[MUSIC] In this Appendix 2, we will describe the phenomenon of diffusion length lifetime on carrier injection by light. Let's look first at the recommendation of electrons on holes. Suppose we expose a semiconductor to the light. We therefore create additional carriers, delta n, delta p, compared to the equilibrium concentrations. Now, suppose that the external excitation is interrupted. So, we have d of delta n over dt. Carriers will therefore recombines, term of -n over 2 0. But in parallel, they can be created by thermal effect, electron hole pair regeneration, g0. So at equilibrium now, n is equal to n 0 and d delta n over dt is 0. So the equations are simplified and we assume that 2n0 for the two values of n corresponding to n equals n 0. Now we will consider for simplicity an n type semi conductor. That is to say small n0 is actually very large as compared to small p0. Likewise, it is assumed that delta n on delta p also much smaller than than n0, which is generally the case. For example, light excitation does not significantly change the number of majority carriers. It affects preferentially minority carriers because majority carriers are already In very large amounts. So n will remain almost constant during the return to equilibrium. We can therefore consider the 2p is independent of delta n. And we see then 2p appears as the lifetime of minority carriers. Let us treat now the carrier injection by light in order to obtain the basic equations of semiconductor devices. I remind you that the current of electrons, for example, has two contributions. The drift contribution, that is to say the drift of charges in electrical field epsilon. Plus a contribution coming from the diffusion mechanism, related to the presence of concentration inhomogeneities in the system. So we have two contributions for electrons and two contributions for the holes. Finally the sum of the current of electrons on holes gives the total current. Consider now the continuity equations, and so we describe evolution of the carriers locally. We take a small volume here and we are therefore interested in the evolution of the number of minority carriers, of NP for example, with time. Then there is a contribution corresponding to creation, g. You can transition between valence and condition bond, thermal translation corresponding to the Boltzmann Law. The second term corresponds to the recombination, it is therefore negative. And the third term will describe the flow of charges that can enter the volume. Electrical neutrality imposes the condition that is given on the last line. Now consider a N type semiconductor, for example, in which we created a nexus carriers at the surface. This is a typical example in photovoltaic application during exposure of semiconductor to the blue light. In such a case, as indicated above, the light is always absorbed close to the surface and not in the bulk. Thus in the volume, there is no creation. The latter taking place only at the surface. So that time, the variation of the minority carriers, which are the hosts in the n-doped semiconductor is giving back d of pn over dt. There is only a term of high combination on the diffusion term. So now, is a steady state as dpn on dt is equal 0. So using the boundary conditions that are given here, you get pn of x which is a concentration of the minority carriers at x, given by the expression here. Once there is a presence of an exponential term minus x over L. So the carries have been created on the surface, they diffuse into the bulk following an exponential low. What is shown here on this curve. So here, I have given the concentration gradient of holes as minority carriers in the n type semiconductor on the division current of holes. The surface expression which is given here will be considered for the calculation of the current in the PN junction, thank you. [MUSIC]