[Slide 1 L5.6] Okay, welcome back.
We are discussing a variety of topics in Unit 5.
The topic for this lecture is compact models.
Now way back in Unit 1,
I said a little bit about compact models.
I'd just like to return to compact models
and say a little bit more.
This is an important topic.
You should know a little bit about compact models.
If you work in semiconductor technology,
you'll wanna learn a lot about compact models.
We really could use a course on compact models.
All I can do in this lecture is just point out some things
that you should be aware of and dive deeper into.
[Slide 2] So in Unit 1 I mentioned
that we can think of two different kinds of compact models.
The models that we have been focusing on in this course
I refer to as compact physical models.
So these are models- simple, analytical models.
The models that we have been developing
are virtual source models
that capture the essential physics.
They sort of summarize our conceptual understanding
of the physical operation of the device.
They can be useful in analyzing experiments
as we discussed in the previous unit:
extracting physically meaningful parameters,
like transmission, mean-free-paths,
series resistances, things like that.
They can be useful in monitoring processes.
So they have a variety of important uses.
This is the kind of model
that we have been discussing in this course.
That's where our focus has been.
[Slide 3] But there's another kind of compact model
as I mentioned in Unit 1.
These I refer to as compact models for circuit simulations.
So these are models that accurately describe
the electrical performance of a device
across a wide range of temperatures,
biases, layout geometries.
They do so in a form that is suitable for use
in numerical circuit simulation programs
so that designers can use these models
to design complex electronic circuits.
Now, the model does not need to be physical.
It could be a set of empirical parameters
that fits the measured characteristics
of the device very well.
But we generally prefer the core of the model
to be a physical model,
and I'll explain why in just a minute.
So these kinds of models are extremely important
because they interface semiconductor technology
to circuit design.
[Slide 4] Now in terms of the second type of model,
the compact model for circuit simulation,
there are two broad classes
that you'll hear people talking about.
There's a table based approach,
and a table based approach constructs large tables
of either measured electrical data or simulated data
and interpolates from that table to describe
the electrical performance of the device smoothly.
A second type of model is the physics based model.
So this is a set of analytical,
or maybe very simple numerical expressions,
that describe a device across a wide range of biases,
a range of different layout geometries
that designers might use,
a range of temperatures
that might be encountered.
Now generally there's a role for each of these.
The table based models are quick to develop.
If you're exploring early technology
and you can get some data,
or you can simulate a new device, for example,
you can quickly produce a model
and start looking at the impact
of this device on applications.
[Slide 5] But it's generally preferred
if we're going to use a model for serious design
that it be physics-based.
Why is that?
Well there are a number of reasons.
One is that it relates the needs of the designers
in terms of circuit performance
to the manufacturing process.
So we can go to the manufacturing process
and we could say we could use a thinner gate insulator.
We need to have a lower series resistance.
The parameters in the model
are not just curve-fitting parameters.
They have physical significance.
You can talk to a semiconductor technologist
and work on those and improve the performance
of the circuit.
Generally these types of models
result in the fewest number of parameters,
and that simplifies the calibration procedure.
When you're going to calibrate the models
and tweak them to accurately describe
a given manufacturing process,
it's easier if there are a relatively small number
of very physical parameters.
They also provide the best basis
for statistical and mismatch modeling of devices.
For example, your manufacturing process might know
that the gate oxide thickness is controlled
to plus or minus x percent.
Then you can directly relate those numbers
into the performance of a circuit.
And as manufacturing processes evolve,
maybe some thicknesses of layers,
some doping densities, some channel lengths change
during the course of the manufacturing process,
since these are physical parameters,
it's relatively easy to go back in the model
and quickly adapt it to the new manufacturing process
and you're in business again.
The major drawback of these models
is that it's very time-consuming
and a long involved process
in order to develop very good models of this kind.
But they're generally the preferred model
if you have a mature, y'know, important,
high volume application that you're working on.
[Slide 6] Now we've discussed this MIT version
of the virtual source model
as we've gone throughout this course
and made it more and more sophisticated.
There are versions of this model
that you can download
and use for circuit design.
But I wouldn't call it an industry-strength,
general purpose model for digital design
because of a number of reasons.
One is we have developed this model
to describe short channel devices,
but designers may have a need for long channel devices,
which behave more like quadratic square law MOSFETs.
We have to be able to smoothly-
the model needs to be able to smoothly go
from a short channel to a long channel
and anywhere in between.
The MVS model doesn't do that.
It doesn't treat a number of second and third order effects.
And, for example, it doesn't treat things like noise,
which are very important to designers.
It doesn't treat the layout dependencies,
the particular geometry of the layout,
of the gate and the transistors,
and these are all very important to designers.
There are a number of other things.
Now you could go back and spend some time
and work and develop this
into an industry-strength industrial model.
But that is a long, involved process
and there are good industry-strength models,
so you want to be very careful about doing it.
It's very difficult for a company
that is committed to one particular model
and has calibrated their manufacturing process
and is using that for a long period of time,
to switch to another model,
even if it turns out to be better.
It's done, but it's done infrequently.
Only when it's important.
[Slide 7] Now one of the other limitations
of our virtual source model
is that it's focused on the source.
We focused on the source for physical reasons.
That allowed us to understand very simply
how these small MOSFETs operate.
But there are issues.
The quadratic square law model of the MOSFET
that was developed in the 1960s.
This is also a source referenced model.
We talk about VGS,
everything depends on whether VGS is greater than VT,
V gate to source.
But problems occur when VDS changes sign.
Most MOSFETs are symmetrical devices.
The terminal with the more positive voltage
is the drain, and the other terminal is the source.
But during circuit operation,
the voltages might switch,
and at some times one terminal might be acting as a drain,
and some times the other.
So it is really best not to formulate models
for circuit design as source referenced models,
because then problems occur when you go through the origin
and VDS switches sign.
Now, it can be done.
In fact, there's a reference here of a very early model
that shows one way of doing a model
that is not referenced to the source.
But this is- over the years people have learned
that one needs to be very careful about this
or artifacts are introduced into the model
as you sweep through VDS equals 0,
and you go from positive to negative terms.
[Slide 8] So the compact modeling community
has developed a number of tests.
This is one of those tests.
If you have a model that's been developed,
you can run it through some of these tests
and see whether it's going to have problems
that might create issues for circuit designers.
One is called the Gummel symmetry test.
This particular test, you set it up
so that we sweep a voltage Vx,
which is attached to both of the terminals,
plus Vx to 1 minus Vx to the other,
we then sweep Vx
from minus the power supply voltage divided by 2,
to plus the power supply voltage divided by 2.
We fix the gate voltage, not the gate to source voltage,
we fix the gate voltage, reference to ground,
and we sweep Vx.
And as we do that, the drain to source voltage
is always twice Vx, so the drain to source voltage
will go from plus VDD to minus VDD.
And while we're doing that, we can monitor
the current and the slope of the current, et cetera.
[Slide 9] So if you do that, you know, qualitatively,
you should get characteristics
that sort of look like this from your model.
And what was discovered
is many models had problems right around the origin,
and they didn't behave the way they were supposed to behave.
This introduced problems,
especially in issues like small signal parameters
and distortion of analog circuits and things like that.
So, designers need these kinds of robust,
very well behaved models for a high volume
or high importance application designs.
But the simpler models,
even if they have some of these issues,
can still be very useful for early stage R&D
and exploring the implications
of a new device on technology, for example.
[Slide 10] Now, let me just say a word
about device research in general.
I've been fortunate in my career
to sort of have it occur
during the golden age of device research.
This is a quote by Herbert Kroemer,
a very famous semiconductor scientist
who won a Nobel prize
for his semiconductor work in 2001
and this is from his Nobel lecture.
So Herb made the point that the application
of any sufficiently novel device will always-
applications will arise to make use of novel new devices.
You invent a device, we'll find an application for it.
That was a very good philosophy for a long time.
But electronics is much more mature today.
Y'know, there's still some of this,
and we still want to look for these possibilities,
but there are many devices available,
many materials available,
semiconductor technology is very sophisticated.
More and more, we're driven today
by what is the impact of this new device on applications.
How can it outperform?
How can it do something that can't be done today?
So there is more and more need for device researchers
to be thinking about applications at an early stage.
What are the implications of my new device
on applications that could be important,
or that people care about?
And for this reason, device and materials scientists
should learn something about compact models
and be able to use them to sort of explore
the impact of their new device or their new material
on applications, even at an early stage of research.
[Slide 11] Okay, so you're looking for a compact model.
Where do you find a compact model?
Unfortunately, there is no single repository
where you can go and find all of the compact models
that have been developed, either open sourced
or the ones that need to be licensed.
There are a couple of places that you can look.
One is the NEEDS website.
There are almost 50 compact models,
open sourced compact models,
that researchers from across the world
have submitted to that repository.
You might be able to find one that suits your purposes;
maybe you can find one that's close that you can modify.
So that might be a good place to begin.
Now the designers need robust, industrial strength models.
There is a coalition of companies that has been formed
to support the development and ongoing support
of these kinds of models.
It's called the Compact Model Coalition.
They have a variety of models that many companies rely on,
that are continuously maintained and supported.
And if you're a member of that coalition,
you can obtain access to those models.
[Slide 12] I also wanna make you aware
of one of the important industry strength MOSFET models.
It's called BSIM.
This is the Berkeley Short Channel IGFET Model.
IGFET is Insulated Gate Field Effect Transistor.
It's what we used to call MOSFETs.
This was developed in 1987, the first version.
It's undergone many versions.
Many of the initial problems of compact models
have been discovered and taken care of in this.
It is widely used by many companies.
Virtually all circuit simulation programs
now will have the BSIM model built into it.
So if you're working on MOSFETs,
it's a model that you want to be familiar with
and very well may be using.
Okay, as I said,
almost any commercial circuit simulation program
that you would encounter will have the BSIM model
as one of its options.
[Slide 13] Well, what if you don't have a model?
What if you have a brand new device
and you have to write your own model?
Well there is a language for doing so.
It's called Verilog-A.
Verilog-A was actually an industry standard model
for modeling analog systems,
basically at a functional level.
But it's been extended,
so that it is now a language
for writing compact models.
It can be used by virtually all, probably all,
commercial simulators will take a Verilog-A script
and will compile it into source code
and run it at native speed
within the circuit simulation program.
Some open source simulators do that, too.
If you're interested in learning about Verilog-A,
I've got a couple of pointers
to additional information here.
[Slide 14] There is also an open source MATLAB based program
that is designed to be an environment for writing,
and experimentally validating the functionality
and suitability of a compact model, running simple circuits
so that you can test its applications in circuits.
Those models then can even be inserted
in some open-source, SPICE engines.
It's also a useful first step
for people who are new to Verilog-A modeling,
but are familiar with MATLAB.
It's a good way to write a model,
get it working, find the issues,
test and debug it before you write your Verilog-A model.
The Verilog-A model then may be more usable
in commercial circuit simulators, at least at this time.
So you can find additional information on MAPP,
this MATLAB based environment, at this website.
[Slide 15] Now before you write the compact model,
you really should take some time to familiarize yourself
with the many lessons that have been learned
in the issues in compact model that can pop up,
all of the things that have been discovered over the years
in making MOSFET models better and better,
and more and more robust.
Many of those lessons learned
can be applied to novel devices as well,
and you should try to acquaint yourself
with some of those lessons.
A good place to begin
is by doing a search for Colin McAndrew,
who has been one of the leaders in this field.
[Slide 16] Alright, so this is just a quick lecture
on some topics in compact modeling
that I wanted to sensitize you to
and to encourage you to learn more about
if you continue to work in semiconductor technology.
So a couple of key points.
Compact models link semiconductor technology
to manufacturing and circuit design.
They really play a very important role.
Now compact models can also be used,
and more and more they're being used,
to link earlier stage research and development
to the design and applications that they may impact.
So if you're going to develop a compact model,
you need a good understanding of the physics
of this new device that you're working on,
because we prefer the models
to be as physics-based as possible.
But you also need to understand
what goes on inside a circuit simulator,
how this complicated system
of nonlinear equations is solved,
because your model must behave robustly
under those numerical algorithms
and in that environment.
And very importantly, you also must understand
the applications that this device might be put to,
because those applications will determine
which characteristics of the device
are the most important ones to focus on
and to get most accurate as you develop a model.
And finally, many of the lessons learned,
and there have been many over the years,
in developing circuit models for MOSFETs,
are more broadly applicable to devices of any kind,
and you should acquaint yourself
with some of those lessons learned
so that you don't have to go through the pain
of learning them for the first time yourself.
You can deal with the new issues
that are specific to your particular device.
[Slide 17] Alright, so that's a little bit about compact models.
We've covered a lot of different topics in Unit 5.
What I'd like to do in the next lecture
is just to quickly review
some of the main points of Unit 5,
and then we'll be wrapping up the course.