current divided by the power is just the ratio of these two:
To understand why this curve increases with wavelength, we need to understand that shorter wavelengths have higher energy. That means that shorter wavelengths are dumping much more energy beyond the minimum required by the bandgap. Therefore they’re putting in much more power compared to the electrical current out. A perfect situation is one where the photon energy perfectly matches the bandgap, which occurs at a wavelength of around 1130 nm. However, above this wavelength, the photons no longer have enough energy to bridge the bandgap, so our responsivity plummets to zero.
You’ll notice that a real silicon cell’s optical responsivity actually falls below the ideal curve. This happens for several reasons. The first is that there are losses from reflection as well as photons that don’t create the right lattice vibrations for absorption (remember that silicon has an indirect bandgap). You’ll also remember that there is the unwanted dark current of the photodiode that leaches away some of our ideal output current. The dropoff at higher wavelengths happens because of the bandgap limit, as expected. At shorter wavelengths, the protective glass on the front of the solar cell starts to absorb most of the incoming light.
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