We are now ready to start discussing the Two-terminal MOS Structure. I know that some of you are eager to get started with the full MOS transistor, but I can assure you that, this week, we are already talking about the MOS transistor. It's just that, we are talking about part of it. Complete MOS transistor models, such as the ones you find in professional, the computer-aided design programs are very complicated and they can have 200 parameters or more. And each parameter is there in order to help describe an effect that is important in the MOS transistors characteristic. The only way to make sense out of this is to take things one at a time. So we will start with the two-terminal MOS structure and understand the phenomena that are already there in that simple structure before, before we go to more complicated ones. We begin with important concept of that Flatband Voltage. So let us begin with a thought experiment. I will assume that we have a special type of MOS structure in which the gate and the body are made out of the same material. And not only that, they are collected together by a wire consisting of the same material. Obviously, this structure is never made as such, but it will help introduce certain concepts here. So it's clear if you stand in the middle of the oxide, that on both sides you see the same thing. So the structure is symmetric, and therefore, you don't expect charges to accumulate anywhere in it. It is everywhere neutral, and so, many things are ideal. Now, let's go to our, to more realistic situation, like this. Now, we have a different material for the gate, compared to the body. Not only that, we may have a contact at the bottom of the body, let's say a metal that contacts the body, and we have two terminals called g for gate and b for body. And they are connected together with a wire, which may consist of yet a different material. As we know from our lecture on contact potentials, there are contact potentials every time one material joins another. But when you go around this, all that counts in the sum of these potentials is the first material and the last material. And in fact, the sum of those contact potentials is the work function potential of the last material minus the work function potential of the first material. And, because they exist, contact potentials, you may have a potential difference between the two plates of this capacitor so to speak. So in this particular example, I'm assuming that the potential happens to be positive here compared to here. So these charges are positive and these charges are negative. The question is what can we do to eliminate these charges and restore the neutral condition in the substrate, just like we had it here, with no charges accumulated anywhere. Clearly, what we have to do is add the potential somewhere in the loop to exactly cancel the existing sum of contact potentials. So I'm going to break this wire here and I'm going to add a voltage source of value phi MS. I'll explain this name in a minute. And this will be such as to exactly cancel the contact potentials here. So the question is, what is the value of phi MS? Since the potential, as we go this way, is the sum of conduct potential, which is the work function potential of the last material minus the work function potential of the first material. This one should be made exactly the opposite. In other words, the work function potential of the first material, the gate material minus the work function potential of the second material, the semiconductor material. M stands for metal, because, in the old days, all gates were made of metal and s stands for semiconductor. So it's clear why this difference is simply called phi MS. So, we have now established that in order to maintain the substrate neutral, we need to insert voltage equal to phi MS in this connection. However, this assumes that we have an ideal MOS structure, otherwise. Real structures, unfortunately, may have charges at the interface between the oxide and the semi conductor, as shown here. Now, there are several types of charges that can exist at the interface or at the oxide, inside the oxide, but you can show that as long as these charges are immobile, you can represent them effectively with a single interface charge here. So, the variety of charges that could be the so-called the oxide fixed charge, you can have the trap charge in the oxide. You can have an interface trap charge right here, which is there because of defects of the structure at these, near the surface. And we will talk about those things later. All of these charges will be represented by a single sheet of charge right at the interface, which will be called the effective interface charge. Now, there is yet another charge that can appear, and that is a mobile charged within the oxide, due mostly to alkali ions, like sodium for example. And in the old days, this was a major problem. It was very difficult to control fabrication processes for this reason. And there are all kinds of anecdotes about what people were observing. For example they were finding that, if they fabricated an MOS transistor, in the early afternoon, it was more unstable and useless than before noon. And the reason turned out to be that the workers that were handling the equipment after having had lunch and having touched potato chips were then coming back. And the sodium on their fingers was enough to contaminate the oxide. Anyway, people learned the hard way, a lot of research was done, and by now the effective interface charge has very small values. And the mobile charge is very small in competing [inaudible]. So now, although, we have canceled the contact potentials by adding this voltage phi MS, we have a charge here, which is positive in this example. And to maintain overall neutrality, you're going to have some negative charges somewhere. Some of the charges are here in the semiconductor and other charges are on the gate. The question is, what can we do now to make the substrate again neutral? We would have to remove the negative charges from here and place all of them there. This is what we would like accomplished. That, one by one, all of these positive charges are mirrored on to these negative charges on the gate. And to do that, we have to modify something. We have to add the voltage here. And the question is what is this voltage? So, let's figure this out. The charge of the interface will be called Q0, and if these charges are the negative of these charges, then the charge over here would be minus Q0. So we have a two plate capacitor, will be called tOX, and the voltage from here to there is the, the charge on this plate divided by the capacitance. And the capacitance is this. The permittivity of the oxide divided by the oxide thickness. Therefore, the potential from here to there is simply the charge on the top leg divided by the oxide capacitance. And I'm going to be using, when I say charge and capacitance, almost always, I'll be talking about charge per unit area, and capacitance per unit area, or area is what you see when you look at the structure from above. But I will maintain the, the short name charge and capacitance. And the primes that you see here will indicate that we're talking about per unit area quantities. So now, if this is the potential we need to have here, then, we'd place here a voltage equal to this potential. And now, what do you have here? You have two voltages. One is phi MS that cancels all of the contact potentials. And the other is precisely the voltage you need to support the voltage across the oxide capacitor without inducing any charges in the body. So the sum of this is the total amount of voltage you need to apply externally, VFB. This is called the flatband voltage, for reasons you will see in a moment. And we have established that the flatband voltage is phi MS minus Q0 prime over C OX prime. This is the flatband voltage. Now, why do we call it the flatband? Notice that what we try to do here is make the semiconductor everywhere neutral. In other words, as you go from the surface towards the bulk, there is no potential change. The corresponding energy band picture looks like this. Here, we have the, the MOS two-terminal structure. This is neutral drop. There is no potential drop as we go in this direction. And if you remember how potential is related to the conduction band edge, that means that the band edge must be horizontal also. So the energy bands are flat. And this is why the amount of all those you need to supply here to accomplish this is called the flatband voltage. In this video, we have discussed the important parameter called the flatband voltage. And, we have seen that the bands are flat when the gate, body voltage is equal to that parameter. In the next video, we will allow the gate, body voltage to take different values and we will see what happens in the semiconductor in such cases.
