Hierarchy of Full Band Structure Models for Monte Carlo Simulation

This paper discusses the various hierarchy levels that are possible when the full band structure is considered. At the highest level, the scatterings are treated using complete k-k’ transition rates, which entail extremely memory intensive computational applications. At the lowest level, the scattering anisotropy is neglected and the scattering rate is considered to be a constant average value on energy isosurfaces of the bandstructure. This model is more practical for device simulation. In between the two extremes, it is possible to design intermediate models which preserve some essential features of both. At all levels of the band structure hierarchy of models, there are similar issues of numerical noise, related to the sampling of real and momentum space that the Monte Carlo method necessarily performs with a relatively small number of particles. We discuss here computationally efficient approaches based on the assignment of variable weights to the simulated particles, in conjunction with careful gatherscatter procedures to split particles of large weight and combine particles of small weight