Geometric and Material Dispersion in Josephson Transmission Lines

Experimental evidence is provided for the presence of two sources of dispersion in Josephson-junction transmission line (JTL's), fabricated using modern trilayer techniques. One source of dispersion is geometric in origin and arises from the counterelectrode overhanging the base electrode beyond the tunneling barrier region. The other dispersive factor is due to the frequency dependence of the magnetic penetration depth, as predicted by the Mattis-Bardeen theory. When both sources of dispersion are taken into account, very good agreement exists between experiment and theory. The presence of strong dispersion in JTL's demonstrates that careful analysis must be exercised to extract information such as junction specific capacitance. The present experimental and theoretical results yield a specific capacitance of 62 +/- 10 fF/mu m(2) for Nb/AlOx-Al/Nb junctions, with the majority of the uncertainty coming from uncertainty in the static penetration depth.