Theoretical Maximum Transistor Switching Speed (based on distances)

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One aspect to this that I can think of is the free electron concentration.

As well, I suspect the laws governing 'nanotransistor' switching will be di fferent from the larger ones.

Quantum effects may dominate at small distances you describe.

After my postings I also googled for maximum cpu hertz to see what it would show up which lead to:

Besides from a few typos here and there I already found one flaw with the reasoning from transistor speed to hertz:

In short: transistor speed does not translate into cpu hertz directly because:

Thanks to the text on this website, which I glanced over and immediatly understood the problem:

I won't quote it here but it basically describes that the size of the CPU matters as well.

The reason is a concept called: "cycles".

A cpu is a complex beast and it needs to do all kinds of things before the cycle is complete... before it calculated one cycle so to speak.

This means the signals have to go across the chip... across many transistors and so forth until finally it's all done and one cycle is complete.

Ofcourse I would assume to make a cpu go as fast as possible it would be a simple as possible chip... to keep these cross over signals as short and as minimal as possible.

However I think it's pretty easy to see that this would slow down the maximum speed by a few factors of 10 or more.

So maybe 1000 times slower. Which more or less matches todays transistor speed at 10 GHz ? (Not researched by it could make sense).

This could mean the actual cpu maximum speed is somewhere between 100 terrahertz to a few petahertz or so.

Bye, Skybuck.

Below I will correct a few typos at *

Hello,

For a while now I've been wondering what the maximum transistor switching speed would be.

Today I tried a google but no* clear answer came up, so I will try to come up/calculate an answer myself.

I share it with you for feedback/verifieing/finding any mistakes I made.

For now I will ignore heat problems and other kinds of problems for example someday somebody might want to build a system that can withstand 1 billion degrees of heat or whatever.

So for such a situation it would be interesting to see what the maximum transistor speed would/could be to give some sense of how far away we are with current/today's technology.

I will make some assumptions:

1. It will be possible to build transistors out of a few atoms. (I suspect it may even be possible to build transistor within an atom, but for now that's too much sci-fi ;))

1. The switching speed for a transistor is solely based on the speed of electrons going back and forth.

So under these simple assumptions the formula* to use to determine maximum transistor (switch) speed seems to be easy:

1. Assume the transistor is 3 atoms thick.

1. Divide this distance by the speed of electricity.

2. Divide this number by 2, to mimic back and forth communication, this last step maybe not required... but seems more realistic for an up and down signal or so. A state change/a switch. (Perhaps this should even be 3... but for now I ll assume 2).

So seems simple enough:

(Minimum Transister Size / Maximum Electron Speed) / 2 = Minimum Transistor Switch Speed.

So time to plug in some numbers, now it gets interesting... would transistor speeds depend solely on distances and electron speeds or is there some hidden third secret limitation/component... for now let's assume not:

According to wikipedia the maximum size of an atom is: 300 picometers

I read that as: (10 to the power of -12) meters.

(Window's environment path so full calculator cannot be started, but I start it via finding it myself. When I enter this into calculator it gives -2 ? LOL wtf ?!) (Or I could try 1 / (10^12) = 0.000000000001

I'll use that for now... may have to re-calculate in Delphi or so to see if it matches... perhaps wikipedia uses wrong notation ? Or perhaps calculator in windows is too limited oh well.

Anyway... on to the maximum speed of an electron.

I googled a bit and so far current theory seems to suggest maximum speed of electricity/electrons is near the speed of light. 90% or so

Speed of light is 299,792,458 metres per second.

So now all we have to do is calculate how many times we can go back and forth, back and forth across our transistor distance and divide that by 2.

((0.000000000001 * 300) / 299792458) = 1.0006922855944561487267301434248e-18

Dividing this by 2 gives:

5.0034614279722807436336507171238e-19

Apperently this is some very smalllllll number. This is exactly how fast a transistor can switch back and forth.

Now the question is how often can it do this per second assuming there is no hidden limitation (perhaps such a hidden limitation could be loss of energy):

To calculate this we would need to divide 1 second by this transistor switching speed to get hertz, mega herts, gigahertz that kind of thing that people are used to:

1 / 5.0034614279722807436336507171238e-19 = 1998616386666666666.6666666666667

So let's divide this by mega and then giga and so forth:

For example 1 megaherts is 1 million hertz. So I will use that, I will also round it down:

1998616386666666666 hertz

1998616386666666 kilohertz

1998616386666 megahertz

1998616386 gigahertz

1998616 terrahertz

1998 petahertz

2 exahertz.

Well surprise surprise... the trees do not grow endlessly forever. Unless some true science-fiction happens.

We are already halfway the maximum speed of computer technology.

This confirms my hunch that I will live to see the day that it all ends. Probably right before my death if I grow old enough ;)

I was born when the PC revolution started, and I will probably die when it ends... though perhaps it will never end... it will just stall.

This little calculation makes me a little bit sad... because 2 exahertz* is not that much... it's still within the 64 bit range.

However it does indicate that our current 4 gigahertz technology is still far off from what is yet to come.

At least the constants that describe our universe* allow for faster speeds. So there should be some way to achieve that eventually.

Be it by super cooling or other techniques. Super heat resistance materials or both.

Bye, Skybuck.

Hi Skybuck,

Currently the minimum feature size of an ordinary MOSFET is limited by leakage currents caused by quantum tunneling between the terminals; I think the smallest practical drain to source length is thought to be about 1 nanometer.

I don't know how you'd build a 3 atom transistor. I don't think it would work like a MOSFET or BJT, at least.

I just looked and it seems a single atom "transistor" has been built; it seems to function more like a relay.

Don't encourage it.

One cannot have a TRANSISTOR less than (about) 100 atoms thick per junction if bipolar or per doped domain to be more general. Doping becomes absurd in that ASS-u-ME-ed region; one atom per 10,000 seems to be a low-end doping level which would limit thickness to the region of 10,000 atoms (adjust for reality). For the sake of discussion, call it 30,000 and one has a "calculated" speed ten thousand times SLOWER than your brain fart.

I never wrote 3 atoms.

I wrote 3 atoms-thick.

I can imagine: One atom for zero. One atom for one. And one atom size in between for spacing.

This is a conservative estimation.

Like you found out... smaller transistor may have been built already and may be usuable in the future :)

Bye, Skybuck.

Interesting, I didn't know you could measure that or a metric existed for it ?

Jamie

How about FETs based on graphene monolayers?

It's nowhere near "single atom" storage, but I gather that people have been demonstrating FETs using single-layer or double-layer graphene channels.

One article I read indicated that potassium doping of such thin layers was able to affect the bandgap.

There's some interest out there in other monolayers - e.g. molybdenum sulphide - which may be superior to graphene.

(tunable band-gap MoS)

"At the upcoming International Electron Devices Meeting (IEDM), an MIT-led team will describe the use of CVD processing to grow uniform, flexible, single-molecular layers of MoS, comprising a layer of Mo atoms sandwiched between two layers of S atoms. They exploited the material's 1.8 eV bandgap to build MoS transistors and simple digital and analog circuits (a NAND logic gate and a 1-bit ADC converter). The transistors demonstrated record MoS mobility (>190 cm^2/Vs), an ultra-high on/off current ratio of 108, record current density (~20 uA/um) and saturation, and the first GHz RF performance from MoS. The results show MoS may be suitable for mixed-signal applications and for those which require high performance and mechanical flexibility."

:-)

[ .. ]

Nice. That's one way to view it. But...

this does not follow. This assumes that you will use a fix number of transitors over the entire course of human history and that the cost for the fix number is fixed. This is not true. First, the number of transitors you get to use has been increasing and even more importantly, in terms of an inflation adjusted dollar per transistor, the price has been falling. The history of technology is we are asymptotically approaching zero, see google("graph of 1/x"), then explain how zero makes you sad, as a price for a computer. Compare price per performance of ENIAC, a PDP-7, z-80 system and new cheap but powerful Android phone. You will see what I mean. Now find the limits of technological advancement that would cause us to deviate from our march to zero. Good luck, I would likely bet against you if you find any limit.

Curve fit, then tell us how much processing power we will have for $500 in 20 years. Then come back in 20, and see how accurate that prediction was.

Anyway, as a sanity check:

'In the past, people have said, maybe it's 50 years away, it's a dream, maybe it'll happen sometime, said Mark B. Ketchen, manager of the physics of information group at IBM's Thomas J. Watson Research Center in Yorktown Heights, N.Y. 'I used to think it was 50. Now I'm thinking like it's 15 or a little more. It's within reach. It's within our lifetime. It's going to happen.' (IBM, March 2012)

[ disclaimer, that's my office building ]

So, that end (see paper for what that sentence refers to) is 2027 for compairson to the end you calculated. They do have a 2060 date or so to hit a single atom on the minimum feature size graph. So, lots of ends in sight, if all you want to do is focus on the end.

isn't normallized for price, but if it were, I think the general trend would be about the same. That one has no end on it, and it is the only one that matters.

You are discussing economy.

In economy there are two driving forces.

Supply and Demand.

You have only looked at supply.

However if there is no demand, no ammount of supply will be "sold".

Even at price zero. Which will probably be somewhat unlikely.

So it will be close to zero. Still not good enough.

If people have to earn 0.00001 dollar to pay for it, they still wouldn't want it if they have no need for it :)

The demand is from people wanting faster computers.

When computers stop becoming faster this demand will fall away.

That's basically my prediction.

However I also predicted there will still be some demand because of repairs for broken computers and replacements and such.

But demand will definetly start to fall once computers do not become faster anymore.

However nobody can predict the future, perhaps there will be other reasons why demand will rise.

However computers is a bit a broad term.... I will narrow it to "PCs". Personal Computers that sit on the desk top as we know it... big/large chunky.

(Perhaps even laptaps and tablets can be counted towards it).

I am not sure what would happen if PCs + Laptops + Tablets + Phones would be put into a graph.

Perhaps then demand for computers is still up... just PCs only are down.

For now that could mean a shift... perhaps a temporarely shift towards mobile computers.

However in the end those will probably collapse somewhat as well... however mobile computers break faster which is kinda ironic :)

Bye, Skybuck :)