When the Boltzmann-Poisson system is the most reliable model for the flow of charged particles
general practice has been to rely on stochastic solvers as Monte-Carlo (DSMC) methods. These solvers are computationally expensive for good resolution and unreliable for transient simulations.
We focus in a rather easy and fast deterministic high order solver to the self-consistent Boltzmann-Poisson system, where the collision operator incorporates acoustical and non-polar optical interactions such a phonon absorption and emission rates.
We have modeled a short based channel flow in a solid semiconductor bounded structure, such as real MOSFET device models and bench-marked our calculations with DSMC solvers In particular, we shall present one and two space-dimension with three phase-velocity -dimension system of equations. They consists of a linear kinetic (non-local) equation solved by WENO methods coupled with the Poisson equation for the force field acting on the particles accounting for long range interactions.
We will focus on the development of the method, simulation results for diodes and MESFET and MOSFET as well as comparisons to other classical models in the field. In particular we compute, deterministically, the evolution probability density function with its first three moments.
Boundary singularities for 2-space dimensions models are described and accurately computed.
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This work has been done in collaboration with J.A. Carrillo, A. Majorana and C.-W. Shu.