Kinetic Monte Carlo Modelling of Organic Photovoltaic Devices

Sammanfattning: Organic photovoltaics (OPVs) is a rapidly growing low-cost PV technology sector that relies on multiple benefits of organic semiconductors viz. being environmental-friendly with a simplified processing/fabrication and tunable properties. While the performance of OPVs has gone up to over 19 % in the last 2 decades, it still lags behind the silicon-PV technology in terms of efficiency and stability. The performance of any solar cell is essentially a combination of three quantities: short circuit current density (jSC), fill- factor (FF), and open circuit voltage (VOC). Of these quantities, especially VOC still offers a scope of further improvement as it falls short of the theoretical achievable limit which requires a better understanding of the various loss channels in an actual device leading to a VOC reduction. Through this thesis, we have developed an understanding of VOC using non-equilibrium models and proposed ways leading to its enhancement.The first step in this study was to develop an understanding of the underlying charge transport mechanism, which relates to the efficiency with which the charges can be extracted at the terminals, or electrodes. Charge transport in any disordered organic semiconductor occurs by a process of hopping, in which charge carriers jump by thermally activated tunneling between localized sites that are randomly distributed in the energy dependent density of states. Thus, among other hopping parameters, the mobility of a charge carrier is crucially dependent on the disorder. We implemented a new semi-analytical hopping model that allows for a consistent extraction of these parameters from the space charge limited conductivity (SCLC) experiments. The model was calibrated against a numerical kinetic Monte Carlo (kMC) model and was used to analyze temperature-dependent SCLC curves for multiple systems used frequently as an active layer in organic solar cells. We observed that there exists a critical ratio between the inter-site distance and the localization length that decides the applicability, or not, of the much-used extended Gaussian disorder model (EGDM). The improved hopping model functions well for both fullerene and non-fullerene-based systems and can also describe the charge transport in electron-only devices, which so far have not been described successfully using EGDM.Having the charge dynamics and other hopping parameters in place, we subsequently developed and calibrated, by independent experiments, a robust and stochastic kMC model that can calculate a full j-V curve of a solar cell correctly. With the full calibration in place with respect to the morphology, recombination rate constant and injection barriers, the motivation was to have a model that can calculate both transients and steady-state j-V curves of a given device. So far, implementing kMC to analyze a full device has been a challenge, especially due to the numerical problems associated with the presence of Ohmic contacts. The calibrated model correctly predicts the device’s j-V and non-equilibrium hopping transport recombination dynamics.A crucial approximation that stems from inorganic solar cells and that is commonly made for organic solar cells as well, is the fast and complete thermalization of charge carriers in the density of states. However, the relaxation of charge carriers in case of organic semiconductors is not as straightforward as in inorganics, but rather a complex two-step process consisting of a fast on-site relaxation followed by a slower global relaxation occurring via hopping to increasingly deep sites. We have shown that the second slow thermalization does not complete within the charge carrier lifetime in the device and leads to a VOC that is 0.1 - 0.2 V higher than the equilibrium value. This is found for both fullerene and high-performing non-fullerene OPV systems.For a given OPV device, there is a significant difference between the upper limit for the efficiency set by theoretical considerations based on the assumption of near-equilibrium (the so-called Shockley-Queisser limit) and the actual measured efficiency. We numerically explored a new funnel-shaped morphology, which can lead to an impactful gain in VOC and efficiency of an organic solar cell. In contrast to the conventional blend morphology, which does not lead to a directed motion of the photogenerated charge carriers, the funnel morphology rectifies the otherwise undirected diffusive motion of ‘hot’ charges, which leads to a higher probability of extraction at the desired contact. We utilized the reciprocity analysis to calculate the gain in VOC and efficiency as compared to a hypothetical equilibrium system of the same material. We found that for an optimized funnel morphology, the efficiency can surpass the near-equilibrium limit.Mixing materials to form a high-performing ternary OPV has emerged as a possible route to improve performance. We performed a review of literature data and deduced that the relative gain in VOC is too small to contribute to a large gain in the efficiency. Instead, the major contribution to the efficiency enhancement is due to gains in the FF and/or jSC. Also, the VOC of the ternary system is found to be tunable relative to the ratio of the added species in the host system. These experimental findings were consistently described by extensive numerical simulations in which the active layer morphology was assumed to give rise to an energetic cascade for at least one of the charge carriers. In contrast, our explicit calculations show that the commonly employed parallel junction model cannot explain the experimental findings.