Electron-phonon relaxation in hot-electron detectors below 1 K

Recently proposed submillimeter hot-electron direct detectors rely on a weak thermal coupling between electrons and phonons. According to the theory, this should occur in impure films. So far, the experimental situation has been somewhat confusing. A number of works have shown a cubic temperature dependence of the electron-phonon relaxation rate below I K. In contrast to the traditional explanation, we show that it was not a clean limit behavior but rather an intermediate temperature asymptotics. In this case, an electron scattering from transversal phonons mediated by vibrating impurities/boundaries dominates. In our recent experiments we reached the dirty limit predicted by the theory in Hf and Ti films. A measured electron-phonon relaxation time followed the T-4 dependence and was a record-long (25 ms) at 40 mK.