Advances in spherical harmonics solvers for the Boltzmann equation

Abstract

Solvers based on a spherical harmonics expansion (SHE) of the Boltzmann equation (BE) are a deterministic alternative to the stochastic Monte Carlo (MC) method. Their numerical properties are very similar to the classical approaches (drift-diffusion or hydrodynamic models), and the same numerical methods can be used (box integration, maximum entropy dissipation scheme (MEDS), Newton-Raphson method, ac analysis, adjoint method, harmonic balance, etc), and the disadvantages of MC are avoided. This is exemplified by simulations of quasi-ballistic transport in nanometric devices.