I think one reason your capacitor charging/discharging argument didn’t stop this number from coming out so small is that information can travel as pulses along the line that don’t have to charge and discharge the entire thing at once.
Sure information can travel that way in theory, but it doesn’t work out in practice for dissipative resistive (ie non superconducting) wires. Actual on chip interconnect wires are ‘RC wires’ which do charge/discharge the entire wire to send a bit. They are like a pipe which allows electrons to flow from some source to a destination device, where that receiving device (transistor) is a capacitor which must be charged to a bit energy Eb>>KBT. The Johnson thermal noise on a capacitor is just the same Landauer Boltzmann noise of En≈KBT. The wire geometry aspect ratio (width/length) determines the speed at which the destination capacitor can be charged up to the bit energy.
The only way for the RC wire to charge the distant receiver capacitor is by charging the entire wire, leading to the familiar RC wire capacitance energy, which is also very close to the landauer tile model energy using mean free path as the tile size (for the reasons i’ve articulated in various previous comments).
Yeah, to be clear I do agree that your model gives good empirical results for on-chip interconnect. (I haven’t checked the numbers myself, but I believe you that they match up well.) (Though I don’t necessarily buy that the 1nm number is related to atom spacing in copper or anything like that. It probably has more to do with the fact that scaling down a transmission line while keeping the geometry the same means that the capacitance per unit length is constant. The idea you mention in your other comment about it somehow falling out of the mean free path also seems somewhat plausible.)
Anyway, I don’t think my argument would apply to chip interconnect. At 1GHz, the wavelength is going to be about a foot, which is still wider than any interconnect on the microchip will be long. And we’re trying to send a single bit along the line using a DC voltage level, rather than some kind of fancy signal wave. So your argument about charging and discharging the entire line should still apply in this case. My comment would mostly apply to Steven Byrnes’s ethernet cable example, rather than microchip interconnect.
Sure information can travel that way in theory, but it doesn’t work out in practice for dissipative resistive (ie non superconducting) wires. Actual on chip interconnect wires are ‘RC wires’ which do charge/discharge the entire wire to send a bit. They are like a pipe which allows electrons to flow from some source to a destination device, where that receiving device (transistor) is a capacitor which must be charged to a bit energy Eb>>KBT. The Johnson thermal noise on a capacitor is just the same Landauer Boltzmann noise of En≈KBT. The wire geometry aspect ratio (width/length) determines the speed at which the destination capacitor can be charged up to the bit energy.
The only way for the RC wire to charge the distant receiver capacitor is by charging the entire wire, leading to the familiar RC wire capacitance energy, which is also very close to the landauer tile model energy using mean free path as the tile size (for the reasons i’ve articulated in various previous comments).
Yeah, to be clear I do agree that your model gives good empirical results for on-chip interconnect. (I haven’t checked the numbers myself, but I believe you that they match up well.) (Though I don’t necessarily buy that the 1nm number is related to atom spacing in copper or anything like that. It probably has more to do with the fact that scaling down a transmission line while keeping the geometry the same means that the capacitance per unit length is constant. The idea you mention in your other comment about it somehow falling out of the mean free path also seems somewhat plausible.)
Anyway, I don’t think my argument would apply to chip interconnect. At 1GHz, the wavelength is going to be about a foot, which is still wider than any interconnect on the microchip will be long. And we’re trying to send a single bit along the line using a DC voltage level, rather than some kind of fancy signal wave. So your argument about charging and discharging the entire line should still apply in this case. My comment would mostly apply to Steven Byrnes’s ethernet cable example, rather than microchip interconnect.