Microscopic Model of Charge Carrier Transfer in Complex Media

TL;DR

This paper develops a microscopic model for charge carrier transfer in complex media, analyzing how environment particles affect carrier velocity and deriving a viscous-like force behavior with an associated friction coefficient.

Contribution

It introduces a dynamic percolation model to describe environment hindrance and analytically derives the velocity profiles and friction coefficient for charge carriers.

Findings

Environment particles exhibit viscous-like behavior at low fields.

Analytical expressions for carrier velocity and environment density profiles.

Derived an analog of the Stokes formula for dynamic percolative media.

Abstract

We present a microscopic model of a charge carrier transfer under an action of a constant electric field in a complex medium. Generalizing previous theoretical approaches, we model the dynamical environment hindering the carrier motion by dynamic percolation, i.e., as a medium comprising particles which move randomly on a simple cubic lattice, constrained by hard-core exclusion, and may spontaneously annihilate and re-appear at some prescribed rates. We determine analytically the density profiles of the "environment" particles, as seen from the stationary moving charge carrier, and calculate its terminal velocity as the function of the applied field and other system parameters. We realize that for sufficiently small external fields the force exerted on the carrier by the "environment" particles shows a viscous-like behavior and define an analog of the Stokes formula for such dynamic percolative environments. The corresponding friction coefficient is also derived.