Analysis of the Temperature Stability of Overdamped ${\hbox{Nb}}/{\hbox{Al-}}{\hbox{AlO}}_{x}/{\hbox{Nb}}$ Josephson Junctions

The temperature stability is one of the most important factors determining the successful application of the Josephson effect to the ac voltage standard or to analog and digital electronics. Whereas SIS hysteretic junctions with an Ambegaokar-Baratoff (A&B) I
_C
(T) behavior exhibit a reduced drift around the working temperature of the liquid helium, metallic-barrier SNS junctions follow a Kulik-Omelianchuck (K&O) behavior with a sharp temperature dependence of Ic in this region. The objective of our research is to study this aspect for overdamped Nb/Al-AlO
_x
/Nb heterostructures with current densities of 10-75 kA/cm
²
and characteristic voltages from 100 to more than 500 muV, that have been fabricated at INRiM. The I
_C
(T) characteristics, measured for Josephson heterostructures with different thickness, s, and exposure, E, essentially deviate from A&B and K&O curves, because of proximity effect caused by the comparatively high value of s (up to 100 nm). We study theoretically two extreme limits: the clean and the dirty limit for the interlayer between the superconducting electrodes and discuss the temperature stability of the junctions characterizing it with the temperature derivative dI
_C
/dT. The combined experimental and theoretical analysis of the problem provides a way for understanding, controlling and improving the design of the Nb/Al-AlO
_x
/Nb junctions in order to enhance their reliability.