## Applicability of the High Field
Model: An Analytical Study via Asymptotic Parameters Defining Domain
Decomposition

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

In this paper, we present a mesoscopic--macroscopic model of self--consistent
charge transport. It is based upon an asymptotic expansion of solutions
of the Boltzmann Transport Equation (BTE). We identify three dimensionless
parameters from the BTE. These parameters are, respectively, the quotient
of reference scales for drift and thermal velocities, the scaled mean
free path, and the scaled Debye length.
Such parameters induce domain dependent macroscopic approximations.
Particular focus is placed upon the so--called high field model, defined by
the regime where drift velocity dominates thermal velocity. This model
incorporates kinetic transition layers, linking mesoscopic to macroscopic
states. Reference scalings are defined by the background doping levels and
distinct, experimentally measured mobility expressions, as well as locally
determined ranges for the electric fields. The mobilities reflect a coarse
substitute for reference scales of scattering mechanisms.
The high field approximation is a formally derived modification of the
augmented drift-diffusion model originally introduced by Thornber some
fifteen years ago.
We are able to compare our approach with the earlier
kinetic approach of Baranger and Wilkins
and the macroscopic approach of
Kan, Ravaioli, and Kerkhoven.

This paper has appeared in VLSI DESIGN 8 (1998), 135--141, and
can be viewed in the following format: