Nonequilibrium electrons in tunnel structures under high-voltage injection

TL;DR

This paper studies the behavior of electrons in tunnel junctions under high voltage, revealing conditions for quasi-equilibrium and the emergence of power-law tails in electron energy distributions, which influence phonon emission.

Contribution

It derives conditions for quasi-equilibrium in nonequilibrium tunnel junctions and describes the formation of power-law tails at high energies due to competing relaxation processes.

Findings

Thermal distribution at low energies when electron-electron relaxation dominates

Development of power-law tails at energies around eV

High-energy phonon emission carrying away injected energy

Abstract

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.