Quasiparticle Recombination and 2A-Phonon-Trapping in Superconducting Tunneling Junctions

The experimental recombination lifetime ref f of quasiparticles in superconducting films in general exceeds the intrinsic recombination lifetime vR by phonon trapping. On the basis of geometric acoustic propagation and reabsorption of phonons emitted in quasiparticle recombination, %ff 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 A~, range 2 with d larger than A w and dominating boundary losses, and range 3, also with d larger than Aw but with dominating bulk losses. For very small d the relation between reff and rR, the intrinsic recombination lifetime, contains only the limiting angle of total reflection of phonons within the superconducting film. Therefore, rR can be directly obtained by reef measurements and from the sound velocities of the film-substrate system. Range 2 is characterized by a linear dependence of %ff on d. In this range it is not possible to obtain za from %fr measurements, however, reef allows a determination of the phonon boundary transmission. Range 3 shows no thickness dependence of %ff on d in the limit of large d values. In this range a further method for obtaining ~R from reff values is suggested.