Heat sources in electronic refrigerators

Tunneling electric current through the normal metal-insulator-superconductor junction is accompanied with heat flow out of normal metal when properly voltage biased. The phenomenon enables cooling of electrons and phonons (under special conditions) in the region below 1 K. At lower bath temperatures two parasitic heat sources decrease refrigerator performance. (i) Due to tunneling of hot electrons from a normal metal electrode to a superconductive one an excess quasiparticle density appears in the superconductor which results in tunneling of electrons back to the normal metal and consequently the normal metal electron temperature increases. This phenomenon is called back tunneling. (ii) Second heat source is the Cooper pair formation: the part of energy released by the formation of Cooper pairs in a superconductor is dissipated in a normal metal. Both contributions are calculated-by considering quasiparticle behavior in the junction region and no free parameters are introduced. Diffusion, tunneling and back tunneling of quasiparticles in the superconductor in equilibrium are considered to calculate temperatures of electrons and phonons in the normal metal electrode. This detailed model explains the increase of normal metal electron temperatures above the bath temperature at lower bath temperatures.