# How far do electrons physically move in a single clock cycle in a (theoretical) 4GHz processor?

I was musing last night about computers and processors and this video of a 6-bit digital adding machine, and I know that 4 GHz seems to be the practical limit of mass-produced CPUs of the current era. Why is that the case? I was trying to imagine something like that 6-bit adding machine * 11 (ok, 10.6666...), lined up side by side, and operating 4 billion times in a second. It's mind-bending to me. XKCD has another take on it.

So, for all of you with much more background in physics than I, I guess there are a few questions rolled into one: Why does 4GHz seem to be the practical limit for processors? Is it that silicon can't switch faster than that (and would another element help)? How far do electrons go in 1/4,000,000,000 of a second, and how long are the electrical paths on, say, a Core 2 Duo processor, and a motherboard? Is 4 GHz the limit because electrons can't get from the processor, say, in and out of memory fast enough while traveling at the speed of light?

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Each electron hardly moves at all in 0.25 ns, even with the tens of amps that flow in such processors.

"For example, in a copper wire of cross-section 0.5 mm2, carrying a current of 5 A, the drift velocity of the electrons is of the order of a millimetre per second."Wikipedia

Fortunately, we don't need the electrons to move very far to carry a wave that moves long distances very fast.

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Interesting. Looking at the article you referenced, they draw the analogy of what we think of as 'electricity' as similar to sound through a gas...a wave that transmits energy rather than an actual blast of air. I had always pictured electrical impulses as these huge torrents of electrons cascading along at near-light-speed, but it's a little more abstract than that. Thanks for clarifying that for me. – atroon Jan 9 '10 at 22:23

It's not the speed of the electrons that matters, that's really slow, but the group propagation velocity of the electric fields that push them around, which is around 1/3 of the speed of light. Given that 2.4GHz has a wavelength of 12 cm roughly, the problem with 4 GHz chips is that the size of the chip die is pretty big compared to the wavelength of the clock, and so it starts to get way too hard to deal with the clock skew.

Also, the power consumption of a CPU increases really fast as the clock speed goes up, and at some point the thing overheats.

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And the group velocity depends on the insulator around the wire, rather than any property of the wire itself, since that's where the field is. – Martin Jan 7 '10 at 16:08
Interesting. Did you mean the chip is pretty small compared to the wavelength of the clock, or am I understanding it wrong? Also, could asynchronous CPUs help with this problem at all? – zildjohn01 Aug 30 '10 at 10:36