Dependence of quasiparticle recombination time on film thickness

Abstract

We find that the measured recombination time of quasiparticles in superconducting aluminum films increases approximately linearly with film thickness as predicted by Rothwarf and Taylor, the lifetime for a thickness of 1000 Å being approximately twice the extrapolated value at zero thickness. They suggest that the reabsorption of phonons, emitted during the recombination of quasiparticles, will lead to an enhancement of the measured quasiparticle recombination time proportional to the film thickness, if the main process competing with phonon reabsorbtion is the direct propagation of phonons into the substrate. Our results are in semi-quantitative agreement with a simple model based on their discussion. The enhancement is expected to depend on the phonon transmission coefficient. We observed essentially no effect when layers of WO 3 or CeO 2, having very high acoustic impedances, were interposed between the aluminum film and substrate. We have, at present, no convincing explanation for this result which casts considerable doubt on the above interpretation of our data.