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Journal of Applied Physics

Superconducting resonator circuits at frequencies above the gap frequency

Gert J. de Lange, J. J. Kuipers, T. M. Klapwijk, R. A. Panhuyzen, Herman van de Stadt, M. W. M. de Graauw

Published Feb 15, 1995• 24 citations
Publisher

Abstract

The frequency response of three superconductive niobium resonating circuits, formed by a Nb microstrip and a Nb tunnel junction, is measured and analyzed at frequencies above the superconducting gap frequency. The circuits are placed in a waveguide system and the frequency response is determined with a Fourier transform spectrometer. The calculated and measured resonance frequencies and bandwidths are in good agreement with the extreme anomalous limit of the Mattis–Bardeen theory on the anomalous skin effect in superconductors [D.C. Mattis and J. Bardeen, Phys. Rev. 111, 412 (1958)]. The observed loss is higher than predicted by this theory, in agreement with previous observations on Nb films. The use of other materials for striplines as tuning circuits for heterodyne superconducting tunnel junction mixers is analyzed.

DOI
10.1063/1.358876

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Three Nb/AlO/sub x//Nb SIS detectors, designed to operate in the 400-550, 550-700, and 600-750 GHz bands, have been studied in direct detection mode using a Fourier-transform spectrometer. All three detectors were of quasi-optical type and had on-chip-integrated-fixed tuned SIS junctions. The tuning ranges of the detectors were selected to cover the interesting region around the superconducting gap frequency of Nb (about 700 GHz). Measurements show detector responses at frequencies above the gap frequency, i.e., up to /spl ap/920 GHz, and that cooling the detectors to 3.1 K improved the direct detection responses about 15% below 700 GHz and about 50% for frequencies up to 800 GHz, compared to the responses at 4.2 K. The 500 GHz SIS detector was also studied in a 440-520 GHz heterodyne receiver set up. Good agreement between modeled tuning circuit characteristics, tuning range of the mixer and the direct detection response bandwidths were found. However, it is essential that the dispersion of the field penetration depth into the superconductor is included in the modeling of the tuning circuits when the detector is operated at frequencies above the superconducting gap.>

IEEE Transactions on Applied Superconductivity•Jan 1, 1995•8 citations
The frequency response of three superconductive niobium resonating circuits, formed by a Nb microstrip and a Nb tunnel junction, is measured and analyzed at frequencies above the superconducting gap frequency. The circuits are placed in a waveguide system and the frequency response is determined with a Fourier transform spectrometer. The calculated and measured resonance frequencies and bandwidths are in good agreement with the extreme anomalous limit of the Mattis–Bardeen theory on the anomalous skin effect in superconductors [D.C. Mattis and J. Bardeen, Phys. Rev. 111, 412 (1958)]. The observed loss is higher than predicted by this theory, in agreement with previous observations on Nb films. The use of other materials for striplines as tuning circuits for heterodyne superconducting tunnel junction mixers is analyzed.
The frequency dependence of the coupling of niobium superconducting transmission lines is measured for frequencies up to and above the superconducting gap frequency. For this purpose superconducting microstrips are integrated in log-periodic planar antennas and the spectral response is measured by means of a Fourier transform spectrometer with 1 μm2 Nb/Al2O3/Nb SIS junctions as detectors. Resonances of microstrips are observed up to 650 GHz, the superconducting gap frequency of niobium, but above that frequency no resonances have been detected. The measured resonance frequencies are in good agreement with a dispersive model for superconducting transmission lines based on the Mattis–Bardeen theory. The radiation coupling is lower than calculated, indicating significant dielectric losses.
The superconductor–insulator–superconductor (SIS) tunnel junction based on Nb material has been investigated theoretically at frequencies of 200–1400 GHz by modeling it as a segment of a superconducting microstrip transmission line and using the Mattis–Bardeen theory of anomalous skin effect. The modeling was used to predict the performance of a flux-flow oscillator (FFO) and a SIS frequency down-converter (mixer). It is shown that in a FFO the internal loss (quasiparticle and surface) limits flux flow to the frequency band of 260–770 GHz. A SIS junction of micron size employed as a mixer for frequency down-conversion demonstrates distributed behavior at frequencies above 550 GHz. We suggest that electrically long SIS junctions of resonant size can be used as self-compensating mixing elements with attractive performance in Nb as well as NbN mixers.
This thesis describes the development, modeling, and optimization of Nb superconducting microstrip tuning circuits for Superconductor-Insulator-Superconductor mixers. The ultimate goal is to extend the quantum limited noise performance of Nb/AlOx/Nb SIS mixers to above the Nb gap frequency (680 GHz). The mixers are intended to be used in the Atacama Large Millimeter Array (ALMA) band 9 frequency range (600-720 GHz). The behavior of Nb microstrip tuning circuits especially above the gap frequency is modeled using the complex conductivity given by the Mattis-Bardeen theory of the anomalous skin effect [72]. A computer code utilizing two-port network theory is utilized to predict and optimize the RF coupling efficiency and bandwidth of the tuning circuits and embedding impedances. The effect of material and geometrical variations on the coupling has been evaluated. The installment of the devices in the waveguide has been found to be a crucial factor explaining the observed scattering in measurement results for nominally identical devices. Despite parameter variations, modeling of the RF coupling efficiency proved to be successful within the limitations set by scattering of the measured results. Using this model, the tuning circuit geometry has been optimized for bandwidth and maximum coupling efficiency. During the work several SIS devices have been fabricated and Fourier transform spectroscopy measurements have been made for RF coupling evaluation. Finally, using simulations, it has been found that application of Nb/AlN/Nb junctions would increase the bandwidth to an extent which should dramatically decrease the sensitivity to parameter variations.
The bandwidth and noise temperature of superconducting-insulating-superconducting (SIS) mixers are strongly determined by the matching between antenna and tunnel-junction. Optimal scientific benefit from Band 9 (600 to 720 GHz) of the Atacama large millimeter array requires a proper design of the matching circuit by taking into account the energy gap of the niobium (680 GHz). In preliminary experiments we have found that tapered structures lead to significant improvements, which suggests that a systematic analysis of optimized geometrical shapes might be beneficial. The tuning circuits are analysed using a model, which includes the Mattis-Bardeen theory for the surface impedance of Nb and which allows arbitrary shapes. We will present simulations and experimental results focusing on the transmission efficiency, which can conveniently be evaluated experimentally by using a Fourier transform spectrometer. We will show how the shape influences the transmission efficiency and relate it to observed noise temperatures of the mixers.
A circuit that produces broadband impedance matching with low-current-density junctions at submillimeter wavelengths for tuning superconductor–insulator–superconductor (SIS) mixers is described; it consists of half-wavelength distributed SIS junctions connected alternately by half-wavelength microstrip lines. It is made of Nb and was designed for two practical source impedances using numerical calculation based on the Mattis–Bardeen theory of the anomalous skin effect at 660 GHz, assuming SIS junctions with a current density of 5 kA/cm 2 . An SIS mixer tuned using this circuit had a large fractional bandwidth of more than 18%, below -10 dB matching, even though the assumed ω C J R N product was about 16. Investigation of the mixer performance using Tucker's quantum theory of mixing showed that it has excellent broadband and low-noise characteristics compared with conventional mixers consisting of half- or full-wavelength distributed elements.
Three Nb/AlO/sub x//Nb SIS detectors, designed to operate in the 400-550, 550-700, and 600-750 GHz bands, have been studied in direct detection mode using a Fourier-transform spectrometer. All three detectors were of quasi-optical type and had on-chip-integrated-fixed tuned SIS junctions. The tuning ranges of the detectors were selected to cover the interesting region around the superconducting gap frequency of Nb (about 700 GHz). Measurements show detector responses at frequencies above the gap frequency, i.e., up to /spl ap/920 GHz, and that cooling the detectors to 3.1 K improved the direct detection responses about 15% below 700 GHz and about 50% for frequencies up to 800 GHz, compared to the responses at 4.2 K. The 500 GHz SIS detector was also studied in a 440-520 GHz heterodyne receiver set up. Good agreement between modeled tuning circuit characteristics, tuning range of the mixer and the direct detection response bandwidths were found. However, it is essential that the dispersion of the field penetration depth into the superconductor is included in the modeling of the tuning circuits when the detector is operated at frequencies above the superconducting gap.>