Quasiparticle lifetimes and tunneling times in a superconductor-insulator-superconductor tunnel junction with spatially inhomogeneous electrodes

The low-energy quasiparticle scattering and recombination lifetimes for a proximity sandwich of two superconductors [ital S] and [ital S][prime] with different bulk energy gaps, are calculated as a function of the spatial coordinate and temperature. The spatial dependence of the order parameter and density of states are calculated on the basis of a microscopic model of the proximity effect, based on the Usadel equations, for dirty superconductors in thermal equilibrium. A zero boundary resistance between [ital S] and [ital S][prime] and a Boltzmann-like energy distribution of the excess quasiparticles are assumed. In the case of a small diffusion time constant an effective quasiparticle relaxation rate into and excitation rate out of the reduced gap region in the [ital SS][prime] sandwich are obtained as a function of (finite, but low) temperature and strength of the proximity effect, determined by the parameter [gamma][sub [ital m]], by averaging over the energies and positions of the quasiparticles. In the same way effective tunneling times for electrons and holes tunneling out of the trap in the [ital SS][prime] sandwich to the other electrode of an [ital SS][prime][ital IS][prime][prime][ital S] junction are determined as a function of temperature, voltage, and [gamma][sub [ital m]].