In this video, we will discuss Ohmic contact. An ohmic contact is a metal semiconductor contact that is non-rectifying and resistive. Ideal ohmic contact will give you zero resistance but in reality, there will be some resistance which you can always add as series resistance at the end of whatever analysis that you're doing. Ohmic contact is a fundamental requirement for any kind of a semiconductor device in order to be able to apply a voltage and also extract current or inject or extract current into and out of the semiconductor. Now, there are two ways to form ohmic contact, the first method is to take a Schottky contact, the rectifying metal semiconductor contact and turn that into an ohmic contact by having, making the effect of the potential barrier negligible. One easy way, straightforward way to achieve this, is to use a heavily doped semiconductor to form a metal semiconductor contact. Now, if you recall, the depletion region width building on the semiconductor side in a Schottky contact goes as this. So, the depletion region width is proportional to the square root of the inverse doping density. So, if your doping density is very, very large, then your depletion region width can become very small. If the barrier width becomes only a few nanometers wide, then the electrons from either side, electrons in metal or electrons in semiconductor either side, can tunnel through, the barrier has become very, very narrow, and there exists a substantial tunneling probability from both sides and therefore you lose the rectifying behavior which is caused by this energy barrier and you have a symmetric current distribution characteristic of a non-rectifying ohmic contact. So, here, this is a situation where you have an energy barrier and the barrier height which is defined by the difference between the semiconductor electron affinity and the metal work function, that's always there, and the band bending here is given by the doping density here and again the band bending is very steep because the doping density is very high, depletion region is very narrow. In this case, you can have an efficient tunneling from metal to semiconductor having a current flowing from metal to semiconductor. If you have an opposite biasing, then this time the electron from the semiconductor side can tunnel through the metal side inducing a current in the opposite direction. Then you can see that if these barriers are very, very narrow, then the difference between these two situations, the forward and reverse bias situation, is almost identical and you should expect the same non-rectifying symmetric current behavior that is required for an ohmic contact. So, here's an example that I took from a book, and this is a metal oxide semiconductor field-effect transistor, which we will discuss later, but I just want to highlight the contact region here. So, there is a source electrode and the drain electrode, and the source and drain electrodes are there to apply voltage and also to pass current. So, you do need ohmic contacts here. In order to have ohmic contact, you create these heavily doped n-type semiconductor region underneath the contacts so that you could have an ohmic contact. So, this is an example of the ohmic contact made by using heavily doped semiconductor to make a metal semiconductor contact. There's an alternative way of creating an ohmic contact, and that is to populate more majority carriers near the contact. So, in a typical Schottky contact, you create a depletion region near the contact, you deplete carriers, mobile carries, you push the carriers away from the contact and create a depletion region, that's Schottky contact. If you somehow can attract more majority carriers near the contact, then you could have a situation that is opposite of Schottky contact, and that contact should behave like an ohmic contact. So, to do this, you have to choose a metal that has a work function, metal work function here, Phi sub m, that is smaller than the work function of semiconductor. So, here is the vacuum energy level, and vacuum to Fermi level is a work function, so this is metal work function, this is the semiconductor work function, and the semiconductor work function is at a lower energy than the metal work function. So in this case, when you form a junction, then when at equilibrium, the Fermi level should line up, and in order to line up these two Fermi levels, you have to have a band bending upward in the semiconductor side and so, equilibrium, energy band diagram should look like this. So, if you see this, then you have a band bending that is in the opposite direction of the normal Schottky contact with n-type semiconductor, and you can see that there is no barrier, electron can just slide along the band diagram and reach metal, and the metal side can also climb up with very little barrier and reach the semiconductor side, and this type of contact, it behaves like an ohmic contact. The charge density and the band bending, all of those things, can be calculated through the same approach that we have used before. Basically, defining the charge density near the contact and solve Poisson's equation in order to calculate the electric field and the potential barrier. So, the charge density is given by the standard equation using the potential, and you can solve the Poisson's equation to find the charge density which is basically the electron density, majority carrier concentration near the contact, and majority carrier concentration has this dependence on x which is basically one over x squared, type dependence. Once again, the mobile carrier distribution here is characterized by this quantity called the Debye length. The Debye length is a number that is commonly used to characterize a mobile carrier distribution, and this is once again, you are attracting majority carriers near the contact, and so the band bending is really caused by the distribution of mobile carrier, majority carriers, and this distribution once again is characterized by the Debye length. So, here is the typical charge density distribution, and the majority carriers congregate near the surface and in this case, majority carriers are electrons, so you have a negative charge building up, and this decaying distribution is characterized by this characteristic length, Debye length, and the equal and opposite charge is building up on the metal surface in order to keep the whole device neutral. From this charge distribution, you can calculate the electric field distribution from the Poisson's equation and the electric field distribution looking like this, and you can see that the electric field direction, the sign of the electric field is positive in this case, which is an opposite sign to the Schottky contact between the metal and n-type semiconductor.
