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

The junction specific capacitance (C
_s
) 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 C
_s
versus specific normal resistance (R
_n
A) relations, which are inconsistent especially at low R
_n
A values, R
_n
A <; 40 Ω·μm
²
. In this paper, we report the Nb/Al-AlO
_x
/Nb SIS junction capacitance data from our recently presented direct microwave (4 GHz) measurements at 4 K for junctions with various R
_n
A values ranging from 8.8 to 68 Ω·μm
²
. 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 R
_n
A values. This susceptance originates from the real part of the response function, I
_KK
, 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 R
_n
A. We provide an improved and more accurate C
_s
(R
_n
A) relation, which can be a reliable and useful tool for circuit designers. The obtained C
_s
(R
_n
A) 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 modeled and the measured noise temperature of the APEX SHeFI band 3\(385-500 GHz) double sideband mixer, we show that the new C
_s
(R
_n
A) relation offers a great potential for improving the performance of SIS mixers.