Dynamics of nonequilibrium quasiparticles in narrow-gap superconducting tunnel junctions

The latest generation of high quality, narrow gap, superconducting tunnel junctions (STJs) exhibits a steady-state and time-dependent behavior which cannot be described satisfactorily by previous treatments of nonequilibrium quasiparticle (qp) dynamics. These effects are particularly evident in experiments using STJs as detectors of photons, over the range from near infrared to x ray. In this paper, we present a detailed theoretical analysis of the spectral and temporal evolution of the nonequilibrium qp and phonon distributions in such STJs excited by single photons, over a wide range of excitation energy, bias voltage, and temperature. By solving the coupled set of kinetic equations describing the interacting excitations, we show that the nonequilibrium qp distribution created by the initial photoabsorption does not decay directly back to the initial undisturbed state in thermal equilibrium. Instead, it undergoes a rapid adiabatic relaxation to a long-lived, excited state, the spectral distribution of which is nonthermal, maintained by a balance between qp creation, recombination, and trapping. The model is able to describe successfully photoabsorption data taken on several different aluminum STJs, using a single set of parameters. Of particular note is the conclusion that the local traps responsible for qp loss are situated specifically in the region of Nb contacts.