Acceleration scheme for particle transport in kinetic Monte Carlo methods

Kinetic Monte Carlo (kMC) simulations are frequently used to study (electro-)chemical processes within science and engineering. kMC methods provide insight into the interplay of stochastic processes and can link atomistic material properties with macroscopic characteristics. Significant problems concerning the computational demand arise if processes with large time disparities are competing. Acceleration algorithms are required to make slow processes accessible. Especially, the accelerated superbasin kMC (AS-kMC) scheme has been frequently applied within chemical reaction networks. For larger systems, the computational overhead of the AS-kMC is significant as the computation of the superbasins is done during runtime and comes with the need for large databases. Here, we propose a novel acceleration scheme for diffusion and transport processes within kMC simulations. Critical superbasins are detected during the system initialization. Scaling factors for the critical rates within the superbasins, as well as a lower bound for the number of sightings, are derived. Our algorithm exceeds the AS-kMC in the required simulation time, which we demonstrate with a 1D-chain example. In addition, we apply the acceleration scheme to study the time-of-flight (TOF) of charge carriers within organic semiconductors. In this material class, time disparities arise due to a significant spread of transition rates. The acceleration scheme allows a significant acceleration up to a factor of 65 while keeping the error of the TOF values negligible. The computational overhead is negligible, as all superbasins only need to be computed once.