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A. Jüngel:
"Numerical simulation of semiconductor devices: thermal and quantum mechanical effects";
Talk: Mathematical Colloquium, University of Split, Split (invited); 2009-05-21.

Numerical simulations of highly integrated electric circuits
are necessary in order to replace costly experiments and to
fulfill the demands due to the technological progress in
microelectronics. Standard modeling approaches employ
simplified models which become questionable in modern,
ultra-small semiconductor devices. Therefore, it is necessary
to model relevant devices in the electric circuit by more
precise physical models.

In this talk, classical and quantum mechanical models for
semiconductor devices are discussed. The heating of electrons
is modeled by the energy-transport equations. They consist of
elliptic cross-diffusion equations for the electron and energy
densities, coupled to the Poisson equation for the electric
potential. A numerical approximation of the equations using
mixed finite elements and numerical simulations of 2D and 3D
transistors are presented. Quantum mechanical effects are taken
into account by the Schroedinger equation, which is discretized
by a pseudo-spectral method. Numerical simulations of a 3D
quantum stub transistor are presented. The results show the
efficiency of the numerical schemes.

Siehe englisches Abstract.

Semiconductors