Let us begin with a discussion of the Extrinsic Source and Drain Resistance.

Extrinsic means the part outside the main part of the transition we've been

discussing, in other words outside the channel.

The n-type source and drain regions we have assumed have a certain resistance,

they're not perfect conductors. So this will be called the extrinsic

source and drain resistances. So the situation can be described like

this. This is the main part of the transistor

we have been discussing, excluding the end type source and drain regions.

This is the series resistance of the n-type source and this is the series

resistance of entire drain. When the drain source current passes

through this resistances, it creates voltage drops with the effect that the

actual VGS that the device C is, is what we call here VGS half.

It is VGS minus the volt that drop across RS.

In other words, it is VGS minus RSIDS. And the actual drain source voltage that

the device sees is the externally applied VDS minus the two voltage drops, RSIDS

and RDIDS, which are lumped together here.

Now, to find the current you need to replace the quantities VGS and VDS in a

given model by VGS half and VDS half, and then show for the current.

After quite some algebra and a few simplifications, which I would skip, you

end up with this relation. So you see, this relation looks like the

source reference strong inversion model only in the denominator it has these

term, beta sub R times VGS minus Vt. And from the analysis, beta sub R turns

out to have this value. So now, you can see that if the

transistors are equal to 0, beta sub R is equal to 0, and the model reduces to the

well-known strong inverse and known saturation model.

Otherwise, as VGS goes up, it tends to decrease this term over here.

Now, this development so far has assumed the constant mobility.

If we now go through the same development, but we assume effective

mobility, then through several of more algebra steps, we find this.

The effective mobility is represented by a term theta times VGS minus VT.

And by the way, I am not including the additional dependence of effective

mobility on VSP, because I'm trying to simplify things and make a point here.

So theta times VGS times VTA is the effect of VGS on mobility, and beta sub R

times VGS minus VT is the effect of the series resistances.

The two effects we're talking about are completely different, but they just

happen to have the same effect in the IV characteristics.

That's why beta sub R has been lumped with theta.

So now, if you take a very small VDS, which is what we have assumed in previous

plots of this kind, and you plot I versus VGS.

You find that the slope tends to decrease at large VGS values .

Because of both the series resistance effect and the effect of mobility effect.

And because both of these effects have the same effect, the same type of effect

on the IV characteristis, sometimes, you may hear the term mobility dependence on

series resistance. Of course, this is incorrect.

The fact that series resistance have the same type of effect on the current as

does the effect in mobility is just a coincidence.

This is a fallacy and an abuse of terms. To reduce the series resistance, which is

of course an undesirable effect, silicides are used.

Silicides are metals that cover the drain and the source such metals for example,

titanium or cobalt are used. They react with silicon and they form

disilicides and the resulting processes are called silicide or salicide process.

And they can reduce here its resistance significantly by a factor of, let's say 5

or 10. Let us now talk about a different topic,

temperature effects. The various quantities we have seen in

the models we have derived such as the flatband voltage.

The thermal potential, the thermal voltage, the mobility, they all depend on

temperature. And if you include the temperature

dependence of these terms, you end up with very complicated equations, but the

main effects that you observe on the IV characteristics can be lumped into the

following two. First of all, the mobility varies with

temperature approximately like this. T sub I is a reference temperature,

typically room temperature. And k3 is a positive quantity from 1.2 to

2. This is a negative exponent, and as the

temperature increases, it makes the mobility go down.

The threshold also varies with temperature.

This is the threshold at the reference temperature, like room temperature, and

as the temperature goes above that, you have a reduction of the threshold given

here, where k4 is typically between half a, half a millivolt per Kelvin to 3

millivolts per Kelvin, degree Kelvin. The combined effects of mobility

dependence on temperature and threshold dependence on temperature makes the

characteristics look like this. Here, now, I'm assuming saturation in

such ration you expect roughly the current to be proportional to VGS minus

VT square. It will not be that, because you have the

mobility dependence on VGS, which interferes with that.

But approximately, if you plot square root of I versus VGS and you don't have

strong mobility effects, you expect a straight line.

So you see a straight line here, almost, and then the effective mobility reduces

the slope like that. If you now increase the temperature, the

curve is move like that. Because the mobility decreases, the slope

decreases, the same also here, and at the same time, the threshold becomes smaller

and smaller. The threshold is approximately the

extrapolated value that you get. If you extrapolate a straight line down

here, what you get here is approximately the threshold.

And the threshold goes to lower and lower values as we increase the temperature.

As a result, the curves seem to be rotating like this.

And sometimes, you find a single point around which they all rotate, there have

been papers written about this point and there have been attempts to utilize it in

circuit design. Now, if we use a logarithmic access here,

so we can see better what happens in moderate and weak inversion, then we end

up with these curves. This point here is this point here.

So, here, you have strong inversion. Here, you have moderate inversion.

And here, you have weak inversion. And where you have exponential behavior,

this is a logarithmic axis, though, and this is why you get a straight line.

So if this is room temperature and you increase the temperature, then you get a

smaller slope like this. So, the slope, the weak inversion slope

tends to deteriorate at high temperatures.

This region here has to do with [UNKNOWN] currents, we will discuss those when we

talk about short channel devices. Another topic is breakdown.

If we exceed the maximum allowed voltage across a p-n junction in the transistor,

like the trained body junction, we get breakdown and large currents can flow in

the reverse bias region. So such values, of course, should be

avoided. You can also get channel breakdown due to

impact ionization where you have an, an electron accelerating, hitting on a

crystal atom and extracting because of its high energy, a whole electron pair.

Now, you've got two electrons, they both accelerate.

They extract more whole electron pairs. So the electrons get to multiply and the

current becomes larger and larger. This is called the Avalanche effect and

the effect on the IV characteristic is this, that you see here.

So normally, you would avoid Applying VDS more than above 1 volt in order to avoid

this region here. Now, both of these effects that I've

mentioned are not effects that destroy your transistor immediately.

Although, impact ionization can compromise the quality of your oxide, but

if you momentarily exceed the maximum safe voltage, and then you go back down,

the device may still work. But there is a third type of breakdown,

oxide breakdown and if you exceed that you just get a short, a permanent short

between the gate and the channel. So for all these reasons, we will be

assuming that none of these breakdown voltages is approached in what we do

unless we say otherwise. Now, let me say something about parameter

extraction. In the various models, we have derived,

we see the same parameters again, and again for example the flatband voltage.

The value of the flatband voltage as it is predicted from physics, may have to be

modified slightly when you use it in a model.

The reason is that, because we have made many approximations, we can help the

model match experiments if we slightly adjust their parameter values.

Let me show you why this is necessary by giving you a simple example.