## Two Carrier Semiconductor Device Models with Geometric Structure and
Symmetry Properties

#### By: Gui-Qiang Chen, Joseph W. Jerome, Chi-Wang Shu, and Dehua
Wang

We introduce a novel two carrier (electro) hydrodynamic model, which
incorporates higher dimensional geometric effects into a one
dimensional model. A rigorous mathematical analysis is carried out for the
evolution system in the case of piezotropic flow,
including realistic carrier coupling.
The proofs are constructive in nature, making use of generalized Godunov
schemes with a novel fractional step, steady-state component, and
compensated compactness. Two important applications are studied.
We simulate:
(1) the GaAs device in the notched oscillator circuit; and,
(2) a MESFET channel, and its steady-state symmetries.
The first of these applications is the well known Gunn oscillator, and we
are able to replicate Monte-Carlo simulations, based upon the Boltzmann
equation. For the second application, we observe the effect of a symmetry
breaking parameter, the potential bias on the drain.

This paper appeared in: Modelling and Computation for Applications in
Mathematics, Science, and Engineering, Oxford University Press (J. Jerome,
ed.), 1998, pp. 103--140, and
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