· · · Repository hosted by TU Delft Library

We present a scaling theory for charge transport in molecular semiconductors with Gaussian energy disorder, which extends standard percolation theory by including bonds with conductances close to the percolating one in the random-resistor network of bonds representing charge hopping. A general and compact expression is given for the charge mobility as a function of temperature and charge concentration, with parameters that are determined for Miller-Abrahams and Marcus hopping on different lattices from numerically exact results. A universal dependence on charge concentration is found and a temperature dependence that differs significantly from other reports.

From a numerically exact solution of the Master equation for hoppingtransport in a disordered energy landscape with a Gaussian densityof states, we determine the dependence on temperature, carrier density, and electric field of the charge carrier mobility. Experimentalspace-charge limited currents in semiconducting polymer-based devices are excellently reproduced with this unified description of the mobility. At room temperature it is mainly the dependence on carrier density that plays an important role, whereas at low temperatures andhigh fields the electric field dependence becomes important. Omission of the carrier-density dependence has led to an underestimation of the hopping distance and the width of the density of states in these polymers.