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Journal of Applied Physics

rf current dependence of the 8.9-GHz impedance of tantalum point-contact Josephson junctions

David E. Claridge

Published Apr 1, 1977• 0 citations
Publisher

Abstract

The complex rf impedance of tantalum point-contact Josephson junctions at 8.9 GHz has been measured as a function of the dc bias current for several values of rf current amplitude. The experimental results agree qualitatively with the predictions of the resistively-shunted-junction model, but discrepancies between the experimental results and the theory suggest that this model does not adequately predict all of the impedance properties of these junctions.

DOI
10.1063/1.323827

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The complex rf impedance of tantalum point-contact Josephson junctions at 8.9 GHz has been measured as a function of the dc bias current for several values of rf current amplitude. The experimental results agree qualitatively with the predictions of the resistively-shunted-junction model, but discrepancies between the experimental results and the theory suggest that this model does not adequately predict all of the impedance properties of these junctions.
For a current-driven Josephson junction shunted by an Ohmic resistance, the dc voltage response and impedance to external high-frequency currents is calculated with a second-order perturbation method based on the unperturbed solution for the time evolution of the voltage as given by Aslamazov and Larkin. The response is proportional to signal power and has three characteristic-frequency regions depending on whether the internal self-generated Josephson frequency, ω0, is larger than, equal to, or smaller than the signal frequency, ω. For ω0< or >ω the response could be expressed by easily observable parameters of the dc voltage-current characteristics. This permits comparison of the predictions with experimental results obtained on point-contact junctions whose dc characteristics were only approximately represented by the simple model chosen for analysis. For ω0≪ω the response is found to be proportional to (i) the slope of the dc characteristic, (ii) the inverse square of the applied frequency, (iii) the inverse battery current in terms of the critical current, and (iv) the voltage amplitude of the inherent Josephson oscillations. For ω0≫ω ``classical'' detection proportional to curvature is obtained. For ω0∼ω resonance detection occurs, which depends to a considerable degree on fluctuations of the average contact voltage. These predictions are in reasonable agreement with experiments in which point-contact junctions were illuminated with klystron radiation at 10 and 90 GHz. Evidence is presented that the voltage fluctuations limiting the resonance response are the result of noise generated in the junction. Comparison of the noise-equivalent power expected from the simple model with measured results suggests that parasitic elements, such as shunt capacity, are not negligible at 90 GHz.
The properties of point-contact Josephson junctions operated as mixers with an external local oscillator at 130 GHz have been studied, and the results compared with predictions of the resistively shunted junction model. It was found that the junction’s output noise could be within a factor of 1.5 of the model prediction based on the thermal-driving noise. When the coupling to the rf source was optimized, a factor of 2 discrepancy was typical. The measured conversion efficiency agreed with the model, within the experimental uncertainty in the equivalent microwave circuit. The best coupling was achieved in full-height waveguide. The best overall performance, measured using the hot/cold source technique, was a single sideband conversion efficiency of 0.30 and a mixer-noise temperature of 180 K (both ±20%). The best junctions were made of Nb, with carefully prepared points. Nonideal behavior in other junctions is ascribed to heating effects. There is some evidence that junctions whose resistance exceeds a threshold value of ∼60 Ω are no longer well described by the RSJ model. A discussion is given of possible improvements in performance with better junctions or improved rf matching.
Point contact Josephson junctions operated as microwave mixers at 36 GHz show conversion gain and lower noise than cooled Schottky barrier diodes in the same application. The noise in such junctions with and without rf bias is explored both experimentally and theoretically. The noise power is found to be about a factor 2 above the thermal noise in the resistively shunted junction model. In contrast to previous reports, the inclusion of a shot noise term in the theory for no rf bias overestimates the observed noise substantially.
Point contact Josephson junctions operated as microwave mixers at 36 GHz show conversion gain and lower noise than cooled Schottky barrier diodes in the same application. The noise in such junctions with and without rf bias is explored both experimentally and theoretically. The noise power is found to be about a factor 2 above the thermal noise in the resistively shunted junction model. In contrast to previous reports, the inclusion of a shot noise term in the theory for no rf bias overestimates the observed noise substantially. (Author)
We describe measurements of the 10 GHz dynamic impedance of niobium point-contact weak links at 2 K, biased below their critical currents. The measured quantity is Γ(ω), the complex reflection coefficient Of the weak link in parallel with a superconducting cavity resonator terminating a waveguide. Measurements were made at several frequencies close to resonance. In order to interpret the results it is only necessary to assume that the weak link is a two-terminal device consisting of a phase-dependent susceptance in parallel with a phase-dependent conductivity, which is connected to the waveguide through a lossless, phase-independent two-port. The data are consistent with the resistively shunted junction model including a phase-dependent conductance with a negative sign. An important feature of this study was the ability to measure the d.c. IV characteristic simultaneously. The point-contacts investigated had nearly ideal IcR products, and exhibited reproducibile structure in the differential conductance at the superconducting energy gap voltage.
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.