[MUSIC] Hello again, I hope you've been learning from the lecture so far. In the previous lectures on crystalline silicone solar cells, you saw how increasing the temperature of a cell decreases its conversion efficiency. Let us now consider this topic in more detail by working through an example question. The question is stated as follows, a given crystalline silicon solar cell displays an open circuit voltage, Voc, of 0.650 volts under standard test conditions and at 25 degrees Celsius. What would the Voc be if the temperature of the panel rises to 80 decrees Celsius? Additionally, we are told that the cell is made from a wafer that is p-doped with a majority carrier density of 10 to the 17th per centimeter cubed. If you wish at this point, you may stop the video and try to solve the problem on your own, if not, let's continue. We're going to consider that the implied Voc, that is the separation between the quasi Fermi levels is is a pretty good proxy for Voc. And that both recombination is the dominate effect for implied Voc. To start with, let's draw the band diagram and add what we know. The band gap of silicone is 1.1 eV and we know that it's a p-doped wafer. So the quasi Fermi level for holes will be closer to the valance band edge. Also, the spacing between the quasi fermi levels will be the implied Voc of 0.65 volts. To calculate the distance between the whole quasi fermi level and the valence band edge, we use the carrier concentration equation from before. Plugging in the numbers, and noting that the valence band effective density of the state is unknown quantity for crystalline silicon. We see that this distance is 0.135 electron volts, and we can add this to the diagram. By simple subtraction, we obtain that the distance between the electron quasi fermi level and the conduction band edge is 0.315 electron volts. This completes our band diagram for the cell under illumination at 25 degrees Celsius. Now we move on to thinking about the case at 80 degrees Celsius. So, what will stay the same in this piece of silicon when we increase the temperature? Well, firstly, the absorption coefficient and band gap won't change significantly. If the absorption coefficient and the band gap don't change that means the generation rate will also remain the same. In reality, the band gap does decrease slightly with increasing temperature but we're going to ignore that effect. Next, we can assume that the carrier lifetime will remain the same. And if the generation rate and lifetime don't change, then the minority carrier concentration will also stay unchanged. Finally, we all ready assume that all the dopant atoms are ionized at room temperature. So there's no reason to think that a change in temperature would affect this. The majority carrier concentration will therefore also remain unchanged. What will change? Well, the positions of the Fermi levels have a temperature term. And so these will move around even if the carrier concentrations are not changing. Let's now calculate the positions of the Fermi levels at 80 degrees Celsius. If we look at the equations used to determine the positions of the quasi Fermi levels, we note that there is a part which is constant. And another that depends linearly on the temperature, measured in degrees Kelvin, of course. We can therefore simply take the values that we calculated at 25 degrees C, and multiply them by the ratio of the two temperatures in Kelvin, of course. Doing so for the whole quasi Fermi level, we see that this level moves away from the valence band edge to the new distance of 0.160 eV, an increase from the old value of 0.135. Doing similarly for the electrons, we get a new distance of 0.373 eV. Doing the subtraction again, the new implied Voc is 0.567, a significant decrease from the old value of 0.650 volts. So, what has happened here? Well, we have to remember that we're looking at an energy diagram, whereas in reality we mostly care about the work that we can extract. If we think of the Voc as a measure of the work that we can extract per electron, clearly, as the temperature increases, we can extract less as work, as more is lost to entropy. Also note one more thing, if we had a much wider band gap semiconductor, since we are subtracting the quasi Fermi energy changes from the total energy band gap, the proportional amount of work lost will be less in percentage than for the small gap cell. For this reason, wide band gap semiconductor-based solar cells are less sensitive to temperature than small band gap semiconductor cells. Through this word problem, I hope you've gained some insight into why the efficiency of a solar cell decreases when the temperature increases. Thank you for your attention and see you again soon.
