We will now revisit the concept of transit time, which we had discussed back when we were providing a review of fundamentals, for our course. And we will talk about the transit time of transistors, and strong inversion and in weak inverse. Let us assume DC operation. 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. If all the carriers were traveling at maximum drift velocity Vd max, then the time they would take to go through the channel would be L over Vd max. But because some of those carriers, especially any other source, are traveling at, at smaller velocity than this, the actual transit time is larger than this limit, and only approaches this value asyntotically. So in this short video, we evaluated the transit time under this DC conditions. these results will turn out to be useful when we want to determine whether a given speed of operation allows the device to behave quasi-statically or not. In the next video, we will talk about transient response using quasi-static modeling.