I remind you that the transit time have been defined in a general way, back in

the introduction, to the main transistor material, as the total charge contained

in a given part of the semiconductor, divided by the rate of change at which

this charge exits. Now in our case, the charge is the mind

tread of the mercelator charge, and the rate of exit of it with respect to time,

is the drain source current. Let's assume strong inversion with a very

small Vds, then we have this result from our previous video, or on the charge

evaluation for Qi. And this is an approximate expression for

the current, where we have neglected the square term of Vds, because we are

assuming that Vds is very small. So dividing the two, we get the transit

time like this. You can see that see that C ox is

contained in both numerator and denominator cancels out, and so is W, and

so is Vgs minus Vt. So finally for very small Vds we get this

result. Notice the dependence on the square of

the length of the device. We have discussed the reason for this

back in our introduction. and notice that the transit time is

invertible portion to Vds. Which makes sense, as the Vds goes to 0,

the transit times becomes infinite, because if Vds is 0, there is no moving

force for the electrons to get out, so they stay there forever.

Let's now talk about saturation, again it's strong inversion.

We have derived this result of, although we've bypassed the algebra, for the

inverserly charge. And this result is the approximate

current in saturation, from our source reference simplified model.

Dividing the two, we get this result. Again, we have an L squared dependence,

but now the driving force turns out to be the gs minus Vt.

In weak inversion saturation, we have this result, back when we discussed weak

inversion operation, we had mentioned that the current is only due to

diffusion. And therefore, the inversal charge per

unit area varies, as a straight line from Qi 0 prime at the source, to 0 at the

drain, in the saturation region. And from that, it is easy to derive this

result from, for Qi. And again, back when we discussed the

current. In weak inversion we had shown this

result, assuming again that we are in saturation.

Dividing the two we find again, that the transit time depends on the square of the

length as before. But the bias voltages in the denomonator

that we had seen in the strong inversion region, where the current was due to

drift. Here, are replaced by two phi t, where

phi t is the thermal voltage. So let's put the results together, and

plot the transit time in the saturation region versus Vgs, the gate source

voltage. Tau versus Vgs.

In the weak inversion region, we have the maximum transit time, the device is the

slowest, and the transit time is independent of Vgs.

Then we enter moderate inversion region, and finally weak strong inversion region.

The strong inversion region equation was this one, as we showed, and it goes like

this. However, the actual transit time never

becomes as low as that, and the reason is that eventually, you approach velocity

saturation. Once you have velocity saturation, the

transit time is limited by how fast the carriers can travel.