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Solar Energy

# Minimizing reflectance of interfaces and contacts

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:

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

2. 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.

Suppose we have a PV cell that converts photons that make it into the PV material to electricity at 25% efficiency (we’ll call this the internal efficiency $$\eta_{cell,int}$$, not to be confused with the normal PV cell efficiency, where the denominator is given by photons incident on the cell). The cell is integrated into a module with a glass cover. If the glass cover reflects 10% of incident sunlight away, and the front surface of the PV cell reflects 30% of incident sunlight away, what is the efficiency of the module (in percent)?

We want to minimize reflectance on the front of the module so that photons can be make it into the PV cell, maximizing the absorbed photons and the collected power. To maximize the photons incident on the module making it into the PV material, we need a better understanding of reflection. When a photon reaches an interface (a difference in the material the photon is traveling through), it has a chance to reflect or transmit. For an interface like air to silver (a common mirror material), most incident photons are reflected. For an interface like air to glass, most incident photons are transmitted.

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.

Silicon has $$n = 3.6$$, what would the chance be for a photon to transmit through an air/silicon interface (in percent)?

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.

Metals tend to have very high indices of refraction and are thus reflective. The front contact fingers on PV cells are made of metal to conduct electrons, but this means that they will block and reflect incident sunlight. Thus, we want to make the contacts as small and narrow as possible. What limits how small we make the contacts?

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.

Suppose the contact pattern in the figure below, where contact fingers $$\SI{100}{\micro\meter}$$ wide are spaced at a $$\SI{2}{\milli\meter}$$ pitch, leads to good electrical properties for collecting current from a PV cell. What is the effective transmittance of the front contact layer (in percent)? You only need to consider shadowing from the contact fingers, you can ignore shadowing that would result from the busbar in your calculation.

There are a few strategies being pursued to minimize the effect of contact shadowing. One strategy is to use front contacts made from materials called transparent conducting oxides (TCOs). This allows the full front side of the cell to be covered by the contact, as sunlight can transmit through the contact to reach the cell. The problem is that they aren’t as conducting as metal and aren’t fully transparent. What is the maximum index of refraction allowable for a TCO to match the optical performance of our previous contact pattern? You can assume that any photons which pass through the air/TCO interface successfully transmit through to the PV material.

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?

While reflectance at the glass and silicon interfaces and shadowing from the contacts can reduce the performance of a silicon PV cell, with proper design we can keep these effects to a minimum. Through the use of anti-reflection coatings and different contacting strategies, real PV cells have achieved effective transmittances above 90%, meanings that over 90% of sunlight incident on the module can successfully make it into the PV cell material. The next two quizzes will look at how to maximize the chance of a PV material absorbing a photon once it has been transmitted through the glass and contacts.

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