Heat sources in electronic refrigerators

Tunneling electric current through the normal metal - insulator - supercond uctor junction is accompanied with heat flow out of normal metal when prope rty voltage biased. The phenomenon enables cooling of electrons and phonons (under special conditions) in the region below 1 K. At lower bath temperat ures two parasitic heat sources decrease refrigerator performance. (i) Due to tunneling of hot electrons from a normal metal electrode to a supercondu ctive one an excess quasiparticle density appears in the superconductor whi ch results in tunneling of electrons back to the normal metal and consequen tly the normal metal electron temperature increases. This phenomenon is cal led back tunneling. (ii) Second heat source is the Cooper pair formation: t he part of energy released by the formation of Cooper pairs in a supercondu ctor is dissipated in normal metal. Both contributions are calculated by co nsidering quasiparticle behavior in the junction region and no free paramet ers are introduced. Diffusion, tunneling and back tunneling of quasiparticl es in the superconductor in equilibrium are considered to calculate tempera tures of electrons and phonons in the normal metal electrode. This detailed model explains the increase of normal metal electron temperatures above th e bath temperature at lower bath temperatures.