0:18

There are two theories, two main theories, that have been developed in the

past concerning flicker noise. One attributes that noise to traps near

the interface, which capture and release carriers.

And this results in fluctuations in the surface potential and corresponding

random fluctuations in the number of carriers in the channel.

The other dominant theory was that we have lattice scattering, phonon

scattering, which we have discussed back when we talked about effective mobility.

And that results in random ability fluctuations.

today the two theories have been combined into a unified theory.

So I could now give you the highlights of each of the two theories and then we will

combine them. the first one is the carrier number

fluctuations in the channel. And it goes like this.

We have traps near the silicon oxide interface which trap and release charge.

1:16

This corresponds to our random varying two zero prime which I remind you is the

effective oxide interface charge for unit area.

That, of course, directly affects VFB, so we have random fluctuations in the

[UNKNOWN] voltage VFB. Now, you will recall that VFB appears as

part of the threshold. It's an additive term to the threshold,

the relation and that we can write at least in strong inversion.

The current as a function of VGS minus VT, so in effect, the VFB appears in a

difference with VGS. So we can represent it, we can represent

the variations of VFB rather, as a voltage source, a noise voltage source,

in series with the gate. And this delta V, the noise voltage of

the source is the delta VFB. And that corresponds to delta Q0 over

Cox, where delta Q0 is a randomly varying Q0 prime.

Now if you, from this relation, if you take the square and then you take the

mean, it follows that. The mean square value of delta V would be

inversely proportional to C prime oxide squared.

And also, the larger the gate area, the more these effects of the value straps

will tend to average out. So you expect that the noise should go

down as the gate area increases. Now if you look at the single trap, as it

captures and releases charges, it turns out that it gives rises to a power

spectral density that corresponds to this so called Lorentzian spectrum which is

shown here. Tau T is the characteristic time that is

related to the average capture and release time.

Now different traps can have very different tau t.

the deeper they are on the oxide, the more the difficulty in capturing and

releasing carriers from the channel, and the larger the tau t becomes.

Now, if you take several traps with various tau t, you get a spectrum as

shown here. So this is for one trap, this is for

another trap, a third trap, and so on. All of them corresponding to the

Lorentzian spectrum with different tau t's.

The interesting thing here is that if you add up all the individual power spectral

density, you get this broken line, shown here.

Which is already pretty close to N1 over f line, which has been drawn in a solid

line over here. So you can see that the superposition of

a large number of the power spectral densities corresponding to individual

traps tends to generate a one over power spectral density.

And therefore, the large variety of the tau t's and the superposition of the

results is what results in one over f. So this of course is not the proof but I

showed you graphically that just with a few drops you tend to get already this

result. So you can imagine with many more traps

this one as it turns out and as it can be shown approaches one of the behavior.

The power spectral density due to flicker noise can be shown to be given by gm

squared times Svf, where Svf is the corresponding power spectral density of

the equivalent noise in the gate. And that Is found to correspond to this,

although we have not proven this, we have already predicted the 1 over f behavior

of in, in this slide. We predicted that does the W times L, the

gate area increases the noise should go down.

And we have also predicted the dependent, the inverse dependence on C ox squared.

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More details and more rigorous proofs are found in the references to the book.

C, this factor here ideally is 1 but it turns out a vary between 0.7, 1.2

depending on fabrication details. The second theory is the mobility

fluctuations due to lattice scattering. And that one turns out to give a similar

relation but you have a bias-dependent factor here, K of VGS.

And sometimes in the literature, PMOS devices are found to conform to this type

of relation. Now, for the unified theory, we have

traps, which capture, release carriers, and this results first of all in

fluctuations in the number of carriers in the channel, which is the same as the

first theory. But you all, they all resolve to

fluctuation in the mobility because of Coulomb scattering.

I remind you, Coulomb scattering is scattering related to, electric charges.

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So this, now, is the dominant theory and combines, in a sense, the other two.

And it leads to an expression of this form.

Where this K of VGS can really vary a lot.

And, it has been reported it can vary up to a factor of 2 for nMOS and up to 50

for certain pMOS devices. Now, buried-channel devices are uncommon

devices today. They used to be used to make depletion

devices in the past. And sometimes they are considered in

research today. This can have a channel that is below the

surface so it is affected less by the phenomena I mentioned.

And some of buried-channel devices have been reported to be significantly quieter

than the surface-channel devices we have been discussing.

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And because you don't have a large number of traps, you don't have enough of the

averaging we have mentioned. So you cannot expect the inverse

dependence on WL. There is no statistical average anymore.

And the noise can be very different from device to device, as you see here.

These are five different devices, made in the same way.

But because they have a very small gate area the number of traps over the gate

area which may be different, and you get very different power spectral densities

For the low frequency noise. This is an 1/f line for your reference.

In addition in saturation if you have traps in the pinch-off region you don't

have much contribution to the noise. Because presumably what happens in the

pinch-off region does not effect the channel to the left of it towards the

source. But in reverse saturation, if you now

interchange, in other words the source and the drain, the traps that used to be

near the pinch-off region are now near the source and they can contribute to

noise. The result is that you can have, for very

small devices, we can have asymmetric behavior.

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Let me expand on this a little bit. things can actually get worse by hot

carriers, let me show you what I mean by that.

Lets say we have a device which we aged for hours in saturation with large VDS

above the normally permitted value of VGS near breakdown so that we have hot

carriers which damage the interface near the drain.

Now we reduce VDS and we keep the device in such rations so damaged area is in the

pinch-off region so it's not felt by most of the channel.

Which is the part of the device that determines the value of the current, so

this transistor is quiet, it doesn't have much noise.

But now if you use the same device in non-saturation, then the channel exists

throughout from source to drain. And therefore the damaged area can

influence your noise in known saturation. Also if you turns device upside down, so

that damaged area is now near the source, and this quiet, undamaged area is near

the drain. Since you have a strong channel near the

source, this area, the traps in this area can contribute to the noise in this

device. Even if this device is in saturation, as

a result both of these devices are noisy. Sometimes you may have just one trap,

which results in random telegraph signals, as they are called or RTS, RTS

noise. So you have a trained current, it has

thermal noise and there are jumps up and down because of one trap tends to capture

and release carriers. And this jump can be large between a

fraction of a percent and let's say 20%. Now, a reasonable question here is if we

can have one trap, is there a possibility that we may have no traps?

And in fact, this is possible. I know of a well-known researcher in the

field, who made such devices with no 1/f noise, which is major news.

unfortunately, he could never make them again.

He made them one day for what ever reason, something went really right with

that process and he got extremely quiet devices with no flicker noise.

from what he tells me, he didn't publish these results, because he could never

reproduce them again. So, if he has those devices sitting on

his shelf to this day, but he cannot reproduce these results.

Anyway this is encouraging news that perhaps with a hard effort devices with,

without flicker noise may be possible. Other causes of the increased noise

include quantum effects. And it has also been reported that halo

implants can contribute to noise, through the factor K1 of VGS, that you have

already seen in one of the formula. Now, as a final note, for both thermal

noise and flicker noise, if you want to incorporate it into an equivalent

circuit, you use the noise source in parallel with the channel.

So this source is shown as this a current source here, that incorporates thermal

and flicker noise. You also have the physical resistances of

gates, drain and body that contribute to noise as well.

And I have to warn you that although this physical resistance it contributes to the

noise, Gsd, which is the source drain small signal transconductance.

This is not a real resistance, it is just a small signal equivalent to represent

the change at the drain source current when you change the drain source voltage.

As such, it does not represent a real resistance, so this one should not have

noise in it. Only the physical resistors here should

have noise. The total power spectral density of this

noise source is the sum of the white noise power spectral density and the

flicker noise power spectral density. In this video, we have concluded our

brief disucssion of noise, we talked about flicker, or 1/f noise.

And we showed how both that noise and thermal noise can be incorporated into an

equivalent circuit, representing the small-signal behavior of the transistor.