0:57

Of course this will be an n channel MS transistor, once the channel is filled

with electrons. Then we have an insulator, commonly

referred to as the oxide, and on top we have a gate.

And I should mention that for economy of space, we're showing the gate as a

shallow region. In reality, as we have seen in more

realistic pictures, it is much taller than what is shown here.

So, the terminals of the transistor is called S for source, B for body, D for

drain and G for gate. The width is W and the length is L.

Now, we will make the following assumptions.

L and W will be large. What does this mean?

It means, very roughly, several times the minimum possible dimensions in a given

fabrication process. And later on we can be more specific than

this. We will assume that the substrate is

uniformly doped throughout. We will assume VSB and VDB never become

negative because if they do then you will be forward biasing the body source or

body drain juncitons. And given that there will never be

forward bias, we can neglect that very small leakage currents in the those

regions for now. And we will also assume that the gate.

The current is 0, because we have a perfect insulator there and that is thick

enough and the body current is also 0. Later on, we will relax these assumptions

but for now we start with a simplified long channel MS transistor as we call it

where all of these things apply. So here is the transitor for now you can

neglect the little square in the middle here.

we have biased it, with voltages referred to the body.

The gate body voltage is VGB. The source body voltage is VSB and the

drain body voltage is VDB. In the particular situation I'm showing

here, I have assumed that VDB is larger than VSB and the transistor as is shown

in this example, is in strong inversion. What does it mean?

It means that VGB is large enough to have placed in the gate plenty of positive

electrons, that will deplete and then invert the semiconductor below the oxide.

So the depletion region is showed here. We have ionized[UNKNOWN] acceptor atoms

going in circles, and we have free electrons in the channel.

Now as we have mentioned before... If you are in strong inversion, then you

have plenty of electrons here in the channel, and you can think of this region

in the channel as an extension of the end regions in the source and the drain.

So think of it as one big n region. Around the source, we have a pn junction,

which we would have even if there were no electrons in the channel, right?

So we have applied VSP which is positive from n to p.

This is a reverse bias and it creates certain depletion region width on the p

side and a much smaller depletion region width on the very heavily[UNKNOWN] side

which for simplicity we are not showing. Because VDB is larger than VSB it will

create a deeper depletion region over here.

So the reverse bias in the source body junction is VSB and the larger reverse

bias in the drain body junction is VDB and in between you have another so to

speak n type region for which the reverse bias increases gradually from VSB toward

VDB. And this is why the depletion region gets

deeper and deeper as you go towards the drain.

Now we're going to pretty soon start neglecting what, what happens very close

to the source and drain regions. So basically our channel will be so long

that we can neglect. The about one depeltion region width

around the source, and about one depletion region width near the drain.

This would be a long channel approximation that we'll, we will adopt

in this material for now. Later on we will relax this assumption.

Now in addition to referring the voltages to the body as I have already mentioned,

sometimes we need to refer the voltages to the source.

And then we have this situation where now we have VGS is the gate to source

potential. VDS is the drain to source potential.

Rather, I should say voltage or potential difference.

And VSB is the voltage between source and body.

This could have been VBS body, refer to the source, but it is common to use the

opposite of it, VSB. Now if you arrange these three voltages

so that between any two terminals in this structure, you get the same, voltages as

we get with this this structure, the two structures behaves identically.

The device doesn't see any difference as far as the externally applied voltages

across it's terminals are concerned, and you get identical behavior from both

structures. Which means that for the right set of

VGS, VSB, and VBS. To emulate this behavior the drain

current here is the same as the drain current here.

So let us plot some IV curves. Each of these curves applies to both, to

each of these strucures. In other words.

Both of these, apply to this structure and the same curves also apply to the

bottom structure. So let's start with the top set of

curves. When the VDB is equal to VSB, the current

is 0 meaning that when visible, that's just equal to this voltage, there's not

difference. A potential across the channel and

therefore the current through the channel is 0 as you can see all of the curves

meet at this point. And then if you start for a given VGB,

let's say for example for VGB equal to VGB 3, we have this curve .

If you start increasing VDB above VSB you start seeing more and more current and

eventually you enter saturation. This is because as you increase VDB you

increase the voltage between drain and source.

And you are in strong inversion, where actually the device operates like a

nonlinear resistor, so the larger the voltage, the larger the current.

So it goes up. If you now increase your VGB even

further, for example, if we go to VGB equal to VGB4, then the same thing

happens but you have more current. For the same VDB.

Now if instead of referring the voltage to the body, you want to refer them to

the source, then you get this set of curves.

Where now the horizontal axis is VDS, other than that, the curves are

identical. In fact, you can get this set of curves

from the curves above them, if you just shift them by VSB.

So, if we now use a arigothimic current axis so that we can see a wide range.

Of current values. We see the strong inverse at near the

top, then as we lower the VGS, we go to moderate conversation and if we lower the

VGS further, we are in wiki version, the darkest of the three regions here.

The limits between weak inversion and moderate inversion, are denoted by VM if

we're talking about VGS. And by a similar symbol if we're talking

about VGB. But for now I will refer everything to

the source and I will be talking about VGS.

And the onset of strong inversion, which is the, the limit point between moderate

inversion and strong inversion will be denoted by VH.

We have, discussed these values when we talked about the 2 terminal and 3

terminal structures. But as you will see, I will be deriving

models that are valued throughout all of the 3 regions.

And these models don't care what VH and VM is.

They're just valued everywhere. So let's talk about regions of inversion

for the MOSFET more precisely now. So we have this, device in the particular

situation that I'm showing here. I have assumed strong inversion.

And we define the regions of inversion for the MOSFET by looking at the most

heavily inverted channel end. In this particular case, the most heavily

inverted channel end. Is the source end, because I have assumed

that VDB was larger than VSB. And you may recall, from our discussion

of the 3 terminal structure, the larger, the reverse bios you're applying to this

terminal, the smaller the[INAUDIBLE] level will be.

Back then, when we talked about the 3, terminal[INAUDIBLE] structure, we were

talking VCD. Where C was the external terminal that

made contact to the channel. Now, the C terminal has become the D

terminal over here. So, the larger VDB is, the lighter the

level of inversion here. So, and because we assume VDB is larger

than VSP. This is the least inverted channel end,

and the source end is the most inverted channel end, so in this case, I will be

looking at the source. So if the most heavily inverted channel

end is weakly inverted, then say the transistor is operating in weak

inversion. If instead, that end is moderately

inverted then, the transistor is set to operate in moderate conversion.

Even that, is strongly inverted then the transistor is set to operate in strong

inversion, as is the case in example that you see in this figure.

11:22

Now I want to empahisize the following. Although this is storngly inverted in

this example, if VDB becomes large enough, then this end of the channel here

will not be strongly inverted anymore. Eventually, if VDB is large enoguh, you

can take this end to moderate inversion or even to weak inversion.

As far as the name of the region of operation for the transistor as a whole

is concerned. You still call it a transistor in strong

inversion simply because around the source, the channel, or rather near the

source, the channel is strongly inverted. This is historically how people have

named inversion regions. Let me now show you what happens in terms

of, potentials in the channel, and the corresponding conduction band edge, e sub

c, versus for example distance c. Assume, in the beginning that I don't

have many positive charges in the gate and that I have not inverted the channel.

The potential is low. Shown by curve a prime, as you see here.

And the corresponding conduction band edge is high, that means that there is a

barrier, qVBI that electrons would have to cross to go from the source region To

the channel region. And because this barrier is high, very

few electrons can make it, and you do not have inversion.

Now if I increase the gate bias, then I have a larger surface potential.

Shown here by. b prime, and that means the corresponding

conduction of that edge goes down, and now you can see that the barrier that the

electrons have to cross is very small in this vicinity, so it's easier for

electrons to cross and they enter the channel.

So let us assume that this allows the, channel and near the source, to be

strongly inverted. If I now, increase the body, the drain

body voltage, then gradually the voltage will increase, the potential will

increase, from the source to the drain, in this direction.

And the corresponding bandage will go down like this.

And that is the case that we had shown in the previous slide.

So this then, this here is a strongly inverted device that corresponds to this

case. Because the drain is more positive the

source, the negatively charged electrons have a tendency to go towards the most

positive potential. So let me now preview what we will be

doing in the next several lectures. We're going to derive several models.

Each of them has something to, that goes with it.

it has a certain set of assumptions, it has a certain accuracy and it has a

certain history. So I'll have to cover all of these models

because they're all used. And some of them are the basis on which

today's CAD models are derived. So we will start with all region models,

which are models that have sets of equations which are valid in all regions

of inversion. I will start with a complete model, then

I will simplify it. And then I will distinguish two cases,

one would be body referenced and the other will be source referenced.

Once we've finished with origin models we'll talk about strong inversion models.

I will start from the complete model and derive a complete strong inversion model,

and then I will talk about a simplified body reference and a simplified source

reference model for strong inversion. And finally we'll go to weak inversion

and derive a body reference model and a source reference model.

So in this introduction, we have seen a simplified view of the long channel MOS

transistor. We saw a set of curves so we didn't prove

anything yet, and so all of that was a rather intuitive introduction.

But starting now, in the next lecture we will start deriving things pretty

rigorously.