Superconducting tunnel-junction refrigerator

The dc current through an S1-S2 tunnel junction, with 2 greater than 1, when biased with eV<1+2, will lower the energy in S1. This energy reduction will be shared by the phonons and electrons. This device is shown to be analogous to a thermoelectric refrigerator with an effective Peltier coefficient *1e. Tunneling calculations yield the cooling power Pc, the electrical power Pe supplied by the bias supply, and the cooling efficiency =PcPe. The maximum cooling power is obtained for eV=(2-1) and t1=T1Tc10.9. Estimates are made of the temperature difference T2-T1 achievable in Al-Pb and Sn-Pb junctions with an Al2O3 tunneling barrier. The performance of this device is shown to yield a maximum cooling efficiency 1(2-1) which can be compared with that available in an ideal Carnot refrigerator of =T1(T2-T1). The development of a useful tunnel-junction refrigerator requires a tunneling barrier with an effective thermal conductance per unit area several orders of magnitude less than that provided by the Al2O3 barrier in the Al-Pb and Sn-Pb systems.