We saw the homo junction. We will now consider the multi-junction that combines several semiconductor materials. Thermalization losses would be strongly reduced in a situation where solar photons are converted practically as their nominal energy. This will be closer to the thermodynamic limit. As shown in the figure, the blue photon are first converted with a semiconductor with large band gap. Lower energy photon are not converted by the first semiconductor. Then the second semiconductor converts the green photons following the red and so on. In fact, this is not always possible with crystalline semiconductors. Right here, we present a variation of the gap depending with the lattice parameter limited to binary compounds, ternary or quaternary siliphine compounds also exist. Crystal growth without defects dislocation stress and so on implies the conservation of lattice parameter epitaxy condition. Only materials lying on the same vertical in this figure can be combined. Thus, silicon can be only combine with wide band gap materials. More than two EV as GAAP or AALP. 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 bandgap materials, binary, ternary or quaternary. A rough estimation can be performed by limiting to the ideal condition. The combination of three different bond achieves a conversion efficiency greater than 50 percent with concentration. Therefore the use of multi-junction allows to significantly overcome the Shockley-Queisser limit. Finally, it can be pointed out that in the case of disorder semiconductor that are amorphous solid network can relax allowing the goals 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 these multi-junction. One can disperse spatially light as shown on the left figure, or can realize a stack with decreasing gap values as displayed on the right figure. The spatial dispersion is not used in practice because of the increase of ground area it represents. With two terminals stacks shown here, the currents must be kept constant as a 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 three order thin films. There are four terminal case. The two junctions are independent from each other which is advantageous for the electrical point of view. The theoretical performance of multiple junction with two or three unit cells are shown in this figure without concentration. Conversion efficiencies of about 50 percent 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-Queisser 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. Is the ideal case. The equivalent circuit was formed by a diode pn junction in parallel with a current source. The circuit shown here is a more realistic version with the presence of two new parameters that will affect the conversion efficiencies. A series on the 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 the electrical losses in the cell. For example, due to inhomogeneities. An electron-hole pair has been created but he is not collected. It can be lost for instance, in the grain boundaries of a polycrystalline material. It is generally assumed that this loss is independent of the photo current. The right curve illustrates the effect of series on parallel resistances which appear at the slopes at the origins. The present of series on parallel resistance decrease the fill factor and then the conversion efficiency. Now, we can summarize the values 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. I_sc, is also affected by the collection of photo generated pairs. Open circuit voltage, as we have seen measures the difference between the quasi-Fermi levels of the np regions. So, other than being increases V_oc. More generally the position of the quasi-Fermi level, depends on the carrier density. For electrons density it varies exponentially with the distance between EC conduction band edge on EF, the Fermi level. Furthermore, V_oc depends logarithmically on the flux. Thank you.
