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Calculation of rf-induced current–voltage characteristics of a measured Josephson tunnel junction

H.-D. Hahlbohm, Axel Hoffmann, H. Lübbig, Holger M. Luther, S. Seeck

Published Oct 16, 1972• 4 citations
Publisher

Abstract

The rf-induced current–voltage characteristics of a small Josephson tunnel junction have been calculated for various values of rf power. The contact parameters (i.e. the capacity, the maximum of the zero-voltage pair-tunnelling current, and the nonlinear quasiparticle characteristic) are correlated to measured values of a Sn–SnO–Sn junction near the transition temperature.

DOI
10.1002/pssa.2210130232

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IEEE Transactions on Magnetics•Mar 1, 1975•4 citations
The rf-induced current–voltage characteristics of a small Josephson tunnel junction have been calculated for various values of rf power. The contact parameters (i.e. the capacity, the maximum of the zero-voltage pair-tunnelling current, and the nonlinear quasiparticle characteristic) are correlated to measured values of a Sn–SnO–Sn junction near the transition temperature.
The microwave response of the dc quasiparticle tunneling current in Josephson tunnel junctions, where the Josephson current is suppressed by an external magnetic field, has been studied quantitatively in order to clarify its characteristics as a probe for the measurement of the junction capacitance. Extensive experiments for both small and long junctions are carried out for distinguishing between microwave behaviors of lumped and distributed constant junctions. It is shown that the observed voltage dependence of the dc quasiparticle tunneling current modified by an applied rf field is in good agreement with a theoretical result which takes into account the influence of the microwave circuit connected to the junction. The comparison between theory and experiment gives the magnitude of the internal rf field in the junction. Together with the applied rf field, this internal rf field leads to the junction rf impedance which is dominated by the junction capacitance in our experimental condition. In the case of lumped junctions, this experimental rf impedance is in reasonable agreement with the theoretical one with the junction capacitance estimated from the Fiske step of the distributed junction fabricated on the same substrate; the obtained ratio of the experimental impedance to the theoretical one is approximately 0.6–1.7. In the case of distributed junctions, however, experimental values of their characteristic impedances are approximately 0.2–0.3 of theoretical values calculated by assuming the one-dimensional junction model and taking account of the standing-wave effect in the junction.
Unexpected partly dramatic temperature dependences were registered for the basic tunnel parameters used to characterize a Josephson junction. Measurements of the magnetic field variation of the microwave-power reflection, i.e., a mapping of the Josephson plasma resonance, enabled determinations of the rf small-voltage resistance RJ, the cosφ amplitude ζ, and the effective junction capacitance C in both Pb-O-Pb and PbTl-O-Pb junctions. The uncertainties in the parameter values are large, particularly in the low temperature values of ζ, for which we confirm earlier estimates of ζ, but as the superconducting transition temperature Tc is approached, ζ increases rapidly and goes through a positive maximum close to +1 before it decreases towards zero at Tc. Also, RJ displays a pronounced maximum in the same temperature interval; it decreases rapidly within a narrow range below the temperature of the maximum before it again increases slowly well below Tc. The location in temperature for the two maxima depends upon the barrier via the critical current density, but seems to be material independent. Well below Tc, the ratios of RJ to the normal-state tunnel resistance are also affected by the barrier transmission. These latter properties seem hard to explain within a model based only on the relaxation of the order parameters in the superconductors. A considerable decrease in C close to Tc can be explained by temperature-dependent surface losses in the junction electrodes. The Q-value associated with these could be determined as a function of temperature. In accordance with previous measurements, the Josephson current IJ is reduced at low temperature in small high-resistance tunnel junctions. Smaller deviations in IJ from theoretical estimates can be explained by strong coupling effects.
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.
It has been found that point-contact Josephson junctions can be clearly classified into bridge-type and tunnel-type by introducing new parameters characterizing their I-V curves. Nearly-ideal tunnel-type junctions with Nb–SuO x –Sn (Film) point-contacts were obtained. Tunnel-type junctions showed larger gap energies than bridge-type junctions in Nb–SnO x –Sn and Nb–NbO x –NbN point-contacts. The submillimeter-wave responses were measured in Nb–Nb point-contacts, and it was found that the contacts with the best performance were bridge-type junctions with a sharp gap structure; tunnel-type junctions showed rather bad performance. On irradiation with laser light, the center of the Shapiro step moved to the lower-current side in bridge-type junctions but to the higher-current side in tunnel-type junctions. These differences can be explained by differences in the heating effects between bridge-type and tunnel-type junctions.
Low βc tunnel junctions have current-voltage characteristics which deviate from the intrinsic quasiparticle characteristic because of the ac Josephson effect. This effect has previously been analyzed for the special case of a pointlike junction in zero applied field. We demonstrate that deviations still occur when the critical current is suppressed by an applied field to a small fraction of its zero field value. The effects are significant for junctions whose length l is comparable to the Josephson penetration length λJ. These are often the junctions of practical interest. We present a simple model to explain the physical origin of these deviations, and also present detailed computer simulations using up to nine segments to model the distributed junction. For l = λJ, and an applied magnetic field which corresponds to the first minimum of the junction threshold characteristic, we find time-averaged voltages which deviate from the quasiparticle characteristic by up to 5%. Their magnitude is proportional to (l/λJ)2 and inversely proportional to the square of the applied field. This dependence can be used experimentally to confirm the observation of the effect.