Chemistry: Doped Semiconductors

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Previously I talked about semiconductors and how we could understand the electrical conductivity in a semiconductor. And now I'm going to show you semiconductor on drugs. That is we're going to dope them. Now why do we want to dope them? It turns out that it's actually really hard to not dope them. It's really hard to get something so absolutely perfectly pure, which is again what I said was necessary for an intrinsic semiconductor. It's really difficult to get them so perfectly pure that their electrical conductivity gets really, really, really small.
And in fact, silicon is probably purified better than anything else on the planet, with the possible exception of uranium. And uranium is used to make bombs, so nobody really knows how pure they can make uranium. In the case of silicon, it's purified to the level of parts per billion. So in other words, the impurity levels are on the order of parts per billion. That's a very small level of impurity.
Let's now talk about the effect of an impurity. What we're assuming is that we're going to make it as pure as we can make it. And then it's so pure that we can now start putting things back in. And the effect of the things that we put back in is going to be predictable. So we're going to purify the silicon really well. And then now we're going to start doping things back in.
And doping can be divided into two categories. There's N-type doping, and there's P-type doping. And it will be really clear why it's N or P. So let's consider silicon now. And we're going to look at N-type doping first. Let me refresh your memory. We have the lower band, so this is a filled band. This is called the valence band. And then we have an empty band up here called the conduction band. And assuming we're at absolute zero temperature, all of the electrons are going to be in the valence band. And there will be no electrons in the conduction band at all.
Now suppose we put a phosphorous in place of one of the silicons in the structure. That phosphorous has five valence electrons, whereas all of its neighboring silicons only have four valence electrons. And we represent that in the energy diagram by an orbital that's a phosphorous atom orbital with one electron in it. Again, phosphorous has five valence electrons. Four of them went to go into the valence bond to form these covalent bonds. And then there's one electron left.
Well what does that get us? At absolute zero, it doesn't get us anything. In other words, when the temperature is as low as it can be, all of the electrons are living down in the valence band, except for one electron that's extra that lives on phosphorous. But as we warm this up, it's reasonable that this electron should be thermally excited in exactly the same way we were talking about thermally exciting electrons from the valence band to the conduction band. Except now this level doesn't have that far to go to get from this atomic level up to the conduction band. So it's much more likely that this electron is going to get excited up into the conduction band.
What does that look like pictorially? It looks like, pictorially, this electronic moving into the conduction band looks like going from the electron living on phosphorous. That's that extra electron leaving phosphorous so that phosphorous becomes positively charged. And now that extra negative charge is delocalized onto one of the silicons. This is an antibonding orbital. In other words, it's an orbital that's delocalized over the entire silicon. Right, this is a molecular orbital theory picture. These are antibonding levels up here. So the effect of this is that the lattice is ever so slightly less stable. It's spread out a little bit more, but not much more, because these are the least antibonding of the antibonding levels. And that electron now is delocalized over the whole solid. And it's actually free to move around.
So this electron can hop around all through the silicon. It can be the charge carrier. The positive charge that's living on phosphorous, it's there permanently, because what it represents is a level here on phosphorous that doesn't have an electron on it. But this is a localized level. This is an atomic orbital on phosphorous. Now we can have a bunch more phosphorouses, but for the most part, they're not going to really talk to each other much. And so we'll just have another atomic phosphorous level, and another atomic phosphorous level, and another atomic phosphorous level. And inside the band gap, it's the electrons that get promoted off of the phosphorous, and into the silicon network that are delocalized, that are free to move around and carry electrical charge. And if you think about what it represents is this silicon has two electrons, so it has a negative charge. It doesn't need any more electrons to form a bond. And then this silicon has one unpaired electron that it wants to make a bond with, but it doesn't have anything to bond with. This negative charge can move all around. So it can move to this silicon, and this silicon, and this silicon, move all about through the whole lattice, and basically you'll just trade forming a bond here for moving a negative charge to this silicon. If you draw it out, you'll see what I mean.
The bottom line is there's a positive charge localized on this phosphorous, and now an electron in the conduction band that's delocalized over the whole silicon. And we call this N-type doping because the phosphorous is contributing an extra electron, a negatively charged particle to the silicon lattice. And it's that negatively charged particle, which is delocalized, which can move about. It's sort of like going from this picture here, the Chinese checkerboard. And then the conduction band is an empty Chinese checkerboard. And then phosphorous is just something that comes along and takes an electron, not out of the amount of the valence band, but phosphorous contributes another electron to the conduction band from somewhere else in the impurity level. And that electron is free to move around in the second Chinese checkerboard. So that's N-type doping.
Now P-type doping is the opposite in the sense that now what we're going to do is we're going to put something on the other side of silicon. So phosphorous is to the right of silicon. We're going to go to the left of silicon. We could do aluminum, but I happen to draw boron, in any case, anything in the group 13. And now boron doesn't have enough electrons to make the four valence bonds that it wants to make in the silicon lattice. And so this silicon has an extra electron, and boron doesn't have an electron to make that bond. What that represents pictorially is here's a boron level, that's sitting inside the gap, but it lives relatively close to the top of the valence band. And what we can do is we can make a hole at the top of the valence band, take an electron from here and put it onto the boron. And if we take an electron here and put it onto the boron, it doesn't take a whole lot of thermal energy. Again it might take a whole lot of thermal energy to go from the valence band all of the way up to the conduction band. But considerably less to go from the valence band onto the boron.
And what does that look like pictorially? What that looks like is going from this picture, which is what I had on the previous slide, to this picture, where one of the silicons somewhere else gave up an electron to form the boron silicon bond that wasn't really complete. Right, boron needs an electron to contribute to that valence bond. Now boron is negatively formal charged. So these are formal charges. And this silicon had to give up an electron. So now this bond doesn't exist. This silicon still has its electron. But this silicon gave up the electron that it was previously using to make this bond, gave it up to the boron, but this positive charge is delocalizable. It is free to move about the lattice, because it represents a hole that we created at the top of the valence band. So I'm going to draw a hole there, and move the electron that was living in that hole before. Now that electron lives on the boron. That's represented by that electron living on the boron as a negative charge. And then there's positive charge of a hole that's free to be delocalized across the whole solid. And this is known as P-type doping, P meaning positive, because we have a positive charge that can be delocalized through the whole solid.
Well it happens to turn out that if you take an N-type dope material and a P-type dope material and you stick them together, you make something called a pn-junction. And a pn-junction acts like a diode, meaning that it passes current in one direction and not in the other direction. And that device turns out to be useful for, for instance, turning AC, or alternating current, into DC, direct current, but it also is a fundamental solid state device that's used for making computers and things like that. And if you take two p-junctions and sandwich them around an n-junction, you get a pnp-junction. And that's what a transistor is. Similarly an NPN is also a transistor. So what I've shown you here is really the basis for all of the semiconductor industry. Obviously it gets more sophisticated, but the basis of it, taking silicon, making it really, really pure and then doping it with levels of impurities so that you can control the number of free carriers, and the conductivity. And then layering them, making junctions like pn, or npn, or pnp, is really the crux of the semiconductor industry.
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Doped Semiconductors Page [2 of 2]