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A. Jüngel:
"Challenges in semiconductor modeling and simulation: nonlinear PDE models and finite-element approximation";
Talk: Fakultätskolloquium der Universität Zagreb, Zagreb, Kroatien; 2008-05-28.

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. The semiconductor devices in the circuits
are usually modeled by equivalent network equations, thus
reducing the computational cost. However, this strategy
becomes questionable in modern circuits, as parasitic effects,
such as device heating and quantum mechanical effects, cannot
be easily incorporated in the network models. 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. Furthermore, the Schroedinger equation
is discretized by a pseudo-spectral method and numerical results of
a quantum transistor (quantum interference device) in 2D and 3D
are shown. The results show the efficiency of the numerical schemes.

Siehe englisches Abstract.

Semiconductors, mixed finite elements, Schrödinger equation