Electron-phonon scattering rates in disordered metallic films below 1 K

We have studied thin disordered metal films at low temperatures under nonequilibrium conditions. The electron temperature was raised above the lattice temperature by applying a dc bias. The Coulomb anomaly and weak localization were used as thermometers for the electrons. We confirm that at temperatures below 1 K the electron temperatures as derived from either the Coulomb anomaly or weak localization are consistent. The electron-phonon energy relaxation rate was measured to be proportional to ${\mathit{T}}^3$. Our results disagree with theoretical calculations of the electron-phonon rates for dirty metals which predict electron-phonon scattering rates proportional to ${\mathit{T}}^4$ for three-dimensional phonons.