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.
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.