Heating effects in high-frequency metallic Josephson devices: Voltage limit, bolometric mixing, and noise

Abstract

In this paper, we analyze nonequilibrium effects within a simple heating approximation for the case of metallic Josephson weak links which have a favorable three‐dimensional cooling geometry. Our principal conclusions are the following: (1) The temperature in the center of the junction with voltage V applied is T_m=[T_b²+3 (eV/2πk)²]^1/2, where T_b is the bath temperature, e is the electronic charge, and k is Boltzmann’s constant. This T_m can be as high as 70 K in Nb point contacts on a high Josephson step; thus the device noise temperature T_N? (1/2)(T_b+T_m) can greatly exceed T_b. (2) The critical current falls approximately as exp(−P/P_o), where P is the power dissipated in the junction and P_o is typically 10 μW for Al, Sn, Pb, and Nb, but much smaller for Nb₃Sn. This leads to a decrease in the amplitude of Josephson steps at high voltages which is in good agreement with data on the best Sn variable‐thickness microbridges and Nb point contacts. In a junction of optimized resistance level, the overall maximum voltage at which microwave‐induced steps can still exceed the noise is predicted to be proportional to T_c[Ωξ (0)/ρ_o]^2/7× (ν₁/T_c)^1/7, where Ω is the solid angle of the three‐dimensional cooling, ξ (0) is the extrapolated coherence length at T=0, ρ_o is the residual resistivity of the metal, and ν₁ is the microwave frequency. (3) The thermal response should be fast enough (∼τ_GL) to allow detection (heterodyne or square law) with bandwidth as large as the energy gap frequency; it is estimated that this bolometric detection effect will dominate true Josephson detection for carrier frequencies above ∼3 THz (i.e., λ≲100 μm) in junctions with resistance 10 Ω or less.