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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.

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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.