In this video, we'll talk about how efficient solar cells can be and the theoretical limits that exist. As we already know, we have the valence band and the conduction band. And this leads to a spectral response. So, from last time we know that if we have a photon coming in, we can excite an electron from the valance band to the conduction band. However, there's two important mechanisms that we need to look at here. So, in one case we have a photon coming in with less energy than the band gap. And in that case there's not enough energy to excite the electron to the conduction band. That means all of this light is wasted. So all of the light with energies less than the band gap is light we cannot use. The other situation is, we have sufficient energy and we actually have more than sufficient energy. That means we promote an electron from the balance band way up into the conduction band. All of the excess energy is lost to a thermalization process, and that means all of this excess energy is lost so we cannot use it to power anything from the solar cell. This give rise to what we call the spectral response of the solar cell, and we can look at what is called the spectral efficiency. In order to illustrate this a little bit better, we can look at this virtual instrument where we can change the band gap of the solar cell or the semiconductor material into solar cell. And then it can calculate for us the spectral efficiency. So you can see now, the curve here represents the solar spectrum of the sun. The green area is the light that we're using to produce energy from this solar cell or the light that we at least potentially can use. If we change the band gap, you'll see this area will shift. So if we increased the band gap, we can see that there's a smaller portion of the spectrum that we're using. And for this reason the spectral efficiency is dropping off. It might be tempting to just say, "Well, let's use a really low band gap material so that we can use the entire spectrum." In that case however, we end up losing a lot of the energy because, we simply lose all of this to thermalization. And in the other direction, we lose most of the energy to simply not having enough energy to overcome the band gap. In between here somewhere there's an optimum. When we talk about a theoretical limit for the efficiency of a solar cell, one thing is the spectral efficiency. The spectral efficiency limits how many of the photons gets converted into electrons and how much energy we carry for each of these electrons. Beyond the spectral efficiency, we also need to look at the voltage that we get out from the solar cell. And the voltage is limited by the band gap. If we have a lifespan gap we can have a large voltage, and for a low band gap we'll end up with a low voltage. And this has a direct effect on the power we can produce from the solar cell. The other important limit is that we cannot have a fill factor of 100 percent. For these reasons combined: The spectral efficiency, the voltage limitation, the fill factor limitation, we end up with a theoretical efficiency limit. So, we can calculate what is typically called The Shockley-Queisser limit. And you can see a depiction here. So, this graph represents the theoretical maximum efficiency we can get out of the solar cell depending on the band gap in electron volts. You can see the wrinkles in this curve, an effect of the solar spectrum that we use. We could calculate a theoretical efficiency for any light spectrum, and that would radically change the efficiency we can get out. But this one is drawn for AM1.5, meaning that it's the spectrum that we typically see. When we look at our virtual instrument, we can see besides the spectral efficiency it also calculates the theoretical efficiency. That means we can find a point of the maximum theoretical efficiency, and this theoretical efficiency is directly this curve we see here. In order to overcome the theoretical efficiency that is put in place mostly by the spectral efficiency, the most obvious solution we can make is to use what is called a tandem solar cell. A tandem solar cell means we basically take one solar cell and put another one underneath it. In this case, we can have the top solar cell using the blue part of the light, the high energy wavelength. And the bottom cell can then use the red light, the photons with less energy. With this tandem structure we can increase the efficiency quite significantly. There are two ways we can create tandem solar cells. One, is stacking two solar cells on top of each other. Like I just described. In this case, we collect the current from each solar cell and we end up with the solar cells with four wires coming out. This can be quite efficient. There's no real limitations except the solar cell on top needs to be transparent to all the light that needs to come to the second solar cell. And this means the contacts needs to be transparent. At the same time, the bottom cell needs a transparent top electrode. So this is quite a big limitation. Another way of making a tandem solar cell is to make a monolithic structure. In a monolithic structure, we put the two cells on top of each other directly with a tunnel junction in between. In this way, we effectively create a serially connected solar cell. The problem is, the current must then be the same for both solar cells. Otherwise, one solar cell limits the other. With the tandem solar cells, we can get a much higher efficiency. This you can see from a virtual instrument I have here. Where we have two different semiconductor materials that we can control individually since you have a green part which represents the top solar cells, and this blue part which represents the bottom solar cell. By changing both parameters, it's possible to find a theoretical limit to a tandem solar cell. We can of course continue in this way and make multi junction solar cells. You might remember from our first week that multi junction solar cells are used in space applications. And in those circumstances provided usually have three or four stacked solar cells on top of each other. Of course, the complexities of making these types of solar cells are increasingly high. And, the efficiency gains we get from using an increasing number of junctions becomes less and less for each additional junction we introduce. In our discussion of the theoretical limits of solar cell efficiency, there are lot of mechanisms that we have not discussed. First and foremost, electrons and holes can recombine. We can have reflection losses from the surface. We can have [inaudible] instances, like we talked about in the last week. All of these loss processes needs to be optimized as much as possible in order to get the highest efficiency solar cells. In many ways, it's encouraging to see, that the laboratory efficiencies for various types of solar cells are getting closer and closer to these theoretical limits. And of course, there's still some way to go, but in many ways it also shows that if you want to improve further we need really to look at something like tandem structures in commercial solar cells.