## Transport Effects and Characteristic Modes in the Modeling and
Simulation of Submicron Devices

#### By: Joseph W. Jerome and Chi-Wang Shu

This paper has two major goals: (1) to study the effect of the common
practice of neglecting the convective terms (inertial approximation)
in the hydrodynamic model in the simulation
of n+/n/n+ diodes and two dimensional MESFET devices; and, (2) to
test analytical criteria, formulated in terms of characteristic values
of the Jacobian matrix, as a
method of determining the impact of first derivative perturbation terms
in this model,
and in related energy transport models. This
characteristic value analysis
can be thought of as generalizing the usual analytical solution of
first order linear systems of ordinary differential equations
with constant coefficients. Concerning (1), we find that the inertial
approximation is invalid near the diode junctions, and near the
contact regions of the MESFET device. In regard to (2), we find a proper
arrangement of terms, expressing the flux, such that the
first derivative part of the system is hyperbolic,
both for the hydrodynamic model and the energy transport model.
For the hydrodynamic model, two forms of the heat conduction term are
studied, including the case of a convective term. This
suggests and validates the use of shock capturing algorithms for the
simulation.

This paper appeared in IEEE Trans. CAD 14 (1995), 917--923.

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