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In this paper, we present results of a discontinuous Galerkin (DG) scheme applied to deterministic computations 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 nano-scale active regions under applied bias. The proposed numerical technique is a finite element method using discontinuous piecewise polynomials as basis functions on unstructured meshes. It is applied to simulate hot electron transport in bulk silicon, in a silicon n + -n-n + diode and in a double gated 12nm MOSFET. Additionally, the obtained results are compared 1 Support from the Institute of Computational Engineering and Sciences and the University of Texas Austin is gratefully acknowledged.2 . Research supported by Italian PRIN 2006: Kinetic and continuum models for particle transport in gases and semiconductors: analytical and computational aspects. 5 to those of a high order WENO scheme simulation and DSMC (Discrete Simulation Monte Carlo) solvers.

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.

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Fast and slow magnetoacoustic shocks are studied in the framework of relativistic magneto-fluid dynamics with the Synge equation of state. An approximate analytical solution is presented in a particular case. The general case is treated by numerical methods.