Effect of Electric Field on Diffusion in Disordered Materials II. Two- and Three-dimensional Hopping Transport

Abstract

In the previous paper [Nenashev et al., arXiv:0912.3161] an analytical theory confirmed by numerical simulations has been developed for the field-dependent hopping diffusion coefficient D(F) in one-dimensional systems with Gaussian disorder. The main result of that paper is the linear, non-analytic field dependence of the diffusion coefficient at low electric fields. In the current paper, an analytical theory is developed for the field-dependent diffusion coefficient in three- and two-dimensional Gaussian disordered systems in the hopping transport regime. The theory predicts a smooth parabolic field dependence for the diffusion coefficient at low fields. The result is supported by Monte Carlo computer simulations. In spite of the smooth field dependences for the mobility and for the longitudinal diffusivity, the traditional Einstein form of the relation between these transport coefficients is shown to be violated even at very low electric fields.

12 pages, 7 figures

References in corpus (1)

• Effect of Electric Field on Diffusion in Disordered Materials I. One-dimensional Hopping Transport

Cited by in corpus (6)

• Encounter-Limited Charge Carrier Recombination in Phase Separated Organic Semiconductor Blends
• Effect of Electric Field on Diffusion in Disordered Materials I. One-dimensional Hopping Transport
• Distribution of charge carrier transport properties in organic semiconductors with Gaussian disorder
• Defect-related Anomalous Mobility of Small polarons in Oxides: the Case of Congruent Lithium Niobate
• Monte Carlo Simulation of Carrier Diffusion in Organic Thin Films with Morphological Inhomogeneity
• Diffusion of a particle in the Gaussian random energy landscape: Einstein relation and analytical properties of average velocity and diffusivity as functions of driving force