Solar Energy
# PV: Engineering and Advanced Concepts

To maximize performance, we want to maximize the absorptance of a PV module. That is, of the solar photons incident on the module, we want to maximize the probability that they are absorbed in the semiconductor material, leading to an electron hole pair. This can be separated into two steps:

We want to maximize the chance that a photon incident on the module makes it into the the PV material

We want to maximize the chance that a photon in the PV material is absorbed.

This quiz will look at the first step, and the second step will be examined in the following quizzes.

The probability of a photon to transmit through an interface is given by the Fresnel equations, and depends on the difference in index of refraction \(n\) of the two media forming the interface, as well as the angle of incidence of the photon. In this quiz, we will only consider reflectance for normally incident light, in which case reflectance is given by: \[R = |\frac{n_1 - n_2}{n_1 + n_2}|^2\] Where \(n_1\) is the index of refraction of the material the photon is coming from and \(n_2\) is the index of refraction of the material the photon is heading towards. Photons which aren’t reflected by the interface are transmitted through it. Thus, the transmittance of an interface is given by 1 minus the reflectance: \[T = 1- R = 1 - |\frac{n_1 - n_2}{n_1 + n_2}|^2\]

If air has \(n = 1\), and glass has \(n = 1.5\), what is the chance that an incident photon transmits through an air/glass interface (in percent)?

Note: index of refraction is a measure of the speed of light in a material. The speed of light in a material \(c\) is given by: \[c = \frac{c_0}{n}\] Where \(c_0 = \SI[per-mode=symbol]{3e8}{\meter\per\second}\) is the speed of light in vacuum. In general, index of refraction varies with wavelength, but in this quiz we will assume an average index of refraction that is constant across the solar spectrum.

Higher mismatch between the indices of refraction across the interface leads to larger chance for reflection. Glass has an index of refraction close to air, so reflectance across an air/glass interface isn’t that large (but a pane of glass has two interfaces - air-to-glass followed by glass-to-air - so it can contribute a ~10% reflection loss, which is significant).

On the other hand, the reflection at an air/silicon interface is very significant, and can drastically lower the efficiency of a silicon PV cell. If we added an intermediate material with \(n = 2\) between the air and silicon, what is overall chance of a photon transmitting through (in percent)?

Note: don’t consider the effect of multiple internal reflections within the intermediate material.

When you add an intermediate index material, even though you’re adding an extra interface, the overall reflectance is reduced because the mismatch between the layers is smaller. This boosts performance, since more photons can make it through the interfaces to the PV cell. To make glass more transparent (or to make more light transmit into silicon), an “anti-reflective coating” (ARC) can be added which has an intermediate index of refraction to reduce the overall interface reflectance.

A common strategy for reducing reflectance into silicon is texturing the surface (i.e., make it rough, adding features like pyramids or pillars). If the texturing is at or smaller than the scale of the wavelength of the incident photon, then the photon sees the index of refraction of the textured surface as an average between the index of refraction of air and of the silicon. This gives the silicon an effective graded index which slowly changes from \(n_{air}\) to \(n_{Si}\), increasing transmittance into the silicon.

If the contacts are too thin and long, the electrical resistance will be high for current traveling through those contacts, leading to large Joule losses. One way to model this would be to increase the series resistance in our PV cell circuit model. Additionally, we want contacts to be close to generated electron-hole pairs, so charge carriers don’t need to travel far to be collected at contacts. The farther a charge carrier needs to travel before being collected, the more likely it is to being lost to recombination.

Thus, there is a balance between the performance of the contacts and contact shadowing (contacts blocking incident sunlight), so real PV cells will have some contact shadowing and some electrical resistance.

Another strategy for addressing contact shadowing is to use rear contacts. Instead of having p and n type layers, with contacts on the front and back, the junction is made with a more complex pattern. Interdigitated n and p contacts are both attached to the back of the cell, so no contacts block the front.

[note: the real structures for rear contact PV cells are more complicated than this, but I'm worried about making the diagram too confusing and introducing new concepts that aren't critical for the overall idea]What is the effective transmittance (in percent) for rear contacts?

The last strategy we’ll consider is using “effectively transparent” contacts. If contacts have a triangular cross section, then light that hits them can still be directed towards the cell. Note that this only works for light near normal incidence. For large incidence angles, sunlight will still be reflected away (and in this case performance might be worse than for normal contacts).

If you have triangular cross-section contacts that have 10% area coverage and reflect 95% of incident sunlight to the cell (the other 5% is reflected out to environment), what is the effective transmittance of the front contact layer?

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