Contributions to Books:

A. Jüngel, J. Milisic:
"A simplified quantum energy-transport model for semiconductors";
in: "ASC Report 04/2010", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2010, ISBN: 978-3-902627-03-2.

English abstract:
The existence of global-in-time weak solutions to a quantum energy-transport
model for semiconductors is proved. The equations are formally derived from the quantum
hydrodynamic model in the large-time and small-velocity regime. They consist of a nonlinear
parabolic fourth-order equation for the electron density, including temperature gradients; an
elliptic nonlinear heat equation for the electron temperature; and the Poisson equation for
the electric potential. The equations are solved in a bounded domain with periodic boundary
conditions. The existence proof is based on an entropy-type estimate, exponential variable
transformations, and a fixed-point argument. Furthermore, we discretize the equations by
central finite differences and present some numerical simulations of a one-dimensional ballistic

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.