A novel Monte Carlo simulation algorithm method for electron transport in complex nanostructured thermoelectric materials*

Monte Carlo (MC) simulation approaches are frequently used for the solution of the Boltzmann Transport Equation (BTE) for electronic and phononic transport in various semiconductor materials and devices. It involves the simulation of particle trajectories rather than the direct solution of partial differential equations. This is particularly useful in nanostructured thermoelectric materials, in which case the details of nano-features and their effect on transport need to be captured accurately.

Here, we developed and present a novel MC ray-tracing algorithm with computational efficiency of at least 2 orders of magnitude compared to existing ensemble algorithms. Our new method is a hybrid between the analytical solutions of the BTE and MC particle based simulations. The method utilizes only a limited number of ray-tracing particles and only one unidirectional fliux injection, allowing it to avoid the statistically challenging subtraction of two opposite going fluxes, and the application of a driving force all together. We simulate nanostructure materials and find a good agreement between the MC results for nanostructured grain boundary and porous domains with Matthiessen’s rule. We believe the new method provides more efficient and user friendly algorithm, which will enable the proper study of highly nanostructured TE materials.