Exact solution to kinetic Monte Carlo simulations and its application to energy materials

In many circumstances kinetic Monte Carlo simulations are used to determine the probabilistic outcome of a process. However, one of the challenges of this method is the need to accumulate enough statistics to reduce errors to a manageable level. Here we show how for this set of problems it is possible to formally extract the exact solution for the probabilistic outcome of a kinetic Monte Carlo process by presenting the kinetic Monte Carlo problem in terms of a master equation. This reduces the solution method to the inversion of a single sparse matrix, from which all the relevant data can be extracted. We have applied this method to tackle two cross-cutting problems in the area of energy applications: the simulation of particle-surface interaction during wide band gap semiconductor epitaxy and the transport of charged species in nanostructured electrodes.