Modeling of Characteristics for Josephson Junctions Having Nonuniform Width or Josephson Current Density

Abstract

Several models, both static and dynamic, for calculating the maximum dc Josephson current versus external magnetic field "characteristic" of tunnel junctions of various geometries are described. The static models have the advantage of short computation times; the dynamic models, although slower, yield additional information on circuit-switching times. The dependence of the characteristics on the junction shape is described. The accuracy of a one-dimensional approximation used in the models has been tested experimentally, and theoretically against a two-dimensional approximation. In both cases, the one-dimensional treatment yields quantitatively good agreement provided the inductance of the junction is included in the model. Junctions defined by an oxide "window" of sinusoidal shape (maximum and minimum width at the center and ends, respectively) have a characteristic in which the side lobes are almost completely suppressed. The characteristics of a wide variety of junction shapes, including interferometers having two or more junctions, have been accurately calculated, permitting the design of devices for specific purposes. IntroductionThe dependence of the maximum dc Josephson current on magnetic field exhibits a simple Fraunhofer diffraction pattern when the junction width W is uniform and the length € is smaller than about twice the Josephson penetration length \j [1,2]. However, for larger values of //Xj, the self-field of the junction current has an increasing influence, and the resultant characteristic depends strongly on the geometry of the junction. Such cases cannot be solved in a simple analytical form and have been the subject of a number of theoretical [3-8] and experimental [4,5,7,9] investigations. With suitably chosen junction geometry the experimental results show good agreement with one-dimensional numerical calculations.

Proximity effects and nonequilibrium superconductivity in transition-edge sensors

“…Critical current versus magnetic field side lobe suppression has been desired for Josephson junction logic and memory applications 39,40 , mixers 41 , optics 42 , antennae design 43 , and superconducting tunnel junction particle detectors 46 . Quartic-shaped Josephson junctions have been produced showing suppression of the first side lobe maxima to as low as only a few percent of the zero-field central peak value.…”

High-resolution superconducting X-ray spectrometers with aluminum trapping layers of different thicknesses

“…The use of this shape was an attempt to reduce the magnetic field required to suppress the dc Josephson current [7]. This suppression is necessary to allow stable operation of the device when biased near zero voltage.…”

A superconducting analog track-and-hold circuit

“…2(a). At least 30 sections are required to properly model the shaped junction [ 5 ] . A simulated equivalent-time response to an arbitrary input signal I,,( t ) is generated from the following sequence: 1) Beginning with all currents and voltages equal to zero, IR is ramped up to IRo = 10 mA to set the circuit in the track …”

“…magnetic flux produced by the gate current Ig couples into J1 suppressing its critical current I,,,. A sine-shaped junction is used because its threshold curve has very low side lobes [5]. In the experimental data of Fig.…”

“…Thus, signal-current changes less than I, ( Zg ) will not be tracked by the circuit and the dynamic range is limited by the ratio I , (0) / I , ( I,). It has been found that a sine-shaped junction with a length of several times the Josephson penetration depth can achieve a critical current suppression ratio I,,, (0) /Im ( I , ) on the order of 50, for all values of Ig greater than about 10 mA [ 5 ] . The resulting dynamic range is 35 dB.…”