It goes like this because once the device turns on at t equal t1, we can apply the

simple square law. Saturation equation we know for strong

inversion. So it goes up until of course vG becomes

constant, and then the transport current becomes constant.

Now, the charging component will be dqD dvG which is a negative constant.

Times dvG dt, the rate of change of the input but that is also constant because

the input goes up as a straight line. So the product of the slope of this and

dqD dvG from here gives you a constant nevative number for iDA.

So, the charging component is 0 then becomes negative.

And a t3, it goes back to 0. Why?

Because now vG is not changing and therefore dvG dt becomes 0.

The total drain current is the transport component plus the charging component so

you add this and this together. And you end up with a wave form that goes

down and then goes up. And then another jump here and goes like

this. Now, how good is this result?

If you compare it to a measured results, obviously for a long time in device, you

find this behavior. So you can see that the quasi-static

model tries to predict this behavior. For example, it does predict that, the

current does not become positive until some time here which is valued over here.

The current starts becoming positive at t equals t2.

The only difference being that the measure of current is 0 before, before

t2. Whereas here, it is predicted to be

negative. So you see problems like this.

You also see another problem here. There is a sudden jump because of the

jump of the charging component as in a real device there is only a gradually

changing current like that. This result cannot be predicted by quasi

static models. One has to do non quasi static modeling

which it will do. But for the time being the question is,

if the speed is slow enough, so we're in quasi-static operation.

How good is the result? And again it depends how close you a,

you, you get to the limit of quasi-static operation.

And empirically it has been found that for, to get reasonable results from a

quasi-static model. You need to have a rise time in your

input wave form, the time it takes for the wave form to go from 0 to it's

maximum value. Which is at least 20 times the transit

time, and I remind you that the transit time is this.

This means that your waveforms have to be slow for quasi-static operation to be

valid. And of course because you have extrinsic

parasitics, which we will discuss shortly in a couple of videos.

You have extra capacity such which necessarily slow your waveforms.

In some cases in practice, speeds are low enough so that for the static model

income do an accurate and adequate job. however once the rise times become short,

was the static models fail. You can save the quasi-static model

statistic stand the reason of validity as follows.

Let's say you have a channel that is too long, so that this condition is violated,

the condition I just showed you on the previous slide.

Notice the L squared dependence. You make L long, eventually.

It would no longer be true that the transit time of a given wave form is

longer than 20 times the transit time. When this happens, you can split the

device into m sections, each of them now has a length L over m.

L over M so, in such a way that, this is smaller then the rise.

You can do it like this. This is the entire length of the channel.

You split it into m segments. And then your model leads segment has a

separate device. Each of these subdevices is assumed to

operate quasi-statically because each length is short enough to allow this to

be true. And then you model this in a very careful

fashion. For example, intermediate points here

correspond to intermediate points here are not associated with the source of the

drain. The source is over here and the drain is

over there. Therefore intermediate points do not

suffer from effects that we discuss when we discuss short channel effects, such as

charge sharing for example. So the only way to really model it is to

really understand what's happening inside the model and be very careful with how

you do it. This is done in some programs where the

number of segments used is typically from 2 to 5.

And it does typically extend the validity of the quasi-static models.

Let me now talk about the drain/source charges.

In saturation we have seen that the drain charges have been given by this

expression. And the source charge is given by this

expression. If you divide one by the other, you find

that the ratio of QD to QS is 40 to 60. So you associate 40% of the inversely

charged with the drain and 60% of it with the source.

There are other partitions that sometimes are used.

One is 50, 50 which is rather arbitrary. And the other is 0 to a 100.

In other words, no charges associated with a drain and no charges associated

with the source. Of course both of these partitions leave

much to be desired but this latter partition 0 to a 100.

Removes the negative part of the drain current plot that we saw a couple of

slides ago and is sometimes used. Sometimes you as a user of a model,

you're asked to choose your partition, so it's good to understand what these

partitions mean and what effect they have.