Effects of noise on the dc and far-infrared Josephson effect in small-area superconducting tunnel junctions

We report investigations of the effect of noise on the Josephson effect in small-area tunnel junctions, both at dc and when the junction is irradiated by 604-GHz laser radiation. The junctions were made of Sn-SnO-Pb layers of ~1 ${\mathrm{\ensuremath{\mu}}\mathrm{m}}^{2}$ area, fabricated on crystal quartz substrates with integral planar resonant dipole antennas. The observed systematic falloff of the ${I}_{c}{R}_{n}$ product with increasing resistance can be accounted for by the thermal activation model (transition-state theory) if an effective noise temperature (presumably extrinsic) of 8\ifmmode\pm\else\textpm\fi{}1 K is assumed. The noise rounding of the high-voltage steps can be fitted with the analytic results obtained by P. A. Lee [J. Appl. Phys.42,325 (1971)] for an overdamped junction, but using a fictitious elevated noise temperature of ~eV/$k$ (~20-30 K for typical steps at ~5 mV) to incorporate the nonthermal shot noise as an effective increase in noise temperature. We have also developed a computer simulation which builds in the effects of the nonlinear quasiparticle resistance of the junctions as well as the voltage-dependent shot noise; it can account for the entire $1\ensuremath{-}V$ curve, including the photon-assisted tunneling steps. Noise currents are found to have much less effect on the finite-voltage Josephson steps than in reducing the ${I}_{c}{R}_{n}$ product, which explains the anomalously high ratios of step widths to measured ${I}_{c}$ that are found experimentally.