Phonon deficit effect and solid state refrigerators based on superconducting tunnel junctions

Sincethe(cid:12)rstdem onstration ofelectron cooling in superconductor{insulator{norm alm etal( SIN ) tunneljunctions,there is growing interest in tunneling e(cid:11)ects for the purpose to develop on{chip refrigeratorswhich can generatecooling in theorderof100 m K in an environm entof0 : 3{0 : 5 K .Thin (cid:12)lm deviceshavetheadvantageofbeing extrem ely com pact,operatein a continuousm ode,dissipate littlepower,and can easily beintegrated in cryogenic detectors.M otivated by such possibilities,we investigate the phonon de(cid:12)cit e(cid:11)ect in thin (cid:12)lm SIS (superconductor{insulator{superconductor) and SIN tunneljunctions. U nder certain circum stances,the phonon absorption spectra ofsuch tunneljunctionshave spectralwindowsofphonon absorption/em ission. W e propose to use phonon (cid:12)ltersto selectthe phonon absorbtion windowsand thusto enhance the cooling e(cid:11)ect.M em branes attached to such tunneljunctionscan becooled