  In a hybrid Superconductor - Insulator - Normal metal tunnel junction biased
just below the gap, the extraction of hot electrons out of the normal metal
results in electronic cooling effect. The quasiparticles injected in the
superconductor accumulate near the tunnel interface, thus increasing the
effective superconductor temperature. We propose a simple model for the
diffusion of excess quasiparticles in a superconducting strip with an
additional trap junction. This diffusion model has a complete analytic
solution, which depends on experimentally accessible parameters. We find that
the accumulated quasiparticles near the junction reduce the efficiency of the
device. This study is also relevant to more general situations making use of
superconducting tunnel junctions, as low temperature detectors.
