Related Experiment Video
Updated: Jun 19, 2026

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
Published on: September 5, 2019
Random walk numerical simulation for hopping transport at finite carrier concentrations: diffusion coefficient and
J P Gonzalez-Vazquez1, Juan A Anta, Juan Bisquert
1Departamento de Sistemas Físicos, Químicos y Naturales, Universidad Pablo de Olavide, 41013, Sevilla, Spain.
Abstract:
The random walk numerical simulation (RWNS) method is used to compute diffusion coefficients for hopping transport in a fully disordered medium at finite carrier concentrations. We use Miller-Abrahams jumping rates and an exponential distribution of energies to compute the hopping times in the random walk simulation. The computed diffusion coefficient shows an exponential dependence with respect to Fermi-level and Arrhenius behavior with respect to temperature. This result indicates that there is a well-defined transport level implicit to the system dynamics. To establish the origin of this transport level we construct histograms to monitor the energies of the most visited sites. In addition, we construct "corrected" histograms where backward moves are removed. Since these moves do not contribute to transport, these histograms provide a better estimation of the effective transport level energy. The analysis of this concept in connection with the Fermi-level dependence of the diffusion coefficient and the regime of interest for the functioning of dye-sensitised solar cells is thoroughly discussed.
More Related Videos
Related Concept Videos
Carrier Transport
Drift Current:
The drift of charge carriers is started by an external electric field (E). Charged particles, such as electrons and holes, experience an acceleration between collisions with lattice atoms. For electrons, this results in a drift velocity (vd) given by:
The Kinetic Model of Gases
Transport Number
Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion
Maxwell-Boltzmann Distribution: Problem Solving
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
Diffusion

