Abstract
Superconducting integrated circuits should be operated at low temperature below a half of their critical temperatures. Thermal heat from a bias resistor could rise the temperature in Josephson junctions, and would reduce their critical currents. In this study, we estimate the temperature in a Josephson junction heated by a bias resistor at the bath temperature of 4.2K, and introduce a parameter β that connects the thermal heat from a bias resistor and the temperature elevation of a Josephson junction. By using β, the temperature in the Josephson junction can be estimated as functions of the current through the resistor.
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