Analytical and Computational Advances for Hydrodynamic Models of
Classical and Quantum Charge Transport
By: Joseph W. Jerome
In recent years, substantial advances have been made in understanding
hydrodynamic models, both from the standpoint of analytical
infrastructure, as well as the parameters which play a decisive effect in
the behavior of such models. Both classical and quantum hydrodynamic
models have been studied in depth.
In this survey paper, we describe several
results of this type. We include, for example, well-posedness
for both classical and quantum reduced models,
and the relaxation drift-diffusion limit as
examples of analytical results. As examples of computational results, we
include some discussion of effective algorithms, but most importantly,
some
information gleaned from extensive simulation. In particular, we
present our findings of the prominent role played by the mobilities in the
classical models, and the role of hysteresis in the quantum models.
All models are self-consistent. Included is discussion of
recent analytical results on the
use of Maxwell's equations. Benchmark devices are utilized: the MESFET
transistor and the $n+/n/n+$ diode for classical transport, and the
resonant tunneling diode for quantum transport. Some comparison with the
linear Boltzmann transport equation is included.
This paper has appeared in VLSI DESIGN 10 (2000), 453--466, and
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