Generalised balance equations for charged particle transport via localised and delocalised states: Mobility, generalised Einstein relations and fractional transport
arXiv:1608.08509 · doi:10.1103/PhysRevE.95.042119
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.
arXiv comment21 pages, 4 figures
References in corpus (8)
- High order fluid model for streamer discharges: I. Derivation of model and transport data
- High Temperature Electron Localization in dense He Gas
- Ab-initio electron scattering cross-sections and transport in liquid xenon
- Electron scattering and transport in liquid argon
- Positronium in a liquid phase: formation, bubble state and chemical reactions
- Analytic solution of the fractional advection diffusion equation for the time-of-flight experiment in a finite geometry
- Solution of a generalised Boltzmann's equation for non-equilibrium charged particle transport via localised and delocalised states
- Fluctuation capture in non-polar gases and liquids