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 term 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 wave-vector space. The problem is three dimensional in the wave-vector 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.