In this book a hierarchy of macroscopic models for semiconductor
devices is presented. Three classes of models are studied in
detail: isentropic drift-diffusion equations, energy-transport
models, and quantum hydrodynamic equations. The derivation of each
of the models is shown, including physical discussions.
Furthermore, the corresponding mathematical problems are analyzed,
using modern techniques for nonlinear partial differential
equations. The equations are discretized employing mixed
finite-element methods. Also, numerical simulations for modern
semiconductor devices are performed, showing the particular
features of the models.
Modern analytical techniques have been used and further developed,
such as positive solution methods, local energy methods for
free-boundary problems and entropy methods.
The book is aimed at applied mathematicians and physicists
interested in mathematics, as well as graduate and postdoc students
and researchers in these fields.
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