On the highest order moment closure problem [semiconductor device modelling applications]

Macroscopic transport models, based on the first six moments of Boltzmann´s equation are a natural extension to the drift-diffusion model (two moments) and the various energy-transport models (three or four moments). To close the system of equations, the sixth moment has to be expressed as a function of the lower order moments. We investigate the influence of the applied closure relation on the numerical properties of the six moments model, comparing three different methods, and propose a new solution to the closure problem. We present results of numerical solutions of six moments models and compare them to self-consistent Monte Carlo data.