The low-field mobility μ of a small concentration of charge carriers hopping among a random distribution of transport sites is studied, as a function of the mean interparticle spacing ρ and the temperature T, for model systems having different site-energy distribution functions. For a uniform density of states our calculations show that the mobility obeys empirical scaling laws similar to those found in the theory of variable-range hopping. For a binary distribution of site energies we observe a crossover as a function of site density between trap-limited conduction and trap-mediated conduction. For a Gaussian density of states our results confirm the quadratic inverse temperature dependence of lnμ found in Monte Carlo studies, although quantitative characterization of this dependence is found to depend sensitively on the degree of spatial disorder in ways that could impact the extraction of microscopic parameters from experimental data.
P. E. Parris, "Low-Field Hopping among Randomly-Distributed Sites with Uncorrelated Energetic Disorder," Journal of Chemical Physics, vol. 108, no. 1, pp. 218-226, American Institute of Physics (AIP), Sep 1998.
The definitive version is available at https://doi.org/10.1063/1.475373
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