Modeling of charge-transport processes for predictive simulation of OLEDs

Abstract

Intensive research is taking place into alternative light sources to replace incandescent and fluorescent lamps. Organic light-emitting diodes (OLEDs) show great promise, with their main potential advantages being high energy efficiency, cheap roll-to-roll production, excellent color rendering and a unique form factor. However, significant challenges must still be overcome, particularly in the areas of luminous efficacy, lifetime and manufacturing. Several approaches to overcoming these challenges have been proposed, but it is difficult to design optimized devices around these approaches. This is because at present this design takes place through trial and error, which makes investigating the full parameter space of material choices and layer stack design virtually impossible. To improve this design process, a predictive OLED model is needed. A full predictive OLED model takes as input the layer stack design, deposition methods and chemical structures of the materials involved, and gives as output the angle-dependent emission spectrum and current-voltage characteristics of the device. This involves molecular dynamics, density functional theory, charge-transport modeling, excitonics and photonics. However, charge-transport modeling by itself already yields useful results, such as current-voltage characteristics and exciton generation locations. In such modeling one three-dimensionally (3D) simulates the charge transport in organic semiconductors, which takes place by hopping of charge carriers between localized sites. Since this 3D simulation is computationally expensive, the results must be translated to a fast one-dimensional drift-diffusion (1D-DD) approach to be of use in the OLED design process. In this translation, 3D simulation is used in two ways: to determine parameters like the charge-carrier mobility, and to validate the results of the 1D approach. Charge-transport modeling and the 3D-to-1D translation are the focus of this work. In this thesis, two 3D simulation methods are used, based on the master equation (3D-ME) and on Monte Carlo simulation (3D-MC). In the 3D-ME method, we determine for each site the probability that there is a charge carrier on this site. We use this method to determine the charge-carrier mobility in bulk systems. Advantages of this method are its speed and direct insight into the spatial distribution of charge carriers. An important disadvantage is that Coulomb interactions between individual charge carriers cannot be taken into account. In the 3D-MC method, we evaluate the full hopping model through explicit Monte Carlo simulation, including all Coulomb interactions. We use it to model charge transport in multilayer structures relevant for modern OLEDs. A first result is a new scaling theory which describes the dependence of the charge- carrier mobility on temperature and carrier density at zero electric field (chapter 3). This scaling theory is based on percolation theory, in which one critical bond determines the charge-transport properties of the entire system. We expand on percolation by considering not just this single critical bond but also the distribution of almost equally difficult bonds in the system. This leads to an accurate, closed-form expression for the mobility, containing three parameters which depend on the specific system considered (such as the type of lattice, the expression for the charge carrier hopping rate between two sites and the shape of the energy disorder). This theory makes it possible for the first time to analyze the effect of assumptions like the lattice and hopping rate. The second result is a description of the electric-field dependence of the mobility in host-guest systems (chapter 4). These are systems in which a small amount of sites act as charge-carrier traps, such as dopants, dyes or naturally occurring electron traps. At low guest concentration charge transport takes place only through the host. The effect of the guest sites is then purely to immobilize a number of carriers. At low electric field, this number can be determined from equilibrium Fermi-Dirac statistics. At finite fields this no longer applies because of field-induced detrapping: the field assists carriers in escaping the guest sites. We quantify this effect by generalizing the Fermi-Dirac distribution to a numerically determined occupation function. This allows an accurate prediction of the mobility, leading to improved simulation of OLEDs containing host-guest systems. The third result is a general description of charge transport at non-zero electric field (chapter 5). This result combines elements of the scaling and field-induced-detrapping theories described above. We show that the mobility factorizes into an ‘intrinsic’ factor and a ‘detrapping’ factor. These are physically separate effects, and we show that they affect the charge transport in devices in different ways. This means that the value of the mobility by itself does not fully describe charge transport at finite electric field. We present a new form of the 1D-DD method that explicitly splits these two factors of the field dependence instead of using the charge-carrier mobility. This method can be used to more accurately model devices in which high electric fields occur. The fourth and final result is a description of how to accurately implement internal organic-organic interfaces in the 1D-DD method (chapter 6). By comparing 3D-MC simulations to 1D-DD results, we determine and quantitatively describe three effects that must be taken into account. First, the charges at the interface are not in equilibrium, which must be taken into account in the boundary condition. Second, there is a discrete surface charge caused by charge carriers accumulating before the interface. Third, the Coulomb repulsion of this surface charge is reduced by Coulomb interactions between the carriers. All three effects can significantly influence the current in multilayer OLEDs and must be taken into account in an accurate 1D model. These charge-transport results have applications in the short, middle and long term (chapter 7). In the short term, the 1D-DD method can be used in characterization of organic semiconductors. Indeed, this approach (without the results in this thesis) has already been successfully used in several organic semiconductors to determine material parameters for a given choice of hopping model. By considering the time or frequency dependence of the mobility it may also be possible to determine which hopping model is appropriate. In the middle to long term, the 1D-DD method will be a valuable tool in OLED device simulation. The 3D-MC method has also proven to be useful in this kind of simulation. These methods are especially powerful when used to complement each other. Double-carrier charge transport and excitonics will have to be analyzed further to complete the 1D-DD method. In the long term, our most valuable result is most likely the insight we have gained into the physics underlying charge transport in organic semiconductors. This will allow us to truly understand OLED operation and come up with new concepts and designs. Some of our results, such as the scaling theory, may also be applicable to other fields of study.