So far we have assumed that the electric fields are not too high.

They were high enough to cause velocity saturation, but in some cases they're

high enough to cause other troubles, which go by the name of hot carrier

effects. This is what we will discuss in this

video. Let us begin by a justification of the

name hat carriers. So, we are discussing now, high fields,

which especially occur near the drain. For example, what we call the pinchoff

region. These result in high kinetic energy of

carriers, in our case, electrons. In the examples we are discussing.

Now, the scattering, the collision that these electrons encounter, randomizes the

carrier velocity. But we have agreed to use an average

velocity, and, called drift velocity, which reaches a limit, the velocity

saturation. But this is only the average velocity.

It's, it, it doesn't talk about the instantaneous velocity of the carriers.

The random kinetic energy of the carriers still increases with the electric field.

And some of those carriers acquire such a high velocity that the value of this

velocity is higher. Then the thermal velocity you would

expect for the given semiconductor temperature.

So this carries for this region, as, are called hot carriers.

Here is now a very messy picture of what hot carriers can do.

They can do a lot of damage. So, this is the gate, this is the oxide,

this is the drain, the body, and this is the depletion region edge.

In the inversion layer we have electrons flowing to the right, shown here.

Negative charges flowing to the right, are equivalent to positive Charges

flowing to the left so I-ds is defined in this way.

Now ,the highly energetic carriers, especially in the high feed region and

the pinchoff region, can impact on silicon atoms and extract electron hold

pairs from them. So here is one hold electron pair.

Here's another hold electron pair. Some of these electrons are attracted by

the positive Potential of the drain. In other words, the field is in such a

direction to make these negative charges flow towards the drain.

The holes will flow in the opposite direction, like this, and they will give

rise to a drain body current, among other things.

Now, this impact of an electron on a silicon atom, that creates an electron

whole pair Is a phenomenon revered to as Impact Ionization and it is also referred

to as Weak Avalanche. In Weak Avalanche we assume that each

electron causes one whole electron pair to be generated.

But of course, the new electrons generated that can also impact on atoms

and cause yet more avalanche effects. Then you wouldn't have weak avalanche

anymore, but for now, we assume we have weak avalanche.

As we said, the first effect is a body current, or substrate current, IDB, which

appears to flow between drain and body, as shown here.

Another effect is, some of these electrons are so energetic that they can

Go into the oxide, and some of them can even come out.

So you have negative charges going out, towards the gate, which is equivalent to

positive charges going in. So suddenly you have a gate current.

Then, some of these can really damage the interface between the semiconductor and

the oxide. They can increase the number of interface

states. We had seen interface states before.

These are states where, which, can captures and release charges.

A poor damaged surface is bad news for the quality of device characteristics.

Worse then that some of these charges can end up in the Oxide.

And the cause an extra oxide charging and eventually all of this phenomena can

contribute to aging of your device. The performance of the transistor

deteriorates with age. So hot electron effects are to be

avoided. Here is the same picture as before, how

would we calculate IDB, the drain body current due to hot electrons.

Let us limit ourselves to the pinchoff region, and take a very short length,

delta x, and find the contribution of, that length to IDB, the total drain body

current. I will call that delta IDB at position x.

First of all because the whole electron pairs generated is expected to be

proportional to the number of electrons that flow here per unit time.

You expect delta IDB to be proportional to delta IDS.

The drain source current. You also expect the contribution to be

proportional to the length. And there is a constant of

proportionality here that I will discuss in a minute that depends in general on x.

And you expect this constant of proportionality to have something to do

with the electric field. Because the higher the electric field.

The more energetic this current becomes and the worst the had electron effect.

Now, if you know, the contribution of elected delta x to the current IDB.

Then you can integrate this over all of the depletion, all of the pinchoff region

from l minus one pinch off region length to l, and find the total drain body

current. This assumes that this Weak Avalanche

phenomenon, or the impact ionization we have described occurs only in the

pinchoff region. If it doesn't only occur only in the

pinch region then instead of LP here we can have another appropriate length.

So here, we see that we have the integral of a sub n of x, where a sub n is this

coefficient, this has been estimated, this is one example of an expression used

sometimes for it. And as you can guess, as the horizontal

field increases, you expect alpha sub-n to be larger and larger and it is from

this relation. So now if you plug this in here and you

estimate the field by sum Soon the two dimensional analysis and after several

steps of them bypassing you end up with this expression.

As I said in the beginning in these set of lectures.

I cannot afford to be very detailed and rigorous.

Both because of the approximation and because of the time limit that we have.

So I'm bypassing a lot of steps. If you're interested, you can look up the

references in the book. This is the equation that gives you the

drain body current, as a function of the drain voltage, the saturation voltage,

and two parameters, K sub I, and V sub I, that are best determined empirically.

So, let's see what this equation looks like.

Same equation here, here's a plot of it. First of all, the train body cart, by the

way, I say IDB here. It should have been IDB so this is D and

this is B. Now the larger the drain volt of these,

these set of curves is obtained for increasing VDS.

the larger the drain voltage. The more the drain body current, because

of course the larger the drain voltage, the more field, the higher the field that

gives rise, to hot electron effects. So you expect that the curves should go

up in this direction. But why do they go up in terms of VGS,

and then do they go down again? So let's look at this.

When you have low vgs values, as vgs goes up, and this is my short hand for going

up, as vgs goes up, the drain source current goes up.

And of course, if the drain source current goes up, you have more charges

flowing per unit time. And the larger number of them will cause

more whole electron pairs to be generated because of impact ionization, and the

larger IDB will be. So you expect this.

But if you keep increasing VGS, what happens now is this.

As VGS increases, VDS prime which is proportional to VGS minus VT, also

increases. But if VDS prime increases then VDS minus

VDS prime which is the potential across the pinchoff region decreases.

And therefore the horizontal field decreases, and if that field decreases,

hot electron effects become less severe, and therefore the drain body, current

closed by then, goes down. This is why this goes down.

So it first goes up, and then goes down like that.

Same picture as before. We have electrons going to the right

equivalent to IDS going to the left. We also have IDB, the drain body current

and we have a total current ID. Now, if you think, close all of, close

all this region, where all these nasty effects happen, into a box.

ID goes in, and IDS and IDB come out. If I can neglect the gate current, I can

write that ID is equal to IDS plus IDB. So, initially, at low fields, where IDB

is very small, you can neglect it. In fact for typical operation, IDB can be

a couple of orders of magnitude smaller then IDS.

You can completely neglect it and you're down here.

But eventually and because of the presence of this exponentials that you

saw on the, in the equations on previous slides.

IDB takes off. And then, this is an indication of severe

hot electron effects. Normally, you would avoid operating the

device in this region, you would limit it to a region where IDB is negligible

compared to IDS. Because among other things, once hot

electron effects start happening, as I said before, the device can be expected

to age. So you can refer to this region as a

breakdown region and you avoid it. Now, another different effects but is,

which is caused by the drain body current.

The drain body current here flows through the up straight.

The up straight has some resistance so the current flowing through it causes a

voltage drop. So as it goes like that it makes the, the

sub straight here positive with respect deeper points in the sub straight.

But the positive potential on the p side can be so high as to forward by us the p

injunction between the body and the source.

The source is to the left it's not shown here.

Once the body to source junction is forward by us.

It turns on. And now you have source which is n.

You have body which is p. And have drain which is n.

This is an n pn bipolar transistor and you've just turned on the pn junction

corresponding to base endometer . Turning on this device can have a very

severe effect because it's current as a bipolar device.

Is a, essentially in parallel with your drain source current.

I will bypass the effects, this, these are not MOS effects but because they

happen, due to the parasitic bipolar transistor I mentioned then.

When you plot VDS versus ID, you find a curve like that.

Notice that I said you plot VDS versus ID because now VDS is a function of ID, not

the other way around. And this behavior clearly is something

you want to avoid. You never want to forward bias the p n

junction, between body and source, under normal circumstances.

So, this is not something that you want to have.

Nevertheless, as it is often the case, people have found use for it, in

electrostatic discharge protection circuits.