[MUSIC] We will be tested in to describe in more detail the characteristics of the p-n junction at equilibrium. I remind you that when contacting the p-type semiconductor with the n-type semiconductor, it creates a space charge region, in which there is an electric field. However, far from the interface area, the space charge zone, the p and the n semiconductors in fact are not affected. So I remind you, here, three questions that this kind of p or n semiconductor away from the interface. Questions that we have already seen before. I remind you, that the number carriers rise exponentially with the distance between the Fermi level on bond edge of condition bond for electrons or valence bonds for holes. And then we have in each case the mass action law Np equal ni squared. Where ni is a constant function of the temperature. The zero indices represent the behavior of p on n semiconductor before contacting sees the interface far from the contact, does not affect the property of the semiconductors. Let's now turn to the barrier height is the p-n junction. Important quantity for photovoltaic applications. I remind you that we contact p on n semiconductor, the Fermi level is constant in the system. In one case, it was close to the conditional bond and the other close to the valence bond far from the interface. The semiconductor properties are unaffected. After the contact, potential by therefore occurs E phi as shown in the figure. In the pink is shown E phi as at the first approximation, the potential that will appear as electrons. So if Vn and Vp denote the electrostatic potentials in the n on p regions, far from the junction. So if phi = Vn- Vp. Therefore E phi in fact is equal to the distance between the Fermi levels. In the previous situation before contacting of n on p regions. Later levels. So we're using expressions that we're shown on the previous slide, we get e5 equal to the bond gap eG + T log of NA and D over NC, NV and A on ND. [INAUDIBLE] concentration of [INAUDIBLE] on [INAUDIBLE] divided by the constant NC on NV as previously seen. Thus, it is shown that E phi is slightly less than the bond gap. Taking the case of crystalline silicon, the gap is about 1.18 interval. So if we take typical values of NA, ND, NC, on NV, the potential barrier ranges about 0.6 volts, just like the lesson's gap. The electric field in the junction is a derivative of the potential previously considered. Let's recall that far from the junction semiconductors are not affected by the contact. So the electrical neutrality is revealed. This is not the case as you know inside the space charge region. In contrast is space charge region as the chemical potential of Fermi level is relatively far from the edges. That means, because of the exponential variations, there are few carriers, therefore the space charge region will appear resisted. Or deeply. The potential is obtained by solving the presence of equation. So there is electrical neutrality far from the junction. It is assumed that the system is in a saturation region, region N on P. So the following expression are obtained away from the junction. In the space charge region we must integrate the Poisson's equation together with electrical neutrality, which gives Nadp where dp corresponds to the width of the area of the space charge the region p equal to ND. The N being the width of the space charge in the region N. So we see that the electric field which is shown here, increases linearly in absolute value. The total width of the space charge zone, dn + dp, is given by this expression here. If you make a numeric application, in the case of silicone, so we have seen that E phi was slightly less than 1 volt, we obtain here that the space charge width is the order of two microns. In summary, in case of silicon, the space-charge region is found very thin. As a solar cell in practical condition has a typical thickness of 200 microns. Thus, so space charge zone represents about 1% of the total thickness of the solar cell. So we have studied the p-n junction at thermodynamic equilibrium. In the following, we'll see how p-n junction in non equilibrium condition. That is to say, when it is submitted to an external bias. Thank you! [MUSIC]