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A. Jüngel:
"Numerical approximation of ultrasmall semiconductor devices";
Hauptvortrag: Colloquium on Applied and Numerical Mathematics, Zürich (eingeladen); 12.04.2010 - 13.04.2010.

Siehe englisches Abstract.

Numerical simulations of highly integrated electronic circuits
help to reduce costly experiments and to accelerate the
technological progress in microelectronics. Typically, only
simplified models are used in industrial applications for reasons
of computing time. However, modern semiconductor devices have
extremely small structures such that a precise modeling of,
for instance, temperature or quantum effects becomes necessary
for accurate simulation results. In this talk, some numerical
techniques are presented which allow for an efficient simulation
of such effects.

In the first part, fluid dynamical diffusion models for
semiconductors with temperature effects are approximated using
mixed finite elements. Numerical simulations of two- and
three-dimensional transistors and electric circuits illustrate
the influence of the temperature. The second part is concerned
with the numerical analysis of a finite-volume scheme of a
quantum diffusion model. Furthermore, time-dependent simulations
of the switching behavior of a quantum transistor, modeled
by the Schroedinger equation and discretized by a pseudo-spectral
method, are presented.

Finite element methods; quantum transistors; spectral method