1:12

Now as q i goes up, because of the charge

balance equation you can expect that q b will change and q g will change.

Since now q g is changing the rate of change of this charge will be

felt outside as a gate current.

So we have i g of t is d q g d t.

Likewise, because there's a change in q b.

1:35

The rate of change of this charge will be felt as a change in the body current.

I remind you that this, variation of qB is not due to

immobile ions moving but rather to holes that either cover or

deplete more acceptor ions.

What about the drain and source currents?

2:03

In order to reason about those two, think of it this way.

What is the drain current?

The drain current is a quantity that is proportional to the rate

at which electrons leave the channel through the drain.

2:16

And what is the source current?

The source current because it is defined in opposite direction for

iD is a negative quantity so I will instead talk about the absolute value.

The absolute value of i s is proportional to the rate at which electrons enter

the channel through the source.

2:38

at any given time, as many electrons would be entering through the source

as living through the drain and if that were the case you could never change Q,

I, but here we want Q, I, to up which means that momentarily.

More electrons should be entering through the source than leaving through the drain.

And in fact, when you plot, i s and i d, this is what you observe.

This is the magnitude of i s, momentarily becomes larger, then

i d and the difference between the two is what allows q i to build up.

Now i sub t here is the transport current.

This is the current you will have obtained if you were using just

the transport card equation which was established for this here operation.

So, clearly, the two currents will be both different from i sub t.

Then eventually the currents merge together because here we reach,

this is steady state.

And when v g goes down, and magnitude of q i must go down momentarily,

i g becomes larger than the magnitude of is which means.

Momentarily, more electrons exit per unit time through the drain that come

into the channel through the source so that the channel can partially empty and

the magnitude of qI can decrease like that.

And then when VG goes up very, very slowly and qI goes up very, very slowly,

the same things will happen but now, because this change lasts for

a longer time, i sub d and the are closer to each other,

4:21

because the longer they are different, over a longer time, is enough to build

the extra q i required here.

Now as I mention already, let's take this part, the mitrodavis and

the mitrodavi different from the transport carbon I sub T,

which would have been obtained using DC type equations.

So this difference I will call I sub DA.

Here is the transport current, here is the actual drain current, and

the difference I will call I sub DA.

I can write that the total drain current is what I would have obtained from DC.

Derived equations plus a new component which is

what we would call the charging component of the drain.

5:27

So we can see that in quasi-static operation

we are not implying that the drain and source currents are the same.

All we're saying when we say a device operates quasi-statically is that

the charges obey DC like laws in terns of the terminal voltages,

but the currents have to be different to allow for QI to change.

6:07

So let me now take this equation, we need to satisfy this equation by the two

charging currents, I'll repeat the equation over here and

what I will do is I will define two fictitious charges, qd and

qs such that the rate of change of qd is equal to iDA and

the rate of change of qs is equal to iSA.

6:37

So, I'm defining two fictitious charges, qd and qs, such

that their derivatives with respect to time, add up to dqi, dt.

The rate of change of the universal air charge.

Now if you define a function only through its derivative it is not defined uniquely,

of course.

But we can agree that we take the simplest possible functions for

q d and q s in such a way that their sum is equal to q i.

Okay.

So this will be called the train charge and

this will be called the source charge and they adapt to the inversal layer charge.

Notice that I will never use qd and qs by themselves, but,

rather, I would use them only to calculate the charging components of the drain

current and the source card, like this.

7:31

Now, to decide what QD and QS is is not a simple matter.

It is discussed in all the appendices of the book and

here I will only show you the solution.

Let us go back to DC operation.

Capital Q sub D is obtained by

integrating the inverse layer charge over the gate area, WDX, but

also waiting Qi prime, there saw that the closer we get to the drag,

the larger x becomes and the larger the waiting factor here becomes.

Go through this integration, you find some function f sub d

of the terminal voltages the same happens for Qs.

Only now the weighting factor becomes larger as you go towards the source,

where x goes towards 0.

And more and more of Qi prime is associated that with the source.

Going through such an integration gives you another

function F sub S over the terminal voltages.

8:43

D x times w, which is the same as the inversal layer charts so

we satisfy this equation.

Now for quasi-static operation the same.

Their functions will be used only.

I will replace VD, VG,

VB and VS by time varying quantities but

I will assume that otherwise, QD is given by the same function fD.

As before.

And the same for qs.

This is consistent with our assumption of quasi-static operation.

9:24

Now the way I showed you as to how to evaluate qs and

qd which of course I didn't go through and I if you're interested,

I would refer you to one of the appendices in the book.

This way is physically and

mathematically sound as you can find from the proof in the book.

9:47

It agrees with results from perturbation techniques which is another way to

solve such problems and it agrees with non-quasi-static

models if the speed is reduced to such an extent that

the non-quasi-static operation in the limit becomes a quasi-static operation.

10:16

And another approach is to assume rather arbitrarily that half of

the inverse solar charges associated with the source and half with the drain.

We will not be using these approaches, rather we will be using the what I

call the physically and mathematically sound approach that I just described.