[MUSIC] Hello, so we studied this previous chapter the band structure of semiconductors. On alpha, solar photon could create electron hole pairs. Now we will look at the separation of electron whole pair on carrier transport to a load circuit in order to use the photogenerated energy. May I remind you the principle of a solar cell. A semiconductor is exposed to solar flux. Some of the photons are reflected. The rest of the photon flux MPGs the semiconductor where it can excite electrons to the condition bond where they act as free electrons. It was some loss by thermalization which corresponds to the photon energy above the bond gap. Now, we will look to the transport expect of the electron that has been created in the semiconductor to an external circuit. We will look as the electron transport mechanism, this electron will reach the contact electron with external circuit in which there is creation of a voltage, thus an energy generated in this circuit. Finally, the electron recombines at the end of the cycle. So we will look first at the Drude model, this kind being the transport of electric charges. Then, we will see how carriers are injected from the light. That is to say, from the solar flux. Then we will study the device which is the basis of the operation of solar cell, the p-n junction. In this context, we'll finally introduce the photovoltaic effect. Then a few words about transport phenomena. Consider a free electron in a crystal. This electron will therefore undergo collisions with funnels of the crystal on values the effects or impurities. This movement of electrons is the solid reverse image on this figure. It may be considered a random motion. In the presence of an electric field, this random motion will be oriented in the opposite direction to the electric field vector. Concentration guidance may also create charge carrier as will be seen later. If we look at the order of magnitude for a free electron in the crystal semiconductor, which is subject to collisions with photons and impurities, the typical time between collisions is about 10 to the -12 or 10 to the -13 seconds. This time is actually very short compared to the lifetime of an electron-hold pair which was therefore created by a photon. For that, the transport properties can then be determined by considering the electrons and holes consist of two gases without interaction. Let us now turn to electrical conductivity. So it is therefore considered a free electron of volume density, n. In the presence of an electric field, the equation of motion is f =- ee, e being the electric field that is equal to -m dv/dt plus the visous term. The presence of a viscous term is necessary. Otherwise the electron is accelerated indefinitely, which does not correspond to the physical reality. In steady state, dv/dt = 0. So v is found proportional to the electric field, and therefore defines the mobility as proportionally constant. Therefore, the electric current density is now obtained from the expression of the velocity on J, is equal to sigma epsilon. Epsilon means the field. Sigma is by definition, so electrical connectivity. It is proportional to the mobility. Therefore, mobility expresses the ability of an electron drift in an electrical field. We treated electrons, the other charge carrier, as we have seen of the holes. Well, we have similar expression for electrons on holes where we define the electron mobility and the hole mobility. The mass m that are considered in these expressions are, of course, the effective mass of electrons on holes. So later we will see the electron mobility on all mobility are equal. Likewise, effective mass of electron on hole are not equal. So far, overall electrical continuity is obtained from the electron on hole clearance. The total electric current is the sum of these two components. Therefore, one obtains full electrical conductivity. The following expression, total electrical conductivity is equal to conductivity electrons plus those of holes. It is therefore related to the mobility of electrons on holes. In an intrinsic semiconductor, the conductivity increases vastly with temperature, which is not the case for the metals. The carrier cation electrons is a conditional bond on holes, is a valence bond, increases with the temperature. So that the conductivity in semiconductor increases rapidly as function of temperature. The Drude model is a simple way to describe also a transport phenomenon that is linked to a concentration gradient which is remedial, that is called diffusion. The diffusion current is due to a inhomogeneity of concentration in the system. By analogy, a coterminal introduced to a location in a river is in the river. Similarly, the presence of a concentration inhomogeneity or diffusion current is created which stands to homogenize the concentration in the medium. We search the paths on concentration gradient. This is what is called Fick's law. The minus thing is related to the process of homogenization. We just obtained the current density distribution for electrons and holes. For each carrier, the total current is equal to the drift current plus the diffusion current. The drift current is relative to an electric field, which may be external and thus the diffusion current is due to concentration gradient in the system. Finally, the total current density is the current density of electrons and holes. At the thermodynamic equilibrium, the current vanish. The presence of a concentration gradient thus induces the creation of electrical field. So now if phi is electrostatic potential, the electric field is equal to the derivative of the potential. So we can consider in fact that the bond AG's Ec, and Ev, which correspond to potential energy are actually shifted by these electrostatic potential. We finally obtain the Einstein relationship that links the mobility on diffusion constant. This relationship is a result of thermodynamic equilibrium. So as the two currents are equal, the diffusion constant is relative to the mobility for electrons on holes. These relationships depends on the temperature. This called Einstein relations. The mobility is relative to the Einstein time, experience by [INAUDIBLE] carriers. That is to say, the interaction time with photons of the network with impurities. So more impurities are present in the semiconductor, more the mobility will be low. We can consider the electron undergoes interaction processes that are independent of each other. The probability of collision is obtained by adding the different contributions, therefore the same for the mobility, which is proportional to the collection time, therefore the inverse of the probability. 1 over mu is equal to 1 over mu interaction with phonons plus, 1 over mu interactions with impurities and so on. We give, on the table, a few orders of magnitude of semiconductor mobility, so in square centimeters per volt and per second. What is generally observed is that electron mobility is larger than the whole mobility, for instance, 2 or 4 times for silicon. In addition, the silicon is not the semiconductor which has the highest mobility. Has higher mobility and also carbon diamond. Mobility measures should drift capacity of your in a analytical field. So more mobility, the faster the electronic device will be, most transistor in a microprocessor for example. Indeed, the first mobility with a low shutter microprocessor cycle. It is noted that a 3,5 compound, such as ionize B, or has a much higher mobility than silicon. This table shows the mobility of crystalline semiconductor. In the case of these other semiconductors are amorphous because the disorders in impurity concentration is much higher than in a perfect system, so that mobility is much smaller. Thus, in the silicon, mobility which is more than 1,000 for the crystalline silicon, in the units, drops to 1, even less than 1 for electrons on the loss of negligible mobility. Thank you. [MUSIC]
