In this video, we will discuss surface effect. So, surface by definition is a defect. Surface is where the periodicity of your crystal structure stops is broken. The chemical nature of the surface is that, there are some atoms sitting on the surface that don't have the sufficient number of neighboring atom that it can bond to. So, the surface contains a lot of incomplete chemical bonds, sometimes called the dangling bonds. So, these dangling bonds and incomplete bonds, produce energy levels that are located within the band gap. Just as the bulk defects and impurities produce energy levels that are located within the band gap. The nature of these defect surface states are not well-known in general, and there are many varieties of defect states that are possible depending on the exact termination of the surface. But in general, the density of surface states is known to be proportional to roughly the two-thirds power of the atomic density. This number for silicon is about 10th to the 15th per square centimeter, which is pretty substantial number. The energy level is spread out over a range because there are many different types of defect states which will have a different energy. So, these surface state energy levels are spread around over a range, and it is generally known to peak around one-third of the band gap from the valence band in silicon and other semiconductors that have a diamond crystal structure. This is not specific to just real surface but also you have a similar situation for any hetero interface, meaning that the interface between two different materials. So, Schottky contact metal semiconductor contact is an example of hetero interface. It's an interface between two different materials semiconductor and metal. At the interface, you should expect a lot of these surface states or interface states producing these energy levels within the band gap located physically at the interface. So, let's consider these Fermi level pinning effect in the Schottky contact. So, when you form a Schottky contact, then if you recall how does a metal semiconductor Schottky contact reach equilibrium, by migrating electrons from an n-type semiconductor to metal, and these migrating electrons leave ionized donors behind, and these ionized donors produce electric fields, and these electric field produces a potential barrier that opposes the migration of electron. So, when these two balance each other out, then you reach equilibrium. Now, this is an ideal Schottky contact case. Now, consider the case where you have a substantial density of surface states as shown here. So, these states before formation of the Schottky contact, when they're isolated, the distribution of these surface states peaks at about one-third of the way into the band gap from the valence band, as I said before. So, most of the states are located below the Fermi level. If you recall the Fermi-Dirac probability function, energy levels located below Fermi level has a very high probability of having an electron there. So, you can imagine that most of these surface states actually have electrons in there. When you form a Schottky contact and when the band bending occurs, then some of these states that originally had electrons get pushed up above the Fermi level. When they are pushed up above the Fermi level, then the probability according to the Fermi-dirac probability function once again, the probability of finding electron in these states are small. Which means that these guys will release the electrons away from it. So, the electrons will be emitted into conduction band and those electrons will then fall into the metal side because metal side has lower energy. So, not only do the conduction band electrons of the anti semiconductor migrate over to metal, you also have an additional source of electrons surface state emitting electrons and providing these carriers to the metal side in order to reach equilibrium. Now, suppose the case where you have a very, very high density of states, and a high density of surface states so that the electrons produced by this surface states here are comparable and to the electrons migrating from the conduction band of the n-type, or consider even more extreme case where the number of electrons emitted from the surface states is greater than the number of electrons migrating over to the conduction band. In that case, the number of electrons emitted by the surface states will be enough to reach equilibrium. So, irrespective of your doping density, you will always reach the same equilibrium state where the Fermi level position, and a Fermi level at equilibrium should be constant throughout the system. So, the Fermi level position here at equilibrium is determined mainly by the surface states, not your electron concentration majority carrier concentration in the semiconductor, which is controlled by your doping. So, in this situation, your Fermi level position is fixed to the energy where the surface state density peaks. Again, that is typically one-third of the way into the band gap from the valence band in many semiconductors. It doesn't matter how lightly or how heavily doped your semiconductor, your Fermi level will always get stuck at that energy level. That phenomenon is called the Fermi level pinning and it takes away a very very important degree of freedom for engineering for semiconductor devices. So, it is detrimental, it is a major source of degradation in semiconductor devices and so it has been a major topic in the development of semiconductor devices to clean up the surface, to reduce the surface state density as much as possible so that you don't suffer the Fermi level pinning and the consequent degradation of the semiconductor device performance.