# Do Not Forget the Temperature Dependence of the Specific Resistivity!

The discovery of high temperature superconductors in 1986 immediately lead to proposals to use these materials for interconnects on chips instead of the Al that was common than (and for about 15 more years).
The reason was that the finite resistivity of Al together with parasitic capacitances (e.g. between two conducting lines on a chip) limits the maximum frequency to
fmax  =   1
R · C
With R = resistance of the longest connection line on the chip and C = parasitic capacitance "seen" by this line.
For R = 0 W as we have it for a superconductor, the maximum frequency is no longer limited by R · C, no matter how large the parasitic capacitances are. Instead, the limit comes from
fmax = (L · C)–1/2
with L = inductance of the line, and this is just another way of saying that the signal propagation is limited by the speed of light.
fmax  =   (L · C)–1/2
Given the resistivity of Al (at room temperature!), a sizeable advantage was seen for the integrated circuits then envisioned.
However, comparing the performance of a chip run with Al at room temperature to a chip run at liquid N2 temperature (77 K), is not the right comparison. After all, you can cool down the conventional chip, too - and that will decrease RAl by a factor of 6 - 8.
The comparison then is quite different. The graph shows the minimum switching time t = 1/fmax as a function of the length of a standard interconnect line about 1 µm2 cross section.
Whereas superconductors would already make an interesting difference for lengths of a few mm (typical line length) in the wrong comparison, the correct comparison only shows an advantage for about 1 cm and larger - line lengths easily avoided by clever design.

2.1.1 Conductors

© H. Föll (Electronic Materials - Script)