Band theory of solids
Conductors insulators and semiconductors
- [Instructor] The key to understanding the electrical properties of material, is to look at the energy diagram, the energy band structure of the solids and focus on the highest energy band which contains electrons in them. I mean, think about it, any material you take, any solid you take, there must be some highest energy band with electrons in it, right? Because there are a finite number of electrons. So you pick that highest energy band. It could be anything I don't know, depending on which material we choose, the band can either have completely filled electrons or maybe partially filled electrons, right? Any of them is possible. So let me just shade this to show filled electrons over here. Let's assume it has partially filled electrons. This is even one of them. And since electrons tend to get excited at higher temperatures and we don't want to look at that right now, let's look at the lowest energy state possible. That's at the lowest temperature possible zero kelvin. So let's assume this is at zero kelvin, zero kelvin. O K. All right. Now, if you take materials like materials like sodium or magnesium or copper or iron, you see I'm talking really about conductors. If you take materials like these, which are conductors, it turns out that if you look at the next available energy band, what you see is that the next higher energy band ends up overlapping with this energy band. As we saw before energy bands can overlap and in good conductors or in metals, they stay overlapped. And so strictly speaking, these are not two different energy bands because once they overlap they become one single giant energy band so I really should get rid of these divisions over here, I'm just gonna decrease their opacity. There you go. So what we have now is one giant energy band with electrons not completely filled there are so many vacant spaces at zero Kelvin. Now think about what will happen if we increase the temperature just a little bit. If we increase the temperature just a little bit, the thermal energy is going to try and excite the electrons, electrons over here a little bit higher. The question is, are the energies allowed a little bit higher? The answer is yes, there are energies allowed. There are so much energy allowed it's just the whole thing is a continuum. Remember they don't have to jump anywhere over here, it's allowed and so as a result, all these electrons, all of them end up becoming free electrons because they can freely move over here. You can sort of think of this like a big classroom with only partially occupied students, the classroom is empty and the kids are going to move around. This is the situation for conductors. So what we're dealing with over here are conductors. On the other hand, if you look at some other material and check their energy bands, we'll see that their highest energy band, again, this is the highest energy band will be completely filled at zero Kelvin, will be completely, completely filled at zero Kelvin. Again, remember, this is O K, zero Kelvin. And now if you look at the next available energy band, you will see it's not only not, it's not overlapping, but there's a huge gap between them. There's a huge energy gap between them and this energy gap is called as the band gap. It's also called as the forbidden energy levels because electrons are forbidden to be anywhere over here. Usually call it as Eg. And if this band gap, Eg, if it is somewhat more than four electron volt, now it's not, again, this is not a very strict thing sometimes you could write five electron volts or four but if it's sort of like more than four electron volts, then we'll call this as an insulator. We'll call this as insulators, all right? So this will be the example for say glass or diamond, they're excellent insulators. Can you see why they end up becoming insulators? Because now if you increase the temperature a little bit and the electrons try to get excited, well now the electrons can't get excited so easily because if you try to excite the electron from here to here, well they can't accept that because remember these energy levels are forbidden. So if you want to excite these electrons, you have to excite them all the way till here and the probability of an electron being excited all the way over there is extremely low even at room temperatures. And so in such materials even at room temperatures, you will find extremely tiny amount of electrons found in this empty band and so only little bit of, or negligible amount of free electrons are found and that's the reason insulators behave like insulators. And if you look at silicon or germanium and focus on their highest energy bands, again, it's found that at zero Kelvin, this is completely filled, zero Kelvin this whole thing is completely filled just like an insulator. All right. But now if you look at it's next available energy band, what you find is situation is very similar to insulator but you can see the difference is that that same band gap, that forbidden energy gap, that band gap is extremely tiny. Usually it's, for Silicon I remember it's for silicon it's about 1.1 electron volt, for germanium about 0.7 electron volt so it's usually found to be less than about two electronic volt we can say somewhere like that, again it's not very rigorous we don't have to worry too much all that matters is very low. And now as a result if you increase the temperature say to room temperature and you try to excite the electrons well, compared to insulators, electrons will get more readily excited over here. So at room temperature, you will find a lot more electrons in this higher energy band ready to conduct compared to that of insulators. But of course they're not as good as conductors because in conductors, you don't have a gap at all there is no band gap and so all the electrons become free over here. Here, a very few amount of electrons can become free, here almost no electrons, almost, I say almost because some electrons will get free and that's the reason these guys end up becoming semiconductors, semiconductors. Now the only one detail we need is to know the names of these two energy bands, all right, this highest field energy band at zero Kelvin, we call that as the valence event. So these bands, the highest field bands are called callers valence bands. So whenever someone says valence bands, what usually comes to my head is it's the highest field band at zero Kelvin and it's most of the cases it's completely filled at least when you take insulator or semiconductor, it is completely filled. And by the way, it's called valance because even in the atoms we have something called valance shells, the final shell which has electrons, right? This, the word comes from there itself. And the next higher band in which conduction takes place like I mean the electrons have to go there to get conduction, we call that as the conduction band. So these bands are called conduction bands, conduction bands. And notice at zero Kelvin, the conduction band is always empty, completely empty at least for insulators and semiconductors. And now you might ask, what do you do for conductors? Well simple, don't define valance bands and conduction bands because you see in conductors, you actually just have one giant band you could call it as a valance band, this whole thing because it is the band with the highest energy electrons. We can also call it as a conduction band because that's the band in which conduction can take please. So they lose their meanings for conductors but they have very specific meanings for insulators or semiconductors.