## A Discontinuous Galerkin Solver for Boltzmann Poisson Systems in Nano Devices

#### Chi-Wang ShuBrown University

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 to those of a high order weighted essentially non-oscillatory (WENO) finite difference scheme simulation and with direct simulation Monte-Carlo (DSMC) results. This is a joint work with Yingda Cheng, Irene M. Gamba and Armando Majorana.

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