Moment Methods

In modern devices large electric fields which rapidly change over small length scales give rise to non-local and hot-carrier effects which begin to dominate device performance.

Macroscopic models which can overcome the limitations of the available energy-transport models are obtained by taking the moment system of equations of the Boltzmann transport equation and truncating it at a suitable order $N$. A consistent transport model based on the first six moments of Boltzmann's equation has been developed at the Institute for Microelectronics. The aim of this research is to increase the numerical robustness of the solution algorithm for the six moments model.

Truncation introduces a ``closure problem'' because the number of unknowns exceeds that of the equations. The main emphasis in this thesis is put on studying different kinds of closure relations for the highest order moment, as this was found to be a critical issue with respect to robustness. Requiring consistency with bulk simulations we give a new solution to the closure problem.