nanoHUB-U Fundamentals of Nanotransistors/Lecture 1.3: MOSFET Device Metrics
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[Slide 1] Welcome back. This is Lecture 3 of Unit 1. In lecture 2, we began to get to familiar with the I-V characteristics of transistors. So in lecture 3, we're going to talk a little more quantitatively about what makes a good transistor. What do device designers look for in those I-V characteristics? So these are called device metrics
[Slide 2] and there are a few device parameters that we will talk about as well. So you remember we talked about hooking the transistor up in different ways so that we had a 2 port device, 2 port circuit. An input and an output. This is a common source connection. The source is common between the input and the output. And then we're interested in understanding these current voltage characteristics. The current that flows from the drain to the source as a function of the voltages on those 3 terminals. And we have transfer characteristics and we have output characteristics depending on which voltage we fix and which voltage we step or sweep.
[Slide 3] So here are the output characteristics. So in this particular curve, we have fixed gate voltage at a specific voltage, VG1. We're sweeping the drain voltage from 0 to the power supply voltage, VDD, possibly 1 volt or so these days. And we get an I-V characteristic that looks like this. These are the output characteristics. If I put smaller voltages on the gate, I get smaller currents. If I put larger voltages on the gates, I get curves that have higher saturation currents. So I get a whole family of characteristics that way.
[Slide 4] If I just look at one of those, each of those have a linear region where we have a small voltage between the drain and the source and a saturation region where the current is less sensitive to drain voltage and tries to saturate. That's for a high voltage. There is a specific drain to source voltage. You can see it's not precise but it sort of separates the linear region from the saturation region. We call that the drain saturation voltage, VDSAT. Now let's look at these I-V characteristics. The slope of the I-V characteristic and the linear region, that is related to the resistance. One over the slope is the resistance of the transistor when it's operating in the linear region as a gate voltage controlled resistance. So we can just take the slope at that specific gate voltage, take 1 over the slope, we'll call that RDS. That's the voltage-- That's the resistance that we would deduce between the drain and the source terminals at that specific gate voltage, VG1. All right. So if it is an experimental characteristic, it's easy to read that slope off and determine that value. In the output region, we also have a slope and that represents the output resistance of that current source in the saturation region. So if we take 1 over that slope at this particular input voltage, VG1, we would get little r sub zero. We call that the output resistance of the transistor. So those are two important parameters.
[Slide 5] Now if we look at the output characteristics, there are several things we should mention. We're assuming that we're above threshold. That is the gate voltage is big enough that current is allowed -- significant current is allowed to flow between the drain and the source. If the gate voltage is not big enough, then we are in, we would call that the sub threshold region. Small leakage currents would flow and those small currents are important these days but they're still too small really to see on a linear scale like this. The linear region is for voltages that are less than VDSAT between the drain and the source. The saturation region is for voltages that are larger than VDSAT. The output resistance is the resistance in the saturation region. And this drain to source resistance is the resistance in the linear region. Normally when we're quoting these values, the gate voltage we'll use to do that will be the biggest gate voltage available in the circuit which is VDD, the power supply voltage. Perhaps 1 volt these days. Okay. Now I want to mention when we discuss some parameters in the next 2 slides that remember that the width of the transistor, the dimension coming out of the page when I draw these cross sections, that we call W. And the current just scales with W. The transistor is twice as wide. Twice as much current flows. So people usually quote the current in microamps per micrometer of width or milliamps per millimeter or amps per meter. You usually quote in current per unit widths because you know, the designers will decide what width they want to use to get the current that they need.
[Slide 6] So we'll have to keep that in mind when we look at some of these units. So let's talk about the first set of device metrics that a designer would look at. So a key one is what device designers would call the on-current. You apply the maximum voltage to the drain. You apply the maximum voltage to the gate. This is the maximum current that you're going to get out of the transistor in this circuit. We call that the on-current. It's usually quoted in microamps per micrometer. Okay. Output resistance, again we're usually interested in the output resistance. We'll see a little bit later why that's important in circuits but we're usually interested in it at the highest gate voltage possible. So we take 1 over the slope in the saturation region. Now notice the units because this is the change in current. It's actually it's a change in drain voltage divided by the change in current but we're measuring the current in microamps per micrometer. So it means that we'll quote this output resistance not in ohms but in ohms dash micrometers. So if my transistor is 1 micrometer wide, I'll have one value. If my transistor is 2 micrometers wide, I'll have half the output resistance because it's like resistors in parallel. So some of the units take a little -- a while to get used to. Now transconductance is another really key figure of merit for a transistor. The transconductance is basically if we change the gate voltage, if we increase it a little bit, what is the increase in the drain, the source current. So it's delta drain to source current divided by the change in gate voltage that produced that delta. So the units are siemens but remember everything is being measured per micrometer. So we typically quote these numbers in microsiemens per micrometer. If you have a transistor that's twice as fat, you'll have twice as much transconductance.
[Slide 7] Okay. So those are some key parameters in the output characteristics. Let's look at the transfer characteristics. So remember in the transfer characteristics, we fixed the drain voltage and we sweep the gate voltage. So if we fixed the drain voltage at some particular VDS, we'll get a curve that looks like that.
[Slide 8] If I look at that a little more carefully, if I fix it at a low drain voltage, now I'm operating in the linear region. And I'm sweeping the gate voltage. And I'll get a characteristic that will look like that. If I fix it at a large drain voltage, now I'm operating in the saturation region, and for small gate voltages the transistor is still off but for a large enough gate voltages the transistor is on. The transition between off and on, you know, it's not a precisely defined quantity. It's when the current -- when significant current begins to flow.
[Slide 9] And we call that the threshold voltage of the transistor. So just looking a little more carefully at that. If I look at, if I apply a large voltage to the gate, let's see. I'm going to apply a large voltage to the drain in this particular curve and do that transfer characteristic, then when I get the gate voltage up to the power supply voltage then I've got the maximum voltage on both the drain and the gate, that's my on-current. If I apply a small voltage between the drain and the source, I get another transfer characteristic, smaller voltage I get less current. Now if I'm interested in the threshold voltage, what I might do is to draw a straight line on this transfer characteristic and find its intercept with 0 current. And I'll call that the threshold voltage but notice that if I do that with a smaller drain voltage, the intercept is different. So people frequently talk about two different threshold voltages. There's a threshold voltage with a device operating in the saturation region and there's a threshold voltage for the device operating in the linear region. Ideally those two would be the same. The threshold voltage would not depend on the voltage we apply to the drain, but in practice, there is some small dependence. We'll talk about the physics of that later. So there is a drain voltage dependent threshold voltage. There's a -- there is actually some current flowing below threshold, too small to see on this plot. The way to see it is to plot the current on a logarithmic scale instead of a linear scale because this leakage current is important. These days we have billions and billions of transistors on a single chip of silicon. Even when they're off, a little bit of leakage current is slowing and when you multiply that by the billions of transistors that are there, this has become quite significant. So we need to look at that off current. So if I plot it on a log scale,
[Slide 10] this is what the transfer characteristic would look like. The same transfer characteristic we showed on the previous slide, just plot it on a log scale. Okay. Now we can read off what we call the off current. So the off current is defined -- we have a large voltage between the drain and the source but we have no voltage on the gate. The transistor is supposed to be off but there is some leakage current flowing. We can just read it off of this log plot now. Now, I might define an arbitrary current. Some current here that's -- I'll say when the current is bigger than this arbitrary current and the transistor is on, when it's less than that current, the transistor is off. So my threshold voltage is going to be, you know, when I hit that arbitrarily defined current. Different people will define it in different ways. It's just another indication that VT is not a precise number if you're comparing VTs with some other lab or some other group, you have to be sure that you understand how each of you is defining threshold voltage because it might not be the same. Okay. Now an important thing to understand is that below threshold, the current goes exponentially with gate voltage. Above threshold, it behaves much more slowly. And we'll talk about that a little bit later. Now below threshold there is an important device parameter that device designers worry a lot about and that's something called the sub threshold swing. So if we look below threshold where the current goes exponentially with gate voltage, straight line on a linear plot. Then I can ask myself, how much change in gate voltage does it take to get a factor of 10 increase in the current? We call that the sub threshold swing and we measure it or quote it in millivolts per decade. It means how many millivolts does the gate voltage have to increase in order for me to get a factor of 10 increase in the drain current. That's the sub threshold swing
[Slide 11] and that's a really important device metric. Okay. We're going to define several of them here and it's important for you to spend some time getting familiar with these because we'll refer to these and talk about the physics of these metrics throughout the course. So let's look at this transfer characteristic. And this, let's say there's an arbitrary current we're looking at here. This is a transfer characteristic plotted with a large voltage between the drain and the source. So we're operating in the saturation region. Let's do the same transfer characteristic at a low voltage between the drain and the source. Typically people would use .05 volts, you know. Sometimes a little bit different. So we get less current but the interesting thing to notice is that we get a horizontal translation in the curve. So if this arbitrary current is the current that I'm defining threshold as. If you're bigger than that, you're on. If you're less than that, you're off. Then what this says is that the threshold voltage has changed. Right? We saw that earlier. There's a VTSAT and VTLIN, threshold voltages in the linear and saturation region. And we're just seeing the same thing here on this log plot. So the I-V characteristics, if it's a good transistor, then these slopes don't change. We just translate the I-V characteristic by an amount horizontally. And we call that drain induced barrier lowering. Lots of terms to remember here. It's called drain induced barrier lowering because that describes the physics of what causes this. And we'll discuss that later in the course but this is measured in millivolts per volt. So it's how many millivolts of horizontal translation or how many millivolts did the threshold voltage change per volt of change in the drain voltage. >From VDD to this small voltage, maybe .05 volts. That's what we call DIBL, drain induced barrier lowering. Okay. So lots of terms.
[Slide 12] Spend some time getting familiar with them. On current. Off current. Subthreshold swing. DIBL. Some device parameters like threshold voltage in both the linear and saturation region. The drain to source resistance. One over the slope in the linear region. The drain saturation voltage which tells me that the division between the linear region and the saturation region of the output characteristics. The output resistance, 1 over the slope of the I-V characteristic in the saturation region and the transconductance. So these are all very important device parameters and device metrics.
[Slide 13] And we're going to discuss the physics of them in the course. So here's an example that you can practice on. Here are some measured I-V characteristics. See if you can deduce the device metrics from these I-V characteristics. And you know, you can do it in eyeball. So these are the output characteristics. My power supply looks like it's 1 volt. This top line here is a gate voltage of 1 volt. That point there which looks like 1.55 milliamps of drain current per micrometer of width. That looks like the on current. If I want the off current, I look over here on the log plot. The off current is defined when I have the maximum voltage on the drain and I have 0 voltage on the gate. That looks like 10 to the minus 7th amps per micrometer. So you can go through these and just kind of eyeball them
[Slide 14] and see if you can get these answers that I got when I went through and just tried to roughly read these curves off. And if you can get these answers, you know then it means you have an adequate understanding of device metrics and device parameters.
[Slide 15] And then one more thing. Remember most of the time, just in the interest of time and because the concepts are the same, I'm going to be talking about N-channel transistors but CMOS technology has just as many P-channel transistors. All of the voltages change sign. All of the currents change direction.
[Slide 16] The I-V characteristics flip around and look like this but they're basically the same. It's just everything is flipped. See if you can derive the device metrics and device parameters. It's the same ones that we did for the N-channel parameters. Do them for the P-channel transistors. And if you can do that, then you understand these device
[Slide 17] parameters well enough that we can continue with the course. So what we've learned in this lecture is how to extract some of these key parameters that we're going to be talking about throughout the course. We've -- most of the course is going to be trying to understand what physics controls these parameters both qualitatively and also quantitatively. You know, how do we get a high on-current. But in the next lecture, what I want to do before we dive into device physics is I want to talk just briefly. Device designers want a high on-current. They want a low off current. You know why? So we need to talk just a little bit about circuit design. Basic CMOS circuit design so we can appreciate why these device metrics are so important in determining the performance of the CPU that you carry around in your laptop or your smartphone or whatever. So the subject of the next lecture will be a brief look at how device metrics relate to circuit performance.