In this lecture, we're going to talk about the use of the law of mass action to determine the minority carrier concentration extrinsic semiconductors. Then we will look at how the charge moves in a diode during operation, as well as formation. Diodes are all over our lives, either from a solar cell, to LED lighting, to rectifying diode. But first, let's take a moment for inquiry. In this case we're asked, why do electrons in the presence of electrostatic field do not undergo continuous acceleration? Well, again, in the presence of this electrostatic field, the electrons are accelerated. However, they undergo scattering events with other electrons and defects, such as grain boundaries, impurities, dislocation. Now, as the number of dislocations or defects increase, there goes the increase in our resistor. Why does it? Due to scattering. Now we're going to look at the formation of a p-n diode. Well, first we need some p-type material and an n-type material. Now we want to make sure we're clear on which is the majority carrier and the minority carriers in each one. We look at the p-type material. We know that holes are the majority carriers, so we're going to have p on the p side, meaning the majority carriers, which are holes, and on the p side, denote the minority carriers or electrons. Similar manner on the n side, n_n denotes the electrons concentration in the n type material, p_n denotes the minority carriers or holes concentration on the n side. To determine the minority carrier concentration, we utilize the law of mass action. Basically, we look at the relationship between the intrinsic concentration and the electron and hole concentration. Let's start off on the n side. Well, we know when we dope it with acceptors, on the p side, I should say, that determines the hole concentration in the p-type material on a problem. Now we want to determine the minority carrier concentration. That's when we use the law of mass action. In this case, we take the square of the intrinsic concentration divided by the acceptor concentration. That gives us the concentration of the electrons or the minority carrier concentration on the p side. Similar manner we have our donor concentration which gives us the electron concentration on the n side. You use the law of mass action to determine the minority carrier concentration. To determine the hole concentration on the inside, we take the square of the intrinsic concentration divided by the acceptor concentration. Now we know the majority carrier concentration on both sides as well as the minority carrier concentration. We're going to make our P-N junction. We got to bring them into metallurgical contact. Basically means say, we're just going to put those two pieces together and make them touch in a intimate manner. We have our carrier concentration. They're going to come together. But notice if I look at the electron concentration, is high on the n side, low on the p side. If I look at the hole concentration on the p side is high, low on the n side, so we have a concentration gradient. The concentration gradient is the driving force for diffusion. Now we're going to get some diffusion from high to low concentration. In this particular case, we're going to get some holes diffusing, and we're going to get the electrons to diffuse. We got holes diffusing, electrons diffusing, but remember, we can have electron-hole annihilation. That basically says, hey, I got a hole plus an electron. That results in annihilation. We're going to get electron-hole annihilation. Now, if we let this go on for some time till we reach thermal equilibrium, now, once we have obtained the thermal equilibrium, we are going to have this region that is depleted of mobile charge. Now, this is what I said, void of mobile charge. That would imply no holes , no electrons present. But what do we have? Well, we have the uncovered ionized donors and acceptors. If you look, we have our partitioning of charge per Poisson's equation. We now have an electrostatic field in place. Anytime you have partition static charge, you set up a field. Well, I actually have potential, then we build up the field, and this field is over the width of the built-in depletion region, or we also refer to that as W_d. The V is the built-in potential. Then I'll be consistent, let me put a W_d. Now we have this electrostatic field. We have this region that is void of mobile charge. Again, there's no mobile charge in this region. We have reached thermal equilibrium. Now you say, hey, what about that high concentration? Well, again, I have the holes here, high concentration. However, if a hole diffuses in, it's going to get swept back because of the high electrostatic field. In a similar manner, and if electron diffuses in, it gets swept back due to the large electrostatic field. Now we have thermal equilibrium. We establish the depletion region where we void a mobile charge. We have this built-in electrostatic field that prevents any subsequent diffusion of majority charge. We've got a diode, so now let's put it.
