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

Abstract

Accurate modeling of electron-hole recombination in organic light-emitting diodes ͑OLEDs͒ 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.

Effects of energy correlations and superexchange on charge transport and exciton formation in amorphous molecular semiconductors: An ab initio study

“…As mentioned in the introduction, the size and sign of the correlation between the on-site HOMO and LUMO energies have an important impact on the exciton formation rate [23]. Figure 8 shows in a scatter plot for all molecular sites in microscopic ab initio calculations for the three considered materials the values of E LUMO ≡ E LUMO − E LUMO versus E HOMO ≡ E HOMO − E HOMO , where E LUMO and E HOMO are the average LUMO and HOMO energies.…”

“…In the case of positive HOMO-LUMO energy correlation (negative correlation between electron and hole energies in the terminology used in Ref. [23]), the probability that electrons and holes are trapped at different sites is larger than in the case of negative HOMO-LUMO energy correlation (positive correlation between electron and holes energies). This leads to a lower exciton formation rate for positive than for negative HOMO-LUMO energy correlation.…”

“…The existence of on-site HOMO-LUMO energy correlation and its sign are of importance for the rate of exciton formation [23]. In the case of positive HOMO-LUMO energy correlation (negative correlation between electron and hole energies in the terminology used in Ref.…”

“…We note that in Ref. [23] the exciton binding energy was assumed to be sufficiently large to prevent unbinding of the exciton, so that effects of a finite exciton binding energy and its possible correlation with the LUMO and HOMO energies were not included. This paper is organized as follows.…”

Monte Carlo study of charge transport in organic sandwich-type single-carrier devices: Effects of Coulomb interactions

“…We note that we have recently shown that in order to properly describe electron-hole recombination in double-carrier devices, it is also necessary to take into account the effects of short-range interactions. 38 If these interactions are included in the mobilities in a double-carrier situation, an accurate description of the recombination rate is found when these mobilities are used in the conventional Langevin expression for this rate. 38 It would therefore be highly desirable to develop a systematic theory for including short-range Coulomb effects on charge-carrier mobilities in disordered organic semiconductors.…”