Here is the structure we have been discussing. The two terminal structure with a bias VGB. It charged on the QG. And reverse under the charge QI. And depletion region charge on QB. And the total the potential drop here is the surface potential, CS. You recall from the previous slide that the surface potential CS versus V G B looks like this. And that it flattens out over here for the following reason. Once c s becomes large enough the electrons start piling up here next to the surface. So a very slight increase in c s is enough to increase the electron concentration in QI a lot. So when you increase v g b you depend a larger inversely charged QI. But a slight increase in CS is enough to give you that QI. So if CS doesn't have to increase much and this is why C is flat and south for that values of VGB. This is characteristic of what we call strong inversion. This is the weak inversion region, the in between region is the moderate inversion region, and this here is the strong inversion region. We are going to concentrate on this part now. So in this part, what is the most important characteristic as far as the service potential goes? It is that the surface potential, it's almost flat, almost constant. It is not t 2 pi F as you very often see in some books. It is 2 pi F plus a certain amount delta phi. Which is significant. Actually this is a realistic plot. So if 2 pi F is, let's say 7x10 of 1 volt, delta pi here can be 2 or 3x10 of 1 volt. It's not negligible. Especially these days that we're talking about very low voltage circuits, and the total voltage you may apply on a device may be a fraction of the volts, so you cannot be ignoring things like that. So now, the total potential here in the strong inversion region, is 2 pi F plus delta phi And it is clear that delta phi is not exactly constant, because this curve is not exactly flat. But more or less, it is constant. It is convenient to use a single value for it, so we will assume that it is constant and the total, 2 pi F + delta phi, in other worlds, the total value of surface potential in strong inversion, will be phi 0. We say that the surface potential is pinned to a certain value in strong inversion. So this is the pinned surface potential value. And as I already mentioned, delta phi is not mentioned at all in some treatments of strong inversion. But I advise you to take it into account. So now, I'm going to use this value for the surface potential, pi 0, inside the simple equation we had developed for the inversion region. Which was this one, if you go back to our general treatment, we had developed this equation which is valid throughout inversion, weak, moderate, and strong. Well, in strong inversion, we can replace psi s by pi 0. And we end up with this. Now this, if you lump all of these terms into one, and you call the result VT0. This will turn out to be the so called threshold voltage, then this equation can be written simply. Like this. So now we have our first very simple equation. The versalier charts per unit area is negative of course, and is proportional to the oxide capacitance. And the difference between the gate back voltage and VT0, the threshold voltage. And VTO from here is given by this expression. So these equations are very commonly used in strong inversion. So what do you see? That QI is a first degree polynomial in strong inversion. Let's plot this. This is of QI because QI itself is negative versus VGB. And in strong inversion, which is over here, you see this behavior. A straight line that goes first to this equation. Now this straight line, if you extend it, it goes like this. It goes as the broken line over here and QI becomes 0 when VGB is equal to VT0. So the equation is wrong there because the exact behavior of QI, if you take our general inversion expressions, goes like this as the solid line, so clearly, the equation is wrong over here, but you don't care because we said that this is the equation for strong inversion. And strong inversion is from this point on. This is strong inversion. From this point on. So the equation is accurate in strong inverse. The slope of this is C'ox. Remember, I'm plotting the magnitude here. And one interesting thing that I should point out here is that VT0, which is a parameter that appears in this strong inversion equation. It, itself, is below the values that correspond to strong inversion. In other words, the equation here is valid from this point on. But in the equation, there is a parameter, VT0, which is outside strong inversion. Now, don't make the mistake to assume that as soon as VGB is above the threshold, you're in strong inversion. You are not. You need a couple of 10th of a vault before you get to strong inversion. We'll talk more about this later on. Notice that we have assumed a uniformly doped substrate, no implantation of other dopants for now, so everything I'm telling you applies to uniform substrates. So we have seen now that we can simplify the general inversion equations to get the really simple equations In strong inversion. And in the next video, I will do the same thing for weak conversion