Quasiparticle recombination and 2Δ-phonon-trapping in superconducting tunnelling junctions

Abstract

The experimental recombination lifetime τeff of quasiparticles in superconducting films in general exceeds the intrinsic recombination lifetime τR by phonon trapping. On the basis of geometric acoustic propagation and reabsorption of phonons emitted in quasiparticle recombination, τeff is calculated as a function of film thickness d taking into account longitudinal and transverse phonon reabsorption, bulk loss processes and acoustical phonon transmission into the substrate. With increasing thickness d three characteristic ranges are found: range 1 with film thickness d small compared to the phonon reabsorption mean free path Λw, range 2 with d larger than Λw and dominating boundary losses, and range 3, also with d larger than Λw but with dominating bulk losses. For very small d the relation between τeff and τR, the intrinsic recombination lifetime, contains only the limiting angle of total reflection of phonons within the superconducting film. Therefore, τR can be directly obtained by τeff measurements and from the sound velocities of the film-substrate system. Range 2 is characterized by a linear dependence of τeff on d. In this range it is not possible to obtain τR from τeff measurements, however, τeff allows a determination of the phonon boundary transmission. Range 3 shows no thickness dependence of τeff on d in the limit of large d values. In this range a further method for obtaining τR from τeff values is suggested.