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.

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