We will now treat the operating principle of a solar cell. First, is the ideal case, that is to say, assuming a perfect behavior. This is what is explained in this slide. I remind you of principle of converting solar energy to electricity, with two conditions to be met. First, we must absorb a photon, that is to say, induce a transition of an electron from the valence bands that is full to the conduction band, which is empty or almost empty. We'll first excite an electron in the conduction band. As this band is empty, it will tend to preferentially populate the lowest energy states. Part of the energy will first be lost by thermalization. The useful energy corresponds to the band gap. It is the optical absorption phenomenon. Coming now to the device aspect, is your p-n junction diode which is characterized by the presence of an electric field as the interface between the n and p regions. It's a photogenerated carriers can diffuse to the space charge region. They will be separated by the field. So separation of the carriers is a second condition to fulfill. Physically, this means that rediffusion length of the carriers is of the order of magnitude of the total thickness of the diode. We'll see that this is a case of solar cells based on crystalline silicon. The ideal operation involve several assumptions. The first is the perfect absorption of all photons that have an energy greater than the band gap. Which implies, the absence of reflection on the front surface of the of the semiconductor. For example. The second assumption is a perfect collection of the photogenerated carriers. So that is to say, lack of recombination in the pn-junction. And then, perfect contact with the metallic electrode. The solar photon conversion mechanism is summarised in these figures. We have seen that forms electrical point of view or cell behaved like a pn-junction out of equilibrium , in parallel with the current source that corresponds to the photogenerated carriers. The characteristic of a non-equilibrium diode follows the Shockley's law: I equals I S exponential minus EV on KT minus one, which is in parallel with the source IL. The final characteristic IV is presented here. We also define two quantities, V or C, which is open circuit voltage which corresponds to I equal zero. And the short circuit current ISC, corresponds to V equals zero. The solar cell acts as a generator in the cell current P equals VI negative. Which is only illustrated here, reversed. The current per unit area, JS, depends on the characteristics of the semiconductor. That is to say, band gap diffusion constant of the carriers, lifetimes of electrons on hold, 2 N and 2 P, doping densities and so on. The VOC is obtained from the expression of the characteristic at I equal zero. We obtain an important consequence for the solar cell operation. VOC depends logarithmically on the photon flux I L, thus for example, VOC increases with the optical concentration. The maximum of the power P equal V I, corresponds to DP over DV equals zero. It can therefore be calculated analytically, as shown here. The short circuit current ISC corresponds to the photon conversion. It is obtained from the interior of the spectrum of solar photons, integrated between EG and infinite. These quantities are reported in the sphere which again, display the fourth quadrant of the curve IV. We define the field factor FF to the ratio Jm Vm, that is to say maximum power divided by area of the rectangle Isc Voc. The more the characteristic will be close to the rectangle, the greater the field factor will be. In practical application, FF can reach 80 percent or even above. This figure shows a theoretical comparison of value semiconductor. The two top graphs correspond roughly, to the crystalline germanium on silicon. More of the band gap decreases, more solar photons are absorbed, leading to an increase of ISC. We observe an opposite behavior for the x axis. VOC depends on the band gap still being slightly lower as we have seen previously. We can evaluate the theoretical maximum conversion efficiency for the value semiconductors. Remember that the solar photons, that have a lower energy band gap are not converting. More the gap is low, more the loss is weak. In contrast, losses by a thermalization vary in the opposite way. These opposing behaviors with EG, lead to a compromise shown in this figure. Band gap of 1.34, slightly higher than crystalline silicon, corresponding to the better compromise between conversion and degradation. These correspond to efficiency of 33 percent. Under ideal operating conditions, is called the Shockley-Queisser Limit. It applies to homojunction, that is to say, a pn-junction based on single semiconductor material. This limit is well below the thermodynamic limit. More than 80 percent. The red dots correspond to the best yields actually achieved. These values are found to be far below the theoretical limits, particularly, for the amorphous silicon thin-films The actual costs are in the order of 25, 26 percent for crystalline silicon instead of 29 percent theoretically. The share of the different solar cell technology is shown in this figure. So crystalline silicon-based industries account for over 90 percent of the global market. We'll come back to these technologies in the next chapter. The thin layer of technology, CDT, amorphous silicon, and so on, represents the rest of the market, barely 10 percent. We have presented in this section the ideal operation of solar cells, based on homojunction. That is to say, considering a single semiconductor material. We will see later how it's possible to overcome the Shockley-Queisser Limit, 33 percent efficiency. Thank you.
