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

摘要

A generalised phase-space kinetic Boltzmann equation for highlynon-equilibrium charged particle transport via localised and delocalised statesis used to develop continuity, momentum and energy balance equations,accounting explicitly for scattering, trapping/detrapping and recombinationloss processes. Analytic expressions detail the effect of these microscopicprocesses on the mobility and diffusivity. Generalised Einstein relations (GER)are developed that enable the anisotropic nature of diffusion to be determinedin terms of the measured field-dependence of the mobility. Interestingphenomena such as negative differential conductivity and recombinationheating/cooling are shown to arise from recombination loss processes and thelocalised and delocalised nature of transport. Fractional transport emergesnaturally within this framework through the appropriate choice of divergentmean waiting time distributions for localised states, and fractionalgeneralisations of the GER and mobility are presented. Signature impacts ontime-of-flight current transients of recombination loss processes via bothlocalised and delocalised states are presented.