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.

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

diode.

http://www.asc.tuwien.ac.at/preprint/2010/asc04x2010.pdf

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