At this point, we have discussed quasi-static operation in detail. And we are ready to apply what we have discussed to the complete transient simulation of transistors. Provided of course the speed of the voltage is applied to them is not to high. So that equals a static operation assumption is valid. We will discuss the transom response evaluation using quasi static models. Using a strong inversion example. So here we have a transistor with body shorted to shores the drain value always held constant at the large value. So as soon as the transistor turns on, it is assumed to be in saturation. And of varying voltage VG. Notice that only VG varies, the other voltages are constant. Now you will recall from our earlier discussion, that the drain current is the transport current that could have been predicted from DC light. Equations, plus a charging component. Now this charging component is dqD dt, where qd is the so-called drain charge in the channel. And that can be written as dqD dvG, dvG dt, so you can relate it to the rate of change of the gate voltage. you may recall that there were three other terms in dqD dt. But here they are 0 because those other terms don't have a dv dt. The dv dt for them is 0 since these voltages are constant. The only varying voltage is the gate voltage. dqD dvG can be evaluated from the drain charge expression which we have shown in the past. It's this one and when you differentiate with respect to vG, you find this constant. Now putting these results together if I assume that vG is a ramp, we get these results. VG is assumed to be 0 at the time t equals 0, then it goes up as a ramp, and then at t equal t3 becomes a constant again. We are making a very simple approximation that the device is practically off. Before vG reaches the threshold voltage vt which happens at time t1 here. And then after that, as soon as it turns on we assume it is in strong inversion. And remains a strong inversion throughout. And because vDD is large, only saturation needs to be considered. Now to find the drain current, we need to know the transport current, and the transport current goes like this. 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. I would say that for speeds that, in which the quasi-static model is valid, 40 to 60 makes sense. or, if that doesn't make sense, it means that probably the speed is so high that you're no longer in quasi-static operation and you have to use non-quasi-static operation. Some issues associated with charge modeling. Sometimes wrong modeling principles are used, for example, time in variance circuit principles are used. Whereas the actual capacitances of the transistor, and we will be talking about capacitances in a couple of lectures. Vary with time because they turn out to be capacitance that the voltage dependent, the voltage is varied with time, the capacitance is varied with time. So you can no longer use circuit concepts from time-invariant circuit. Another problem is that sometimes transcapacitance terms are omitted. For example the gate current is assumed to be dqG dvG, dvG dt, for as we know that the correct expression contains other terms. in addition to dqG dvG, which is the second term over here we have dqG dvD and dqG dvB and dqG dvS. These terms are called transcapacitance and they have to be there for correct modeling. Then sometimes in the software, implementation of a model, current to evaluate it, and the charges are found by integrating the currents. Now if the currents have an error, then when you integrate the error accumulates and that will give you wrong charges. And finally, in some models there is a non-continuity in, in charge voltage relations. Which results in discontinued capacitors. We will discuss this effect when we talk about capacitors. Some other effects very briefly. In short channels of course you have velocity saturation that you need to take into account. And you have something called the transient transport current. Because the drain is so close to the channel that it even affects it under DC conditions, and of course the transport current is also affected. I will not discuss these effects, there are references to papers in the literature discussing them if you're interested, and they're listed in the book. There's one more effect I would like to discuss. Charge pumping. Consider a transistor that has been turned on. It has a gate voltage that is large, and then suddenly the voltage goes down. Now there is some capacitance between the gate and the inverse layer. And when you suddenly push the potential in the gate down, because the capacitance maintains momentarily a fixed voltage across it. When the potential in the gate goes down, the potential in the invasion layer goes down, becomes more negative than before. And that can be so negative that it can turn on the parasitic effective junction if you like between the invasion layer and the body. This is called charge pumping. It is as difficult effect to model, and again a discussion of it can be found in the references in the book. So in this video we talked about how we can evaluate the transient response of resistors. Using posistatic modelling . And we saw certain limitations of such modeling. In the next video, we will talk about non posistatic modeling. That can take you to much higher speeds.