Specific Capacitance Dependence on the Specific Resistance in Nb/Al-AlOx/Nb Tunnel Junctions

Journal article, 2017

The junction specific capacitance (Cs) is an essential parameter in designing tuning circuitry for Superconductor-Insulator-Superconductor (SIS) mixers. However, our knowledge of the junction capacitance only relies on the few available empirically obtained Cs vs. specific normal resistance (RnA) relations, which are inconsistent especially at low RnA values, RnA < 40 Ω.μm2. In this paper, we report the Nb/Al-AlOx/Nb SIS junction capacitance data from our recently presented direct microwave (4 GHz) measurements at 4K for junctions with various RnA values ranging from 8.8 to 68 Ω.μm2. New insight is provided into the extraction of the true geometrical specific capacitance of SIS junctions. We show that, even at such low microwave frequencies, the so-far-neglected nonlinear susceptance is significant, especially for junctions with low RnA values. This susceptance originates from the real part of the response function, IKK, which can be calculated through the Kramers-Kronig transform of the DC tunnel current. The new specific capacitance, which accounts for this contribution is presented as a function of RnA. We provide an improved and more accurate Cs (RnA) relation, which can be a reliable and useful tool for circuit designers. The obtained Cs (RnA) relation is compared with those available in the literature, and the possible reasons giving rise to the disparity among these relations are discussed. By comparing the modelled and the measured noise temperature of the APEX SHeFI band 3 (385–500 GHz) DSB mixer, we show that the new Cs (RnA) relation offers a great potential for improving the performance of SIS mixers.