Cryogenic cooling using tunneling structures with sharp energy features

Thermoelectric cooling, based upon the extraction of hot electrons and holes from a metallic electron gas, holds unrealized potential for refrigeration at cryogenic temperatures. We discuss the performance of two such electronic refrigerators: the quantum-dot refrigerator (QDR) and the normal-insulator-superconductor (NIS) refrigerator. We obtain the QDR base temperature using a numerical simulation and verify the validity of certain simplifying assumptions which allow refrigerating performance to be summarized on a diagram of ambient temperature versus electronic temperature. In this way, we find that the best refrigeration is obtained with the electronic distribution far from the equilibrium Fermi-Dirac function and the temperature reduction achieved is limited by the rate at which phonons are absorbed. We predict that, with sufficient thermal isolation, electronic devices could be cooled to a small fraction of the ambient temperature using these solid-state refrigerators. The NIS refrigerator should be capable of cooling thin-film devices from above 300 mK to below 100 mK; the QDR will cool macroscopic metallic samples in the μK or nK range. We also discuss topics related to thermoelectric refrigeration including other cryogenic thermoelectric cooling schemes, the validity of the linear-response theory of thermoelectric effects, the refrigerating efficiency of an optimized thermoelectric refrigerator, and the overall cooling power of thermoelectric refrigeration.