The other theory assumes shot noise, and of course from the general expression for

shot noise that I showed you in the previous video, you get this result.

So, if you look at them, they're exactly the same.

And in fact, you can show that even in between the saturation point and VDS

equal zero. Even if you use shot noise, you get

exactly the same result, as you get if you assume thermal noise.

So two different theories that give you the same result which has generated some

controversy. And you can find references to that in

the book. So, here we show the power spectral

density versus VDS, in general has the shape that we also show in weak

inversion. But it saturates at this value here.

For, for comparison, I have the drain current versus VDS.

In weak inversion you will recall that the current saturates within three to

five [UNKNOWN], in other words thermal voltages, and so does the power spectral

density. Now, small-dimension effects, of course

if I don't mention small-dimension effects like I didn't in the previous

slides, it is implied that we're talking about long channel transistors only.

But if we have small dimension affects, the power spectral density versus VDS,

with VGS, as a parameter, may look something like this.

And we have to take into account channel length modulation, which can be handled,

through the pinch-off region length. We need to take a talk on velocity

saturation, hot electron effects possibly if they are present, and drain-body, body

current shot noise. [INAUDIBLE] you will recall that there is

a leakage current between drain and body. This shows shot noise and because the

drain-body current is part of the drain current, it will have a direct effect on

it. In addition, because the drain-body

current passes through the body resistance Rb, It modulates the internal

VSB. The internal source to body volt.

It's, and through the body transconductance it modulates the current

as well. So both of these effects will contribute

to current noise in the drain current. You also get gate tunneling current shot

noise, you have very thin oxides. people define an excess noise factor like

this. You take the power spectral density

predicted by the long channel theory and the factor which you must multiply that

in order to get the actually observed short channel noise power spectral

density, is called the excess noise factor.

This excess noise factor has been claimed to be large, for example, 2 to 5 but this

has been questioned. and it actually depends on whether you

have hot electron effects, or you don't. Now, elaborate computer aided design

models do include noise due to these effects, but unfortunately the results

are very complicated analytically. So I will not present them and I will

refer you to references in the book instead.