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Nonequilibrium electrons in tunnel structures under high-voltage injection

We investigate electronic distributions in nonequilibrium tunnel junctions subject to a high voltage bias $V$ under competing electron-electron and electron-phonon relaxation processes. We derive conditions for reaching quasi-equilibrium and show that, though the distribution can still be thermal for low energies where the rate of the electron-electron relaxation exceeds significantly the electron-phonon relaxation rate, it develops a power-law tail at energies of order of $eV$. In a general case of comparable electron-electron and electron-phonon relaxation rates, this tail leads to emission of high-energy phonons which carry away most of the energy pumped in by the injected current.