[MUSIC] We have studied the contacts semiconductor metals at thermodynamic equilibrium. So as in the p-n junction, we'll take the contact, metal-semiconductor junction out of equilibrium. That is to say, in the presence of an external voltage. We will use the same arguments as for the p-n junction out of equilibrium. We first consider the case where the metal work function is greater than that of the semiconductor. We have revealed, in this case, a presence of potential bias at equilibrium. As for the p-n injunction out of equilibrium, the behavior will change depending on the scene of the applied external voltage. The forward bias corresponding to Ve positive, that is to say, to a more negative potential for the semiconductor side. So according to the scene of Ve, the height of the potential barrier will increase or decrease. So resistive region is the only affected by Ve. So now, we'll assess the current flowing between the metal on the semiconductor. As for the p-n junction, there are two components. The first one, which is from the metal to the semiconductor, and the opposite one that goes from the semiconductor to the metal. The thermal equilibrium is characterized by the absence of current. It means that J1 on J2 are strickly opposite. So the application of Ve changes the barrier. The current J2 forms the semiconductor to the metal, that is, exponentially with Ve. Since the barrier increases or decreases, depending on Ve. In contrast, the opposite current, J1, is oriented in the favored direction of the barrier. It is therefore, not affected by application of the potential Ve. So we see that J2 prime varies exponentially with Ve. J1 exponential, eVe over kT. J1 not be affected by the potential bending, low to the Schottky's low, when there's obtained rectifier effect, in this case. Let us read now, the opposite case, in which the metal function is smaller than the semiconductor. You have seen that with space-charge region, here was much thinner, in this case. Since there was a region in which edge of the condition bond was smaller than the Fermi level energy. So instead, to the case corresponding to the presence of a resistive layer between the two connective regions and on metal, the application of an electric field will, in this case, affect the wall semiconductor. Thus, in the forward or reverse bias, the bond bending will take place on the much larger thickness. It is found that there is no potential bias at the interface between the semiconductor and the metal. Even in the reverse case, take into account typical values of on. This potential value is the order of magnitude of 0.1 electron volt. That is to say, one-tenths of the width of the bond gap of silicon. So, in electrical terms, this is called ohmic behavior. In the previous case, where the metal work function was greater than that of the semiconductor, a potential barrier was created at interface. It correspond to a so called Schottky diode. That is to say, when we put a p-n junction in contact with metal, it actually creates another diode in series. Why in the second case was an ohmic like behavior? So the choice of the metal will be very important in practical applications in order to obtain an ohmic contact. Thank you. [MUSIC]