nanoHUB-U Fundamentals of Nanotransistors/Lecture 1.2: The MOSFET as a Black Box
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[Slide 1] Hello and welcome back. So this is Lecture 2 of Unit 1. Now as you know, this is a course about what goes on inside a nanoscale transistor. How the electrons and holes flow through these incredibly small devices. But what we're going to be doing in Lecture 2, is we're going to be treating these transistors as a black box. We're going to ask if we apply voltages to the terminals, what currents flow. And we're going to define some terms that we're going to need to deal with for the rest of the course. 

[Slide 2] So here's our cross sectional view of a silicon MOSFET. 

[Slide 3] Here's a cartoon sketch of that same MOSFET. So you can see all of the key elements. The source and the drain. These are N-Type, so this would be an N channel silicon MOSFET. We apply voltages to the three terminals. You know, we won't worry about the fourth terminal. For the time being we'll just ground that because it doesn't play a major role. We have between the gate electrode and the channel itself a thin layer of insulating layer. Traditionally it's been silicon dioxide. These days it's being replaced by some other materials. And the critical dimension of the transistor is the channel length L. And we'll be talking a lot about that. Now this is the cross sectional view. If you look down on the top of the transistor, this is what it looks like. So you can see the contacts here for the drain. Here and here. We put metal down. That exposes the silicon surface, so we can make a contact -- electrical contact to the silicon surface there. So this is the source contact. This gate is going across the width of the transistor. This width, W. This is the width of the transistor coming out of the page in this cross sectional view. So this is what the transistor looks like from the side view. And from what the -- and from the top view. So keep that in mind as we discuss transistors. 

[Slide 4] Now here's our engineer's black box. Now engineers like to think about any device as a black box that can be characterized from its terminals. So that's what we're going to do for this course. Treat it as a black box. The rest of the course is about what goes on inside. Now there are lots of different kinds of transistors. Most of them operate in similar ways. We're going to be focusing on the MOSFET. There are different flavors of MOSFET's. You know, silicon on insulator MOSFET's. FinFet's. There are III-V transistors. I mentioned HEMT's earlier. There are junction field affect transistors. There are bipolar transistors. All of these transistors operate through the same, general physical principals that we will be discussing in this course. Although we'll spend most of our time on MOSFET's. And a little bit of time on HEMT's. There are a lot of other kinds of transistors that operate on different physical principals. Mostly these are being explored in research as possible replacements for silicon. Or possible complements to traditional transistors, as we continue to evolve transistor technology. Our focus will be on the first class of devices. 

[Slide 5] So here's our bulk silicon MOSFET again. You know, from time-to-time it'll be inconvenient to draw this physical structure. And we'll simply draw this circuit schematic. So you can see the source. The drain. The gate. The channel is on, depending on the voltage of the gate. So that's the dash line here. And there may be a body contact. Some transistors there is. And some transistors there isn't. We'll say a little bit about it in the course, but not a whole lot. 

[Slide 6] Now this MOSFET, let's think of it as an engineer's two-port device. In a two-port device we have an input port and we have an output port. So we need a positive and negative terminal for the input. We need a positive and negative terminal for the output. Now the body contact is separate. In some transistors it's not even there. So we basically have three terminals. But we need four. Two for the input and two for the output. So there are different ways that we can do that. One way that we can do that is we can hook the transistor up in what we would call a common source mode. In the common source mode, this source terminal is common between the input and the output. Now we have an input between the gate and the source. And an output between the drain and the source. So if we hook the transistor up in that way, we say we're hooking it up in the common source mode. Now there are two different ways that we can plot the current versus voltage characteristics in this mode. The first way, we could fix the output voltage. We could fix the voltage between the drain and the source. And we could sweep the input voltage -- the voltage at the gate. And we could plot the output current. So output current versus input voltage. We call that the transfer characteristic. Because it relates the output to the input. Alternatively, we could plot it in a different way. We could fix the input voltage at a specific voltage. We could plot the output current as we sweep the voltage between the two output terminals. We call that the output characteristics. So get familiar with the terminology, if you haven't seen this before. Because we'll be using this routinely throughout the course. 

[Slide 7 ] Now what we want to do in this course, is to understand the current versus voltage characteristics of transistors. The simplest device, I guess, is a resistor. A resistor has a very simple current versus voltage characteristic. An ideal resistor is just linear. Current is proportional to voltage. The constant of proportionality is one over the resistance or the conductance. The higher the resistance, the less current. The lower the resistance, the more current. So that's a device with a very simple current versus voltage characteristic. 

[Slide 8] Now there's another device that electrical engineers like to define. We'll call it an ideal current source. The property of an ideal current source, is it doesn't matter what voltage we put across its terminals, we always get the same current independent of the voltage. So that we would call an ideal -- mathematically ideal current source. 

[Slide 9] Now at the simplest level, the output characteristics of the transistor would look like this. If I apply a small voltage between the drain and the source, the device will operate like a resistor. The particular value of the resistance will be determined by the voltage that I apply at the gate. If I apply a large enough voltage between the drain and the source, the device will operate like an ideal current source. The particular magnitude of the current will be determined by the voltage that I apply to the gate. So that's the basic output characteristic of a transistor -- of all transistors that we're going to be trying to explain in this course. Two different regions -- there's a region we call the linear region -- where the device operates as a gate-voltage controlled resistor. And there's a saturation region. Where the current saturates, and the device operates as a gate-voltage dependent current source. 

[Slide 10] Now of course there is no such thing as an ideal current source. You know, electrical engineers can build pretty good ones. But none is ideal. There's always some dependence of the current on the voltage across the two terminals. And the way we can model that, is by putting a resistor in parallel with the current source. Now the larger the voltage across these two terminals, the more current I get through the resistor. So when you sum the two, you get a current versus voltage characteristic that looks like this. We say now that we have some output resistance to the current source. 

[Slide 11] A real MOSFET looks like this red line here. It looks linear for small drain-to-source voltages. And it tries to saturate for large drain-to-source voltages, but it can't saturate completely. There is some output resistance of the MOSFET. So that's what the IV characteristic looks like for this device. 

[Slide 12] Those are the IV characteristics we're going to try to explain. Basic IV characteristic has two regions. Has a linear region. A region we're going to call the saturation region, even though it doesn't saturate completely. And the voltage that we apply between the drain and the source that separates those, if the voltage is small, compared to this drain saturation voltage -- V DSAT -- than we're in the linear region. If the voltage is big compared to the drain saturation voltage, then we're in the saturation region. That's the basic IV characteristic. 

[Slide 13] Now I showed that for one particular voltage on the gate. If I do that by applying different voltages on the gate, I'll get a family of output characteristics that look like this. If I apply a smaller voltage, I get less current. If I apply a larger voltage to the gate, I get more current. And it looks something like this. If I apply no voltage to the gate, or a very small voltage, I'll have essentially no current. It'll be so small; it'll be a leakage current. That it's hard to see on a linear scale like this. We call that the sub-threshold region. But again, above threshold, the two key regions are the linear region and the saturation region. Depending on the magnitude of this voltage I apply 

[Slide 14] between the drain and the source. So you want to get familiar with going back and forth between output characteristics and transfer characteristics. So if you look at these output characteristics. And the dividing line between the linear region and the saturation region is this critical voltage we call the drain saturation voltage -- V DSAT. If I plot the transfer characteristics, what I'm going to do is fix the drain voltage somewhere, and then sweep the voltage on the gate. Now if I fix the drain voltage at a small voltage, so that I'm operating in the linear region. And then sweep the gate voltage, I'll get a transfer characteristic that will look something like this. All right? If the gate voltage is low; the device is not turned on. I only have leakage current. I'm in sub-threshold. Then the device turns on and I get current. If I pick a larger drain voltage, so that I am out here in the saturation region and do this plot, I'll get more current. Again, the device will be off until I apply a large enough drain current -- gate voltage, I'm sorry. And then the device will turn on and I'll get more and more current. The critical voltage that separates the region from which the transistor is off. And the region when the transistor is on, is called the threshold voltage. Okay, so if you're not familiar with transistors, there are lots of terms that we're defining in this lecture and that you need 

[Slide 15 ] to get familiar with and try to keep straight. Okay, now I've been talking about what we call an n-channel MOSFET. The current that is flowing, is flowing due to electrons. The source is a source of electrons. And the drain is where the electrons go out. And the electrons flow across the channel. When I apply a gate voltage that is bigger than this critical threshold voltage, then the source and the drain are connected by a region with high electron concentration. The current flows across. The positive voltage on the drain attracts the negatively charged electrons from the source. They flow across and out the drain contact. Negatively charged electrons flowing out the contact, give us a positive current flowing in. Now modern day technology is C-MOS technology. The C is for complementary. It means every -- for every N-channel device, there is a P-channel device. And a P-channel device looks like this. In a P-channel device, the source is a source of positive charge carriers or holes. And those positive charge carriers go out of this P-type drain. And there's a channel across there. Now, everything changes sign. When I apply a negative gate voltage, if it's negative enough -- if it's more negative than the threshold voltage, which is negative for this device, then I create a channel of positive carriers/holes. The negative voltage on the drain attracts the positively charged holes from the source. They flow across the channel. The positive carriers flow out. Positive carriers flow out means the drain current flows in the opposite direction. So just in the interest of time, I'm mostly going to be talking about how N-channel MOSFET's work. But you should get familiar with being able to translate back and forth between N-channel and P-channel. Basically all the voltages change sign. All the currents change directions. That's all there is to it. 

[Slide 16 ] Now we've defined some terms. We're beginning to get a little bit familiar with the IV characteristics of these devices. We want to eventually relate those IV characteristics to what's going on inside. But a question you might ask now is, you know, how do we determine whether we have a good MOSFET or not? Now device engineers do this by defining a few key metrics. They look for a few key parameters in these IV characteristics that can tell them whether this device will perform well in the complicated circuits that we build these days. And that's the subject of the next lecture. Device metrics. So I'll see you for the next lecture.