Refrigerator with phonon filters: An application of the phonon deficit effect in superconducting tunnel junctions

Nonequilibrium phenomena in thin solid films can result in cooling effects. These types of effects were predicted theoretically a while ago, and only recently were demonstrated experimentally in superconductor-insulator-normal metal (SIN) tunnel junctions. Since then, there is a growing interest in tunneling effects for the purpose to develop on-chip refrigerators. Thin film devices have the advantage of being extremely compact, operate in a continuous mode, dissipate little power, and can easily be integrated in cryogenic detectors. Currently these refrigerators can generate cooling in the order of 100 mK in an environment of 0.3–0.5 K. There are reasons to expect that this performance can be enhanced but a fundamental investigation of underlying principles is required. One of the outcomes of this type of analysis is the phonon deficit effect. In this article we investigate the phonon deficit effect in thin film superconductor-insulator-superconductor and SIN tunnel junctions. Depending on circumstances, the phonon absorption spectra of such tunnel junctions have spectral windows of phonon emission and/or absorption. We demonstrate that the phonon deficit mechanism can stand for the experimental results with SIN tunnel junctions. In addition, application of the theory of this effect allows us to propose using phonon filters to select the phonon absorption windows and thus to enhance the cooling effect. We discuss a particular superlattice design of corresponding phonon filters.