[MUSIC] We saw the homojunctions. We will now consider the multi-junctions that combine several semiconductor materials. Thermalization losses would be truly reduced in a situation where solar photons are converted practically as their nominal energy. This will be closer to a thermodynamic limit. As shown in the figure, the blue photon are first converted with a semiconductor with a large band gap. Lower energy photon are not converted by the first semiconductor. Then the second semiconductor converts the green photons following the right, and so on. In fact, this is not always possible with crystalline semiconductors. Right here, we present the variation of the gap depending with the lattice parameter. Limited to binary compounds, ternary or quaternary compound also exist. Crystal grows without defects, dislocation, stress, and so on, implies the conservation of lattice parameter epitaxial condition. Only materials lying on the same vertical in this figure can be combined. Thus, silicon can be only combined with wide band gap materials, more than 2 eV as GaP or AlP. However, germanium gap, 0.7 eV, has a situation much more favorable since it can be combined with gallium arsenide, gap 1.3 eV, and other large band gap materials, binary, ternary, or quaternary. What estimation can be performed by limiting to the ideal condition. So combination of three different band achieves a conversion efficiency greater than 50% with concentration. Therefore, the use of multi-junction allows to significantly overcome the Shockley-Queisser's limit. Finally, it can be pointed out that is the case of these other semiconductor that are amorphous. So solid network can relax, allowing the [INAUDIBLE] of a semiconductor on top of another. These materials are well suited for the fabrication of multi-junctions. In practice, there are two ways to proceed to achieve this multi-junction. One can disperse spatially light, as shown on the left figure, or can realign your stack with decreasing gap value as displayed on the right figure. So spatial dispersion is not used in practice because of the increase of the ground area it represents. With two-terminal stacks shown here, the current must be kept constant in the multi-junction, which requires a constraint on the thickness of the unit cell to tune optical absorption. Devices with three or four terminals involve inserting electrodes between the elementary cells, which is inconsistent with the epitaxial conditions required for crystalline materials, conservation of the lattice parameter, but possible with these other thin films. The four-terminal's case, the two junctions are independent from each other, which is advantageous from the electrical point of view. The theoretical performance of the multiple junction with two or three unit cells are shown in this figure, without concentration. Conversion efficiencies of about 50% can be obtained with three cells, even in the case where the rear cell is crystalline silicon. The multi-junction, therefore, allow to significantly overcome the Shockley's limit. We consider up to now, solar cells operating in theoretical condition. We will now discuss the values limitation in conversion efficiency. Let's return to the equivalent circuit of a solar cell. In the ideal case, the equivalent circuit was formed by a diode, PN junction, in parallel with the current source. The circuit shown here is a more realistic version with the presence of two new parameter that will affect the conversion efficiencies with series and parallel resistance. Series resistance may be related to the quality of the semiconductor contacts with metal, as we have seen on any resistance in the device, such as resistive depletion zone. The series resistance expresses all these parasitic effects. More generally, it is affected by carrier mobility. The parallel resistance represents electrical losses in the cell, for example, due to inhomogeneities. An electron-hole pair has been created, but is not collected. It can be lost, for instance, in the grain boundaries of a polycrystalline material. It is generally assumed that this kind of loss is independent of the photo current. The right curve illustrate the effect of series and parallel resistances, which appear as the slopes at the origins. The presence of series and parallel resistance decrease the field factor and then the conversion efficiency. Now we can summarize the various origins of limitation of the conversion efficiency. The short-circuit current is directly dependent upon the photon flux. Since it corresponds to the integral of the converted spectrum, then the short-circuit current depends on the conversion area. It is directly affected by the optical losses, including the reflection of the front surface exposed to the radiation. ISC is also affected by the collection of photogenerated pairs. Open-circuit voltage, as we have seen, measures the difference between the quasi-Fermi levels of the N and P regions. So other doping increases VOC. Marginally, the position of the quasi-Fermi level depends on the carrier density for electrons' density varies exponentially with the distance between EC, conduction band edge, and EF, the Fermi level. Furthermore, VOC depends logarithmically on light flux, thank you. [MUSIC]