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Journal of Applied Physics

Origin of ’’capacitance’’ in superconducting microbridges

Y. Song

Published Jun 1, 1976• 37 citations
Publisher

Abstract

The geometrical interelectrode capacitances of superconducting microbridges are too small to account for the observed hysteresis in their I-V characteristics. We propose a new model of microbridges in finite voltages, in which the relevant time constant is the supercurrent relaxation time τR. From an analysis of the experimental I-V curves it follows that τR can be identified with the pair relaxation time within a numerical factor. By equating τR/2π to the time constant C/G of the shunted Josephson junction model, we obtain values of C in reasonable agreement with those typically obtained from I-V characteristics.

DOI
10.1063/1.322985

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IEEE Transactions on Magnetics•Mar 1, 1991•3 citations
The geometrical interelectrode capacitances of superconducting microbridges are too small to account for the observed hysteresis in their I-V characteristics. We propose a new model of microbridges in finite voltages, in which the relevant time constant is the supercurrent relaxation time τR. From an analysis of the experimental I-V curves it follows that τR can be identified with the pair relaxation time within a numerical factor. By equating τR/2π to the time constant C/G of the shunted Josephson junction model, we obtain values of C in reasonable agreement with those typically obtained from I-V characteristics.
Some types of Josephson junctions such as long microbridges, S-N-S junctions, and junctions with a series palastic inductance are known to have nonsinusoidal current-phase relations which can be approximated by linear-periodic functions. In this paper the equivalent circuit equation of the resistively shunted junction model with linear-periodic current-phase relation is solved. The heights of zeroth and first constant-voltage steps in the I-V characteristics and the impedance at these steps are obtained analytically. This analysis shows that the impedance at the first step lies on a semicircle in the impedance plane with its center at the impedance of the zeroth step. The calculated impedance is compared with the experimental results by Claridge et al. The theory presented here can explain some features of experimental results which differ considerably from predictions based on a sinusoidal current-phase relation. Among these are the value of bias current corresponding to the center of the first step, and the appearance of ’’shoulders’’ in the imaginary part of the impedance at the first step.
We have studied the current-voltage characteristics of small area tunnel junctions at temperatures below 1 K. The junctions were made in an edge geometry with a Nb base electrode and had areas less than .05 μm2and critical currents in the nA range. Although the measured I-V characteristics resemble those of ordinary hysteretic junctions, the supposed zero-voltage portion of the curve proved to have a finite slope and to deviate from zero voltage. For these junctions it is apparently possible for occasional 2π phase slips to occur without switching to the usual voltage state. This behavior can be explained either by macroscopic quantum tunneling or by a model in which the effective shunt conductance of the junction is frequency dependent.
We have performed a transient analysis of a Josephson interferometer in which feedback has been introduced to sharpen the transfer function. We examine the case for junctions with small, but finite, capacitance, so that the junction I-V characteristics have a small hysteresis. We find that no significant changes in switching times occur when feedback is introduced. The transfer function for the interferometer calculated in our ac analysis, which includes finite junction capacitance, is somewhat different from the one determined by a simple dc analysis that assumed zero capacitance.
The technique of ’’shadow evaporation’’ has been used to fabricate superconducting-normal-superconducting Josephson microbridges and SQUID’s with bridge widths of about 0.2 μm and lengths of 0.1 μm or less. The devices consist of vanadium banks and gold bridges and have static current-voltage characteristics that are consistent with the resistively shunted junction model down to at least 0.4 TC. Refined versions of this technique may be useful for batch fabrication of single and multibridge Josephson devices.
An experimental study of small superconducting microbridges in order to examine parameter conditions (i.e., junction resistance and junction inductance) necessary for these junctions to exhibit the Josephson effect is described. Nb variable thickness junctions with very narrow width (<50 nm) and short length (<100 nm) were fabricated using electron beam lithography. The junctions which showed the Josephson effect were thinned by ion beam etching, and consequent changes of junction characteristics were measured. The experimental results indicate that the Josephson effect disappears at some critical resistance. These parameter limits of the Josephson junction are compared with theory.