In this video I want to give you a slightly historical perspective on,
transistor scaling. The first term which, comes to our mind,
when we think about, transistor scaling is, of course, Moore's Law.
And, that is, named after, Mr., Gordon Moore.
Mr. Gordon Moore initially started his career at Shockley
laboratories in Palo Alto. Then he with seven other people
including Bob Noyce They formed this other compnay called Fairchild Semiconductor.
Subsequently he left Fairchild Semiconductor to form Intel.
And this is a very famous set of people. They are also known as the treacherous
eight, and they are in many ways responsible for
the establishment of Silicon Valley as we know it.
And Mr. Moore also as a, as a result
of his entrepreneurial pursuits So has done pretty well for himself.
But the thing I want to bring out is this article that Mr. Moore wrote in
1965 in Electronics magazine.
And while he was still working at Fairchild,
Fairchild Semiconductor. And, this was a magazine article.
It didn't have too many technical details.
But it had this one figure which became famous,
and is known, often referred as Moore's law.
So at this, this was, this article was written in 1965.
And, there are only very few, demonstrations of, integrated, integrated
circuits or integrated components, on a chip at that particular time.
So at,
what, Mister Moore did, was, he looked at, the limited
amount of data he had. And in fact here only four data points, so
it's not a way, it's, his hypothesis was based on a very limited set of data.
And what he saw was this number of components was increasing twice, you
know, it was increasing exponentially
every year.
And in the year of 1965 it
has approximately two to power seven components.
So it had around 128 components at that particular time.
So what he predicted was this trend will continue and what he predicted in this
article was by 1975. You'll have 65,000 components.
Or you'll have looking at this graph, our predictor was assuming this law would
continue by 1965, you will sorry 1975, you'll
have. two to power, 16, or approximately 65,000
components on one particular chip. And
even though it was based on a very limited set of data,
actually it turned out to be true and that's why he became Moore's law
became very famous but it was not a, very technical article. It didn't
tell you, tell us how this will happen, in fact this was a magazine article and this
is another cartoon from this article which says that soon
a microprocessor or computers would become commodities, so like you like you
sell like you sell lotions or you sell cosmetics.
One day you will have stalls which will be selling selling computers.
And you know why this all sound very normal?
Remember the year The article remember was in 1965, which was 20 years before
the first personal computer, the first Apple two or Macintosh came along.
The person who gave more details on how
Moore will progress or how the transistor scaling
will actually happen. Was Bob Dennard from
IBM, who's a inventor for the one transistor,
one capacitor DRAM. So here's a picture of Bob, with a big
smile and showing this one transistor and one capacitor
DRAM that we saw earlier that we saw used inside the iPhone and
he wrote a couple of papers starting in the year
1972. So he
had a paper in the IEDM conference
in 1972. He also had a article on
On IEDM73, which again, which gave some details
on how these scaling will actually happen. But, altogether which
is most famous, and what he is most remembered for and what
is called as Dennard's scaling, is this article,
JSSC written in 1974.
It has over 1,200 citations. It's one of the most
cited articles from this journals. And what he did in this article was he
laid out the, he laid the rules at, by which scaling of transistors will happen.
And this is described in this very simple table.
So this was the first table in this article.
And what, what it says was to scale the transistors.
What we need to do is scale the oxide thickness of our
electric by the scaling factor. So he defined the scaling factor.
He calls K and he took, he said the nominal value of k, let's assume it's 1.4.
And what he says that we need to scale all our dimensions.
That is we need to scale our outside thickness.
we need to scale the length.
We need to scale the width of the transistors.
Each by this factor. one by k, so if K is one, 1.4, we
need to make each of our lengths to be one over 1/1.4, or 0.7.
And he also said we need to reduce the voltage By the same amount.
So we need to scale our voltage also by 0.7.
And then what he said was then if we do all these things our current will actually
scale or decrease by 1 over K as well. So let's actually check that assumption.
So what he said was that. Scale each of these by 0.7,
so we scale W by 0.7, we scale L by 0.7,
so this thing remains unchanged.
They said let's scale the, the oxide thickness
so this, this, this scales by 0.7, alright.
Then it says let's.
All the voltages including the drain voltage, the source
voltage, as well as the threshold voltage, by 0.7.
So if we do that then we scale this by 0.7 squared, and we can see that,
in fact, the current does become 0.7. So that's what it says if, if we scale all
these dimensions by 0.7 we also scale the voltage by 0.7.
Then our current will in fact scale by 0.7.
And then what this is the capacitance, the capacitance which is
simply given by And the capacitance is, which is simply given by
the area, the gate capacitance, which is essentially simply given
by the area by the thickness, is simply proportional to
the W L by t ox, and if we scale
all of those dimensions then what he said was this capacitance.
Will also scale by this factor so this capacitance so the gate
capacitance will also become 0.7 and then the transistor delay which is essentially
CV over I so we have scaled our C by 0.7. We have also scaled our
voltage by 0.7 and our current by 0.7 so our delay which is CV over I which is also.
The transistor delay will also scale by 0.7
Which is a good thing, because we will get faster transistors.
And, then he said, though, our power dissipation per transistor.
Which is given by
v or I, will eventually scale by 0.7 squared
So, this will in fact become half.
So the 0.7 squares.
0.49, or we can say roughly. 0.5.
And what he says more importantly was a power
density so everything, all the dimensions has all the width and the length
have
scaled by this factor 0.7. So the density of circuits
has increased by W L square, so the density of the circuit has become twice.
And at the same time the power consumption has become half So he says the power
density which is CV over which is VI/A
will remain the constant because your power dissipation
essentially became half.
But your area also decreased by half so this power density would remain the same.
Or your your chips won't become any hotter neither would they become any cooler.
But if you do this, if you scale, everything by, by this factor, K, by this
factor K, which is 1.4, your power density does not, increase.
This is also known as constant, electric, field scaling, because
if you look He scaled the, the voltage, by 0.7.
He also scaled the dia, the dielectric thickness of the oxide by 0.7, so
the electric field through the dielectric, so if we think about the electric field
which is perpendicular.
in the perpendicular direction is given by this voltage we apply
on the gate divided by the oxide thickness so this remained constant.
Similarly, if you think about the electric
field in this lateral dimension, that's again
determined by a drain voltage divided by
our gate length so that also remained constant.
So, this, this is also known
as constant fields Scaling, because the fields remain constant.