Moore's law dead? Or just in need of an update.
 

I find it interesting that Moore's law "died" around the time fabrication companies decided to set an upper limit on the cost of their fabs, which I believe is around 14 billion or so.

So, my question to the group is...

Since you guys are all good at math, can you adjust Moore's law mathematically to account for the fact that the cost of fabrication plants becomes fixed?

In other words, I'm suggesting the 19 month rule assumed unlimited money for fabs, and once we account for that error, we just have a new doubling rule that simply takes longer to accomplish a doubling.

And, yes, I know it's just an artificial way of doing things, but since it's held up so well I think we should try to account for why it doesn't work anymore.

My education got cut short by schizophrenia, so I'm out of my league with exponential math, but does 25.36 months make sense as a new doubling time?

I'll explain my "reasoning," with quotes around reasoning since I may be making an an error.

From what I remember, the cost of fabs was doubling every 4 years, so that's an exponential growth of about 20% per year. 19 months is the Moore's law doubling rule that I'm most familiar with. So can we take the 20% and say 1.2^(19/12) times the 19 months?

That's 25.36 months, but, as I said, I'm kind of out of my league when we get into exponential math.

[QUOTE=jasong;474198]My education got cut short by schizophrenia, so I'm out of my league with exponential math, but does 25.36 months make sense as a new doubling time?

I'll explain my "reasoning," with quotes around reasoning since I may be making an an error.

From what I remember, the cost of fabs was doubling every 4 years, so that's an exponential growth of about 20% per year. 19 months is the Moore's law doubling rule that I'm most familiar with. So can we take the 20% and say 1.2^(19/12) times the 19 months?

That's 25.36 months, but, as I said, I'm kind of out of my league when we get into exponential math.[/QUOTE]

it would depend on what type of compounding was being used (or if no compounding was being used, the bond rate):

[url]https://www.investopedia.com/terms/c/continuouscompounding.asp[/url]
[url]https://www.investopedia.com/terms/c/compounding.asp[/url] etc.
[url]https://www.investopedia.com/terms/b/bond.asp[/url]

[QUOTE=jasong;474197]Since you guys are all good at math, can you adjust Moore's law mathematically to account for the fact that the cost of fabrication plants becomes fixed?[/QUOTE]

It's not obvious how to adjust it, because it's not clear how price of fabs related to price of chips. You're suggesting that there is an inverse relationship -- more spending on fabs means less expensive chips -- but what relationship should we assume?

This [url=https://arstechnica.com/gadgets/2016/07/itrs-roadmap-2021-moores-law/]Ars Technica article[/url] might be of interest. Also, the article has a link to a (very lengthy) report that goes into a lot more detail...

The price of a processed silicon wafer is not something that fabs will share lightly. What is known is that FINFETs and double/tripple plattering increased the cost dramatically in the last years. Also the new technologies/processes require huge investments. That is possibly the reason that there are only 4 major fab companies left: Intel, TSMC, Global Foundries and Samsung. Of which GF and Samsung are working together on some processes to reduce costs.

Moore's "law" is not really a law, more an observation/trend that lasted for a long time. At one point you can't really put more transistors on a square millimetre due to quantum and heat effects. It can extent a little by going vertical/stacked chips, but in the end we're confined by the laws of physics.

Hopefully quantum computers will save the day......

[QUOTE=Dr Sardonicus;474252]Also, the article has a link to a (very lengthy) report that goes into a lot more detail...[/QUOTE]

The ITRS as been frozen at 2015; its successor is the IRDS:
[url]https://irds.ieee.org/reports[/url]

[QUOTE=VictordeHolland;474299]The price of a processed silicon wafer is not something that fabs will share lightly. What is known is that FINFETs and double/tripple plattering increased the cost dramatically in the last years. Also the new technologies/processes require huge investments. That is possibly the reason that there are only 4 major fab companies left: Intel, TSMC, Global Foundries and Samsung. Of which GF and Samsung are working together on some processes to reduce costs.

Moore's "law" is not really a law, more an observation/trend that lasted for a long time. At one point you can't really put more transistors on a square millimetre due to quantum and heat effects. It can extent a little by going vertical/stacked chips, but in the end we're confined by the laws of physics.

Hopefully quantum computers will save the day......[/QUOTE]

I'm not much of a Moore's law purist, I think of it as twice the awesomeness for the same price every 1.5 to 2 years, which is obviously not a thing anymore.


One thing to note is that twice the awesomeness for the same price is proportionately equivalent to the same amount of awesomeness for half the price. In other words, if the fabs can learn to do what they can already do, but cheaper, than that "fulfills" Moore's law in my mind.

In reference to the fab price question, my assumption is that there's still exponential growth possible, even if the the companies have reached their pain point with maximum cost of fabs. I was basically trying to calculate Moore's law with the assumption all subsequent fabs would stay at approximately the same price. In other words, Moore's Law may have been incomplete all this time, and the 1.5 to 2 years only applies if you can keep increasing what you spend on your fabs. So double exponential growth goes back to exponential growth.

[QUOTE=Dr Sardonicus;474252]This [url=https://arstechnica.com/gadgets/2016/07/itrs-roadmap-2021-moores-law/]Ars Technica article[/url] might be of interest. Also, the article has a link to a (very lengthy) report that goes into a lot more detail...[/QUOTE]

As the Ars Technica article mentioned about extreme UV:
[QUOTE]As you may know, extreme ultraviolet (EUV) has been waiting in the wings for years now, never quite reaching full readiness due to its extremely high power usage and some resolution concerns. In the mean time, chip makers have fallen back on increasing levels of multiple patterning—multiple lithographic exposures, which increase manufacturing time (and costs).[/QUOTE]
but I'm reading that it really might be implemented real soon now:
[URL="https://spectrum.ieee.org/semiconductors/nanotechnology/euv-lithography-finally-ready-for-chip-manufacturing"]EUV Lithography Finally Ready for Chip Manufacturing[/URL] -- This long-awaited technology will extend the life of Moore’s Law (IEEE Spectrum)

My takeaway from the IEEE Spectrum article is this:
[QUOTE]Today’s state-of-the-art process is called 193-nm immersion lithography. As the name implies, light with a wavelength of 193 nm shines through a patterned surface called a photomask. That process casts the pattern through water onto the silicon wafer, where it is fixed by a photosensitive chemical and then etched onto the wafer. The problem is that light can’t directly define features smaller than its own wavelength. And 193 nm is so much longer than the size of the features modern chips need. These days it takes a host of optical tricks and work-arounds to make up the difference. The most costly of these is the use of as many as three or four different photomasks to produce a single pattern on a chip. With today’s most complex processors, that means a wafer could need some 80 trips though the lithography tool.

EUV lithography’s reason for being is that it uses 13.5-nm light, which is much closer to the size of the final features to be printed. With it, [B]manufacturers can turn three or four lithography steps into one. For its 7-nm EUV process, GlobalFoundries will replace 15 steps with just 5. John Lin, TSMC’s director of litho equipment and mask technology, says his company plans a similar reduction.

While that will make the work at 7 nm faster and cheaper, it’s the nodes beyond where EUV will be absolutely crucial. “If you didn’t use EUV for 5 nm, it’d be more than 100 [lithographic steps],” says Patton. “That’d be insane.”[/B]

Patton makes it sound as though EUV lithography arrived just in time, and in a way it has. But it has been a decades-long journey with many moments when one expert or another declared it dead. Its arrival in production now still seems a bit unbelievable to some observers.[/QUOTE]

I've read an article one/two years ago about an AI designing a piece (fixation of the steel cable if memory serve ) with better performance than human designed one. Is it time to let computer try their hand at this?

[QUOTE=firejuggler;476981]I've read an article one/two years ago about an AI designing a piece (fixation of the steel cable if memory serve ) with better performance than human designed one. Is it time to let computer try their hand at this?[/QUOTE]

It's already pretty integrated, as I understand. I don't think lithography would be practical at the sizes and complexities we use it at without photomasks heavily optimized by computer.

New Moore's law doubling rule(check my math and reasoning)
 

People say Moore's law is dead, but I say the law is incomplete. I believe Moore's law, as it stands, is incomplete.

We've been under the impression that Moore's law is based on exponential growth and doubles every 19 months or so. Not quite. I believe Moore's law, the 19 month version, is based on DOUBLE-exponential growth, and now we're down to regular exponential growth.

So, where is that extra exponential growth, where did it go? I believe it went away when the fabrication plants started seeing predicted needs of over 13 billion dollars or so to build a fabrication plant. Basically, I'm saying that Moore's law is only true if you're willing to double the amount you spend on a fabrication plant every 4 years.(If I'm wrong about the 4 year doubling, I'm a bonehead and will have to start over)

Anyway, and here is the part where I may be a damn fool, but if I am, please feel free to correct my math, because I think my basic idea is sound.

Anyway, here are my equations. Very simple equations, especially for this forum, but still at the limits of my ability.

x^19=2 (x is the approximate growth per month of the "awesomeness" of a computer chip, and yes, it's just an average)

y^48=2 (y represents the increase in the cost of a fabrication plant per month, and, yes, is just an average. Feel free to correct this amount, either the math or the number of months assumption)

Screwing around in Google I get

x=1.0371550444462
y=1.0145453349375

Here's where I get iffy on whether I'm doing math or hocus pocus.

x times (1 divided by y) equals the adjusted Moore's law rule.
x*(1/y) I first wrote it out as text because the forum is international and didn't want to confuse someone who otherwise might be helpful.

If it's not hocus pocus(in other words, simply wrong) then the new Moore's law rule increase per month is

1.02228555859

Which means a doubling about every 31.5 months, or 2 years 7.5 months.

So, unless, again, it's hocus pocus, any doublings that happen in less than approximately 3 years are on track.

*winces as he posts*

[QUOTE=jasong;492929]... DOUBLE-exponential growth ...[/QUOTE]Please explain what you mean by this term.

x=(y^2)^2?

x=2^(2^y)?

[QUOTE=retina;492930]Please explain what you mean by this term.

x=(y^2)^2?

x=2^(2^y)?[/QUOTE]

[url]https://en.m.wikipedia.org/wiki/Double_exponential_function[/url] but probably not.

Jason, I count 8 Moore's law threads that you have started over the years. Stop adding new ones.
Posts 12-15 in this thread were moved here from a new thread.

[QUOTE=jasong;492929]People say Moore's law is dead, but I say the law is incomplete. I believe Moore's law, as it stands, is incomplete.

We've been under the impression that Moore's law is based on exponential growth and doubles every 19 months or so. Not quite. I believe Moore's law, the 19 month version, is based on DOUBLE-exponential growth, and now we're down to regular exponential growth.

So, where is that extra exponential growth, where did it go? I believe it went away when the fabrication plants started seeing predicted needs of over 13 billion dollars or so to build a fabrication plant. Basically, I'm saying that Moore's law is only true if you're willing to double the amount you spend on a fabrication plant every 4 years.(If I'm wrong about the 4 year doubling, I'm a bonehead and will have to start over)[/QUOTE]

The basic idea being that we should use one scaling law from before this change and a different one after it.

I'd be more comfortable with this if you had data on the amount of money spend on fabs. Then we could look for where the transition was and switch laws. Or better yet, we could have a law that takes fab spending into account such that if it doubled every 4 years we get the first law and if it stayed constant we'd get the second law and it would smoothly interpolate between the two if it grew in intermediate rates.

You seem to be very interested in Moore's law. Are you interested enough to gather the relevant information?

[QUOTE=jasong;492929]Anyway, and here is the part where I may be a damn fool, but if I am, please feel free to correct my math, because I think my basic idea is sound.

Anyway, here are my equations. Very simple equations, especially for this forum, but still at the limits of my ability.

x^19=2 (x is the approximate growth per month of the "awesomeness" of a computer chip, and yes, it's just an average)[/QUOTE]

There are two big problems here. First, you really need to decide what you mean by awesomeness. Moore used transistor count, but does that really capture what you are interested in? Second, you have only one variable, but you need two: one for the awesomeness, whatever you decide that it is, and another for the time. The awesomeness should be a function of the time. If you take my suggestion above, you'll need three: the awesomeness would be a function of the time and capital investment.

The remainder of the calculations are meaningless as they rely on your one-variable equation.

[QUOTE=CRGreathouse;493295]The basic idea being that we should use one scaling law from before this change and a different one after it.

I'd be more comfortable with this if you had data on the amount of money spend on fabs. Then we could look for where the transition was and switch laws. Or better yet, we could have a law that takes fab spending into account such that if it doubled every 4 years we get the first law and if it stayed constant we'd get the second law and it would smoothly interpolate between the two if it grew in intermediate rates.

You seem to be very interested in Moore's law. Are you interested enough to gather the relevant information?[/quote]
I'll try Googling it, any recommendations on the terms?

The 4x estimate is based on what I've read, maybe I mis-remembered.

Edit: Oh, about the awesomeness part, I meant the ability to do more calculations. I know that technically, Moore's Law has to do with transistors, but performance is what people actually want. I don't know, honestly, if Moore's law holds up if you change it to being twice the performance every two years for the same cost.


[quote]There are two big problems here. First, you really need to decide what you mean by awesomeness. Moore used transistor count, but does that really capture what you are interested in? Second, you have only one variable, but you need two: one for the awesomeness, whatever you decide that it is, and another for the time. The awesomeness should be a function of the time. If you take my suggestion above, you'll need three: the awesomeness would be a function of the time and capital investment.

The remainder of the calculations are meaningless as they rely on your one-variable equation.[/QUOTE]
I've reached the limits of my abilities with the stuff I've already done, not sure I'm capable of doing what you say. But I'll try and get the info you want.

[QUOTE=jasong;493409]I'll try Googling it, any recommendations on the terms?[/QUOTE]

semiconductor fabrication (fab)
Intel
GlobalFoundries
TSMC (Taiwan Semiconductor Manufacturing Company)
UMC (United Microelectronics Corporation)
Samsung

[QUOTE=jasong;493409]Oh, about the awesomeness part, I meant the ability to do more calculations.[/QUOTE]

Right -- but how do you quantify that? Number of cores times clock speed? GFLOPS (measured how)? A benchmark like Linpack, Dhrystone, or Whetstone?

[QUOTE=jasong;493409]I don't know, honestly, if Moore's law holds up if you change it to being twice the performance every two years for the same cost.[/QUOTE]

And this is what you get to find out! But it won't be Moore's -- you'll be measuring something other than transistors and benchmarking more than just time, so definitely it's its own thing. :cool: