The Van Roosbroeck System: Basic properties, Discretization, and Numerical Solution Methods
Klaus GaertnerWeierstrass Institute for Applied Analysis and Stochastics
Date: Tuesday, October 2, 2007 at 12:00 PM
Room: PARB 126
Abstract
The van Roosbroeck system is a well posed but highly nonlinear system of 3 PDE's describing the transport of electrons and holes in semiconductors and their interaction via the Poisson equation. The discretization should preserve the basic analytic properties like: free energy functional, dissipativity, uniqueness close to equilibrium, bounds for steady state solutions for grids with prescribed properties for any step size. This goal can be reached for boundary conforming Delaunay grids and the proofs limit possible averages of coefficient functions. Based on these properties solution algorithms can be tailored to solve the linearized equations. Direct methods are used to get preconditioners for solving the complete problem iteratively. Finally an example is discussed without - fitting the theory exactly - and with avalanche generation: 1, 4, and 16 elementary cells of a CoolMOS like device are considered up to avalanche generation levels sufficient to compare the sensitivity of design variants.
Presenter Bio
Klaus Gaertner was born in Zittau, Germany. He studied theoretical physics in Dresden (Germany), and received the PhD degree in nuclear reactor physics. After working ten years in the field of neutron transport and diffusion theory, he joined the Karl-Weierstrass-Institute for Mathematics in Berlin, Germany, in 1982. Since this time, his main interest has been in numerical problems connected with degenerate elliptic and parabolic PDE's, especially semiconductor device models. 1992 he joined the Interdisciplinary Center for Supercomputering of the ETH, Zurich, Switzerland. Numerical problems related to device modeling have been in the focus at the ETH Integrated Systems Lab (1994 -- 1998). Now he is with the Numerical Mathematics and Scientific Computing group at WIAS, Berlin. The interests are essentially unchanged: the time is shared among qualitative properties of discretizations, real world applications (3d charge transport in semiconductors) and solution methods for linear systems (coauthor of pardiso).
