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A Domain Decomposition Method for Silicon Devices

#### By: Carlo Cercignani, Irene Gamba, Joseph W. Jerome and Chi-Wang Shu

A mesoscopic/macroscopic model for self-consistent charged transport under
high field scaling conditions corresponding to drift-collisions balance
was derived by Cercignani,
Gamba, and Levermore in [4]. The model was summarized in
relationship to
semiconductors in [2].
In [3], a conceptual domain decomposition method was
implemented, based upon use of the drift-diffusion model in highly-doped
regions of the device, and use of the high-field model in the channel,
which represents a (relatively) lightly-doped region. The hydrodynamic
model
was used to calibrate interior boundary conditions.
The material parameters of GaAs were employed in [3].
This paper extends the approach of [3].
(1)
Benchmark comparisons are described
for a Silicon $n^+-n-n^+$ diode.
A global kinetic model is simulated with Silicon parameters. These
simulations are sensitive to the choice of mobility/relaxation.
(2)
An elementary global domain decomposition method is presented.
Mobilities are selected consistently
with respect to the kinetic model.
This study underscores the significance of the asymptotic
parameter defined below, as the ratio of drift and thermal
velocities, as a way to measure the change in velocity scales. This
parameter gauges the effectiveness of the high field
model.

This paper appears in
Transport Theory and
Statistical Physics vol. 29 (2000), 525--536.
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