Electron-phonon relaxation and excited electron distribution in gallium nitride

TL;DR

This paper develops a comprehensive theory for energy relaxation and electron distribution in highly excited semiconductors, specifically applied to gallium nitride, highlighting the significance of high-energy tails in electron behavior.

Contribution

The paper introduces a new theoretical framework for non-equilibrium electron distributions in irradiated semiconductors, including the impact of electron-phonon interactions and high-energy tails.

Findings

High-energy tail significantly influences charge transport in irradiated GaN.

Electron-phonon relaxation rate determines the shape of the high-energy tail.

Non-Fermi 'tail' contribution is comparable to the low-energy Fermi-like component under certain conditions.

Abstract

We develop a theory of energy relaxation in semiconductors and insulators highly excited by the long-acting external irradiation. We derive the equation for the non-equilibrium distribution function of excited electrons. The solution for this function breaks up into the sum of two contributions. The low-energy contribution is concentrated in a narrow range near the bottom of the conduction band. It has the typical form of a Fermi distribution with an effective temperature and chemical potential. The effective temperature and chemical potential in this low-energy term are determined by the intensity of carriers' generation, the speed of electron-phonon relaxation, rates of inter-band recombination and electron capture on the defects. In addition, there is a substantial high-energy correction. This high-energy 'tail' covers largely the conduction band. The shape of the high-energy 'tail' strongly depends on the rate of electron-phonon relaxation but does not depend on the rates of recombination and trapping. We apply the theory to the calculation of a non-equilibrium distribution of electrons in irradiated GaN. Probabilities of optical excitations from the valence to conduction band and electron-phonon coupling probabilities in GaN were calculated by the density functional perturbation theory. Our calculation of both parts of distribution function in gallium nitride shows that when the speed of electron-phonon scattering is comparable with the rate of recombination and trapping then the contribution of the non-Fermi 'tail' is comparable with that of the low-energy Fermi-like component. So the high-energy contribution can affect essentially the charge transport in the irradiated and highly doped semiconductors.