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In a hybrid Superconductor - Insulator - Normal metal tunnel junction biasedjust below the gap, the extraction of hot electrons out of the normal metalresults in electronic cooling effect. The quasiparticles injected in thesuperconductor accumulate near the tunnel interface, thus increasing theeffective superconductor temperature. We propose a simple model for thediffusion of excess quasiparticles in a superconducting strip with anadditional trap junction. This diffusion model has a complete analyticsolution, which depends on experimentally accessible parameters. We find thatthe accumulated quasiparticles near the junction reduce the efficiency of thedevice. This study is also relevant to more general situations making use ofsuperconducting tunnel junctions, as low temperature detectors.

Quasiparticle diffusion based heating in superconductor tunneling micro-coolers