Time-dependent solutions to the Boltzmann-Poisson system in two spatial dimensions and three-dimensional velocity space are obtained by using a recently developed high order WENO scheme. The collision operator of the Boltzmann equation models the scattering processes between electrons and phonons which are assumed to be in thermal equilibrium. In this paper, the deterministic numerical solutions for a double gate silicon MOSFET are compared with Monte Carlo simulations. The main aim of this investigation is to show how direct solutions of the Boltzmann transport equation coupled with the Poisson equation can, through comparisons, suggest improvements of the DSMC algorithms such as, in particular, the charge assignment to the mesh, the treatment of the boundary conditions and the free flight duration. © Springer Science+Business Media LLC 2007.
- Boltzmann Transport Equation (BTE)
- Boltzmann-poisson system for semiconductors
- Direct Simulation Monte Carlo (DSMC)
- Double Gate Metal Oxide Semiconductor Field Effect Transistor (DG-MOSFET)
- Weighted Essentially Non-Oscillatory (WENO) schemes