Probability density function for the critical current asymmetry of a HTS dc SQUID

A de SQUID consisting of grain boundary Josephson junctions may often be asymmetric owing to the large critical-current spread. In this work, the probability density function (PDF) for the critical-current asymmetry of high-transition-temperature-superconductor (HTS) dc SQUID was investigated. To model the critical-current spread in the grain boundaries, we assumed that the barrier thickness of the Josephson junction fluctuated according to a log-Weibull distribution. The resultant PDF for the critical-current spread that fits the histogram data of critical currents reported in literature was the gamma distribution. With the proposed distribution function, the corresponding PDF for the critical-current asymmetry parameter of a HTS dc SQUID was derived and compared with the experimental result. The proposed gamma distribution function is useful in modeling devices, such as the SQUID array and the superconducting quantum interference grating, consisting of many grain-boundary Josephson junctions.