Nonequilibrium conditions and diffusive transfer of primary excitations in superconducting tunnel-junction detectors.

Abstract

The nonequilibrium behavior of superconducting tunnel junctions in the high-injection regime is examined. A model based on asymmetric coupled diffusion equations for quasiparticles and phonons, including a phonon escape term, is presented. A solution consisting of a two-dimensional perturbative algorithm to the equation of phonons and a self-iterative expansion to the quasiparticles equation has been developed. A characteristic length scale L = (D/sub p/d/u)/sup 1/2/ associated with phonon propagation and the detector geometry where D/sub p/ is the diffusion coefficient for the phonon pulse, d is the detector film thickness, and u is the average phonon velocity. The quasiparticles and phonon pulses almost uncouple with similar spatial and time distributions and with a minimum escape rate of the phonons when L/sup 2/ is equal to XT/..mu../sub min/, where X is a numerical factor, T is the intrinsic phonon transmission probability at the film substrate boundaries and ..mu.. is a phase-space factor defined by ..mu..(i,j) = (Pi/sup 2//4)((2i+1)/sup 2/ /a/sup 2/+(2j+1)/sup 2//b/sup 2/), when i,j = 0,1,2,. . . . The parameters a and b are half the longitudinal and transverse dimensions of the junction film. The implications of these new results on previous experimental measurements are discussed.