In previous lecture, we learned the concept of the Schottky barriers. This slides starting with the Schottky barrier on their bias equations. This is the forward bias of the Schottky contact, and this is the reverse bias of Schottky contact. In forward bias, contact potential is reduced and the huge electron that has a higher energy than barrier, which is following the Boltzmann distribution, they go to the other side and current flowing in one direction. Then reverse bias, potential barrier is increased, no current is flowing, so current is almost zero. This is the same thing of the p-n junction p-n diode. Then for reverse bias, current is not flowing, forward bias, current flowing and increasing exponentially. So I equal I_0 exponential applying voltage per nkT minus 1, and I_0 is reverse saturation current. Obviously, this reverse saturation current is influenced by the Schottky barrier. Because if Schottky barrier high, then reverse current almost lower. In rectifying diode, current transport is mainly due to the majority carrier, therefore, there are no recombination. If you go back to the p-n junction, transport of a p-n junction is mainly due to the minority carrier of the diffusion. So majority carrier of the whole go to the other side of a n-type semiconductor becomes of minority excess carrier, and they recombine in the ocean of the majority carrier electron and recombine and then they get concentration gradient and current flowing by recombination. Here, current is flowing, electron flowing to the metal and there is no recombination. Also operate by the majority carrier without recombination. Therefore, this Schottky barrier is faster device compared to the p-n diode and can be used in high frequency, high switching speed devices of the metal to p-type semiconductor instead of the n-type semiconductor. For the p-type semiconductor, the work function is the opposite metal. Work function is less than the semiconductor work function. This is metal work function, and this is the semiconductor work function of the p-type silicon. If you make contact, holes in opposite to the n-type, holes in p-type is much stable in the metal because this is based on electron, so holes are more stable in high energy of band diagram. So hole accumulation, and there is a depletion of a fixed charge of the boron at the junction of the p-type semiconductor. This is the built-in potential, and this is the Schottky barrier. What is a built-in potential in this band diagram? In this band diagram, potential is increased until the Fermi energy is equal. They moved this much, which is the built-in potential is Pi s minus Pi m. For the Schottky barrier, Schottky barrier is where your counterpoint is not changing, so this is the Schottky barrier. So Schottky barrier is E_g minus this, which is the Pi m minus Chi. On forward bias, barrier is lower for the hole. Therefore, on the forward bias, you should apply positive voltage. The p-type region, barrier is lower and holes are easily moving to the p-type semiconductor to the metal. Reverse bias barriers increase, so almost no carrier can be moving. We learned the Schottky contact, now let's learn ohmic contact. Metal to n-type silicon only contact is drawn in here. It's opposite to the metal to n-type silicon Schottky contact. In here, metal work function should be less than n-type silicon semiconductor work function. So metal work function is lower than semiconductor work function of n-type silicon. In this case, electron in metal side is more stable at the lower energy of n-type semiconductor. They move from metal to n-type, and accumulated in n-type silicon. However, these n-type silicon is not depletion, but the accumulation of the majority electron in n-type semiconductor. This is to differentiate the Schottky contact because the Schottky contact they're generating the depletion region in N-time region. This is the accumulation. Then band diagram of the n-type silicon will go up until the Fermi energy is equal. So the Fermi energy is equal, and then n-type accumulation, which means that E_c is close to the E_f, in junction region, means there are a lot of electron compared to the neutral region. Now, barrier is a very low between the metal to semiconductor, electron can freely moving, current are freely moving in both directions with a minimum resistance. In ohmic contact between the metal to semiconductor has a minimum resistance, and the linear IV characteristic in both direction. Also, this ohmic contact, there is no depletion region, that is a very important thing. Ohmic contact for the metal to p-type silicon, metal work function should be higher than semiconductor work function of the p-type semiconductor. Here's the metal work function, which is higher than p-type semiconductor work function shown in here. Holes in a metal side is more stable in higher energy of the E_v of a p-type semiconductor, because this is based on electron. Positive charge are more stable in higher energy, therefore holes accumulation in p-type semiconductor, this is not the depletion, but this is the majority hole accumulation. Then there will be bending until the Fermi energy is equal and the hole carriers can be moving freely between the both direction because there is almost degree over energy barrier. So contact resistance. Practical way to making our ohmic contact, especially for the MOSFET device, they're making a source drain region with a heavy doping. For the case of a metal semiconductor contact with the lower doping is dominated by the thermionic emission, which is the carriers can go over the barrier by thermionic energy. However, contact with the metal semiconductor, contact with a high doping concentration of semiconductor, barriers at the junction, although the Schottky barrier is a little high, but highly doping is done it and then they bend the width of a barrier is extremely narrow, let's say the one nanometer or something, then a lot of carriers in high doping region can tunneling through the extremely narrow Schottky barrier, and the huge current is flowing. So high doping source drain region, especially for MOSFET, is ohmic contact, and then the current flowing mechanism is tunneling. Then here's my questions. What is the definition of the high doping? Is the 10_17 is high doping? Or 10_18? Or 10_9? Or 10_20? This graph shows the definition of the high doping for the tunneling ohmic contact. As you can see, even in the doping concentration of the 10_19 has a very high contact resistance. So they are not ohmic contact. But when you achieve 10_20 of the high doping, contact resistance is almost to decrease by the 10_5 order, and then this becomes a ohmic contact. So definition of a high doping should be 10 to the, maybe 20, its depending.