In a companion presentation, we have discussed the theory of a mesoscopic/
macroscopic model, which can be viewed as an augmented drift-diffusion model. Here,
we describe how that model is used. The device we consider for this presentation is the
one dimensional GaAs n+−n−n+ structure of length 0.8μm. First, a full Hydro-
Dynamic (HD) model, proven reliable when compared with Monte Carlo simulations, is
used to simulate the device via the ENO finite difference method. As applied to the full
device, the new model is not necessarily superior to traditional Drift-Diffusion (DD).
Indeed, when we plot the quantity η= μ0E/kT0/m, where μ0 is the mobility constant
and E=−ϕ′ is the electric field, we verify that the high field assumption η › 1, required
for the high field model, is satisfied only in an interval given approximately by [0.2, 0.5].
When we run both the DD model and the new high field model in this restricted interval,
with boundary conditions of concentration n and potential ϕ provided by the HD
results, we demonstrate that the new model outperforms the DD model. This indicates
that the high field and DD models should be used only in parts of the device, connected
by a transition kinetic regime. This will be a domain decomposition issue involving
interface conditions and adequate numerical methods.
