Three-dimensional modeling of charge transport, injection and recombination in organic light-emitting diodes

Organic light-emitting diodes (OLEDs) are ideally suited for lighting and display applications. Commercial OLED displays as well as OLED white-light sources are presently being introduced to the market. Essential electronic processes in OLEDs are the injection of electrons and holes into an organic semiconductor, their transport through the semiconductor, and their radiative recombination. In these processes an important role is played by the energetic disorder present in the organic semiconductor. This disorder leads to the localization of electronic states to specific sites. Charges move via a hopping process from one site to another. This hopping process involves quantum-mechanical tunneling assisted by a coupling to lattice vibrations. The energies of the sites are often taken to be distributed according to a Gaussian density of states (DOS). With these ingredients, the electronic processes taking place in OLEDs have been intensively investigated in the last two decades. However, this has not yet led to a satisfactory and complete OLED model that includes these processes in a consistent way, taking into account three-dimensional effects at the microscopic level. The goal of this thesis was to make an important step into this direction. In this thesis, the motion of charge carriers is evaluated by means of calculations based on the Pauli master equation and by means of Monte-Carlo simulations, which are both introduced in Chapter 2. The Pauli master equation describes the time-averaged occupational probabilities of a three-dimensional assembly of sites. This equation can be solved by means of an iterative calculation scheme, after which relevant quantities like the current and the charge-carrier mobility can be obtained. In the Monte-Carlo approach, the actual motion of the charges is simulated in time. The advantage of Monte-Carlo simulations over master-equation calculations is that Coulomb interactions between the charges can be taken into account in a consistent manner. In Chapter 3 it is shown that Coulomb interactions only influence the mobility in the case of high carrier densities and low electric field strengths. In this regime, taking into Coulomb interactions significantly decreases the mobility. This decrease is attributed to the trapping of charge carriers by the Coulomb potential well formed by the surrounding charges. For high electric field strengths and low charge-carrier densities, the mobility with Coulomb interactions agrees quite well with the mobility obtained without taking into account Coulomb interactions. In Chapter 4 the charge-carrier transport in single-carrier single-layer devices consisting of a disordered organic semiconductor sandwiched in between two metallic electrodes is studied by means of master-equation calculations. The effects of space charge, image-charge potentials close to the electrodes, finite injection barriers, and the complete dependence of the charge-carrier mobility on the temperature, the carrier density and the electric field are taken into account. The obtained three-dimensional current density is very inhomogeneous, showing filamentary regions that carry most of the current. Nevertheless, the total current agrees quite well with that of a one-dimensional continuum drift-diffusion model. For very thin devices with a high injection barrier and a high disorder strength (large width of the Gaussian DOS), the one-dimensional continuum drift-diffusion model underestimates the current. In this regime, the current can be described very well by a model assuming injection and transport over one-dimensional straight filaments. In the master-equation approach followed in Chapter 4, Coulomb interactions between charges were only taken into account in a layer-averaged way, because the approach cannot account explicitly for Coulomb interactions in a consistent way. To study the influence of explicitly taking into account Coulomb interactions between charges, the studies of the single-carrier single-layer devices were repeated with Monte-Carlo in Chapter 5. It was found that in the absence of an injection barrier taking into account Coulomb interactions explicitly leads to a decrease in the current as compared to master-equation calculations. This decrease can be rationalized by studying the three-dimensional current density distributions. Taking into account explicit Coulomb interactions leads to a change in the pattern of the filamentary current pathways, which in turn leads to a decrease of the total current. The case of spatial correlations in the energetic disorder was also studied. For this case the filamentary current pathways are broader and the effects of taking into account explicit Coulomb interactions are smaller. Traditionally, the rate of recombination between electrons and holes is described by the Langevin formula, which contains the sum of the electron and hole mobilities as a factor. In Chapter 6 the question of the validity of this formula for electron-hole recombination in disordered organic semiconductors is addressed. One of the main assumptions made in deriving the Langevin formula is that charge-carrier transport occurs homogeneously throughout the semiconductor. As shown in Chapters 4 and 5, however, this is generally not the case in organic semiconductors. Nonetheless, it is found from double-carrier MonteCarlo simulations of recombining electrons and holes that the recombination rate can be very well described by the classical Langevin formula, provided that a change in the chargecarrier mobilities due to the presence of carriers of the opposite type is taken into account. Deviations from the Langevin formula at finite electric field are found to be small at the field scale typical for OLEDs. In Chapter 7, the time-dependent relaxational properties of charge transport are studied. When a charge is injected in a disordered organic semiconductor, its mobility will gradually decrease because of energetic relaxation of the charge into the tail of the DOS. This relaxation process was studied by inserting charges randomly in an assembly of sites with a Gaussian DOS and following the time dependence of their mobility. For short simulation times the mobility was found to be almost independent of the carrier density. However, when the mobility has decreased to a value somewhat higher than the steady-state mobility, the time-dependent mobility branches off and relaxes to the carrier-density dependent steady-state mobility. The obtained results can be used in studying the response of organic devices to a small additional ac voltage. Finally, in Chapter 8 overall conclusions and outlook for the three-dimensional modeling of OLEDs are presented. The results presented in this thesis should be considered as a first step towards the development of a predictive model for state-of-the-art OLEDs.