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=(Dpd/u)1/2 associated with phonon propagation and the detector geometry where Dp 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 L2 is equal to XT/μmin, where X is a numerical factor, T is the intrinsic phonon transmission probability at the film substrate boundaries and μ is a phase-space factor defined by μ(i,j) =(Π2/4)[(2i+1)2 /a2+(2j+1)2/b2], 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.

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