Efficient evaluation of Coulomb interactions in kinetic Monte Carlo simulations of charge transport.

The application of predictive and reliable modeling techniques for the simulation of charge transport in functional materials is an essential step for the development of advanced platforms for electronics, optoelectronics, and photovoltaics. In this context, kinetic Monte Carlo (KMC) methods have emerged as a valuable tool, especially for the simulation of systems where charge transport can be described by the hopping of charge carriers across localized quantum states, as, for example, in organic semiconductor materials. The accuracy, computational efficiency, and reliability of KMC simulations of charge transport, however, crucially depend on the methods and approximations used to evaluate electrostatic interactions arising from the distribution of charges in the system. The long-range nature of Coulomb interactions and the need to simulate large model systems to capture the details of charge transport phenomena in complex devices lead, typically, to a computational bottleneck, which hampers the application of KMC methods. Here, we propose and assess computational schemes for the evaluation of electrostatic interactions in KMC simulations of charge transport based on the locality of the charge redistribution in the hopping regime. The methods outlined in this work provide an overall accuracy that outperforms typical approaches for the evaluation of electrostatic interactions in KMC simulations at a fraction of the computational cost. In addition, the computational schemes proposed allow a spatial decomposition of the evaluation of Coulomb interactions, leading to an essentially linear scaling of the computational load with the size of the system.