Classical and quantum semiconductor device modeling and simulation

The numerical simulation of modern semiconductor devices, like deep
submicron transistors or tunneling diodes, using microscopic models is
usually costly and time consuming. In recent years, fluiddynamical models
are derived, which contain the main physical phenomena and which can be
solved efficiently.

In this talk, a model hierarchy of classical and quantum fluid equations
for semiconductor devices is introduced and two models of this hierarchy
are discussed in detail: the quantum drift-diffusion equations and
the energy-transport models. A positivity-preserving numerical scheme
for the quantum drift-diffusion model is derived and numerical convergence
is proved. A simple 1D resonant tunneling diode is simulated showing
the expected physical behavior. Moreover, the classical energy-transport
equations are discretized using adaptively refined mixed finite elements
and a 2D MOSFET is numerically simulated.