Electron-hole recombination in disordered organic semiconductors : validity of the Langevin formula

Accurate modeling of electron-hole recombination in organic light-emitting diodes (OLEDs) is essential for developing a complete description of their functioning. Traditionally, the recombination rate is described by the Langevin formula, with a proportionality factor equal to the sum of the electron and hole mobilities. In the disordered organic semiconductors used in OLEDs these mobilities have been shown to depend strongly on the carrier densities and on the electric field. Moreover, the energetic disorder leads to percolating pathways for the electron and hole currents, which may or may not be correlated. To answer the question whether the Langevin formula is still valid under such circumstances we perform Monte Carlo simulations of the recombination rate for Gaussian energetic disorder. We vary the disorder energy, the temperature, the densities, and mobility ratio of electrons and holes, the electric field, and the type of correlation between the electron and hole energies. We find that at zero electric field the Langevin formula is surprisingly well obeyed, provided that a change in the charge-carrier mobilities due to the presence of charge carriers of the opposite type is taken into account. Deviations from the Langevin formula at finite electric field are small at the field scale relevant for OLED modeling

Modeling of the transient mobility in disordered organic semiconductors with a Gaussian density of states

The charge-carrier mobility in organic semiconductors is often studied using non-steady-state experiments. However, energetic disorder can severely hamper the analysis due to the occurrence of a strong time dependence of the mobility caused by carrier relaxation. The multiple-trapping model is known to provide an accurate description of this effect. However, the value of the conduction level energy and the hopping attempt rate, which enter the model as free parameters, are not a priori known for a given material. We show how for the case of a Gaussian density of states both parameters can be deduced from the parameter values used to describe the measured dc current-voltage characteristics within the framework of the extended Gaussian disorder model. The approach is validated using three-dimensional Monte Carlo modeling. In the analysis, the charge-density dependence of the time-dependent mobility is included. The model is shown to successfully predict the low-frequency differential capacitance of sandwich-type devices based on a polyfluorene copolymer