At this point we have finished with, the modeling of MOS transistors, under DC excitation. We are now, in a position to take a look at professional compact models, used for circuit simulation. This material is taken out of sequence, and it comes from chapter ten in the book. compact models used for circuit simulations are very large models where the various effects we have discussed, and many more, are combined into a single model. In this series of videos, I will discuss the type of considerations that go into the making of this models how such models can be designed and tested. Of course, we will be very brief. We can only touch upon this very extensive subject. There is much more in chapter ten of the book. In the first video in this series, we will discuss several types of models that are available. And we will talk about what properties a good model should have to be useful in a circuit simulator. Let me begin by a summary of what types of models are available out there. We start with Monte Carlo simulations. These are particle simulations where individual carriers are assigned physical properties and they are tracked. Large numbers of simulations are run. with many carriers, and the statistical behavior of these carriers is predicted very accurately. So Monte Carlo simulations take into account detailed physical descriptions of individual carriers. Then we have moment methods. Still very physics-oriented. Both Monte Carlo and moment methods are accurate, in terms of their physics, but they are very inefficient computaionally, and therefore they're not suitable for the analysis of circuits containing[UNKNOWN] transistors. They are mostly used for device research. We then have drift-diffusion models which are a simplified form of moment methods and the emphasis on detail mobility formutaltion. And then we have physical compact models, which is the type of model we've been discussing in this class. There are also empirical compact models that rely less on physics and more on equations that have empirically been found to, to give the correct shape, for let's say[UNKNOWN] characteristics and other types of behavior. Then we have black box models that are a form of curve fitting. And even more so, we have table look up models that are tables of data and interpolation. For black box models and especially for table lookup models, you have measurements and you fit curves to them. They don't have predictive ability. In other words if you would like to know what happens if you change a certain physical parameter, you cannot do it with these models. But you can do it with physical compact models. So, as you can see, physical compact models are a compromise between accuracy of physics and computational efficiency. So, in this direction the list. Goes towards more accurate physics and in this direction we go towards computational efficency. And as you can see physical compact models are at about the middle. So physical compact models are widely used for the analysis of circuits and we will concentrate on them. Physical compact models as I already mentioned, are compromised with an accuracy and simplicity. They have many parameters.They will have several of hundreds of parameters in fact. Nevertheless, a model with many parameters doesn't necessarily predict things correctly. It's just that if you have equations with many parameters, you always have room to adjust the values of those parameters to fit given experimental data. But if you want to predict, then you need a model that is physically based and correct. The number of parameters by itself is not guaranteed that you have predicted power. I would now like to discuss what properties a good physical compact model must have. Of course, we expect accuracy of drain-current equations charges extrinsic parasitics. I, we will discuss this topic later on. Extrensic refers to outside the main part of the transistor. In other words outside the channel. Things like source and drain, serious resistance,[INAUDIBLE] to the substrate and so on. Leakage, currents, and so on. All of these ofcourse have to be predicted accurately, but this is not enough. The equations that the model uses must be continuous, and even their derivatives up to high order must be continuous. This turns out to be important for small signal modeling, which we will be covering shortly. For numerical robustness and for prediction of distortion, for example in RF circuits or audio circuits. Now let's, let me give you an example here of what can happen if the model is not. Does not satisfy what I just mentioned. So here we have the drain current versus the drain source voltage. The dots are measurements, and the solid line is supposed to be a model that has fit the data very well. And here we have the same experimental data and another model that fits the data equally well. But it so happens that this one has a certain curvature in the saturation region whereas this one is escentially a straight line in the saturation region. Let us now assume that we have assigned so little variation of the drain source voltage around a certain point, in both cases the same variation. You can see that because this curve here is curved a sinusoidal variation of the independent variable VDS will result is in a non-sinosodal variation of the dependent vairable, IED. So the peak of the sinosodial would be compressed. And here the value would be expanded. So clearly you see that you start with a sinosoid and you get a largely distorted sinosoid in the drain current. Now if you go to this model, because this is a straight line. Sinusoidal variations in VDS result in sinusoidal variations in the current. So, what does this example show you? It shows you that two models that are equally good in terms of predicting the current, can give you totally different predictions in terms of. The detailed wave forms, how distorted they are, for example, this model predicts not distortion and this model predicts a heavy degree of distortion. Therefore, what counts is not only how well you match the data, but also whether you predict correctly the detailed shape of the curves. Continuing with the properties of good physical models. we need to have a correct formulation that makes physical sense. We need to include non-quasi-static operation and we will cover non-quasi-static operation later on in this course. this operation is the what happens when the voltages of the terminals of the device are varying very fast. And the charges inside have difficulty following. It should predict white and one over F noise this again are topics we will cover. in the near future. It should cover all intrinsic effects, meaning those that have to do with the main part of the device between source and drain, and extrinsic effects that have to do out, with the parts of the device outside the intrinsic part. All of the above properties should be satisfied for all expected bias ranges or all V G S, all V D S, all V S P. They should be satisfied for all temperatures of interest. And they should be satisfied for all W and L, the geometrical dimensions. Of interest. Ideally, we should have one set of model parameters, independent of geometric dimensions. So, for example new zero, the constant that appears in the mobility expression, should not have one value for a given w, and a different value for another w. There should be no out of range numerical issues. What does this mean? When a computer solves the non linear equations of the transistor. In fact of many transistors in the circuit. it tries to converge to a solution by trying. Different values and at some times it may assign, to, to temporarily to, as a drain source voltage, a value that exceeds, the, the normal range of the transistor. Although you would never use that transistor with such a voltage you want to make sure that the model does not contain formulas that blow up when you apply such large voltages to them. So, because, i-if that happens, then you may reach overflow and you may not be able to reach convergence. There should be, ideally, flags that warn you when you try to use a model outside its region of validity. There should be as few parameters as possible, and they should be independent parameters. For example, you would not use as one parameter, the doping concentration and as a different parameter the threshold voltage. Because the threshold voltage depends already on the doping concentration. So instead you would use oxide thickness, doping concentration and so on. The model should include not only inversion but also depletion and accumulation. It should be computationally efficent and robust. And it should be symmetric for symmetric devices. On the other hand it should allow for non symmetric devices. The model should be linked to an efficient parameter extraction routine and we will have a lot to say about parameter extraction later on in this set of lectures. And it should pass standard benchmark tests. I will give you a few examples later on in this set of lectures. In this video we introduced several types of models and we summarized the properties a good physical compact model should have. And we said that physical compact models are a compromise between detailed modeling of physics and computational efficiency. In the next video we will talk about what considerations one should have in mind when they try to produce a compact physical model.