Theory and simulation of charge transport in disordered organic semiconductors

Charge transport in polymeric or small-molecule organic semiconductors used in organic light-emitting diodes (OLEDs) occurs by hopping of charges between sites at which the charges are localized. The energetic disorder in these semiconductors has a profound influence on the charge transport: charges will try to find the easiest pathway through the semiconductor, leading to percolation effects. We extend the standard percolation theory for charge transport in disordered semiconductors, valid at zero temperature, to finite temperatures within the context of a scaling theory [1]. Within this scaling theory, we are able to describe hopping transport for different types of lattices and hopping rates, and for uncorrelated as well as correlated energy disorder, as a function of temperature and carrier density [2]. The resulting mobility function can be used in the modelling of charge transport in OLEDs and other organic devices. Simulation of charge transport in complex multilayer white OLEDs for lighting applications is essential for their rational design. In these OLEDs the electronic processes in the various layers -injection and motion of charges as well as generation, diffusion, and radiative decay of excitons- should be concerted such that efficient, stable, and colour-balanced electroluminescence occurs. We show that it is feasible to carry out Monte Carlo simulations of charge transport, recombination, and exciton diffusion in such complex OLEDs, as demonstrated for a hybrid multilayer OLED combining red and green phosphorescent layers with a blue fluorescent layer [3]. The simulated current density and emission profile agree well with experiment. The experimental emission profile was obtained with nanometre resolution from the measured angle- and polarization-dependent emission spectra. The simulations elucidate the crucial role of exciton transfer from green to red and the efficiency loss due to excitons generated in the interlayer between the green and blue layer. The perpendicular and lateral confinement of the exciton generation to regions of molecular-scale dimensions, revealed by our study, demonstrate the necessity of molecular-scale instead of conventional continuum simulation.