Now, when you increase VCB, what will the charge of the electrons do here, what will

the inversion layer charge per unit area do?

Take a case in strong inversion, for example.

You have a lot of electrons in the inversion layer.

In a sense, the inversion layer is an extension of the n plus region.

And sometimes, the combination of the inversion layer and the body is called the

field induced n-p junction because the gate field created a lot of electrons here

and made the surface look like an n-type region.

So now, if you increase VCB, you are increasing the reverse bias between the n

and the p, both for the p-n junction and for the combination of inversion layer and

body. And what happens when you increase the

reverse bias, the depletion region width widens.

However, because V, VGC is kept constant, the voltage between the gate and the

inversion layers stays fixed. So, that means that across this capacitor,

you have a fixed potential. So, the amount of charges that we have on

the gate remain approximately fixed when you increase VCB, they don't change.

Now, these positive charges on the gate must be mirrored into negative charges, in

the substrate, in the body. Before, you have the bunch of electrons

universal layer and some accept our ions in depletion region.

Now, because you have increase the reverse bias of the p-n junction, you have more

negatively charged acceptor ions so you need fewer electrons in the inversion

layer, and therefore, the level of inversion will decrease.

So, we have seen, then, that when we keep VGC constant and when we increase VCB, QI,

the inversion layer transfer unit area goes down in magnitude.

And this is the definition of the body effect.

The body effect means that when the voltage between C and B goes up, the

magnitude of the inversion layer charge goes down, provided we keep VGC fixed.

And, of course, if we want to restore QI to the previous level, we must increase

VGC. So, here is then a set of curves versus

VCB. The VL, VM, and VH are the onset of weak,

moderate, and strong inversion. So, VL, VM, and VH are the values of VGC

at which you get to the beginning of weak inversion, the beginning of moderate

inversion, and the beginning of strong inversion.

They all go up with VCB as you can see, consistent with the body effect, and even

the body threshold goes up in the same way.

So, for example, if we take the beginning of moderate inversion VM, which is this

curve over here, it turns out to be given by this.

You may feel that already you already can predict this from what we have already

said. But a more careful derivation of this is

given in the book. The gamma quantity here is this, we have

already seen it before, and it is called the body effect coefficient because it is

instrumental in describing the body effect.

So, let's now look at the threshold. This is the threshold equation, we have

seen it before. The effect of VCB is shown here.

And you can see that the VCB goes up, the threshold goes up.

Vcb sometimes is called the back gate bias.

We will see later why this name has stuck. We also see that the influence of VCB on

the threshold is stronger if gamma is larger.

So, if you plug the increase of VT, compared to its value on VCB 0, this is,

we're plugging here VT minus VT0 versus VCB, you see that it goes up, and the

larger the value of gamma the worse things get.

Of course, such large values here are unreal, unrealistic.

There have been in the past devices with large gammas but of course, we try to keep

the body effect low for reasons that we will see when we get to the MOS

transistor. I would like to finish this slide by

saying that this is one of the manifestations of the body effect.

The body effect, as I already mentioned, is not only about threshold, it's

something more general. Okay.

Anew definition that we will need in our discussion of the MOS transistor is the

pinchoff voltage. So, let's take this structure, and now

back to referring everything to the body terminal.

The strong inversion approximation that we have shown is this one, QI is a

first-degree polynomial with VGB. And in this equation, we have the

threshold referred to the body which depends on VCB.

And I remind you, this was the expression for that threshold.

So now, you can see that if you keep VC, VGB the same, we keep VGB the same, but we

increase VCB, what will happen? The threshold will go up.

So, in this difference, it will have the effect of reducing the magnitude of QI and

eventually, this equation predicts that when VCB is so large that the VTB becomes

equal to VGB, QI will become 0. So, let's look at the plot.

This is what the plot looks like. This equation here is this plot, the

broken line. And, indeed, it shows that, eventually, QI

goes to 0. But when QI has a very small value, and it

is close to 0, we're not in strong inversion.