Delocalisation in Device-Scale Drift-Diffusion Models

In organic semiconductors, even small amounts of delocalisation can considerably enhance charge and exciton transport as well as charge separation. We recently developed delocalised kinetic Monte Carlo (dKMC), the first computational method able to describe the motion of partially delocalised charges [1] and excitons [2] in organic semiconductors on mesoscopic time and length scales, while considering the critical influence of energetic disorder, quantum-mechanical couplings, and polaron formation. dKMC has revealed new, basic physics of transport in organic semiconductors and can explain why mobilities predicted by traditional kinetic Monte Carlo are usually too low, showing that delocalisation over just a few molecules can increase mobilities by orders of magnitude [1,2]. Similarly, applying dKMC to the two-body problem of charge separation reveals a decisive enhancement of internal quantum efficiency (IQE) from a small amount of delocalisation [3,4].<br/><br/>In this talk, I will show that the benefits of delocalisation—first identified on the mesoscopic scale—also improve performance on the macroscopic, device scale. To do so, we have parametrised drift-diffusion models using dKMC to arrive at the first delocalisation-aware device models.<br/><br/>Our parametrisation relies on several new computational approaches. The first is jumping kinetic Monte Carlo (jKMC), a model that approaches the accuracy of dKMC, but with a computational cost comparable to conventional KMC [5,6]. Rates entering jKMC are simple modifications of ordinary Marcus hopping and can be used to include delocalisation effects in any existing KMC code. The low computational cost of jKMC also allows us to carry out the first calculations of all remaining parameters necessary for drift-diffusion models, which could not be computed by fully quantum techniques. These include steady-state mobilities, generation rates, and carrier recombination rates, processes that we show are also significantly affected by even modest delocalisation.<br/><br/>Putting all the ingredients together, our delocalised drift-diffusion code [7] can compute JV curves while faithfully capturing charge and exciton delocalisation. The results confirm the importance of delocalisation in device performance and help explain recent high-performance blends that defy explanation using classical models.<br/><br/>[1] Daniel Balzer, Thijs J.A.M. Smolders, David Blyth, Samantha N. Hood, and Ivan Kassal,<br/>Chem. Sci. 12, 2276 (2021).<br/>[2] Daniel Balzer and Ivan Kassal, J. Phys. Chem. Lett. 14, 2155 (2023).<br/>[3] Daniel Balzer and Ivan Kassal, Sci. Adv. 8, eabl9692 (2022).<br/>[4] Daniel Balzer and Ivan Kassal, arXiv:2308.15076 (2023).<br/>[5] Jacob T. Willson, William Liu, Daniel Balzer, and Ivan Kassal, J. Phys. Chem. Lett. 14, 3757 (2023).<br/>[6] Jacob T. Willson, Daniel Balzer, and Ivan Kassal, arXiv:2308.13194 (2023).<br/>[7] Tom Grayson and Ivan Kassal, in preparation (2024).