Generalized balance equations for charged particle transport via localized and delocalized states: Mobility, generalized Einstein relations, and fractional transport

摘要

A generalized phase-space kinetic Boltzmann equation for highly nonequilibrium charged particle transportvia localized and delocalized states is used to develop continuity, momentum, and energy balance equations,accounting explicitly for scattering, trapping and detrapping, and recombination loss processes. Analyticexpressions detail the effect of these microscopic processes on mobility and diffusivity. Generalized Einsteinrelations (GER) are developed that enable the anisotropic nature of diffusion to be determined in terms of themeasured field dependence of the mobility. Interesting phenomena such as negative differential conductivityand recombination heating and cooling are shown to arise from recombination loss processes and the localizedand delocalized nature of transport. Fractional transport emerges naturally within this framework through theappropriate choice of divergentmean waiting time distributions for localized states, and fractional generalizationsof the GER and mobility are presented. Signature impacts on time-of-flight current transients of recombinationloss processes via both localized and delocalized states are presented.