Universal Disorder in Organic Semiconductors Due to Fluctuations in Space Charge

This thesis concerns the study of charge transport in organic semiconductors. These materials are widely used as thin-film photoconductors in copiers and laser printers, and for their electroluminescent properties in organic light-emitting diodes. Much contemporary research is directed towards improving the efficiency of organic photovoltaic devices, which is limited to a large extent by the spatial and energetic disorder that hinders the charge mobility. One contribution to energetic disorder arises from the strong Coulomb interactions between injected charges with one another, but to date this has been largely ignored. We present a mean-field model for the effect of mutual interactions between injected charges hopping from site to site in an organic semiconductor. Our starting point is a modified Fr\ {o}hlich Hamiltonian in which the charge is linearly coupled to the amplitudes of a wide band of dispersionless plasma modes having a Lorentzian distribution of frequencies. We show that in most applications of interest the hopping rates are fast enough while the plasma frequencies are low enough that random thermal fluctuations in the plasma density give rise to an energetically disordered landscape that is effectively stationary for many thousands of hops. Moreover, the distribution of site energies is Gaussian, and the energy-energy correlation function decays inversely with distance; as such, it can be argued that this disorder contributes to the Poole-Frenkel field dependence seen in a wide variety of experiments. Remarkably, the energetic disorder is universal; although it is caused by the fluctuations in the charge density, it is independent of the charge concentration