0:07

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.

11:50

We know that this is not correct. We have revised the threshold and instead

of 2 phi f, we use phi 0, where phi 0 is 2 phi f plus a few tenths of a volt,

delta phi. And that gives you a more accurate value

for the threshold. Now, how is threshold measured?

There are at least three ways. One is to keep VDS very small and plot

the non-saturation current and extrapolate, and this here is

approximately VT, if VDS is very small. Another is to go to the saturation

region, plot the square root of the current versus VGS.

And provided you don't have severe effective mobility reduction, this is

expected to be a straight line, at least, over part of the region and when you

extrapolate this is VT. Simply because the square root of i is

expected to be proportional to vgs minus vt.

Yet another way that sometimes threshold is measured is this.

People take a specific value of a current for a given [UNKNOWN] and they find the

value of the[UNKNOWN] that gives them this current and they called this the

threshold. Sometimes this is called the

constant-current threshold. And the other two are called extrapolated

thresholds. Now look at this, we have a classical

threshold, we have a revised theshold We have a, an extrapolated threshold from

the non-saturation region, then we have a extrapolated threshold from the

saturation region and we have a constant current threshold.

All five quantity sometimes are called threshold.

So when you hear the term threshold, the right question to ask is which threshold?

Changing subjects, p-channel transistors. Now, p-channel transistors are formed on

and n-type substrate and they have p-type source and drain.

14:56

The more negative VDS becomes, the more the holes will give rise to a current,

and the current increases. So as you can see, you go from

non-saturation to saturation like this. And as you make the gate voltage more

negative, you pile up more negative charges on the gate, which invert the

surface more, more holes than to pile up at the surface and the larger the

current. So as you make VGS from minus 1.4 to

minus 1.8, you get the larger current in magnitude.

Of course, the current is negative for the reason I already mentioned.

If instead of VSB equal 0, we have VSB equal to minus 2, then because of the

body effect, the curves shrink. So now, to represent the IV

characteristics we, can use equations of the same type that we have used for

n-channel devices with some rather obvious algebraic sign changes.

For example, in the non-saturation region, we need the minus sign here to

make sure that the current comes out to be negative.

With this quantities we don't have to worry, because VDS, although it is

negative, it is square. And although VGS minus VT and VDS are

both negative, the product is positive. So this behaves the same way as before.

We need a negative sign only here to predict the negative current.

the threshold voltage due to the body effect will be given by this equation

where VT0 is given by this. Now, phi 0 is a negative quantity in the

p-channel k, so you need a negative sign to make it positive and take this square

root over here. And just like the more positive VSB was

in the n-channel transistor, the more the magnitude of the threshold became

positive. Here, the more negative VSB is, the more

negative the threshold will become for the p-channel device.

So because VSB is negative in this case, we need another minus sign over here to

make it positive. And to get the correct direction in which

the threshold changes, you need the minus here.

So it takes a little time to go through this and appreciate why we have minus

signs at the places that we have them. Please go through this yourselves and

make sure you understand. Notice that VSB has to be negative, it

cannot be positive, because VSB is the voltage between the p type source and the

n type body. If you use the VSB that was positive, you

would be [UNKNOWN] this junction, so VSB has to be either 0 or negative.

So, and so on, this is how you treat p-channel transistors.

Even [UNKNOWN] programs treat p-channel transistors as if they were N- channel

transistors, they use the same model for them, and then, they make the appropriate

sign changes. Now, let me talk about several transistor

types. We have discussed n-channel devices and

p-channel devices. the plots you see here are current versus

VGS for a very small values of VDS. This is the type of plot we've seen

before. And we have said, that if you extrapolate

from the portion that you see a straight line, if you, hopefully, see a straight

line portion, you'd get approximately the threshold.

All of these curves are assumed to be at zero VSB, so no body effect is included.

So, if the threshold that you get is positive, you call the device an

enhancement type device, because when VGS is 0, you get very little current.

And if you want to get a significant current, you have to enhance the channel

with electrons by applying a positive VGS.

On the other hand, if it, the 0 turns out to be negative, then we call this device

the depletion device, because with 0 VDS, VGS, we already have a significant amount

of current. And if you want to deplete the current of

cariers you have to apply a negative value for VGS.

Similarly for p-channels VT0 is negative for the enhancement type device and

positive for the depletion type device. At this point we have finished our

discussion of the long channel [UNKNOWN] transistor Under DC bias.

Starting in the next installment of videos, we will be talking about short

channel effects.