Nonequilibrium in metallic microstructures in the presence of high current density

Thin narrow films with a cross section of about ${10}^{\mathrm{\ensuremath{-}}10}$ ${\mathrm{cm}}^{2}$ have been studied under nonequilibrium conditions. Working at liquid-helium temperature, with current densities up to ${10}^{7}$ A/${\mathrm{cm}}^{2}$, corresponding to electric fields up to 0.3\ifmmode\times\else\texttimes\fi{}${10}^{6}$ V/m, we raised the electron temperature ${\mathit{T}}_{\mathit{e}}$ considerably above the phonon temperature ${\mathit{T}}_{\mathrm{ph}}$. We tried to use weak localization and the Coulomb anomaly of the resistance as thermometers. Weak localization worked very well, but in the case of the Coulomb anomaly we found inconsistencies. We predict that the Coulomb anomaly shows non-ohmic behavior. Our experimental data suggest an Eliashberg function ${\mathrm{\ensuremath{\alpha}}}^{2}$F(\ensuremath{\Omega}) which is linear in \ensuremath{\Omega}. We can give upper limits for the escape time of the phonons from the film into the quartz. The evaluation with our weak-localization thermometer yields consistent results.

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