On Analytical Modeling of Hopping Transport of Charge Carriers and Excitations in Materials with Correlated Disorder.

Spatial-energy correlations strongly influence charge and exciton transport in weakly ordered media such as organic semiconductors and nanoparticle assemblies. Focusing on cases with shorter-range interparticle interactions, we develop a unified analytic approach that allows us to calculate the temperature and field dependence of charge carrier mobility in organic quadrupole glasses and the temperature dependence of the diffusion coefficient of excitons in quantum dot solids. We obtain analytic expressions for the energy distribution of hopping centers, the characteristic escape time of charge/exciton from the energy well stemming from energy correlations around deep states, and the size of the well. The derived formulas are tested with Monte Carlo simulation results, showing good agreement and providing simple analytic expressions for analysis of charge and exciton mobility in a broad range of partially ordered media.