Phonon deficit effect and solid state refrigerators based on   superconducting tunnel junctions
  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. Motivated by such possibilities, we investigate the phonon deficit effect in thin film $SIS$ (superconductor--insulator--superconductor) and $SIN$ tunnel junctions. Under certain circumstances, the phonon absorption spectra of such tunnel junctions have spectral windows of phonon absorption/emission. We propose to use phonon filters to select the phonon absorbtion windows and thus to enhance the cooling effect. Membranes attached to such tunnel junctions can be cooled in this way more effectively. We discuss a particular superlattice design of corresponding phonon filters. 
G.G. Melkonyan, H. Kroger and A.M. Gulian