Computationally efficient Monte Carlo electron transport algorithm for nanostructured thermoelectric material configurations

Monte Carlo statistical ray-tracing methods are commonly employed to simulate carrier transport in nanostructured materials. In the case of a large degree of nanostructuring and under linear response (small driving fields), these simulations tend to be computationally overly expensive due to the difficulty in gathering the required flux statistics. Here, we present a novel MC ray-tracing algorithm with computational efficiency of at least an order of magnitude compared to existing algorithms. Our new method, which is a hybrid of analytical Boltzmann transport equation and Monte Carlo uses a reduced number of ray-tracing particles, avoids current statistical challenges such as the subtraction of two opposite going fluxes, the application of a driving force altogether, and the large simulation time required for low energy carriers. We demonstrate the algorithm's efficiency and power in accurate simulations in large domain nanostructures with multiple defects. We believe that the new method we present is indeed more robust and user friendly compared to common methods, and can enable the efficient study of transport in nanostructured materials under low-field steady-state conditions.