Generation and recombination in semiconductors

- [Narrator] In the previous video, we spoke about electrons and holes in an intrinsic semiconductor. But in this video, we'll go a little deeper and explore how people calculate the number of electron holes that are available in a semiconductor at any temperature. We'll talk a little bit about that. So to understand this, we need to speak about two very important processes that happen in semiconductors. One of them is called generation or thermal generation. We're just gonna call that generation. This is something that you already know. We'll talk about it. And the second one is called recombination. These two processes will be the key to understanding everything in semiconductors later on. Generation is something that we already spoke about, the process that electrons absorb their own energy and jump to conduction band and become free. That process itself is called as thermal generation. It's called generation because due to the process, we have generated a free electron and a hole, I mean, we've not created an electron. The electron was already there but it was not free to move before, but now it is free. So it sort of created that's the idea behind generation. Recombination is exact opposite. You see when these electrons and holes are moving through the solid, sometimes electrons and holes can come very close to each other. And when they do, the electrons will fall back into the holes. So they might fall back into the hole. And when they do, the free electron is lost because it's no longer free, but the free hole is also gone. And so as a result, that's destruction of charge carriers. So recombination is where electrons and holes recombine. And as a result, they destroy charge carriers. Generation is the process in which we create charged carriers. So there are two opposite effects. And one thing that always confuse me is that I actually always think that these electrons are all here and these holes are down over here. How can they ever come close to each other? But remember, this is an energy diagram. So this can be misleading. Electrons are not like on the top floor and the holes are on the ground floor. Electrons or holes are pretty much in the same space because they're in the same crystal, they're on the same solid. So they can definitely when they're moving randomly come very close to each other and recombination can happen. Now think about this, at any given temperature, let's say room temperature, I always like taking room temperature. If you have silicon say at room temperature, then the number of electrons and holes at that temperature must be fixed number. It cannot keep on changing. It must be fixed, but generation is continuously happening. Continuously electron hole pairs are being created. And recombination is happening. Continuously, electron hole pairs are being destroyed but the number has to remain fixed. Can you see that for every electron hole pair that is created, an electron hole pair must be destroyed at least on an average. So we can say that at any temperature, at a constant temperature or we could say at thermal equilibrium that's the word that people like to use, at thermal equilibrium. This means at constant temperature equal, equilibrium, the number of hole pairs created per second let's say, should be quite a number of hole pairs destroyed per second on an average. And so we could say, in other words the generation rate, generation rate, which is the rate at which electron hole pairs are being created, that should be equal to the recombination rate. It has to be. Recombination rate. All right, now let's think about this. What does generation rate depend on? Well, since generation is happening due to thermal energy, we could say generation rate depends on temperature. It should only depend on temperature for any given material. So we could say generation rate is some function of temperature. And as a function, just think of it as some expression, some formula, which has temperature in it and a bunch of other constants all there. And we say this because we can sort of intuitively say that, see if the temperature were to increase, then more thermal energy means more generation That makes sense. But at the same time, we don't know exactly how they're related to each other. We can't say it's directly proportional because we don't know that if double the temperature, the generation rate might double. We don't know that. In fact it turns out it's not to be so. So it's a little bit of complicated relationship. And if you're taking the advanced semiconductor course you might even know, you might even learn what that function is. But for us, it's not important. All that matters is some function of temperature. Similarly now comes the question. What does the recombination rate depend on? I mean, we know that it's equal to generation rate, but independently if you think about it, what does this number depend on? Well, recombination is electrons falling into the holes. So we could say sort of, again that there are more electrons and more holes available then there are more chances that they fall. Does that make sense? In fact, think of it this way. If you've just one electron and one hole, just say one electron, one hole. There's some chance, very tiny chance of recombination. But if you now have two holes, then the number, the chance of recombining doubles, does that make sense? With two holes, you have twice the chance of falling. If you have three holes there are thrice the chance of falling. Does that make sense? So can you say the recombination rate is in fact proportional to the number of holes? It's proportional to the number of holes, but you can also say the same thing about electrons. If you had doubled electrons, well then, twice the chances of electrons falling down because you have two of them and if a triple them, twice the chance. So you can also say it's proportional to the number of electrons. And since it's proportional, you could say some constant. We can put some constant K times this. And at thermal equilibrium, these two must be equal to each other. And one more detail we can add is for our intrinsic or pure semiconductor, where all atoms are Silicon, the number of free electrons must be equal to the number of holes, that's because every electron that jumps on here must have left one hole behind. So if you have like hundred free electrons there must be exactly a hundred holes, no more, no less. And therefore we could say for our pure semiconductor, the number of holes must be equal to the number of electrons. And we usually write this as N sub I, I stands for intrinsic pure. And so if you plug that, we can now write our equation as some function of temperature has to be equal to K, some constant which is dealing with this recombination, times, NI squared because you're multiplying these two. You get now NI squared. And if you look at this equation carefully, you can calculate what F is, you will know what that function is. And you also know what K is, if we do more rigorous physics. Which means, we can figure out the value of NI. And that is amazing if you think about it, that the fact that you can sit at home and take a piece of paper and you can work out the math and figure out the number of electrons and holes that can be found inside a silicon crystal, that is amazing. You can do that. And people have done that. So we'll just take the result. It does it if you calculate the number of electrons and holes at room temperature, that value at room temperature, roughly turns out to be about 10 to the power 10 per centimeter cube. And first time when I saw this, I was like, wow, that's a lot of electrons and holes. Why do we call it as a semiconductor? Why you don't we call this a conductor? 10 billion electrons and holes per centimeter cube. That's a lot. Well, we need to get some perspective. So let's do that. Let's get a little bit of perspective. That seems like a lot of number, but we need to think about the number of atoms present per centimeter cube. It turns out that if you take silicon, then it has about 10 to the 22 atoms available per centimeter cube, which means 10 to the 22 atoms contribute to 10 to the 10 electrons. So how many items contribute for one electron? We can just cross multiply and figure this out. This has helped us understand the sense of this number. So if you cross multiply, you get 10 to the 22 divided by 10 to the 10, that is 10 to the 12, 10 to the 12 atoms contributed one electron and one hole. If you think of it this way, that is depressingly low. It's like a trillion atoms. You have to beg a trillion atoms to get one free electron, one hole. And that is very low. In contrast, if you take copper, you get one atom roughly gives you one electron, sort of gives you the sense of how different these two materials are. And that's the reason why we call this as a conductor because now every atom gives you one free electron. I'm talking about free electron, but over here, 10 to the 12 atoms gives you one free electron one hole, very tiny. That's why we call it as semiconductors.