We treated the p-n junction at equilibrium, in which the chemical potential is constant in the system. We'll now study the non-equilibrium p-n junction, more specifically, we will now connect the semiconductor electrodes to load circuits, so as to apply an external voltage VE, to the p-n junctions. So here, we summarize the three possible cases. Small a, the p-n junction is at equilibrium, Ve equals zero. So no external field. There is therefore a potential barrier at the junction as we have seen previously. And then, small b and small c, we will apply a forward or reverse voltage. That is to say, we can change the c of the voltage so as to vary the height of the potential barrier that exist between the region n and p. Under these conditions, the system is not anymore in Fermi dynamic equilibrium. Consider the effect on the p-n junctions of the application of an external voltage. As noted earlier, the N and P sides contain many carriers. However, the interface is the depletion region, which is very thin, a few microns and has very few carriers. In electrical terms, this means that the depletion regions is much more resistive than the N and the P regions. And thus, the potential drop across the p-n junction mostly takes place in this interface region. So the chemical potential of the Fermi level is not constant because an external voltage is applied to the system. However, away from the interface we can consider that the semiconductor is not affected by this applied voltage. We can thus consider as a bulk zones N and P, have not been affected by electric field. So we can consider a Fermi level in this area. As the system is not in Fermi dynamic equilibrium, we will say quasi- Fermi level. So the quasi-Fermi level corresponds to the Fermi level that we mentioned earlier is a N and P region, far from the interface. And thus, the applied potential is in fact equal to the difference of the quasi-Fermi levels in the P and N regions. We will now study the effect of two types of possession, reverse or forward. The reverse bias is the situation described here. The external potential is such that the potential barrier which opposes the diffusion of majority carriers is increased. So, the current of majority carriers which was already very low is not significantly affected. Let's consider the minority carriers. It can be shown in annex four that the presence of external voltage modifies the carrier concentration at the edge of the space charge region. As shown in this appendix four, the presence of an electrical field creates an inmaginity for minority carriers at the edge of the space charge region. Since there is an inimaginity in the p region for example, this inmaginity will result in the current diffusion for minority carriers. But for the minority carriers, the potential barrier is in a favorable way to the transport. So, the minority carrier can diffuse to the edge of the space charged region, they will be driven by the potential difference between the P and N regions. Being a minority carriers current, It will be weak. The minority carriers being driven by the barrier, it will depend very little on VE. So in summary, in case of reverse bias, minority carrier current is weak and almost independent of the applied voltage. The presence of this concentration gradient at the edge which induces a diffusion carrier and therefore a reverse bias current has to be demonstrated. Let us consider now the case of the forward bias. In this case, it reduces the barrier height for the majority carriers. Under these conditions, the diffusion of holes, for example, from P side to the N side is favored. So the majority carriers can diffuse more easily through the space charge region. So current will therefore increase strongly since it is a current of majority carriers and this current will increase with external voltage. This current is therefore expected to rise exponentially with the applied voltage. So it is seen as response of the P-N junction to an external excitation is very asymmetrical depending on the sign of the applied voltage. So we evidence rectifier effect. Which in the case of forward bias, a current that is going very happily with the voltage. We present in a qualitative description, so I invite you now to refer to Appendix four for the current calculation in the non-equilibrium P-N junction and in particular, the Shockley's law. This law is very important because it is the origin of the current in a solar cell. Indeed, this current determined in annex four is very asymmetrical. With reverse polarization, the current is low and weakly affected by separate voltage. While with a forward bias, the current increases exponentially with VE. Scale where expanding is lower curve to highlight the asymmetric response effect, this is called rectifier effect. So the current itself is given by the Shockley's law as displayed here. So it varies exponentially as a function of applied voltage. Exponential minus of eV over kT, where Js is a constant, which is given in annex four. As your response is very asymmetrical, the first application of the diode P-N junction is an AC rectifier. Indeed, according to the sign of the voltage, the current will be very low on that. The diode allows to transform an alternating current into DC current. In particular, it is the principle of the inverter that are used in photovoltaic applications, since solar cell produces DC current and so the inverter converts the DC current into alternative current. This is also the principle of light emitting diodes that are related to the radiative recombination of the injective carriers to the electrodes of the diode. Finally, the diode is a basic principle of solar cell, I will receive now. Let's describe finally the photovoltaic effect, and therefore, the principle of solar cells linked to a P-N junction. The photovoltaic effect is due to P-N junction exposure to sunlight or light exposure. When the P-N junction is exposed to light the photons that have higher energies as a band gap will therefore create electron-hole pair and will therefore create a current in the P-N junction. The P-N junction is displayed here at equilibrium with the electric field Epsilon, that is related to the potential barrier as shown before. If it creates an electron-hole pair in the P-N injunction and if this electron-hole pairs can diffuse till the space charge region, they will be separated by the electric field. But these pairs will therefore create an electric field, Epsilon prime, that will oppose the permanent electric field. Thus, exposing the P-N junction to the light leads to the occasion of electron-hole pairs, which are separated and therefore contribute to the decrease of the potential barrier. This is equivalent to applying a forward bias. The appearance of the potential difference appearing across the junction is the photovoltaic effect. The maximum value of the voltage which appears is lower than the band gap. Upon exposure to light, we obtain an equivalent behavior to a P-N junction in forward bias. The characteristics of the junction is thus given by the Shockley's law, since this is equivalent to a non-equilibrium P-N junction. In the presence of light, an additional photocurrent appeared in the opposite direction to the direct current. So, if P is a photon flux and eta, quantum yield, that is to say the number of electrons-hole pair created by a photon and finally created and this current will be, 2η eP. The factor two, takes into account of the presence of two different carriers. In other words, it causes in a shift of the characteristic curve corresponding to the Shockley's law by a quantity If. And so, we see that especially the current voltage characterizing go through the negative I(V) product, short current. As if I(V) is negative, energy is recovering. Well, so we define two quantities, the short circuit current will correspond to V equals zero and for I equal to zero, the corresponding voltage is open circuit voltage. It was therefore, during this chapter of presenting the P-N junction at equilibrium and the non-equilibrium conditions and finally the photovoltaic effect. We will study in the next chapter, Silicon metal contacts before looking specifically at the solar cell operation. Thank you.
