3. Device Equations

In *MINIMOS-NT* carrier transport can be treated by the drift-diffusion (DD) and
the hydrodynamic (HD) transport models. For either carrier type the transport
model can be chosen independently. In addition, the lattice temperature can
be treated either as a constant or as an unknown governed by the lattice heat
flow equation. These equations will be reviewed in Section 3.1.
It is worth mentioning that there is some confusion in the literature
about the HD transport model. When deriving the HD model from Boltzmann's
transport equation, the average carrier energies *w*_{} read

with

The resulting equation system for the most general case is very complex and
time consuming to solve. Simplifications should be made whenever possible,
e.g., DD model instead of HD model or to completely neglect carrier transport
by assuming a constant quasi-Fermi level for the respective carrier
type. However, the validity of these simplifications must be carefully
investigated. This is normally done by comparison of simulation results for
different equation sets. Despite the obvious fact that depending on the
equation set different principal physical effects are taken into account,
e.g., self- and carrier-heating, the influence on the models for the physical
parameters is more subtle. The main reason for this is that in the case of
the HD model, information about the average carrier energy is available in
form of the carrier temperature. Many physical parameters depend on this
average carrier energy, e.g., the mobilities and the energy relaxation times.
In the case of the DD model the carrier temperatures are assumed to be in
equilibrium with the lattice temperature, that is
*T*_{C} = *T*_{L}, hence, all
energy dependent parameters have to be modeled in a different way. The
carrier energies are estimated using the local energy balance equations which
give expressions for the carrier temperatures as a function of the local
electric field. These expressions, however, are only valid under homogeneous
conditions. Models for the physical parameters for the DD and HD case will be
called consistent when they deliver equivalent results under these homogeneous
conditions as will be shown.

1999-05-31