Now let's talk about the opposite case, the low-high profile.

now instead of an acceptor implant, we use a donor implant.

Which means that if we have a p-, p-type substrate here, we have, we implant Donor

ions, and depending on the relative concentration between n and that the p,

the final implanted region here can end up being p with lower doping

concentration, or even n. For now we will assume it stays p so we

have this is the initial substrate doping, this is the implanted donor

concentration. So, you have to take this and subtract

that, because they are of the opposite type, to get the overall concentration.

And again, you can approximate this like that for a simple model.

So as you go from the surface towards the balk?

You start with the low and you go to high.

Now this is why this is called a low high profile, the final, the approximate

doping concentration you end up in the implant with the difference between the

initial substrate concentration you started with minus an I who and I is an

approximation. It's an operative value over here.

The threshold is still given by the same expression as before, only now because

you encounter the low doping and then the high doping has VSB increases and

eventually the depletion rate can extend outside the implant.

That is when you see the large concentration and gamma becomes more

important. So this k2, it has now a positive value

for the low/high profile in order to make this one an effective correction to the

rest of the body effect equation. Now, real profiles of course are as I

mentioned. The approximate Gaussian curves.

They are too complicated to get manageable analytical results, so people

use approximations. And these approximations work because of

several reasons. First of all, the variation of the doping

with depth is gradual. It's not true that as you increase Vsb in

the depletional region. Becomes deeper and deeper.

Suddenly, you reach the limit point between the implanted and the unimplanted

region. You just see a gradually changing doping

concentration with depth, nothing drastic happens.

Also the details of the Qb variation are obscured by the integral in our drift

equation. I'll remind you that the drain current

has a drift term and a diffusion term. And the drift term looks like this.

And what matters int his current is not QB itself, it's only the integral of it.

So the details of QB prime are obscured inside this integral.

The diffusion equation looks like this. Here, you do see QB by itself.

But in both of these equations, the main terms, which is the first-order term here

and the square-law terms over there, the first-order term here.

All of these terms do not involve Q'B prime, and that is why If you don't model

Qb prime very accurately, you can still get accurate expressions for the count.

Now's some models use an effective doping, which is made a fraction of the

surface potential in an effort to model implanted devices.

Now If you do this, if you've got an effective doping that depends on the

surface potential, effectively you're making the body effect coefficient a

function of Vsb. This is just a mathematical convenience

to help you model the device. In other models, what they do is they

make an effective doping a function of Vgb.

Again, this is just a mathematical convenience.

Of course, it doesn't mean that the concentration itself changes as you

change VGB, but in equations that we used to have that relates VGB to the surface

potential. there is a term that depends on substrate

doping. They make that term a function of VGB.

And now for a given VGB, you can use the same equation to get the value of the

surface potential, which we used to do for the old region model.

Some problems that can occur with the iron implantation, if the device is not

designed properly or sometimes even if it is.

you can get a log I versus Vgs, here we emphasize the weak inversion region, and

when you have a large Vsb then you get the curve on the right, here.

And this happens because for large Vsb the bottom of the depletion region is

outside the implant,it is in the lightly doped substrate.

And a lively dope substrate means that you have a small gamma, and therefore a

small factor n, which affects the slope of the weak inversion region, so it looks

like that. Now, when VSB is 0, the depletion region

is shallow and it is inside the implant. And then gamma, because of the large

doping consideration there, gamma is large and n is large and you get a

smaller slope. But in addition, as you vary VGS the

depletion region depth varies, an it moves over various parts of the implant.

In other words, it goes over, a region where the doping concentration of the

implant gradually changes. From high to low.

And, therefore, as you increase VGS, the slope even changes.

So when you see things like that, there may be an indication that the implant has

something to do with such effects. Now, pMOS devices are like nMOS devices

but here they have a p type source and drain, an n type body.

And when these regions are implanted, the pole is also implanted, so the pole

typically p, p plus. And if you implant.

This one with extra donors you can adjust the effective body doping near the

surface and modify the threshold of the pMOS devices.

I would very briefly like to mention buried-channel devices.

These are devices that are not used today.

They used to be used for, to make depletion-mode devices, and in device

research they are being considered even today.

Now, the implant type for such devices is the same as low to high, you remember to

get the low to high profile. You start with a, a P-type substrate and

you implant donors. But now, in this case, we implant with

even more donors than we have acceptors, so in other words, the implant, here, the

peak of NI is above NAB. This is the substrate concentration.

This is the implant concentration versus depth.

So then in order to get the com, combined concentration of the two, you have to

subtract the two. And because this is larger in [INAUDIBLE]

than this one, you end up with a net donor concentration near the surface.

And and accept the consideration in the bulk.

So, the device looks like it is p type in the bulk and N type near the surface.

Now, depending on the value of the gate potential, you can even deplete the

surface here. And then you end up with a channel that

is formed by the n type region, except for the depleted part near the top.

So you have a channel where the current flows below the surface.