A direct solver for 2D non-stationary Boltzmann-Poisson Systems for Semiconductor Devices: A MESFET simulation by WENO-Boltzmann schemes

We present preliminary results of a high order WENO scheme applied to deterministic computations for two dimensional formulation of the transients for the Boltzmann-Poisson system describing electron transport in semiconductor devices. The collisional form models optical-phonon interactions which become dominant under strong energetic conditions corresponding to nanoscale active regions under applied bias. We treat the Boltzmann Transport equation in a spherical coordinate system for the phase velocity space. The problem is three dimensional in the phase velocity space and two dimensional in the physical space, plus the time variable driving to steady states. The new formulation avoids the singularity due to the spherical coordinate system.