On the structure of the energy distribution function in the hopping regime

TL;DR

This paper investigates how the dispersion of transport coefficients influences the energy distribution function of charge carriers in the hopping regime, revealing two distinct regimes based on temperature and disorder.

Contribution

It introduces a detailed analysis of the energy distribution function structure considering transport coefficient dispersion in the hopping regime, with explicit expressions for different densities of states.

Findings

Two regimes in energy relaxation processes identified

Below a characteristic temperature, dispersion dominates the energy distribution

Above the characteristic temperature, energy diffusion governs the distribution

Abstract

The impact of the dispersion of the transport coefficients on the structure of the energy distribution function for charge carriers far from equilibrium has been investigated in effective-medium approximation for model densities of states. The investigations show that two regimes can be observed in energy relaxation processes. Below a characteristic temperature the structure of the energy distribution function is determined by the dispersion of the transport coefficients. Thermal energy diffusion is irrelevant in this regime. Above the characteristic temperature the structure of the energy distribution function is determined by energy diffusion. The characteristic temperature depends on the degree of disorder and increases with increasing disorder. Explicit expressions for the energy distribution function in both regimes are derived for a constant and an exponential density of states.