DSMC versus WENO-BTE: A double gate MOSFET example

Time-dependent solutions to the BoltzmannPoisson system in two spatial dimensions and threedimensional velocity space are obtained by using a recently developed high order WENO scheme. The collision operator of the Boltzmann equation models the scattering processes between electrons and phonons which are assumed to be in thermal equilibrium. In this paper, the deterministic numerical solutions for a double gate silicon MOSFET are compared with Monte Carlo simulations. The main aim of this investigation is to show how direct solutions of the Boltzmann transport equation coupled with the Poisson equation can, through comparisons, suggest improvements of the DSMC algorithms such as, in particular, the charge assignment to M. J. Cáceres ( ) Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain e-mail: [email protected] J. A. Carrillo ICREA Department de Matemàtiques, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Spain e-mail: [email protected] I. Gamba Department of Mathematics and ICES, The University of Texas at Austin, USA e-mail: [email protected] A. Majorana Dipartimento di Matematica e Informatica, Università di Catania, Catania, Italy e-mail: [email protected] C.-W. Shu Division of Applied Mathematics, Brown University, Providence, RI 02912, USA e-mail: [email protected] the mesh, the treatment of the boundary conditions and the free flight duration.