Measurements and modeling of phonon cooling by electron-tunneling refrigerators

We demonstrate cooling of the electrons and phonons of a silicon nitride (Si-N) membrane by solid-state refrigerators based on normal metal/insulator/superconductor (NIS) tunnel junctions. We report a temperature reduction of the Si-N membrane from 260 mK to 240 mK, while the electrons in the normal metal of the refrigerator are cooled to 145 mK. We explain the mechanism for cooling an isolated membrane and make quantitative comparisons between experiment and a finite-element thermal model. The model indicates that increasing the thermal conductivity of the cold-fingers, improving the transparency of the tunnel junctions, and reducing the power load through the membrane will make it possible to cool the membrane from 260 mK to below 170 mK. The refrigeration of a membrane makes it possible to integrate other cryogenic devices that require sub-Kelvin temperatures for optimal performance, such as thin-film sensors. We demonstrate this integration by combining NIS refrigerators with an x-ray Transition-Edge-Sensor (TES).