Generalised balance equations for charged particle transport via localised and delocalised states: Mobility, generalised Einstein relations and fractional transport

TL;DR

This paper develops a comprehensive kinetic framework for charged particle transport that incorporates localized and delocalized states, revealing new insights into mobility, diffusion, and fractional transport phenomena, with implications for understanding complex transport behaviors.

Contribution

It introduces a generalized Boltzmann equation approach that explicitly models microscopic processes and derives novel relations like the generalized Einstein relations and fractional transport models.

Findings

Reveals how microscopic processes affect mobility and diffusivity.

Derives generalized Einstein relations for anisotropic diffusion.

Shows fractional transport naturally arises from divergent waiting time distributions.

Abstract

A generalised phase-space kinetic Boltzmann equation for highly non-equilibrium charged particle transport via localised and delocalised states is used to develop continuity, momentum and energy balance equations, accounting explicitly for scattering, trapping/detrapping and recombination loss processes. Analytic expressions detail the effect of these microscopic processes on the mobility and diffusivity. Generalised Einstein relations (GER) are developed that enable the anisotropic nature of diffusion to be determined in terms of the measured field-dependence of the mobility. Interesting phenomena such as negative differential conductivity and recombination heating/cooling are shown to arise from recombination loss processes and the localised and delocalised nature of transport. Fractional transport emerges naturally within this framework through the appropriate choice of divergent mean waiting time distributions for localised states, and fractional generalisations of the GER and mobility are presented. Signature impacts on time-of-flight current transients of recombination loss processes via both localised and delocalised states are presented.